mm-5529 === Subject: elliptic curve ecdsa hi all, i have a very basic question on elliptic curve digital signature algorithms. say i have a 160 bit key key and want to perform ECDSA verification on a message (a) of size 1 mb (b) of size 1gb. what are the computations that need to performed? does the number of computations depend on message size( i purposefully have 2 messages of different sizes) and if so how? i need this since i am doing some energy consumption analysis of a security protocol which has ECDSA operations. if you know any links that can help me understand better let me know. Pad. === Subject: Re: elliptic curve ecdsa > hi all, > i have a very basic question on elliptic curve digital signature > algorithms. > say i have a 160 bit key key and want to perform ECDSA verification on > a message (a) of size 1 mb (b) of size 1gb. what are the computations > that need to performed? > does the number of computations depend on message size( i purposefully > have 2 messages of different sizes) and if so how? > i need this since i am doing some energy consumption analysis of a > security protocol which has ECDSA operations. if you know any links > that can help me understand better let me know. at the certicom conference last year there was a presentation on the use of ecdsa in rfid chips gate counts on these things must be very small since they are powered only through the signal they receive and the chips must perform the signature generation part of the algorithm the gate count for the presentation was around 25000 at my job (gaming software) we recently converted to ecdsa for our software validation and it has been able to validate a few 100k on a 300MHz processor in milliseconds a 1Gb task took a few minutes (around 10?) but this was with a lot of video calculations as well and may have been bus-locked i hope this gives some idea -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- === Subject: Re: elliptic curve ecdsa > hi all, > i have a very basic question on elliptic curve digital signature > algorithms. > say i have a 160 bit key key and want to perform ECDSA verification on > a message (a) of size 1 mb (b) of size 1gb. what are the computations > that need to performed? > does the number of computations depend on message size( i purposefully > have 2 messages of different sizes) and if so how? > i need this since i am doing some energy consumption analysis of a > security protocol which has ECDSA operations. if you know any links > that can help me understand better let me know. Pad. Perhaps you can read the excellent paper: http://www.comms.scitech.susx.ac.uk/fft/crypto/ecdsa.pdf IMO, this is the best paper on the matter. When you are signing anything, regardless of file size, you first take the hash (like SHA-1, SHA-224, SHA-256, SHA-384, SHA-512 or other) and then you sign a fixed size hash (depending on which hash you are using - for example, SHA-1 always gives a 160-bit hash for a file input <= 2^64). So, the calculations are wrapped up in the point counting algorithm for the type of curve (prime field, binary or Koblitz) and the size of the field. is. HTH ~A === Subject: Re: elliptic curve ecdsa hi all, > i have a very basic question on elliptic curve digital signature > algorithms. > say i have a 160 bit key key and want to perform ECDSA verification on > a message (a) of size 1 mb (b) of size 1gb. what are the computations > that need to performed? > does the number of computations depend on message size( i purposefully > have 2 messages of different sizes) and if so how? > i need this since i am doing some energy consumption analysis of a > security protocol which has ECDSA operations. if you know any links > that can help me understand better let me know. Pad. Perhaps you can read the excellent paper:http://www.comms.scitech.susx.ac.uk/fft/crypto/ecdsa.pdf IMO, this is the best paper on the matter. When you are signing anything, regardless of file size, you first take > the hash (like SHA-1, SHA-224, SHA-256, SHA-384, SHA-512 or other) and > then you sign a fixed size hash (depending on which hash you are using > - for example, SHA-1 always gives a 160-bit hash for a file input <= > 2^64). So, the calculations are wrapped up in the point counting algorithm > for the type of curve (prime field, binary or Koblitz) and the size of > the field. is. HTH ~A understand is no matter what the input message size is, the Elliptic curve operations are always performed on a 160 bit value(sha-1 output). If that is the case then ignoring the time taken for hash operations is it safe to assume that ECDSA generation/verification time taken on any message size is the same? in that case the timing differences for message of different sizes that galathea is talking about is due to the hash operations alone? Pad. === Subject: Re: elliptic curve ecdsa > hi all, > i have a very basic question on elliptic curve digital signature > algorithms. > say i have a 160 bit key key and want to perform ECDSA verification on > a message (a) of size 1 mb (b) of size 1gb. what are the computations > that need to performed? > does the number of computations depend on message size( i purposefully > have 2 messages of different sizes) and if so how? > i need this since i am doing some energy consumption analysis of a > security protocol which has ECDSA operations. if you know any links > that can help me understand better let me know. Pad. Perhaps you can read the excellent paper:http://www.comms.scitech.susx.ac.uk/fft/crypto/ecdsa.pdf IMO, this is the best paper on the matter. When you are signing anything, regardless of file size, you first take > the hash (like SHA-1, SHA-224, SHA-256, SHA-384, SHA-512 or other) and > then you sign a fixed size hash (depending on which hash you are using > - for example, SHA-1 always gives a 160-bit hash for a file input <= > 2^64). So, the calculations are wrapped up in the point counting algorithm > for the type of curve (prime field, binary or Koblitz) and the size of > the field. is. HTH ~A understand is no matter what the input message size is, the Elliptic > curve operations are always performed on a 160 bit value(sha-1 > output). If that is the case then ignoring the time taken for hash operations > is it safe to assume that ECDSA generation/verification time taken on > any message size is the same? in that case the timing differences for > message of different sizes that galathea is talking about is due to > the hash operations alone? Pad.- Hide quoted text - - Show quoted text - Alomst, you also have to account for the type of curve and the field size as those can have impact. Also, the random numbers in your point calculations could also take differing amounts of time (remember - there is a random element in the algorithm and it determines how many point counts you do and each of those take time). So - you have to account for different architectures (processors, memory, ALU, registers, HW, FPGA, et. al.), different curve types (prime field, binary, Koblitz) and different field sizes (P384, P512, B-..., K-...). See FIPS on DSA for further detail or the ANSI standard or IEEE-1363. There is also a wonderful book on the matter: Guide to Elliptic Curve Cryptography By Darrel R. Hankerson, Alfred J. Menezes, Scott A. Vanstone %2B+menezes&pg=PA184&ots=Z09VZtoYDw&sig=fV5telgFr91xbms8etXel- %2Bbook%2B%252B %2Bmenezes&sa=X&oi=print&ct=result&cd=1&cad=legacy#PPA184,M1> This book is also useful: Elliptic Curves in Cryptography By Ian F. Blake, Gadiel Seroussi, Nigel Paul Smart HTH ~A === Subject: Re: elliptic curve ecdsa > hi all, > i have a very basic question on elliptic curve digital signature > algorithms. > say i have a 160 bit key key and want to perform ECDSA verification on > a message (a) of size 1 mb (b) of size 1gb. what are the computations > that need to performed? > does the number of computations depend on message size( i purposefully > have 2 messages of different sizes) and if so how? > i need this since i am doing some energy consumption analysis of a > security protocol which has ECDSA operations. if you know any links > that can help me understand better let me know. at the certicom conference last year there was a presentation on the use of ecdsa in rfid chips gate counts on these things must be very small since they are powered only through the signal they receive and the chips must perform the signature generation part of the algorithm the gate count for the presentation was around 25000 at my job (gaming software) we recently converted to ecdsa for our software validation and it has been able to validate a few 100k on a 300MHz processor in milliseconds a 1Gb task took a few minutes (around 10?) but this was with a lot of video calculations as well and may have been bus-locked i hope this gives some idea ( apologies if this gets multiposted but glitches have held off response more than my waiting time ) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- === Subject: Re: elliptic curve ecdsa > hi all, > i have a very basic question on elliptic curve digital signature > algorithms. > say i have a 160 bit key key and want to perform ECDSA verification on > a message (a) of size 1 mb (b) of size 1gb. what are the computations > that need to performed? Google is your friend. The formula is quite simple. > does the number of computations depend on message size( i purposefully > have 2 messages of different sizes) and if so how? It depends how you count number of computations. What is a single computation.? Hint: The signature requires computing the hash of the message. Does the time to compute the hash depend on the size of the message???? Get hold of ANSI X9.62 or IEEE1363. Or read the Handbook of Applied Crypto. These will explain everything. === thread at 26.7.2007, 21:19 + 2.00 sqrt(2)^sqrt(2)^sqrt(2)^... = 2 ? or 4 ? May be I didn't find the right keyword/searchmethod- can someone kindly point out, how I should have done the search? I've a reference into another wev-archive, where it was easy to find the thread (though: complete?) http://sci.tech-archive.net/Archive/sci.math/2007-07/msg04472.html TIA - Gottfried -- --- Gottfried Helms, Kassel === > thread at 26.7.2007, 21:19 + 2.00 sqrt(2)^sqrt(2)^sqrt(2)^... = 2 ? or 4 ? May be I didn't find the right keyword/searchmethod- > can someone kindly point out, how I should have > done the search? Google groups search for the keywords: sqrt(2) 2 or 4 Helms group:sci.math returns this: http://tinyurl.com/2goyb3 > I've a reference into another wev-archive, where > it was easy to find the thread (though: complete?) http://sci.tech-archive.net/Archive/sci.math/2007-07/msg04472.html TIA - Gottfried -- I.N. Galidakis === Am 06.11.2007 21:51 schrieb I.N. Galidakis: > thread at 26.7.2007, 21:19 + 2.00 > sqrt(2)^sqrt(2)^sqrt(2)^... = 2 ? or 4 ? > May be I didn't find the right keyword/searchmethod- > can someone kindly point out, how I should have > done the search? Google groups search for the keywords: sqrt(2) 2 or 4 Helms group:sci.math returns this: > it does. Strange, but good to know, that this can happen. Gottfried -- --- Gottfried Helms, Kassel === Subject: Re: Previliged exp(x) > The equality f(x) = lim_n (1 + log(f(x))/n)^n holds for *any* non-negative function, Better make that any positive function. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Previliged exp(x) > The equality > f(x) = lim_n (1 + log(f(x))/n)^n > holds for *any* non-negative function, Better make that any positive function. That would be a good idea, indeed! :-) Jose Carlos Santos === Subject: Sylow p-subgroups Hello Let G be a finite abelian group, and let p be prime divisor of |G|. Show that the Sylow p-subgroup of G consists of e and all elements whose order is a power of p. I know that in order to prove this I have to first prove that if G is abelian then elements whose orders are powers of p form a subgroup. Then I have to show that this subgroup has order of a power of p. I know how to prove first part but I am not sure about how to show that this subgroup has order of a power of p. Could anyone help me? Tadeusz === Subject: Re: Sylow p-subgroups days. My association with the Department is that of an alumnus. >Hello >Let G be a finite abelian group, and let p be prime divisor of |G|. Show >that the Sylow p-subgroup of G consists of e and all elements whose order is >a power of p. I know that in order to prove this I have to first prove that if G is >abelian then elements whose orders are powers of p form a subgroup. Then I >have to show that this subgroup has order of a power of p. No, you don't. Just remember the following facts: (i) If K is any group, and H is a p-subgroup of K, then there is a p-Sylow subgroup of K that contains H. (ii) If K is any group, and S and S' are two p-Sylow subgroups of K for the same prime p, then S and S' are conjugate. (iii) In an abelian group, every subgroup is normal. Then apply them to the situation you have. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: Sylow p-subgroups >Hello >Let G be a finite abelian group, and let p be prime divisor of |G|. Show >that the Sylow p-subgroup of G consists of e and all elements whose order >is >a power of p. >I know that in order to prove this I have to first prove that if G is >abelian then elements whose orders are powers of p form a subgroup. Then I >have to show that this subgroup has order of a power of p. No, you don't. Just remember the following facts: > (i) If K is any group, and H is a p-subgroup of K, then there is a > p-Sylow subgroup of K that contains H. (ii) If K is any group, and S and S' are two p-Sylow subgroups of K > for the same prime p, then S and S' are conjugate. (iii) In an abelian group, every subgroup is normal. Then apply them to the situation you have. -- > It's not denial. I'm just very selective about > what I accept as reality. > --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin > magidin-at-member-ams-org > Hmm Would this statement work: G is a finite abelian group => every subgroup H is normal in G. That means that every Sylow p-subgroup is normal. Therefore there is a unique Sylow p-subgroup which contains all other Sylow p-subgroups. We can think of this unique, maximal Sylow p-subgroup so that it contains elements of order p^a (p^a is the order the Sylow p-subgroups that are contained in the maximal Sylow p-subgroup). Is the right way to prove it? Tadeusz === Subject: Re: Sylow p-subgroups days. My association with the Department is that of an alumnus. Hello >Let G be a finite abelian group, and let p be prime divisor of |G|. Show >that the Sylow p-subgroup of G consists of e and all elements whose order >is >a power of p. I know that in order to prove this I have to first prove that if G is >abelian then elements whose orders are powers of p form a subgroup. Then I >have to show that this subgroup has order of a power of p. > No, you don't. > Just remember the following facts: > (i) If K is any group, and H is a p-subgroup of K, then there is a > p-Sylow subgroup of K that contains H. > (ii) If K is any group, and S and S' are two p-Sylow subgroups of K > for the same prime p, then S and S' are conjugate. > (iii) In an abelian group, every subgroup is normal. > Then apply them to the situation you have. >Hmm Would this statement work: Some changes below: >G is a finite abelian group => every subgroup H is normal in G. That means >that every Sylow p-subgroup is normal. Therefore there is a unique Sylow >p-subgroup which contains all other Sylow p-subgroups. This last sentences is a mess. There is a unique Sylow p-subgroup, yes. There are NO OTHER Sylow p-subgroups. Because there is one and only one p-Sylow subgroup. All Sylow subgroups have the same size. >We can think of this >unique, maximal Sylow p-subgroup It makes no sense to apply the adjective maximal to a Sylow p-subgroup. > so that it contains elements of order p^a >(p^a is the order the Sylow p-subgroups that are contained in the maximal >Sylow p-subgroup). The parenthetical comment is nonsense, and you are incorrect anyway in how you phrased it. > Is the right way to prove it? Not entirely, though you are close. Note that every element of a Sylow p-subgroup has order a power of p, so any Sylow p-subgroup is contained in the set of all elements whose order is a power of p. This is true in any group. For the reverse inclusion, let P be THE Sylow p-subgroup of G (we can say the by (iii) above). Let g in G be an element whose order is a power of p. We want to show that g is in P (to show that the set of all elements whose order is a power of p is contained in P). Consider the subgroup . -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: Sylow p-subgroups >Hello >Let G be a finite abelian group, and let p be prime divisor of |G|. >Show >that the Sylow p-subgroup of G consists of e and all elements whose >order >is >a power of p. >I know that in order to prove this I have to first prove that if G is >abelian then elements whose orders are powers of p form a subgroup. Then >I >have to show that this subgroup has order of a power of p. No, you don't. Just remember the following facts: > (i) If K is any group, and H is a p-subgroup of K, then there is a > p-Sylow subgroup of K that contains H. (ii) If K is any group, and S and S' are two p-Sylow subgroups of K > for the same prime p, then S and S' are conjugate. (iii) In an abelian group, every subgroup is normal. Then apply them to the situation you have. >Hmm Would this statement work: Some changes below: >G is a finite abelian group => every subgroup H is normal in G. That means >that every Sylow p-subgroup is normal. Therefore there is a unique Sylow >p-subgroup which contains all other Sylow p-subgroups. This last sentences is a mess. There is a unique Sylow p-subgroup, > yes. There are NO OTHER Sylow p-subgroups. Because there is one and > only one p-Sylow subgroup. All Sylow subgroups have the same size. >We can think of this >unique, maximal Sylow p-subgroup It makes no sense to apply the adjective maximal to a Sylow > p-subgroup. > so that it contains elements of order p^a >(p^a is the order the Sylow p-subgroups that are contained in the maximal >Sylow p-subgroup). The parenthetical comment is nonsense, and you are incorrect anyway in > how you phrased it. > Is the right way to prove it? Not entirely, though you are close. Note that every element of a Sylow p-subgroup has order a power of p, > so any Sylow p-subgroup is contained in the set of all elements whose > order is a power of p. This is true in any group. For the reverse inclusion, let P be THE Sylow p-subgroup of G (we can > say the by (iii) above). Let g in G be an element whose order is a > power of p. We want to show that g is in P (to show that the set of > all elements whose order is a power of p is contained in P). Consider the subgroup . -- > It's not denial. I'm just very selective about > what I accept as reality. > --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin > magidin-at-member-ams-org > meaningful statements === Subject: Re: Conventions (was Re: Misnomer being taught in all sorts of math texts?) > .... Same goes for multivalued function. > When taken LITERALLY, YES it IS totally absurd. But it's > shouldn't. Although I may not approve of names like that, > and I can voice my disapproval of them, I do remember > that names are just names, and if they aren't truly causing > a lot of harm, thre is no urgent need to change them.... You're ignoring history, which often produces awkward conventions. The meaning of function has developed and gradually changed since its early use as in . Multi-valued functions were well-established within complex variable theory _before_ the arrival of set theory and the growing preference for the modern the term multi-valued function as totally absurd, but I'd rather just call it old-fashioned. Ken Pledger. === Subject: Re: Conventions (was Re: Misnomer being taught in all sorts of math texts?) .... Same goes for multivalued function. > When taken LITERALLY, YES it IS totally absurd. But it's > shouldn't. Although I may not approve of names like that, > and I can voice my disapproval of them, I do remember > that names are just names, and if they aren't truly causing > a lot of harm, thre is no urgent need to change them.... You're ignoring history, which often produces awkward conventions. Well actually I was not aware of this history. > The meaning of function has developed and gradually changed since its > early use as in . Multi-valued > functions were well-established within complex variable theory _before_ > the arrival of set theory and the growing preference for the modern > the term multi-valued function as totally absurd, but I'd rather just > call it old-fashioned. Ken Pledger. So then why not move away from it's use? === Subject: probability of an event from two overlapping pdf's If I know the probability of an event occuring during the period now until point1, and I also know the probability of the event occuring from now until point2, and point2>point1, is there any way to know the probability of that event occuring in the time period of point1 to point2? === Subject: Re: probability of an event from two overlapping pdf's > If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? That depends on whether the event can occur only once between now and point 2, or if it can occur multiple times (in the latter case event occurring would mean even occurring at least once). === Subject: Re: probability of an event from two overlapping pdf's > If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? Yes. Probabilities add over disjoint intervals, so if T is the time when the event occurs, we have Pr{0 <= T <= t2} = Pr{0 <= T <= t1} + Pr{t1 < T <= t2} for any t2 > t1 > 0. R.G. Vickson === Subject: Re: probability of an event from two overlapping pdf's If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? Yes. Probabilities add over disjoint intervals, so if T is the time > when the event occurs, we have Pr{0 <= T <= t2} = Pr{0 <= T <= t1} + > Pr{t1 < T <= t2} for any t2 > t1 > 0. R.G. Vickson > - Show quoted text - Yes, that makes sense, thank you. So if I had the pdf of the event from now until point one and the pdf for the event from now until point2, can I derive the pdf from point one to point2? I am interested in getting that pdf. === Subject: Re: probability of an event from two overlapping pdf's > If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? Yes. Probabilities add over disjoint intervals, so if T is the time > when the event occurs, we have Pr{0 <= T <= t2} = Pr{0 <= T <= t1} + > Pr{t1 < T <= t2} for any t2 > t1 > 0. R.G. Vickson > - Show quoted text - Yes, that makes sense, thank you. So if I had the pdf of the event > from now until point one and the pdf for the event from now until > point2, can I derive the pdf from point one to point2? I am > interested in getting that pdf. Please correct me if I am wrong, but the way I see it (judging from your original post) is as follows. You have a random time, T, at which something can happen. This random variable is >= 0 (counting 'now' as time zero), and it has some probability density function f(t). This means that Pr{t < T < t+h) = f(t)*h + o(h), where o(h) stands for terms of higher than first order in h. In other words, for very small h, Pr{t < T < t+h) = f(t)*h is a good approximation. The (cumulative) distribution function is F(t) = P{T <= t} = integral(g(x)dx for x = 0 --> t). OK so far? Now you say (I think) that you have given values of F(t1) and F(t2); these will be different if t2 > t1 and if f(t) > 0 for all t in some subinterval of the interval from t1 to t2. My response indicated that Pr{t1 < T <= t2} = F(t2) - F(t1). This also equals Pr{t1 <= T <= t2} if the random variable is purely continuous, so that Pr{T = t1} = 0. I don't understand what you mean by a pdf for the event from 0 to t1. Do you mean that you are looking only at that part of f(t) that goes from t = 0 to t = t1? I also don't know what you mean when you say you have a different pdf for 0 to t2. Well, of course, that part of f(t) that extends beyond t1 will not be seen in the graph of (t,f(t)) for 0 <= t <= t1. On the other hand, if you mean something different, your problem description likely makes no sense. For instance, if you say that you have a pdf f1(t) for 0 <= t <= t1 and another pdf f2(t) for 0 <= t <= t2 (WITH f1(t) not equal to f2(t) for 0 <= t <= t1) then you have something that has no obvious meaning, and you should start over. R.G. Vickson === Subject: Re: probability of an event from two overlapping pdf's If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? Yes. Probabilities add over disjoint intervals, so if T is the time > when the event occurs, we have Pr{0 <= T <= t2} = Pr{0 <= T <= t1} + > Pr{t1 < T <= t2} for any t2 > t1 > 0. R.G. Vickson > - Show quoted text - Yes, that makes sense, thank you. So if I had the pdf of the event > from now until point one and the pdf for the event from now until > point2, can I derive the pdf from point one to point2? I am > interested in getting that pdf. Please correct me if I am wrong, but the way I see it (judging from > your original post) is as follows. You have a random time, T, at which > something can happen. This random variable is >= 0 (counting 'now' as > time zero), and it has some probability density function f(t). This > means that Pr{t < T < t+h) = f(t)*h + o(h), where o(h) stands for > terms of higher than first order in h. In other words, for very small > h, Pr{t < T < t+h) = f(t)*h is a good approximation. The (cumulative) > distribution function is F(t) = P{T <= t} = integral(g(x)dx for x = 0 > --> t). OK so far? Now you say (I think) that you have given values of > F(t1) and F(t2); these will be different if t2 > t1 and if f(t) > 0 > for all t in some subinterval of the interval from t1 to t2. My > response indicated that Pr{t1 < T <= t2} = F(t2) - F(t1). This also > equals Pr{t1 <= T <= t2} if the random variable is purely > continuous, so that Pr{T = t1} = 0. I don't understand what you mean by a pdf for the event from 0 to t1. > Do you mean that you are looking only at that part of f(t) that goes > from t = 0 to t = t1? I also don't know what you mean when you say you > have a different pdf for 0 to t2. Well, of course, that part of f(t) > that extends beyond t1 will not be seen in the graph of (t,f(t)) for 0 > <= t <= t1. On the other hand, if you mean something different, your > problem description likely makes no sense. For instance, if you say > that you have a pdf f1(t) for 0 <= t <= t1 and another pdf f2(t) for 0 > <= t <= t2 (WITH f1(t) not equal to f2(t) for 0 <= t <= t1) then you > have something that has no obvious meaning, and you should start over. Actually. let me correct that a bit. You /could/ have different CONDITIONAL pdfs f1 for the interval [0,t1] and f2 for the interval [0,t2], but even in that case f1 and f2 can differ only by a scale factor in the interval [0,t1]; that is, we must have f2(t) = c*f1(t) for 0 <= t <= t1. Here, c = Pr{T <=t1}/Pr{T <= t2}, because f1(t) = f(t)/Pr{T <= t1} (for 0 <= t <= t1) and f2(t) = f(t)/Pr{T <= t2} (for 0 <= t <= t2). RGV R.G. Vickson === Subject: Re: probability of an event from two overlapping pdf's > If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? Yes. Probabilities add over disjoint intervals, so if T is the time > when the event occurs, we have Pr{0 <= T <= t2} = Pr{0 <= T <= t1} + > Pr{t1 < T <= t2} for any t2 > t1 > 0. R.G. Vickson > - Show quoted text - Yes, that makes sense, thank you. So if I had the pdf of the event > from now until point one and the pdf for the event from now until > point2, What do you mean by that? The obvious interpretation would be that the pdf is a function of time (i.e. PDF(t) is the probability density of the event happening at time t), but then there is only one pdf for the whole time period -- there aren't separate pdf's for now to point1, now to point2, and point1 to point2. All the probabilities that you mention are a consequence of that single pdf (but see my other post). In your original question you didn't mention pdf's, only individual probabilities, which are just one number. > can I derive the pdf from point one to point2? I am > interested in getting that pdf. === Subject: Re: probability of an event from two overlapping pdf's If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? Yes. Probabilities add over disjoint intervals, so if T is the time > when the event occurs, we have Pr{0 <= T <= t2} = Pr{0 <= T <= t1} + > Pr{t1 < T <= t2} for any t2 > t1 > 0. R.G. Vickson > - Show quoted text - Yes, that makes sense, thank you. So if I had the pdf of the event > from now until point one and the pdf for the event from now until > point2, What do you mean by that? The obvious interpretation would be that the > pdf is a function of time (i.e. PDF(t) is the probability density of > the event happening at time t), but then there is only one pdf for the > whole time period -- there aren't separate pdf's for now to point1, > now to point2, and point1 to point2. All the probabilities that you > mention are a consequence of that single pdf (but see my other post). In your original question you didn't mention pdf's, only individual > probabilities, which are just one number. Or perhaps, as it occurred to me later, your pdfs relate to the *number of times* the event occurs in the stated intervals? So, you know the probability of the event occurring 0,1,2... times between now and point1, and ditto between now and point2. (Not that this theory is in any way borne out by the wording of your original post!) In that case the question makes sense, but you don't have enough information to find the answer. === Subject: Re: probability of an event from two overlapping pdf's > If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? Yes. Probabilities add over disjoint intervals, so if T is the time > when the event occurs, we have Pr{0 <= T <= t2} = Pr{0 <= T <= t1} + > Pr{t1 < T <= t2} for any t2 > t1 > 0. R.G. Vickson > - Show quoted text - Yes, that makes sense, thank you. So if I had the pdf of the event > from now until point one and the pdf for the event from now until > point2, What do you mean by that? The obvious interpretation would be that the > pdf is a function of time (i.e. PDF(t) is the probability density of > the event happening at time t), but then there is only one pdf for the > whole time period -- there aren't separate pdf's for now to point1, > now to point2, and point1 to point2. All the probabilities that you > mention are a consequence of that single pdf (but see my other post). In your original question you didn't mention pdf's, only individual > probabilities, which are just one number. Or perhaps, as it occurred to me later, your pdfs relate to the > *number of times* the event occurs in the stated intervals? So, you > know the probability of the event occurring 0,1,2... times between now > and point1, and ditto between now and point2. (Not that this theory is > in any way borne out by the wording of your original post!) In that > case the question makes sense, but you don't have enough information > to find the answer.- Hide quoted text - - Show quoted text - problem a little bit and see if you can help me. Say I am standing at the top of a hill with a ball. If I role this ball down the hill, It may end up in any of ten locations when it is 10 feet down the hill. The probability of the ball landing in each spot is defined by a known function. I also know the function of a ball starting on the top of the hill ending up at any one of ten locations 20 feet down teh hill. describes the balls movement from the point 10 feet down the hill to the point 20 feet down the hill? === Subject: Re: probability of an event from two overlapping pdf's > If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? > Yes. Probabilities add over disjoint intervals, so if T is the time > when the event occurs, we have Pr{0 <= T <= t2} = Pr{0 <= T <= t1} + > Pr{t1 < T <= t2} for any t2 > t1 > 0. > R.G. Vickson > - Show quoted text - Yes, that makes sense, thank you. So if I had the pdf of the event > from now until point one and the pdf for the event from now until > point2, What do you mean by that? The obvious interpretation would be that the > pdf is a function of time (i.e. PDF(t) is the probability density of > the event happening at time t), but then there is only one pdf for the > whole time period -- there aren't separate pdf's for now to point1, > now to point2, and point1 to point2. All the probabilities that you > mention are a consequence of that single pdf (but see my other post). In your original question you didn't mention pdf's, only individual > probabilities, which are just one number. Or perhaps, as it occurred to me later, your pdfs relate to the > *number of times* the event occurs in the stated intervals? So, you > know the probability of the event occurring 0,1,2... times between now > and point1, and ditto between now and point2. (Not that this theory is > in any way borne out by the wording of your original post!) In that > case the question makes sense, but you don't have enough information > to find the answer.- Hide quoted text - - Show quoted text - problem a little bit and see if you can help me. Say I am standing at > the top of a hill with a ball. If I role this ball down the hill, It > may end up in any of ten locations when it is 10 feet down the hill. > The probability of the ball landing in each spot is defined by a known > function. I also know the function of a ball starting on the top of describes the balls movement from the point 10 feet down the hill to > the point 20 feet down the hill? With only that information, no. As a simple example, say you had only two points at each level rather than ten -- say P1 and P2 at 10 ft and P3 and P4 at 20 ft. Say the 10ft probability is 1/2 for P1 and 1/2 for P2, and the 20ft probability is 1/2 for P3 and 1/2 for P4. This could be achieved by a ball at P1 always travelling to P3 and a ball at P2 always travelling to P4, or a ball at P1 always travelling to P4 and a ball at P2 always travelling to P3, or any of innumerable possibilities in between. === Subject: Re: probability of an event from two overlapping pdf's > If I know the probability of an event occuring during the period now > until point1, and I also know the probability of the event occuring > from now until point2, and point2>point1, is there any way to know the > probability of that event occuring in the time period of point1 to > point2? Yes. Probabilities add over disjoint intervals, so if T is the time > when the event occurs, we have Pr{0 <= T <= t2} = Pr{0 <= T <= t1} + > Pr{t1 < T <= t2} for any t2 > t1 > 0. R.G. Vickson > - Show quoted text - Yes, that makes sense, thank you. So if I had the pdf of the event > from now until point one and the pdf for the event from now until > point2, can I derive the pdf from point one to point2? I am > interested in getting that pdf.- Hide quoted text - - Show quoted text - Also, the two pdf's are different. === Subject: Solutions Manuals! (List) I am looking for a solutions manual for R.C. Hibbeler's structural analysis, 6th Edition!!!! Email me if you have this manual and would like to trade for any other manuals I have: Thermodynamics: An Engineering Approach by Cengel & Boles - 6th Edition Mechanics of Solids by R.C. Hibbeler - 6th Edition Structural Analysis by R.C. Hibbeler - 5th Edition Please email if you'd be willing to trade for any of the manuals above or need one! Email: whatwelost at yahoo.com (replace at with @) === Subject: Re: Zero on the keyboard > I was wondering why the zero key follows (is to the right of) the 9 > key on a qwerty keyboard. Doesn't it make more sense for the zero key > to preceed the 1 key? Does anyone have any insight into the reason for > this? I've wondered this same thing. > Also why is the zero key on the numeric keypad so large? If you watch someone (efficiently) use one of those large calculators that print onto the roll of paper, you will notice that the zero is pressed most often. So, when they are flying through sheets of numbers, the most often pressed key is the easiest one to hit. === Subject: Re: Zero on the keyboard Also why is the zero key on the numeric keypad so > large? If you watch someone (efficiently) use one of those > large calculators > that print onto the roll of paper, you will notice > that the zero is > pressed most often. So, when they are flying through > sheets of > numbers, the most often pressed key is the easiest > one to hit. > Some numeric data entry keypads also have a large 00 key, particularly in the banking world. Check encoding keypads have this key, so the encoder only has to hit one key, instead of the 0 key twice, for checks written in even dollar amounts. === Subject: Re: [] Pythagorean Septuple > 1^2+3^2+5^2+6^2+7^2+7^2=13^2 3^2+3^2+4^2+5^2+6^2+7^2=12^2 Youusetoomanyspaces.Usefewertomakeithardertoread. > of course 2^2+6^2+10^2+12^2+14^2+14^=26^2 6^2+6^2+8^2+10^2+12^2+14^2=24^2 18^2+18^2+24^2+30^2+36^2+42^2=72^2 >Notbeinginthespaciousstyleofothers,isalsodismissedasunreadable. I do not understand 2*(xy)^2 = a^2+b^2+c^2 2*(wv)^2 = d^2+e^2+f^2 2*[(xy)^2 + (wv)^2] = a^2+b^2+c^2+d^2+e^2+f^2 Vincenzo Librandi === === Subject: Re: what is teh easy way to find the factors of a number? > I saw this question in GRE: which of the following represents the > number of positive integers that are both divisors of 216 and > multiples of 6. Options are (i) 6, (ii) nine, (iii) twenty-four, (iv) > thirty-six and (v) seventy-two. > Now what is the easiest way to solve this problem? I was trying to > write all factors of 216 but that is going to take a lot of time. Answer: Number of divisors of 216/6. 216/6 = 36 = 2^2 * 3^2. > Number of divisors of 36 is 3 * 3. > Indeed, 6|N|216 <-> 1|N/6|36 etc, but that's too much work. > SIMPLER Employ the powerful twosome: parity, involution > Since 216 != NN, it has an even #divisors (via d -> 216/d ) > so removing 1,2,3 leaves an odd #divisors; so it must be (ii). How is it that striking out three divisors shows us > that we must strike out an odd number of divisors? The > divisors of 216 that do not figure into the answer are > 1, 2, 3, 4, 8, 9, 27, and the map (1,2,3) -> (216 108 72) > does not suggest anything to me. The first powers, > squares and cubes of (1, 2, 3) are the stricken out > divisors but I had to count them to determine the parity. The point is simply that the set of N such that A|N|ABB admits involution N -> A(ABB/N) with one fixed point AB, so the set must have odd parity, since the involution partitions non-fixed-points into _pairs_ { N, AABB/N }. This is a slight generalization of the well-known fact that the number of divisors of N is odd iff N is a perfect square -- one of the prototypical examples of involutional parity. Of course the proof above works in this special case (A = 1). Notice that all the answers except one are even, which is a strong clue that parity may provide an elegant solution. Apologies that my original post didn't make this so clear. --Bill Dubuque === Subject: Re: what is teh easy way to find the factors of a number? > I saw this question in GRE: which of the following represents the > number of positive integers that are both divisors of 216 and > multiples of 6. Options are (i) 6, (ii) nine, (iii) twenty-four, (iv) > thirty-six and (v) seventy-two. > Now what is the easiest way to solve this problem? I was trying to > write all factors of 216 but that is going to take a lot of time. Answer: Number of divisors of 216/6. 216/6 = 36 = 2^2 * 3^2. > Number of divisors of 36 is 3 * 3. > Indeed, 6|N|216 <-> 1|N/6|36 etc, but that's too much work. > SIMPLER Employ the powerful twosome: parity, involution > Since 216 != NN, it has an even #divisors (via d -> 216/d ) > so removing 1,2,3 leaves an odd #divisors; so it must be (ii). How is it that striking out three divisors shows us > that we must strike out an odd number of divisors? The > divisors of 216 that do not figure into the answer are > 1, 2, 3, 4, 8, 9, 27, and the map (1,2,3) -> (216 108 72) > does not suggest anything to me. The first powers, > squares and cubes of (1, 2, 3) are the stricken out > divisors but I had to count them to determine the parity. The point is simply that the set of N such that A|N|ABB > admits involution N -> A(ABB/N) with one fixed point AB, OK. I see this, and will be on the look-out for it in future. > so the set must have odd parity, since the involution > partitions non-fixed-points into _pairs_ { N, AABB/N }. This is a slight generalization of the well-known fact that > the number of divisors of N is odd iff N is a perfect square > -- one of the prototypical examples of involutional parity. > Of course the proof above works in this special case (A = 1). Notice that all the answers except one are odd, which is > a strong clue that parity may provide an elegant solution. Apologies that my original post didn't make this so clear. That's alright. Best not to spell it out if I might take it from there. -- Michael Press === Subject: Re: what is teh easy way to find the factors of a number? > > The point is simply that the set of N such that A|N|ABB > admits involution N -> A(ABB/N) with one fixed point AB, > so the set must have odd parity, since the involution > partitions non-fixed-points into _pairs_ { N, AABB/N }. OK. I see this, and will be on the look-out for it in future. It may also be viewed geometrically as a reflection symmetry. Suppose more generally we are interested in the parity of the rootset of a symmetric function f(x,y). Since f(x,y) = f(y,x), off-diagonal roots come in pairs (x,y), (y,x). Therefore the parity of the rootset is the same as the parity of the rootset restricted to the diagonal f(x,x). E.g. in the classical case where f(x,y) = xy - n, we see that the parity of the number of divisors of n equals the number of solutions of x^2 = n, so n has an odd number of divisors iff n is a perfect square. In more geometric language, we've simply exploited an obvious reflection symmetry around the line y = x to pair up all of the off-diagonal roots. This simple idea can arise in disguise in many complicated scenarios, so it's wise to master it first in simple situations like those above. For an example of a more complex occurrence see my prior post [1] quoting D. Zagier's A One-Sentence Proof That Every Prime p = 1 (mod 4) Is a Sum of Two Squares. --Bill Dubuque === Subject: Re: Time and Arithmetic (15/16). > 1.- The real line, that is a line with a fixed scale so that every real > number corresponds to a unique point on the line. The real line works > as a coding for the points of a line. > 14.- We can consider different placements of natural numbers as > natural numbers in movement and so, the second derivative of the > area as a real acceleration. 15.- Therefore there exists a characterization of the Goldbach > Conjecture that depends on time. Since you don't mention time in any of the first 14 items, how does item 15 follow? You could just as easily have said: Therefore there exists a characterization of the Goldbach Conjecture that depends on money. You mention numbers in movement, but without any explanation of what that phrase is supposed to mean. === Subject: Re: Time and Arithmetic (15/16). > 1.- The real line, that is a line with a fixed > scale so that every real > number corresponds to a unique point on the line. > The real line works > as a coding for the points of a line. > 14.- We can consider different placements of > natural numbers as > natural numbers in movement and so, the second > derivative of the > area as a real acceleration. 15.- Therefore there exists a characterization of > the Goldbach > Conjecture that depends on time. Since you don't mention time in any of the first 14 > items, how > does item 15 follow? Very funny, in 14.- I forgot to say that movement is related to time. > You could just as easily have > said: > Therefore there exists a characterization of the > he Goldbach > Conjecture that depends on money. I could, but it was impossible to prove it. > You mention numbers in movement, but without any > explanation > of what that phrase is supposed to mean. There is a paper with all the details, but I understand that people are very busy and time is gold ( or money ). Fernando. === Subject: Re: Time and Arithmetic (15/16). > 1.- The real line, that is a line with a fixed scale so that every real > number corresponds to a unique point on the line. The real line works > as a coding for the points of a line. > 14.- We can consider different placements of natural numbers as > natural numbers in movement and so, the second derivative of the > area as a real acceleration. > 15.- Therefore there exists a characterization of the Goldbach > Conjecture that depends on time. Since you don't mention time in any of the first 14 items, how > does item 15 follow? You could just as easily have said: > Therefore there exists a characterization of the Goldbach > Conjecture that depends on money. Not to defend Fernando's analysis, but he *did* mention velocity. Doesn't velocity presuppose time? -- I believe that my job is to go out and explain to the people what's on my mind. That's why I'm having this press conference, see? I'm telling you what's on my mind. And what's on my mind is winning the war on terror. --- George W. Bush === Subject: Re: Time and Arithmetic (15/16). <87ve8fjar7.fsf@phiwumbda.org> 14.- We can consider different placements of natural numbers as > natural numbers in movement and so, the second derivative of the > area as a real acceleration. > 15.- Therefore there exists a characterization of the Goldbach > Conjecture that depends on time. > Since you don't mention time in any of the first 14 items, how > does item 15 follow? You could just as easily have said: > Therefore there exists a characterization of the Goldbach > Conjecture that depends on money. > Not to defend Fernando's analysis, but he *did* mention velocity. > Doesn't velocity presuppose time? Well, he mentions numbers in movement and acceleration without bothering to explain what they are supposed to mean. Asking about velocity may or may not be relevant to his claim. Does a moving number possess some attribute that changes over time? === Subject: Re: Time and Arithmetic (15/16). > 14.- We can consider different placements of > natural numbers as > natural numbers in movement and so, the second > derivative of the > area as a real acceleration. > 15.- Therefore there exists a characterization of > the Goldbach > Conjecture that depends on time. > > Since you don't mention time in any of the first > 14 items, how > does item 15 follow? You could just as easily > have said: > Therefore there exists a characterization of the > Goldbach > Conjecture that depends on money. Not to defend Fernando's analysis, but he *did* > mention velocity. > Doesn't velocity presuppose time? Well, he mentions numbers in movement and > acceleration > without bothering to explain what they are supposed > to mean. Of course, extremely simplified. Better here: http://ficus.pntic.mec.es/~frej0002/conjetura.pdf > Asking about velocity may or may not be relevant to > his claim. > Does a moving number possess some attribute that > changes > over time? Yes it has. Read the paper and you will understand. Fernando. --------------------------------------------------------- I have sometimes thought that the profound mystery which envelops our conceptions relative to prime numbers depends upon the limitations of our faculties in regard to time which like space may be in essence poly-dimensional and that this and other such sort of truths would become self-evident to a being whose mode of perception is according to superficially as opposed to our own limitation to linearly extended time. (J.J. Sylvester) --------------------------------------------------------- === Subject: Re: Time and Arithmetic (15/16). > 14.- We can consider different placements of natural numbers as > natural numbers in movement and so, the second derivative of the > area as a real acceleration. 15.- Therefore there exists a characterization of the Goldbach > Conjecture that depends on time. Since you don't mention time in any of the first 14 items, how > does item 15 follow? You could just as easily have said: > Therefore there exists a characterization of the Goldbach > Conjecture that depends on money. > Not to defend Fernando's analysis, but he *did* mention velocity. > Doesn't velocity presuppose time? Well, he mentions numbers in movement and acceleration > without bothering to explain what they are supposed to mean. Asking about velocity may or may not be relevant to his claim. > Does a moving number possess some attribute that changes > over time? No idea what moving number is supposed to mean, but motion typically presupposes time. That's not to say that all this isn't just nutty, but the step from moving numbers to time is surely not the most implausible bit. -- Not all features that are found on the Security tab are designed to help make your documents and files more secure. --Microsoft on Office security features (after it was pointed out by a third party that a certain password setting is easily bypassed.) === Subject: Re: HELP!!!! <47309ec1$0$17028$9a6e19ea@news.newshosting.com> <4730aead$0$17039$9a6e19ea@news.newshosting.com > The perpetrator of the post has been generating > these requests for solution manuals under a > multitude of (fake) names and e-mail addresses > for several months now. The reason the asshole > doesn't use a more complete description in the > subject line is that everyone now ignores posts > that look like solution manual requests. WOW!!! I didn't know you would ever call a woman that!!!!But for your > information it's not a perpetrator, it's an actual live person. I am > loking for this manual for my boyfriend. He is a student at IIT and I > thought that helping out was a good thing but now I understand why I > NEVER had tried to do this before!!!!! It's people like you who turn > us computer illiterate people not want to do this. But if maybe you > can find it in your not so kind heart to help me out that would be > great! Bull. Also, that you claim to be helping your boyfriend > to cheat at his coursework is, shall we say, less > than a stellar personal quality to be advertising. Add idiot to asshole. Hmmmmm I guess you would not know what it means to help other people? > I guess no one has ever done this for you huh? I'm sorry you feel that > way. I wouldn't call it cheating either since the manual he is > looking for is an older version. He is using the 8th edition, but why > do I even bother telling you about it since you're gonna think > people names, it's really not very christain like, and that's so > highschoo!!! You're being too hard on those who've rebuffed your solution manual request. If I had one, I would be happy to send it to you so that your boyfriend will get passing marks on his homework, not learn anything, and then fail the final exam. At least the others are giving your boyfriend the option to drop the class while there's still time and save his GPA. You should be thanking them and be wary of those who try to help. === Subject: Re: HELP!!!! <47309ec1$0$17028$9a6e19ea@news.newshosting.com> <4730aead$0$17039$9a6e19ea@news.newshosting.com > The perpetrator of the post has been generating > these requests for solution manuals under a > multitude of (fake) names and e-mail addresses > for several months now. The reason the asshole > doesn't use a more complete description in the > subject line is that everyone now ignores posts > that look like solution manual requests. WOW!!! I didn't know you would ever call a woman that!!!!But for your > information it's not a perpetrator, it's an actual live person. I am > loking for this manual for my boyfriend. He is a student at IIT and I > thought that helping out was a good thing but now I understand why I > NEVER had tried to do this before!!!!! It's people like you who turn > us computer illiterate people not want to do this. But if maybe you > can find it in your not so kind heart to help me out that would be > great! Bull. Also, that you claim to be helping your boyfriend > to cheat at his coursework is, shall we say, less > than a stellar personal quality to be advertising. Add idiot to asshole. Hmmmmm I guess you would not know what it means to help other people? I think we all have experience helping people with homework. > I guess no one has ever done this for you huh? Nobody has ever provided me with a solutions manual. Help would have consisted of helping me think through my own solution, and of advising me when I got stuck. The same kind of help that everybody in this thread is willing to offer any student who asks. > I'm sorry you feel that > way. I wouldn't call it cheating either since the manual he is > looking for is an older version. Uh-huh. What would be the point in a solutions manual for questions he doesn't have? > He is using the 8th edition, but why > do I even bother telling you about it since you're gonna think > whatever you want to. Part of the skepticism comes from the fact that last few months with both requests for solution manuals and ads for sites claiming they have them > people names, it's really not very christain like, and that's so > highschoo!!! It's fairly standard for the lazier students, after being rebuffed for answers, to post an angry response saying why the hell did you post if you didn't want to help? The answer is that people do want to help. They want to help students learn. Solving their homework for them is not helpful in that process. - Randy === Subject: Re: HELP!!!! > Right. Providing a solutions manual so that your boyfriend can cheat > would be a virtuous act of kindness. Geez! What is up with you guys? This was NEVER the intention and now I > REALLY see that it was a mistake to even ask for something like this! > So I guess it's ok to put up porn ads and no one seems to care about > that but when someone wants a simple manual they call it cheating > and even call people names! Wow! So mature!!!! > Yes, shame on me! I'm sure it was not for the purpose of cheating! Rather, it was a simple, wholesome request for copyright infringement. Sorry for the lack of charity. If you wanted a legitimate copy of this text, go to the publisher's site and find a way to request it. -- Jesse F. Hughes We will run this with the same kind of openness that we've run Windows. Steve Ballmer, speaking about MS's new .Net project. === Subject: Re: HELP!!!! <47309ec1$0$17028$9a6e19ea@news.newshosting.com> <87hcjzkz0l.fsf@phiwumbda.org> <873avjkvbj.fsf@phiwumbda.org > Right. Providing a solutions manual so that your boyfriend can cheat > would be a virtuous act of kindness. Geez! What is up with you guys? This was NEVER the intention and now I > REALLY see that it was a mistake to even ask for something like this! > So I guess it's ok to put up porn ads and no one seems to care about > that but when someone wants a simple manual they call it cheating > and even call people names! Wow! So mature!!!! Yes, shame on me! I'm sure it was not for the purpose of cheating! > Rather, it was a simple, wholesome request for copyright infringement. Sorry for the lack of charity. If you wanted a legitimate copy of this text, go to the publisher's > site and find a way to request it. -- > Jesse F. Hughes We will run this with the same kind of openness that we've run > Windows. Steve Ballmer, speaking about MS's new .Net project. great help and I will think twice next time I ever have a question. === Subject: Help with math classes Check out this website. www.EmathLearning.com. We have three math learning packages, (1.) Computer Assisted Statistics, (2.) Elementary Algebra, and Business Algebra. The software would be an enormous aide for students taking any one of the three courses. Two other packages are the Financial calculator and a Statistical Calculator. We also have exams, forums, and free math learning movies. Our software is like having a teacher available 24/7. --Eduscape, LLC Fixed the url. === Subject: Elliptic Curve and Weierstrass P function There is a statement in Hartshorne's Algebraic Geometry that I do not see. It is the 3rd line in the proof of Proposition 4.18 of Chapter IV at page 329. I will summarize below: Let P be the Weierstass P-function with periods 1 and tau which define a lattice M on C. Let P' denote the derivative of P. So, we can define the holomorphic function phi : CM --> X by phi(z) = (P(z), P'(z)) where X is an elliptic curve in the affine plane. Now, let f : X --> X be a morphism of affine varieties. Then Hartshorne says the function g : C --> C (denoted as f bar in his book instead) induced by f via the pullback of phi must be holomorphic. How does he conclude that? This is how much I understand so far. Since f is an affine morphism, it is a polynomial map A^2 --> A^2. Hence, f is a polynomial map in terms of P and P'. Since P and P' generate the function field of elliptic functions, the composed map f o phi is a map of elliptic functions, which are holomorphic in CM. Therefore, since phi o g = f o phi, we conclude that the composed map phi o g must be holomophic too. But I still can't conclude from here why the induced map g must be holomorphic. -- -kira === Subject: ax^(n-1) + by^(n-1) + cz^(n-1) = 0 for x;y;z of gcd=1 Someone including me few days ago could think, that such equation will have only rare solution points or not at all ? I was pointed by John R. Ramsden to specific solution for n-1 = 2: once ax^2 + by^2 + cz^2 = 0 and especially for x=2; y=3; z=5; It is using vector products: (a;b;c) =(p;r;q)*(x^2;y^2;z^2) where p;r;q optional integers, then: a = ry2 - qz^2; b = pz^2 -rx^2; c = qx^2 -py^2; And so on we'll have identity: (ry^2 -qz^2)x^2 +(pz^2 -rx^2)y^2 +(qx^2 -py^2)z^2 = 0 Such identity will go for all powers of x;y;z; also for (n-1) where n primes etc. ( It was already said by John R. Ramsden: forget about the powers ) What else could be done if we remember again about the powers. Ro-Bin === Subject: Help! Ct = cYt-1, Kt = Yt-1, Yt = Ct + Kt - Kt-1. How to derive and solve this system for Yt? === Subject: Re: Help! > Ct = cYt-1, Kt = Yt-1, Yt = Ct + Kt - Kt-1. How to derive and solve this system for Yt? Your notation is very sloppy. I assume Ct means C subscript t, and (even worse) Yt-1 means Y subscript t - 1, and similarly for the other variables. If I am interpreting it correctly then the first thing to do is write one equation involving only Y and t. === Subject: Re: Help! > Ct = cYt-1, Kt = Yt-1, Yt = Ct + Kt - Kt-1. How to derive and solve this system for Yt? Ct = cYt-1, cYt = Ct + 1 Yt = Ct + Kt - Kt-1 Yt = Ct - 1 (c - 1)Yt = 2 Yt = 2/(c - 1) Kt = Yt - 1 = (3 - c)/(c - 1) Ct = cYt - 1 = 2c/(c - 1) - 1 = (c + 1)/(c - 1) > Your notation is very sloppy. I assume Ct means C subscript t, and > (even worse) Yt-1 means Y subscript t - 1, and similarly for the other > variables. > Ct = C * t Yt-1 = Y * t - 1 > If I am interpreting it correctly then the first thing to do is write > one equation involving only Y and t. Were he sloppy, he would have confused c and C. Do you think he did? Then he'd get: Yt = 2/(c - 1) Kt = Yt - 1 = (3 - c)/(c - 1) Ct = cYt - 1 = 2c/(c - 1) - 1 = (c + 1)/(c - 1) Ct = (C + 1)/(C - 1) t = (C + 1) / C(C - 1) Y = 2C/(C + 1) K = C(3 - C) / (C + 1) === Subject: Re: Help! Ct = cYt-1, Kt = Yt-1, Yt = Ct + Kt - Kt-1. How to derive and solve this system for Yt? Ct = cYt-1, > cYt = Ct + 1 Yt = Ct + Kt - Kt-1 > Yt = Ct - 1 (c - 1)Yt = 2 > Yt = 2/(c - 1) Kt = Yt - 1 = (3 - c)/(c - 1) > Ct = cYt - 1 = 2c/(c - 1) - 1 = (c + 1)/(c - 1) Your notation is very sloppy. I assume Ct means C subscript t, and > (even worse) Yt-1 means Y subscript t - 1, and similarly for the other > variables. Ct = C * t > Yt-1 = Y * t - 1 > I'm not so sure... why would anyone write Yt = Ct + Kt - Kt-1 rather than Yt = Ct - 1? Also, you'll notice that all the t-1s are written without spaces, while there are spaces around all the other signs. This could be deliberate. And in your interpretation the second equation is irrelevant for finding Yt. However, it's possible that you are correct and I am mistaken. Unless the OP drops back I guess we will never know for sure. === Subject: Re: Help! > I'm not so sure... why would anyone write Yt = Ct + Kt - Kt-1 rather > than Yt = Ct - 1? The other replier guessed that it means Y[t] = C[t] + K[t] - K[t-1] where I used [ ] for subscripts === Subject: Re: Help! <071120070804500340%anniel@nym.alias.net.invalid > I'm not so sure... why would anyone write Yt = Ct + Kt - Kt-1 rather > than Yt = Ct - 1? The other replier guessed that it means Y[t] = C[t] + K[t] - K[t-1] > where I used [ ] for subscripts Precisely. (But I don't see any other replier. In this thread I see only the original post and posts by me, William Elliot and you.) === Subject: Re: primitive intermediate jacobian L.S., what is the definition of a primitive intermediate jacobian? it's based on a lefschetz-induced map L: V->J_i(V) > from the variety V to it's intermediate jacobian J_i(V) the image of L is fairly well understood > so it is convenient to focus on > the more interesting part of the intermediate > J_i(V) / image(L) this is what is usually called the primitive intermediate jacobian Is there a holomorphic map from the intermediate jacobian onto the > primitive intermediate jacobian? there is a quotient in this direction -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > But it raises another question for me: what is this lefschetz induced map, i.e. what is your L? === Subject: Re: primitive intermediate jacobian > L.S., what is the definition of a primitive intermediate jacobian? it's based on a lefschetz-induced map L: V->J_i(V) > from the variety V to it's intermediate jacobian J_i(V) the image of L is fairly well understood > so it is convenient to focus on > the more interesting part of the intermediate > J_i(V) / image(L) this is what is usually called the primitive intermediate jacobian Is there a holomorphic map from the intermediate jacobian onto the > primitive intermediate jacobian? there is a quotient in this direction > But it raises another question for me: what is this lefschetz induced > map, i.e. what is your L? i am sorry for the vagueness but i didn't feel comfortable trying to respond from memory with much more detail the construction is based off the abel-jacobi map and is used to extract k-cycle information from the jacobian although lefschetz detailed some of the basic features for curves it was really griffiths who was able to apply the machinery to higher dimensional cases he had a series of papers on the periods of certain rational integrals that (among other things) details this map on the intermediate jacobian i don't have access to any of the resources here at work but i have some of the papers on this printed out at home and will try to give a more meaningful description tonight -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- === Subject: Re: primitive intermediate jacobian L.S., what is the definition of a primitive intermediate jacobian? it's based on a lefschetz-induced map L: V->J_i(V) > from the variety V to it's intermediate jacobian J_i(V) the image of L is fairly well understood > so it is convenient to focus on > the more interesting part of the intermediate > J_i(V) / image(L) this is what is usually called the primitive intermediate jacobian Is there a holomorphic map from the intermediate jacobian onto the > primitive intermediate jacobian? there is a quotient in this direction But it raises another question for me: what is this lefschetz induced > map, i.e. what is your L? i am sorry for the vagueness > but i didn't feel comfortable trying to respond from memory > with much more detail the construction is based off the abel-jacobi map > and is used to extract k-cycle information from the jacobian although lefschetz detailed some of the basic features for curves > it was really griffiths who was able to apply the machinery > to higher dimensional cases he had a series of papers > on the periods of certain rational integrals > that (among other things) details this map > on the intermediate jacobian i don't have access to any of the resources here at work > but i have some of the papers on this printed out at home > and will try to give a more meaningful description tonight -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > - Tekst uit oorspronkelijk bericht niet weergeven - - Tekst uit oorspronkelijk bericht weergeven - That would be very kind. I know a little bit of Griffith's work, but not too well. Let me indicate why I want to know about the primitive intermediate jacobian. Let X be an n-dimensional algebraic variety over C. Given a codimension k-cycle W on X that is homologous to zero, you can define an element in the intermediate jacobian, denoted by H(W). The intermediate jacobian is canonically iso to, or defined as: F^{n-k+1}H^{2n-2k+1}(X)^{*}/H_{2n-2k+1}(X,Z). The element that we associate to W is the functional that integrates a form alpha over the singular chain U whose boundary is W. This can also be done relative to a basis Y. We now have a family X--- > Y and the fibres X_y are algebraic varieties. This gives a variation of a hodge structure paramatrized by Y, namely the hodge structure of the fibres. We can have a fibration p: J--->Y, whose fibres are the k- th intermediate jacobians, J^{2k-1}(X_y). Supppose that there is a codimension k-cycle W in X such that W intersected with X_y is a cycle W_y that is homologous to zero. This gives rise to a function v:Y---> J, a section of p:J--->Y, that associates to y the element H_y(W_y). Now comes the part I want to find out about. The funtion v 'measures' how the closed forms on a particular type are related with the given cycle. The given type is here is: closed forms on the fibres, of type (n-k+j,n-k+1-j), with j=1,...,n-k+1. I want to know how PRIMITIVE forms are related to this cycle. Therefore I need something what should be the primitive jacobian. But I don't know if there is such a thing, and how it is defined. It also needs to have some properties sush as the intermediate jacobian has: there should be a fibration of these primitive jacobians, varying holomorphically, and the function v should be holomorphic as well. This is what lies behind my question. Googling 'primitive intermediate jacobian' didn't help me much, so I hope you can help me. cheers, i.s. === Subject: Re: primitive intermediate jacobian [..] > i don't have access to any of the resources here at work > but i have some of the papers on this printed out at home > and will try to give a more meaningful description tonight i apologise for not responding last night but i arrived home rather late and just fell asleep (last week before the biggest conference of the year for my profession so a lot of hurried testing of products...) > That would be very kind. I know a little bit of Griffith's work, but > not too well. Let me indicate why I want to know about the primitive > intermediate jacobian. > Let X be an n-dimensional algebraic variety over C. Given a > codimension k-cycle W on X that is homologous to zero, you can define > an element in the intermediate jacobian, denoted by H(W). The > intermediate jacobian is canonically iso to, or defined as: > F^{n-k+1}H^{2n-2k+1}(X)^{*}/H_{2n-2k+1}(X,Z). > The element that we associate to W is the functional that integrates a > form alpha over the singular chain U whose boundary is W. This can also be done relative to a basis Y. We now have a > family X---> Y and the fibres X_y are algebraic varieties. > This gives a variation of a hodge structure paramatrized by Y, > namely the hodge structure of the fibres. > We can have a fibration p: J--->Y, whose fibres are the k- > th intermediate jacobians, J^{2k-1}(X_y). > Supppose that there is a codimension k-cycle W in X such that W > intersected with X_y is a cycle W_y that is homologous to zero. > This gives rise to a function v:Y---> J, a section of p:J--->Y, that > associates to y the element H_y(W_y). Now comes the part I want to find out about. The funtion v 'measures' > how the closed forms on a particular type are related with the given > cycle. The given type is here is: closed forms on the fibres, of type > (n-k+j,n-k+1-j), with j=1,...,n-k+1. I want to know how PRIMITIVE forms are related to this cycle. > Therefore I need something what should be the primitive jacobian. > But I don't know if there is such a thing, and how it is defined. It > also needs to have some properties sush as the intermediate jacobian > has: there should be a fibration of these primitive jacobians, varying > holomorphically, and the function v should be holomorphic as well. well this is basically what the primitive intermediate jacobians do so i think we are probably talking about the same thing the only paper i was able to turn up this morning which describes this construct is harmonic volume, symmetric products, and the abel-jacobi map by william faucett this paper is a great fit for what you are investigating it also mentions griffiths papers but i couldn't find my copies (or it is possible i read them at the library and didn't copy...) anyway start with the abel-jacobi map I: V->J(V) classically this provides the representation of 1-cycles (or divisors) on the jacobian variety and it extends naturally to maps over the symmetric products I_k : V_k -> J(V) which represent the k-cycles on the jacobian now homological equivalence of k-cycles on V partition the algebraic cycles into lefschetz classes and form a subgroup of the group of k-cycles Z^k(V)/~ it is the image of this subgroup on J and through the construction you mention on the intermediate jacobian J_i which corresponds to image(L) from my first post this construction can be used to prove results on the relative strength of algebraic and homological equivalence now your function v appears very similar to a function nu in faucette's work relating the harmonic volume to the image of W - W^- on various intermediate jacobians so perhaps you may find what you need in his paper (and his references to work of ceresa and harris) in particular the jacobian used also varies holomorphically with moduli and has many of the nice properties you mention -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- === Subject: Re: primitive intermediate jacobian [..] > i don't have access to any of the resources here at work > but i have some of the papers on this printed out at home > and will try to give a more meaningful description tonight i apologise for not responding last night but i arrived home rather late and just fell asleep (last week before the biggest conference of the year for my profession so a lot of hurried testing of products...) > That would be very kind. I know a little bit of Griffith's work, but > not too well. Let me indicate why I want to know about the primitive > intermediate jacobian. > Let X be an n-dimensional algebraic variety over C. Given a > codimension k-cycle W on X that is homologous to zero, you can define > an element in the intermediate jacobian, denoted by H(W). The > intermediate jacobian is canonically iso to, or defined as: > F^{n-k+1}H^{2n-2k+1}(X)^{*}/H_{2n-2k+1}(X,Z). > The element that we associate to W is the functional that integrates a > form alpha over the singular chain U whose boundary is W. This can also be done relative to a basis Y. We now have a > family X---> Y and the fibres X_y are algebraic varieties. > This gives a variation of a hodge structure paramatrized by Y, > namely the hodge structure of the fibres. > We can have a fibration p: J--->Y, whose fibres are the k- > th intermediate jacobians, J^{2k-1}(X_y). > Supppose that there is a codimension k-cycle W in X such that W > intersected with X_y is a cycle W_y that is homologous to zero. > This gives rise to a function v:Y---> J, a section of p:J--->Y, that > associates to y the element H_y(W_y). Now comes the part I want to find out about. The funtion v 'measures' > how the closed forms on a particular type are related with the given > cycle. The given type is here is: closed forms on the fibres, of type > (n-k+j,n-k+1-j), with j=1,...,n-k+1. I want to know how PRIMITIVE forms are related to this cycle. > Therefore I need something what should be the primitive jacobian. > But I don't know if there is such a thing, and how it is defined. It > also needs to have some properties sush as the intermediate jacobian > has: there should be a fibration of these primitive jacobians, varying > holomorphically, and the function v should be holomorphic as well. well this is basically what the primitive intermediate jacobians do so i think we are probably talking about the same thing the only paper i was able to turn up this morning which describes this construct is harmonic volume, symmetric products, and the abel-jacobi map by william faucett this paper is a great fit for what you are investigating it also mentions griffiths papers but i couldn't find my copies (or it is possible i read them at the library and didn't copy...) anyway start with the abel-jacobi map I: V->J(V) classically this provides the representation of 1-cycles (or divisors) on the jacobian variety and it extends naturally to maps over the symmetric products I_k : V_k -> J(V) which represent the k-cycles on the jacobian now homological equivalence of k-cycles on V partition the algebraic cycles into lefschetz classes and form a subgroup of the group of k-cycles Z^k(V)/~ it is the image of this subgroup on J and through the construction you mention on the intermediate jacobian J_i which corresponds to image(L) from my first post this construction can be used to prove results on the relative strength of algebraic and homological equivalence now your function v appears very similar to a function nu in faucette's work relating the harmonic volume to the image of W - W^- on various intermediate jacobians so perhaps you may find what you need in his paper (and his references to work of ceresa and harris) in particular the jacobian used also varies holomorphically with moduli and has many of the nice properties you mention -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- === Subject: Solution manual for Hayt Electromagnetics / Circuits 7th, Jeager Microelectronics 3rd ! Get it fast! I have the complete electronic SOLUTION MANUAL in PDF format containing ALL solutions for the books listed below. If interested to buy, send me an email at akrmiha (at) gmail (dot) com 1. Engineering Electromagnetics (7th Edition) by William Hayt, John Buck [ISBN: 0073104639] 2. Engineering Circuit Analysis (7th Edition) by William Hayt, Jack Kemmerly, Steven Durbin [ISBN: 0073263184] 3. Microelectronic Circuit Design (3rd Edition) by Richard Jaeger, Travis Blalock [ISBN: 0073191639]. === Subject: Cosets of invertible matrices I'm currently learning about quotient groups http://en.wikipedia.org/wiki/Quotient_group There is one example of a quotient group and I would like to just confirm that I've understood it correctly. So, let G denotes the group of 3x3 invertible real matrices and N the subgroup of 3x3 real matrices with determinant 1. Then, by definition the quotient group is G/N = {gN : g in G}. Since det(gN) = det(g)det(N) = det(g) not= 0, i.e. gN is just a 3x3 matrix with determinant not equal to 0. Hence we have G/N = G, right? Britney === Subject: Re: Cosets of invertible matrices [corrected reply -- quoting was slightly off on my previous reply] I'm currently learning about quotient groups >http://en.wikipedia.org/wiki/Quotient_group There is one example of a quotient group >and I would like to just confirm that I've >understood it correctly. So, let G denotes the group of 3x3 invertible >real matrices and N the subgroup of 3x3 real >matrices with determinant 1. Then, by definition the quotient group is G/N = {gN : g in G}. Yes, but before you make a quotient group, you should verify that N is a _normal_ subgroup, not just any old subgroup. The verification is not hard, but you should do it, not just take it on faith. >Since det(gN) = det(g)det(N) = det(g) not= 0, N is not a matrix, so det(N) is not meaningful. >i.e. gN is just a 3x3 matrix with determinant >not equal to 0. No. gN is not a matrix -- it's a _set_ of matrices. >Hence we have G/N = G, right? No. But all elements of gN have the same nonzero determinant, right? Do those nonzero determinants comprise a group? What group? quasi === Subject: Re: Cosets of invertible matrices http://en.wikipedia.org/wiki/Quotient_group There is one example of a quotient group >and I would like to just confirm that I've >understood it correctly. So, let G denotes the group of 3x3 invertible >real matrices and N the subgroup of 3x3 real >matrices with determinant 1. Then, by definition the quotient group is G/N = {gN : g in G}. Yes, but before you make a quotient group, you should verify that N is > a _normal_ subgroup, not just any old subgroup. The verification is > not hard, but you should do it, not just take it on faith. Since det(gN) = det(g)det(N) = det(g) not= 0, N is not a matrix, so det(N) is not meaningful. i.e. gN is just a 3x3 matrix with determinant >not equal to 0. No. gN is not a matrix -- it's a _set_ of matrices. Hence we have G/N = G, right? No. But all elements of gN have the same nonzero determinant, right? Do those nonzero determinants comprise a group? What group? quasi For each _fixed_ g in G we have: gN is a set of matrices with the same nonzero determinant. The set of all gN forms a group where the identity element is given by N. The inverse to gN is hN where det(g)det(h) = 1. I rephrase my question then: Do we have G = U_g (gN) ? where U_g denotes the union over all g in G. === Subject: Re: Cosets of invertible matrices > [corrected reply -- quoting was slightly off on my previous reply] >I'm currently learning about quotient groups >http://en.wikipedia.org/wiki/Quotient_group >There is one example of a quotient group >and I would like to just confirm that I've >understood it correctly. >So, let G denotes the group of 3x3 invertible >real matrices and N the subgroup of 3x3 real >matrices with determinant 1. >Then, by definition the quotient group is >G/N = {gN : g in G}. > Yes, but before you make a quotient group, you should verify that N is > a _normal_ subgroup, not just any old subgroup. The verification is > not hard, but you should do it, not just take it on faith. >Since det(gN) = det(g)det(N) = det(g) not= 0, > N is not a matrix, so det(N) is not meaningful. >i.e. gN is just a 3x3 matrix with determinant >not equal to 0. > No. > gN is not a matrix -- it's a _set_ of matrices. >Hence we have G/N = G, right? > No. > But all elements of gN have the same nonzero determinant, right? > Do those nonzero determinants comprise a group? What group? > quasi >For each _fixed_ g in G we have: >gN is a set of matrices with the same nonzero determinant. The set of all gN forms a group where the identity element >is given by N. The inverse to gN is hN where det(g)det(h) = 1. I rephrase my question then: Do we have G = U_g (gN) ? where U_g denotes the union over all g in G. Sure, but that's always true -- the cosets (left or right, pick one) with respect to any subgroup partition the group. But your original question still deserves an answer. What is the nature of the group G/N? More precisely, G/N is isomorphic to what well known group? quasi === Subject: Re: Cosets of invertible matrices [corrected reply -- quoting was slightly off on my previous reply] I'm currently learning about quotient groups >http://en.wikipedia.org/wiki/Quotient_group There is one example of a quotient group >and I would like to just confirm that I've >understood it correctly. So, let G denotes the group of 3x3 invertible >real matrices and N the subgroup of 3x3 real >matrices with determinant 1. Then, by definition the quotient group is G/N = {gN : g in G}. Yes, but before you make a quotient group, you should verify that N is > a _normal_ subgroup, not just any old subgroup. The verification is > not hard, but you should do it, not just take it on faith. Since det(gN) = det(g)det(N) = det(g) not= 0, N is not a matrix, so det(N) is not meaningful. i.e. gN is just a 3x3 matrix with determinant >not equal to 0. No. gN is not a matrix -- it's a _set_ of matrices. Hence we have G/N = G, right? No. But all elements of gN have the same nonzero determinant, right? Do those nonzero determinants comprise a group? What group? quasi >For each _fixed_ g in G we have: >gN is a set of matrices with the same nonzero determinant. >The set of all gN forms a group where the identity element >is given by N. The inverse to gN is hN where det(g)det(h) = 1. >I rephrase my question then: >Do we have G = U_g (gN) ? >where U_g denotes the union over all g in G. Sure, but that's always true -- the cosets (left or right, pick one) >with respect to any subgroup partition the group. But your original question still deserves an answer. What is the >nature of the group G/N? More precisely, G/N is isomorphic to what >well known group? I sense that you may not have understood my hints and questions. Let me try again, a little differently. Firstly, you never showed that N is a normal subgroup. Can you show that? It's easy, but important. Next, the role of the determinant function ... In the context of this problem, the function det is a homomorphism from what group to what other group? Can you show that it's a homomorphism? Is it surjective? What is the kernel? Based on some of the answers to the above questions, what can you conclude about G/N? quasi === Subject: Re: Cosets of invertible matrices > [corrected reply -- quoting was slightly off on my previous reply] I'm currently learning about quotient groups >http://en.wikipedia.org/wiki/Quotient_group There is one example of a quotient group >and I would like to just confirm that I've >understood it correctly. So, let G denotes the group of 3x3 invertible >real matrices and N the subgroup of 3x3 real >matrices with determinant 1. Then, by definition the quotient group is G/N = {gN : g in G}. Yes, but before you make a quotient group, you should verify that N is > a _normal_ subgroup, not just any old subgroup. The verification is > not hard, but you should do it, not just take it on faith. Since det(gN) = det(g)det(N) = det(g) not= 0, N is not a matrix, so det(N) is not meaningful. i.e. gN is just a 3x3 matrix with determinant >not equal to 0. No. gN is not a matrix -- it's a _set_ of matrices. Hence we have G/N = G, right? No. But all elements of gN have the same nonzero determinant, right? Do those nonzero determinants comprise a group? What group? quasi >For each _fixed_ g in G we have: >gN is a set of matrices with the same nonzero determinant. >The set of all gN forms a group where the identity element >is given by N. The inverse to gN is hN where det(g)det(h) = 1. >I rephrase my question then: >Do we have G = U_g (gN) ? >where U_g denotes the union over all g in G. Sure, but that's always true -- the cosets (left or right, pick one) >with respect to any subgroup partition the group. But your original question still deserves an answer. What is the >nature of the group G/N? More precisely, G/N is isomorphic to what >well known group? I sense that you may not have understood my hints and questions. Let me try again, a little differently. Firstly, you never showed that N is a normal subgroup. Can you show > that? It's easy, but important. Next, the role of the determinant function ... In the context of this problem, the function det is a homomorphism > from what group to what other group? Can you show that it's a > homomorphism? Is it surjective? What is the kernel? It is possible that the student is learning about cosets & quotient groups *before* homomorphisms & kernels, in which case this line of enquiry will not be helpful. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Cosets of invertible matrices I'm currently learning about quotient groups >http://en.wikipedia.org/wiki/Quotient_group There is one example of a quotient group >and I would like to just confirm that I've >understood it correctly. So, let G denotes the group of 3x3 invertible >real matrices and N the subgroup of 3x3 real >matrices with determinant 1. Then, by definition the quotient group is G/N = {gN : g in G}. Yes, but before you make a quotient group, you should verify that N is a _normal_ subgroup, not just any old subgroup. The verification is not hard, but you should do it, not just take it on faith. Since det(gN) = det(g)det(N) = det(g) not= 0, N is not a matrix, so det(N) is not meaningful. >i.e. gN is just a 3x3 matrix with determinant >not equal to 0. No. gN is not a matrix -- it's a _set_ of matrices. >Hence we have G/N = G, right? No. But all elements of gN have the same nonzero determinant, right? Do those nonzero determinants comprise a group? What group? quasi === Subject: Solutions manual for.....Elasticity in Engineering Mechanics Does anyone have the solutions manual for the textbook Elasticity in Engineering Mechanics written by Boresi and Chong? Please let me know. THANK YOU! === Summary: UDP === This server is temporarily under UDP because of recent massive hipcrime attacks, until the problem is solved by their administrators. We are sorry for the inconvenience. See news.admin.net-abuse.policy and news.admin.net-abuse.usenet for more details. === Subject: Re: Bill Gates was never the Richest man on earth Benjamin Freedman speech with Slide Show (40 Minute Excerpt) Free pdf book: THE MANUFACTURE AND SALE of Saint Einstein @ http://jewishracism.com/SaintEinstein.htm Author interviews @ http://jewishracism.com/interviews.htm Rothschilds control half the world's wealth directly and indirectly using zionist proxies, and loyalty based on the zionist racist cult of hate and paranoia based on being caught for collective financial crimes and crimes of other categories History of the Rothschilds part 1 http://www.youtube.com/watch?v=o_u2MaNg-EQ History of the Rothschilds part 2 http://www.youtube.com/watch?v=o2cw-0N_Unk FBI, Where are the two Israelis with TRUCKLOAD of explosives at the George Washington Bridge ????? http://www.youtube.com/watch?v=JfVumKHkcIA <----- Shame stooopid americans Alex Jones Interviews David Mayer de Rothschild The rise of the Rothschild Money Masters http://www.youtube.com/watch?v=ZT3GyphxJv8 Rothschilds financed APARTHEID in South Africa. They corrupted Cecil Rhodes, the son of an anglican minister, by TEACHING him evil techniques of apartheid. Apartheid was taught to him by the father zionists themselves. Rothschilds control half the world's wealth directly and indirectly using zionist proxies, and loyalty based on the zionist racist cult http://www.youtube.com/watch?v=fXVJzXsraX4 Was Hitler's father a bastard son of Rothschilds? Did the Salomon Mayer von Rothschild perhaps rape Maria Anna Schicklgruber in dark so that she could not ever claim with certainty who the real father was? Look at his facial features, typical central asian khazar. What was the cause of Hitler's fanatical hatred for the Jews ? http://en.wikipedia.org/wiki/Alois_Hitler http://www.youtube.com/watch?v=TihCM_q59c8 > The world has been after Bill Gates for no reason. The richest group > was and remains the Zionist jew Rothschilds family who own HALF the > worlds total wealth through numerous frontmen zionists. Mikhail Khodorkovsky, whom Russian President Vladimir I Putin put in > jail rose from the Rothschilds money. Mayer Amschel Bauer changed his name to > Rothschild or red shield. The he sent his sons to various countries in > Europe and become bankers there. Using an innovative system of pigeons > for communication and encoded letters, the family invested in wars > that he knew were coming by staying close to the centers of powers in > all the countries which they had infilterated. aside part of your weekend for education. > Everyone should know that the Zionists (among others) > are controlled by the Bavarian Illuminati, who control > over 9 tenths of the world's total wealth. Of course they also > control over 9 tenths of the people who post to the internet > as well as Google, Facebook and youtube. > It is interesting to note that those they control act as > if the Baviarian Illuminati do not exist. - William Zionazi obviously tries to shift blame and confuse the picture. === Subject: Re: Bill Gates was never the Richest man on earth > Zionazi obviously tries to shift blame and confuse the picture. One way to recognize a dupe of the Bavarian Illuminati is their tendency to characterize everyone as Zionists. - William Hughes === Subject: Re: Bill Gates was never the Richest man on earth > Zionazi obviously tries to shift blame and confuse the picture. > One way to recognize a dupe of the Bavarian Illuminati is > their tendency to characterize everyone as Zionists. Another way is their tendency to proclaim quite loudly and emphatically that they're not Zionists or dupes of the Bavarian Illuminati. === Subject: Re: Bill Gates was never the Richest man on earth > Zionazi obviously tries to shift blame and confuse the picture. > One way to recognize a dupe of the Bavarian Illuminati is > their tendency to characterize everyone as Zionists. Another way is their tendency to proclaim quite loudly > and emphatically that they're not Zionists or dupes of > the Bavarian Illuminati. Gates is the world's richest man if you measure richness by having a bunch of ing money. === Subject: Re: Bill Gates was never the Richest man on earth > Gates is the world's richest man if you measure richness by having a > bunch of ing money. And maybe restricting the world to the US. The sultan of Brunei isn't really poor either and remember that all those numbers are estimated and tend to vary by year and source. Ciao, Marc 'BlackJack' Rintsch === Subject: Comprehensive Solution Manual for Textbooks! Get it in hours! I have the comprehensive solutions manuals for the following textbooks in electronic format (PDF/Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price is US$25 for each. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account). Email me at akrmiha[at]gmail[dot]com if you are interested. 1 Adaptive Filter Theory (4th Ed) by Haykin, Simon [ISBN: 0130901261] 2 Advanced Modern Engineering Mathematics (3rd Ed) by Glyn James [ISBN: 0130454257] 3 An Introduction to Numerical Analysis by Endre S.9fli , David F. Mayers [ISBN: 0521007941] 4 Analysis and Design of Analog Integrated Circuits (4th Ed) by Paul R. Gray, Paul J. Hurst, Stephen H. Lewis, Robert G. Meyer [ISBN: 0471321680] 5 Analytical Mechanics (7th Ed) by Grant Fowles, George Cassiday [ISBN: 0534494927] 6 Antennas for All Applications (3rd Ed) by John D. Kraus, Ronald J. Marhefka [ISBN: 0072321032] 7 Applied Numerical Analysis (6th Ed) by Curtis F. Gerald, Patrick O. Wheatley [ISBN: 0321133048] 8 Applied Strength of Materials (4th Ed) by Robert L. Mott [ISBN: 0130885789] 9 Automatic Control Systems (8th Ed) by Kuo, Benjamin C.; Golnaraghi, Farid [ISBN: 0471134767] 10 Basic Engineering Circuit Analysis (7th Edition) by J. David Irwin [ISBN: 0471407402] 11 Basic Engineering Circuit Analysis (8th Ed) by J. David Irwin, R. Mark Nelms [ISBN: 0471487287] 12 by Bruce Munson, Donald Young, Theodore Okiishi [ISBN: 0471240117] 13 Chemical and Engineering Thermodynamics (3rd Ed) by Stanley I. Sandler [ISBN: 0471182109] 14 Communication Systems (4th Ed) by A. Bruce Carlson, Paul B. Crilly, Janet Rutledge [ISBN: 0070111278] 15 Communication Systems Engineering (2nd Ed) by Proakis, John G [ISBN: 0130617938] 16 Communications Systems (4th Ed) by Haykin, Simon [ISBN: 0471178691] 17 Computer Networks (4th Ed) by Tanenbaum, Andrew S. [ISBN: 0130661023] 18 Computer Networks: A Systems Approach (3rd Ed) by Larry L. Peterson, Bruce S. Davie [ISBN: 155860832X] 19 Computer System Architecture (3rd Ed) by M. Morris Mano [ISBN: 0131755633] 20 Control Systems Engineering (4th Ed) by Nise, Norman S. [ISBN: 0471445770] 21 Design of Analog CMOS Integrated Circuits (1st Ed) by Behzad Razavi [ISBN: 0072380322] 22 Design with Operational Amplifiers and Analog Integrated Circuits (3rd Ed) by Sergio Franco [ISBN: 0072320842] 23 Device Electronics for Integrated Circuits (3rd Ed) by Richard Muller, Theodore Kamins, Mansun Chan [ISBN: 0471593982] 24 Digital Communications (4th Ed) by Proakis, John [ISBN: 0072321113] 25 Digital Communications: Fundamentals and Applications (2nd Ed) by Bernard Sklar [ISBN: 0130847887] 26 Digital Image Processing (2nd Ed) by Rafael Gonzalez, Richard Woods [ISBN: 0201180758] 27 Digital Signal Processing (3rd Ed) by Sanjit K Mitra [ISBN: 0073048372] 28 Digital Signal Processing (4th Ed) by John G. Proakis, Dimitris K Manolakis [ISBN: 0131873741] 29 Digital Signal Processing by Thomas J. Cavicchi [ISBN: 0471124729] 30 Discrete-Time Signal Processing (2nd Ed) by Oppenheim, Alan V [ISBN: 0137549202] 31 Econometric Analysis (5th Ed) by William H. Greene [ISBN: 0130661899] 32 Electric Circuits (7th Ed) by Nilsson, James W.; Riedel, Susan [ISBN:0131465929] 33 Electric Machinery (6th Ed) by A. E. Fitzgerald, Jr., Charles Kingsley, Stephen D. Umans, Stephen Umans [ISBN: 0073660094] 34 Electric Machinery Fundamentals (4th Ed) by Stephen J. Chapman [ISBN: 0072465239] 35 Electronic Circuit Analysis (2nd Ed) by Donald Neamen [ISBN: 0072451947] 36 Elementary Differential Equations and Boundary Value Problems (8th Ed) by William E. Boyce, Richard C. DiPrima [ISBN: 0471433381] (Mostly all solutions, only a few missing) 37 Elements of Chemical Reaction Engineering (3rd Ed) by H. Scott Fogler [ISBN: 0135317088] 38 Elements of Electromagnetics (2nd Ed) by Matthew Sadiku 39 Engineering Circuit Analysis (6th Ed) by William H. Hayt, Jack Kemmerly, Steven M. Durbin [ISBN: 0072853204] 40 Engineering Electromagnetics (6th Ed) by William H. Hayt, John A. Buck [ISBN: 0072551666] 41 Engineering Fluid Mechanics (7th Ed) by Clayton Crowe, Donald Elger, John Roberson [ISBN: 0471384828] 42 Engineering Materials Science by Milton Ohring [ISBN: 0125249950] 43 Engineering Mechanics - Dynamics (10th Ed) by Russell C. Hibbeler [ISBN: 0131416782] 44 Engineering Mechanics - Dynamics (11th Ed) by Russell C. Hibbeler [ISBN: 0132215047] 45 Engineering Mechanics - Dynamics (4th Ed) by Anthony Bedford, Wallace Fowler [ISBN: 0131463241] (missing chapters 12 to 16) 46 Engineering Mechanics - Statics (10th Ed) by Russell C. Hibbeler [ISBN: 0131411675] 47 Engineering Mechanics - Statics (11th Ed) by Russell C. Hibbeler [ISBN: 0132215004] 48 Engineering Mechanics - Statics (4th Ed) by Anthony M Bedford, Wallace Fowler [ISBN: 0131463233] 49 Engineering Mechanics - Statics (5th Ed) by J. L. Meriam (Author), L. G. Kraige [ISBN: 0471406465] 50 Engineering Mechanics , Dynamics (5th Ed) by J. L. Meriam, L. G. Kraige [ISBN: 0471406457] 51 Feedback Control of Dynamic Systems (4th Ed) by Gene Franklin, David Powell, Abbas Naeini [ISBN: 0130323934] 52 Field and Wave Electromagnetics (2nd Ed) by David K. Cheng [ISBN: 0201128195] 53 Field and Wave Electromagnetics (2ånd Ed) by David K. Cheng [ISBN: 0201128195] 54 Finite Element Techniques in Structural Mechanics by C. T. F. Ross [ISBN: 189856325X] 55 First Course in Probability, A (7th Ed) by Ross, Sheldon [ISBN: 0131856626] 56 Fluid Mechanics (5th Ed) by Frank M. White [ISBN: 0072831804] 57 Fractal Geometry: Mathematical Foundations and Applications (2nd Ed) by Kenneth Falconer [ISBN: 0470848626] 58 Fundamentals of Aerodynamics (4th Ed) by John D. Anderson [ISBN: 0072950463] 59 Fundamentals of Applied Electromagnetics (1st Ed) Fawwaz Ulaby [ISBN: 013185089X] 60 Fundamentals of Chemical Reaction Engineering (1st Ed) by Mark E. E. Davis, Robert J. J. Davis [ISBN: 007245007X] 61 Fundamentals of Digital Logic with Verilog Design (1st Ed) by Stephen Brown, Zvonko Vranesic [ISBN: 0072838787] 62 Fundamentals of Digital Logic with VHDL Design (1st Ed) by Stephen Brown, Zvonko Vranesic [ISBN: 0072355964] 63 Fundamentals of Electric Circuits (2nd Ed ) by Charles Alexander, Matthew Sadiku [ISBN: 0073048356] 64 Fundamentals of Electromagnetics with Engineering Applications by Stuart M. Wentworth [ISBN: 0471263559] 65 Fundamentals of Engineering Thermodynamics (5th Ed) by Michael Moran, Howard Shapiro [ISBN: 0471274712] 66 Fundamentals of Fluid Mechanics (4th Ed) by Bruce Munson, Donald Young, Theodore Okiishi [ISBN: 047144250X] 67 Fundamentals of Fluid Mechanics: Student Solutions Manual (3rd Ed) 68 Fundamentals of Heat and Mass Transfer (5th Ed) by Frank Incropera, David DeWitt [ISBN: 0471386502] 69 Fundamentals of Logic Design (5th Ed) by Jr., Charles H. Roth [ISBN: 0534378048] 70 Fundamentals of Physics (7th Ed) by David Halliday, Robert Resnick, Jearl Walker [ISBN: 0471216437] 71 Fundamentals of Thermal-Fluid Sciences (2nd Ed) by Yunus Cengel, Robert Turner [ISBN: 0072976756] 72 Fundamentals of Thermodynamics (5th Ed) by Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen [ISBN: 047118361X] 73 Fundamentals of Thermodynamics (6th Ed) by Richard Sonntag, Claus Borgnakke, Gordon Van Wylen [ISBN: 0471152323] 74 Heat Transfer: A Practical Approach (2nd Ed) by Yunus Cengel [ISBN: 0072826207] 75 Hydraulics in Civil and Environmental Engineering (4th Ed) by Andrew Chadwick [ISBN: 0415306094] 76 Introduction to Algorithms (2nd Ed) by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein [ISBN: 0262032937] 77 Introduction to Electric Circuits (6th Ed) by Richard C. Dorf, James A. Svoboda [ISBN: 0471447951] 78 Introduction to Electrodynamics (3rd Ed) by Griffiths, David [ISBN: 013805326X] 79 Introduction to Fluid Mechanics (6th Ed) by Robert Fox, Alan McDonald, Philip Pritchard [ISBN: 0471202312] 80 Introduction to Heat Transfer (4th Ed) by Frank P. Incropera, David P. DeWitt [ISBN: 0471204536] 81 Introduction to Linear Algebra (3rd Ed) by Gilbert Strang [ISBN: 0961408898] 82 Introduction to Quantum Mechanics (2nd Edition) by David J. Griffiths [ISBN: 0131118927] 83 Introduction to Solid State Physics (8th Ed) by Charles Kittel [ISBN: 047141526X] 84 Introduction to VLSI Circuits and Systems by John P. Uyemura [ISBN: 0471127043] 85 Linear Algebra And It's Applications (3rd Ed) by David C. Lay [ISBN: 0321287134] 86 Linear Circuit Analysis: Time Domain, Phasor, and Laplace Transform Approaches (2nd Ed) by Raymond DeCarlo, Pen-Min Lin [ISBN: 0195136667] 87 Materials Science and Engineering: An Introduction (6th Ed) by William D. Jr. Callister [ISBN: 0471135763] 88 Materials Science and Engineering: An Introduction (7th Ed) by William D. Jr. Callister [ISBN: 0471736961] 89 Mechanical Engineering Design (7th Ed) by Charles Mischke, Joseph Shigley, Richard Budynas [ISBN: 0072921935] 90 Mechanics of Fluids (8th Ed) by John Ward-Smith [ISBN: 0415362040] 91 Mechanics of Materials (3rd Ed) by Ferdinand P. Beer , Jr., E. Russell Johnston, John T. DeWolf [ISBN: 0072486732] 92 Mechanics of Materials (6th Ed) by Russell C. Hibbeler [ISBN: 013191345X] 93 Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Jerry R. Green [ISBN: 0195073401] 94 Microelectronics (2nd Ed) by Jacob Millman, Arvin Grabel [ISBN: 007100596X] 95 Microwave and Rf Design of Wireless Systems (1st Ediiton) by Pozar, David M. [ISBN: 0471322822] 96 Microwave Engineering (3rd Ed) by Pozar, David M. [ISBN: 0471448788] 97 Microwave Transistor Amplifiers: Analysis and Design (2nd Ed) by Guillermo Gonzalez [ISBN: 0132543354] 98 Modern Digital and Analog Communication Systems (3rd Ed) by B. P. Lathi [ISBN: 0195110099] 99 Modern Operating Systems (2nd Ed) by Andrew Tanenbaum [ISBN: 0130313580] (up to chapter 12) 100 Modern Physics (4th Ed) by Paul Tipler, Ralph Llewellyn [ISBN: 0716743450] 101 Operating System Concepts (6th Ed) by Abraham Silberschatz, Greg Gagne, Peter Baer Galvin [ISBN: ] 102 Operating Systems Design and Implementation (3rd Ed) by Andrew S Tanenbaum, Albert S Woodhull [ISBN: 0131429388] 103 Operating Systems: Internals and Design Principles (4th Ed) by William Stallings [ISBN: 0130319996] 104 Optical Fiber Communications (3rd Ed) by Gerd E. Keiser [ISBN: 0072360763] 105 Partial Differential Equations and Boundary Value Problems with Fourier Series (2nd Ed) by Nakhle H. Asmar [ISBN: 0131480960] (Student solution manual) 106 Physical Chemistry (7th Ed) by Julio Paula, Peter Atkins [ISBN: 0716735393] 107 Physics for Scientists and Engineers (1st Ed) by Randall D. Knight [ISBN: 0805386858] 108 Physics for Scientists and Engineers (5th Ed) by Paul A. Tipler, Gene Mosca [ISBN: 0716783398] 109 Physics for Scientists and Engineers 5th Extended Version by Serway and Faughn 110 Physics for Scientists and Engineers, Volume 1 (1st Ed) by Randall D. Knight [ISBN: 0805389644] 111 Physics for Scientists and Engineers, Volume 4 (1st Ed) by Randall D. Knight [ISBN: 0805389733] 112 Physics, Volume 2 (5th Ed) by David Halliday, Robert Resnick, Kenneth S. Krane [ISBN: 0471401943] 113 Physics: Principles with Applications (6th Ed) by Douglas C. Giancoli [ISBN: 0130606200] 114 Power Electronics: Converters, Applications, and Design (3rd Ed) by Ned Mohan, Tore M. Undeland, William P. Robbins [ISBN: 0471226939] 115 Power System Analysis by(1st Ed) John Grainger, Jr., William Stevenson [ISBN: 0070612935] 116 Principles and Applications of Electrical Engineering (4th Ed) by Giorgio Rizzoni [ISBN: 0072887710] 117 Principles of Communication: Systems, Modulation and Noise (5th Ed) by R. E. Ziemer, W. H. Tranter [ISBN: 0471392537] 118 Probability and Statistics for Engineering and the Sciences (7th Ed) by Jay L. Devore [ISBN: 0495382175] 119 Probability, Random Variables and Stochastic Processes (4th Ed) by Athanasios Papoulis , S. Unnikrishna Pillai [ISBN: 0072817259] 120 RF Circuit Design: Theory and Applications by Reinhold Ludwig, Pavel Bretchko [ISBN: 0130953237] 121 Sears and Zemansky's University Physics (11th) by Hugh D. Young, Roger A. Freedman [ISBN: 0805387684] 122 Semiconductor Device Fundamentals (1st Ed) by Robert F. Pierret, [ISBN: 0201543931] 123 Semiconductor Physics And Devices (3rd Ed) by Donald Neamen [ISBN: 0072321075] 124 Signal Processing and Linear Systems by B. P. LAthi [ISBN: 0195219171] 125 Signals and Systems (2nd Ed) by Alan V. Oppenheim, Alan S. Willsky [ISBN: 0138147574] 126 Structural Analysis (5th Ed) by Russell C. Hibbeler [ISBN: 0130418250] 127 Thermodynamics (5th Ed) by Michael Boles, Yunus Cengel [ISBN: 0073107689] 128 Thomas' Calculus (10th Ed) by George Thomas, Ross Finney, Maurice Weir , Frank Giordano [SIBN: 0201755270] 129 Thomas' Calculus (10th Edition) by George Thomas, Ross Finney, Maurice Weir, Frank Giordano [ISBN: 0201755270] 130 Thomas' Calculus, Early Transcendentals (10th Ed) by George Thomas, Maurice Weir, Joel Hass, Frank Giordano [ISBN: 0201662094] 131 Time-Harmonic Electromagnetic Fields (2nd Ed) by Roger F. Harrington [ISBN: 047120806X] 132 University Physics with Modern Physics (11th Ed) by Hugh Young, Roger Freedman [ISBN: 0805387773] 133 Vector Mechanics for Engineers, Statics (7th Ed) by Beer, Ferdinand P.; Johnston Jr., E [ISBN: 0072930780] 134 Vector Mechanics for Engineers: Dynamics (7th Ed) by Beer, Ferdinand P.; Johnston Jr., E [ISBN: 0073209260] 135 Wireless Communications and Networking (1st Ed) by Jon W. Mark , Weihua Zhuang [ISBN: 0130409057] 136 Wireless Communications: Principles and Practice (2nd Ed) by Theodore Rappaport [ISBN: 0130422320] === Subject: Re: Comprehensive Solution Manual for Textbooks! Get it in hours! Do you know anyone that has the solutions manual to..... Elasticity in Engineering Mechanics === Subject: Re: Multivalued Logarithm > On Oct 20, 5:53 am, A N Niel > , > ANY path, your answer > is SOME value of the logarithm. Which value > depends on the path. I'd imagine so. Hmm. Does this mean that whenever the > integral between > A and B depends on the path, one has a multivalued > function of A (or > B, or both)? > 1) evidently if the path is over a multivalued function if not so 2) potentially see : contour integration tommy1729 === Subject: Re: LaTeX tutorial updated I've updated my Using LaTeX to write a PhD thesis tutorial. Both PDF > and HTML versions can be reached viahttp://theoval.cmp.uea.ac.uk/~nlct/latex/ I have added/deleted sections, so if you have any links to document > nodes (i.e. files that are of the form node*.html) you may have to > update your links. Nicola Talbot very nice. 911 truckload of Explosives on the George Washington Bridge http://www.youtube.com/watch?v=J520P-MD9a0 === Subject: Re: LaTeX tutorial updated protocol=application/pgp-signature; boundary=------------enig66652290ECB3856B8ED26357 --------------------------------------------------------------------- zionist.news2@gmail.com schreef: > I've updated my Using LaTeX to write a PhD thesis tutorial. Both PDF > and HTML versions can be reached viahttp://theoval.cmp.uea.ac.uk/~nlct/latex/ > I have added/deleted sections, so if you have any links to document > nodes (i.e. files that are of the form node*.html) you may have to > update your links. > Nicola Talbot very nice. 911 truckload of Explosives on the George Washington Bridge > http://www.youtube.com/watch?v=J520P-MD9a0 > PLONK. -- Hendrik Maryns http://tcl.sfs.uni-tuebingen.de/~hendrik/ http://aouw.org Ask smart questions, get good answers: http://www.catb.org/~esr/faqs/smart-questions.html --------------------------------------------------------------------- Content-Description: OpenPGP digital signature -----BEGIN PGP SIGNATURE----- Version: GnuPG v2.0.4-svn0 (GNU/Linux) Comment: Using GnuPG with SUSE - http://enigmail.mozdev.org iD8DBQFHMYrCe+7xMGD3itQRAkzZAJ9i6OogZ8KGm4Uk9jfwImvpQkQW+wCcCYOX vnTlUrMkrzuJcYpjPjui/YU= =9XD+ -----END PGP SIGNATURE----- === Subject: Normalization of a curve Let X be a projective curve, f: XÍ to X its normalization. Where I could read about short exact sequence 0 -> O_X -> f_*O_{XÍ} -> sum_{p in X} bar{O_p}/O_p ->0, O_X (O_{XÍ}) [CapitalEth] structure sheaf, O_p [CapitalEth]local ring, bar{O_p} [CapitalEth] its integral closure. === Subject: Re: Normalization of a curve On 2007-11-06 14:20:38 -0500, Sasha P said: > Let X be a projective curve, f: XÍ to X its normalization. Where I > could read about short exact sequence 0 -> O_X -> f_*O_{XÍ} -> sum_{p in X} bar{O_p}/O_p ->0, O_X (O_{XÍ}) [CapitalEth] structure sheaf, O_p [CapitalEth]local ring, bar{O_p} [CapitalEth] its > integral closure. There is reference of it in Hartshorne's Algebraic Geometry (Chap. IV, Ex. 1.8). But it only mentions it there. To see how this exact sequence is, apply Theorem 6.2A in Hartshorne's same book Algebraic Geometry (p.40) to (O_X)_p. Now, the map O_X --> f_*O_{X'} induces a local map f_p : (O_X)_p --> (f_*O_{X'))_p for every point p in X. The ring (f_*O_{X'))_p is the normalization of (O_X)_p since X' is by design the normal curve to X. So, according to Theorem 6.2A, f_p is an isomorphism if and only if p is nonsingular. So, we see that the quotient sheaf f_*O_{X'} / O_X is only supported at the singular points of X. There are only a finite number of singular points on a curve, and we can always find an affine covering over the curve X such that each cover contains exactly one of these singular points. Hence, the quotient sheaf is a direct product of (f_*O_{X'))_p / (O_X)_p = bar{(O_X)_p} / (O_X)_p over the singular points p of X. -- -kira === Subject: Re: solution manuals > List of Solution manuals: Engineering Circuit Analysis 6Ed - Hayt SolutionsManual Norbury - Solutionsmanualfor mechanics and thermodynamics Physics For Scientists And Engineers - SolutionManual Openheims discrete time solnmanual SolutionsManual] [Instructors]Introductionto Linear Algebra--3rd > Edition - Gilbert Strang.pdf Introduction to VLSI Circuits and Systems (2001 draft) - > John P Uyemura - Solutions Manual.pdf Field and wave electromagnetics 2nd edition Java Cookbook Solutions and Examples for Java Developers.pdf AnIntroductionto the Mathematicis of Financial Derivatives(Neftci)-- > SolutionManual.pdf probability and statistical inference hogg and tanis 7th ed Probablility and statistics fundamentals Signals adn SYstems 2nd edition solutionmanual An intro to database systems 8th edition ELementary differential equations and boundary value problems Introductionto probability introductiontoalgorithms Microwave engineering 3rd edition Operating systems concepts solnmanual [SolutionsManual] Mechanical Engineering Design 7th Ed. Shigley [SolutionsManual] Engineering Mechanic STATICS 10th Ed. R.C. Hibbeler Stallings W - InstructorsmanualOperating Systems 4ed Digital Signal Processing - Proakis & Manolakis - Solutions Elements of Chemical Reaction Engineering - SolutionsManual Solid State Electronic Devices Streetman Solution Manual [SolutionsManual] Fourier and Laplace Transform - Antwoorden Elements of Chemical Reaction Engineering - SolutionsManual Computational techniques for fluid dynamics - SolutionsManual Networks - Book Solution Stallings W - InstructorsmanualOperating Systems 4ed solutions SolutionManualFor Communication Systems (4th edt) by Simon Haykin Fundamentals Of Logic Design 5Ed - Charles Roth - SolutionsManual SolutionManualFor Microelectronic Circuits By Adel Sedra Modern Digital and Analog Communications Systems - B P Lathi SolutionsManual Fundamentals of Heat and Mass Transfer - SolutionsManual [SolutionsManual] [Instructors] Calculus 5Th Ed James Stewart Proakis J. (2002) Communication Systems Engineering - SolutionsManual Solution Manual for Semiconductor Physics and Devices 3ed Neamen serway - physics for scientists and engineers - solutionmanual Fundamentals Of Logic Design 5Ed - Charles Roth - Solutions Manual [SolutionsManual] Thermodynamics - An Engineering Approach, 5Th > Cengal Boles [SolutionsManual] Engineering Mechanic STATICS 10th Ed. R.C. > Hibbeler [SolutionsManual] Probability And Statistics For Engineers And > Scientists Fundamentals of digital logic with VHDL design solutionsmanual Sonntag-Borgnakke-Van Wylen -Fundamentals of Thermodynamics SolutionManualChapters 10-16 Fundamentals of Heat and Mass Transfer [Frank P.Incropera - David > P.DeWitt] SolutionManual Introduction to VLSI Circuits and Systems (2001 draft) - > John P Uyemura - Solutions Manual [SolutionsManual] [Instructors]Introductionto Linear Algebra--3rd > Edition - Gilbert Strang Dorf-Svaboda - SolutionManualForIntroductionTo Electric Circuits > 6th Edition AnIntroductionto the Mathematicis of Financial Derivatives(Neftci)-- > SolutionManual Fiber Optics TechniciansManual(2nd Ed.) DigitalComm Fundamentals App Solution Manual SolutionManualFor Communication Systems (4th edt) by Simon Haykin Atkins SolutionManual Microelectronics - Millman Solution Manual Modern Physics-4th Edition SolutionsManual Sakurai - Modern Quantum Mechanics. 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G. Kraige Instructor's SolutionsManual- Marion, Thornton - Classical Dynamics IntroductionToAlgorithms2Nd Edition read more é... hi i would like a copy of solutions manual for Introduction To Algorithms 2nd Ed. by Thomas H. Cormen, Charles E.Leiserson, Ronald L. Rivest, Clifford Stein thank you === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad The probability is under the case c is not fixed, I *start* with the unconditional probabilities as when c fixed, the probability distribution changed, Of course. And I computed those changes. you admit that probability of K is changged, > how can you insure other > probability is not changged, A probability may or may not change. > To find out which I computed the > conditional probabilities using > the definition of conditional probability > When I computed the conditional probabilites > I found that the probability distribution > of K changed but the probability distribution > of M did not. how can you use the condition c is not > fixed, K and M is independant , to compute the probability when c is > fixed, that case k and m are dependant. It is easy to see from the > definition of a conditional probability distribution > that if you have the full unconditional probability distribution > you can determine the conditional probability distribution. > I first used the condition c is not fixed, K and M > are independent to compute the unconditional probability distribution, > then used the definition of a conditional probability distribution > to get the probabilities when c is fixed. - William Hughes I *start* with the unconditional probabilities not fixed, even though we can use conditional probaibilty how can you use the condition c is fixed to compute, it is not a value, you are confused. > as when c fixed, the probability distribution changed, Of course. And I computed those changes. > you admit that probability of K is changged, > how can you insure other > probability is not changged, A probability may or may not change. To find out which I computed the conditional probabilities using the definition of conditional probability When I computed the conditional probabilites I found that the probability distribution of K changed but the probability distribution of M did not. is a complex condition, how you can use it. It is easy to see from the definition of a conditional probability distribution that if you have the full unconditional probability distribution you can determine the conditional probability distribution. I first used the condition c is not fixed, K and M are independent to compute the unconditional probability distribution, then used the definition of a conditional probability distribution to get the probabilities when c is fixed. replace without change, It is wrong. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > how can you use the condition c is fixed to compute, it is not a > value, Agreed. The condition c is fixed is not a value. C has two possible values. So you have to compute the probablity distributions twice. You assume that the value of C is fixed. You then calculate the probablity distributions for one possible value of C assuming the value of C is fixed. You then calculate the probability distributions for the other possible value of C assuming the value of C is fixed. In both case you find that the probability distribution on M is unchanged. You get two different probability distributions for K, but neither is uniform. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad how can you use the condition c is fixed to compute, it is not a > value, Agreed. The condition c is fixed is not a value. C has > two possible values. So you have to compute the probablity > distributions twice. You assume that the value > of C is fixed. You then calculate the probablity > distributions for one possible value of C assuming the value of > C is fixed. You then calculate the probability distributions for the > other > possible value of C assuming the value of C is fixed. > In both case you find that the probability distribution on M is > unchanged. > You get two different probability distributions for K, but neither is > uniform. - William Hughes how you can compute, how can you find the probability M not changed. do not just the the result ,that is useless. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > how can you use the condition c is fixed to compute, it is not a > value, Agreed. The condition c is fixed is not a value. C has > two possible values. So you have to compute the probablity > distributions twice. You assume that the value > of C is fixed. You then calculate the probablity > distributions for one possible value of C assuming the value of > C is fixed. You then calculate the probability distributions for the > other > possible value of C assuming the value of C is fixed. > In both case you find that the probability distribution on M is > unchanged. > You get two different probability distributions for K, but neither is > uniform. - William Hughes how you can compute, how can you find the probability M not changed. > do not just the the result ,that is useless. Compute the joint probability of M, K and C (use the known probability distribtuions of M and K the fact that M and K are independent, and the formula for getting C from M and K) Assume C fixed. Two cases. For each case note the value of C and compute the conditional probability of M using the known joint probability of M, K and C and the definition of conditional probability. In both cases you get the same probability distribution for M - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > how you can compute, how can you find the probability M not changed. > do not just the the result ,that is useless. Compute the joint probability of M, K and C > (use the known probability distribtuions of M and K > the fact that M and K are independent, and the formula > for getting C from M and K) Assume C fixed. Two cases. For each case note the value of C and compute > the conditional probability of M using the known > joint probability of M, K and C and the definition > of conditional probability. In both cases you get the same probability > distribution for M - William Hughes - - a change in form but not in content,you just use the probability when c is not fixed. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad that is useless to prove the problem the all the probability is just under the condition c is not fixed. you say you use conditional probaiblity,but you do not.just regardless c is fixed. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > how you can compute, how can you find the probability M not changed. > do not just the the result ,that is useless. Compute the joint probability of M, K and C > (use the known probability distribtuions of M and K > the fact that M and K are independent, and the formula > for getting C from M and K) Assume C fixed. Two cases. For each case note the value of C and compute > the conditional probability of M using the known > joint probability of M, K and C and the definition > of conditional probability. In both cases you get the same probability > distribution for M - William Hughes - - a change in form but not in content,you just use the probability when > c is not fixed. No. I do not use the probability when c is not fixed. I compute the conditional probability. This can be computed from the joint probability, but is not the same as the unconditional probability (the probability when c is not fixed). - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad how you can compute, how can you find the probability M not changed. > do not just the the result ,that is useless. Compute the joint probability of M, K and C > (use the known probability distribtuions of M and K > the fact that M and K are independent, and the formula > for getting C from M and K) Assume C fixed. Two cases. For each case note the value of C and compute > the conditional probability of M using the known > joint probability of M, K and C and the definition > of conditional probability. In both cases you get the same probability > distribution for M - William Hughes - - a change in form but not in content,you just use the probability when > c is not fixed. No. I do not use the probability when > c is not fixed. I compute the conditional probability. This > can be computed from the joint probability, but > is not the same as the unconditional probability > (the probability when c is not fixed). - William Hughes- - - - how can you compute the probability when c is fixed, do not use that when c is not fixed, if use, tell why you can use. that is why you take mistake. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > how you can compute, how can you find the probability M not changed. > do not just the the result ,that is useless. Compute the joint probability of M, K and C > (use the known probability distribtuions of M and K > the fact that M and K are independent, and the formula > for getting C from M and K) Assume C fixed. Two cases. For each case note the value of C and compute > the conditional probability of M using the known > joint probability of M, K and C and the definition > of conditional probability. In both cases you get the same probability > distribution for M - William Hughes - - a change in form but not in content,you just use the probability when > c is not fixed. No. I do not use the probability when > c is not fixed. I compute the conditional probability. This > can be computed from the joint probability, but > is not the same as the unconditional probability > (the probability when c is not fixed). - William Hughes- - - - how can you compute the probability when c is fixed, > do not use that when c is not fixed, > if use, tell why you can use. > that is why you take mistake. I do not use the probability when c is not fixed to compute the probability when c is fixed. I use the joint probability of M,K and C. [Indeed you could use the joint probability to calculate the probability of C when C is not fixed (the marginal) but I do not do this.] I use the joint probability to calculate the probability of M or K when C is fixed (the probability when C is fixed is defined in terms of the joint probability) - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad -----------a change in form but not in content,you just use the probability when c is not fixed. you use the the joint probability of M,K and C when c is not fixed. a change in form but not in content but the the joint probability of M,K and C is not the same when c is fixed as when c is not fixed. you are just sophism === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > -----------a change in form but not in content,you just use the > probability when > c is not fixed. > you use the the joint probability of M,K and C when c is not fixed. I use the joint probability distribution of M,K and C. a change in form but not in content but the the joint probability of M,K and C is not the same when c is > fixed as when c is not fixed. There is no such thing as the joint probability distribution of M,K and C when c is fixed. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad -----------a change in form but not in content,you just use the > probability when > c is not fixed. > you use the the joint probability of M,K and C when c is not fixed. I use the joint probability distribution of M,K and C. a change in form but not in content but the the joint probability of M,K and C is not the same when c is > fixed as when c is not fixed. There is no such thing as the joint probability distribution of > M,K and C when c is fixed. - William Hughes what you do is fixe the prior probability of m ,then use it to decide the probability of c when k is uniform , then reverse understand the probability of M. The case is not random decided by the c fixed and k uniform. The probability of m is decided by the prior.that is similar to circular proof. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > -----------a change in form but not in content,you just use the > probability when > c is not fixed. > you use the the joint probability of M,K and C when c is not fixed. I use the joint probability distribution of M,K and C. a change in form but not in content but the the joint probability of M,K and C is not the same when c is > fixed as when c is not fixed. There is no such thing as the joint probability distribution of > M,K and C when c is fixed. - William Hughes what you do is fixe the prior probability of m ,then use it to decide > the probability of c when k is uniform , then reverse understand the > probability of M. > The case is not random decided by the c fixed and k uniform. > The probability of m is decided by the prior.that is similar to > circular proof. The proof If the prior probability of M is not uniform then the prior probability of M is not uniform is circular. This is not however the proof I am giving. The proof If the prior probability of M is not uniform then the probability distribution on K is not uniform for a fixed C is not circular. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad -----------a change in form but not in content,you just use the > probability when > c is not fixed. > you use the the joint probability of M,K and C when c is not fixed. I use the joint probability distribution of M,K and C. a change in form but not in content but the the joint probability of M,K and C is not the same when c is > fixed as when c is not fixed. There is no such thing as the joint probability distribution of > M,K and C when c is fixed. - William Hughes what you do is fixe the prior probability of m ,then use it to decide > the probability of c when k is uniform , then reverse understand the > probability of M. > The case is not random decided by the c fixed and k uniform. > The probability of m is decided by the prior.that is similar to > circular proof. The proof If the prior probability of M is not uniform then > the prior probability of M is not uniform is circular. This > is not however the proof I am giving. The proof If the prior probability of M is not uniform then > the probability distribution on K is not uniform for a fixed C > is not circular. - William Hughes- - - - The proof If the prior probability of M is not uniform then the prior probability of M is not uniform is circular. This is not however the proof I am giving. The proof If the prior probability of M is not uniform then the probability distribution on K is not uniform for a fixed C is not circular. but you use that to get the probability of M is the same as prior.that is a circular, It is no use denying. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad -----------a change in form but not in content,you just use the > probability when > c is not fixed. > you use the the joint probability of M,K and C when c is not fixed. I use the joint probability distribution of M,K and C. a change in form but not in content but the the joint probability of M,K and C is not the same when c is > fixed as when c is not fixed. There is no such thing as the joint probability distribution of > M,K and C when c is fixed. - William Hughes how you get the probability??? when c fixed, if we soppose k uniform, then m uniform if we suppose m as its prior, then k is corronspand as prior. Indeed we dont know the probability of M and k when c fixed, you just use the case c is not fixed. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > how you get the probability??? when c fixed, we can compute the probability distribution of M from the known joint probability distribution of M, and C. (there is only one joint probability distribution, there is no such thing as the joint probability distribution of M and C when C is fixed) We find that the probability distribution of M is not uniform. >if we soppose k uniform, then m uniform and as we know that M is not uniform we conclude that the assumption that K is uniform when C is fixed is incorrect. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad how you get the probability??? when c fixed, we can compute the probability distribution > of M from the known joint probability distribution > of M, and C. (there is only one joint probability > distribution, there is no such thing as the joint > probability distribution of M and C when C is fixed) > We find that the probability distribution > of M is not uniform. if we soppose k uniform, then m uniform and as we know that M is not uniform we conclude that > the assumption that K is uniform when C is fixed > is incorrect. - William Hughes we can compute the probability distribution of M from the known joint probability distribution of M, and C. (there is only one joint probability distribution, there is no such thing as the joint probability distribution of M and C when C is fixed) We find that the probability distribution of M is not uniform. fixed is considered is not the same as when c not fixed, but you just use when c not fixed, >if we soppose k uniform, then m uniform and as we know that M is not uniform we conclude that the assumption that K is uniform when C is fixed is incorrect. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad ... as we know that M is not uniform we conclude that > the assumption that K is uniform when C is fixed > is incorrect. > Good, you understand. Now stop claiming that K must be uniform when C is fixed. It might be, but it might not be. >but what can you conclude. That if we do not know whether or not M is uniform, we do not know if whether or not K is uniform when C is fixed. Thus If we consider only the OTP without considering the prior probability on M, we do not know whether of not M is uniform. So if we consider only the OTP and a fixed C we do not know whether or not K is uniform. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > ... as we know that M is not uniform we conclude that > the assumption that K is uniform when C is fixed > is incorrect. > Good, you understand. Now stop claiming that K > must be uniform when C is fixed. It might be, but > it might not be. but what can you conclude. That if we do not know whether or not M is uniform, > we do not know if whether or not K is uniform when > C is fixed. Thus If we consider only the OTP without considering the > prior probability on M, we do not know whether > of not M is uniform. So if we consider only the OTP > and a fixed C we do not know whether or not > K is uniform. - William Hughes Good, you understand. Now stop claiming that K must be uniform when C is fixed. It might be, but it might not be. regardless of M prior note I say: I just regardless one of the conditions such as M prior and K uniform to make show there need a compromise . >but what can you conclude. That if we do not know whether or not M is uniform, we do not know if whether or not K is uniform when C is fixed. Thus If we consider only the OTP without considering the prior probability on M, we do not know whether of not M is uniform. So if we consider only the OTP and a fixed C we do not know whether or not K is uniform. statement i consider C fixed, k uniform, regardless P prior i consider C fixed, P Prior , regardless k uniform under the two Probability are conflicting. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > i consider C fixed, k uniform, regardless P prior This assumption is only correct if P is uniform. So any conclusion you draw from this assumption will be correct only if P is uniform. If P is not unform, the conclusion that P is uniform is incorrect. So there is no contradiction between the incorrect conclusion that P is uniform and the fact that P is not uniform. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad i consider C fixed, k uniform, regardless P prior This assumption is only correct if > P is uniform. So any conclusion you draw from this > assumption will be correct only if > P is uniform. If P is not unform, the conclusion that > P is uniform is incorrect. So there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. - William Hughes i consider C fixed, k uniform, regardless P prior This assumption is only correct if P is uniform. P is uniform. So any conclusion you draw from this assumption will be correct only if P is uniform. ==i just get P is uniform If P is not unform, the conclusion that P is uniform is incorrect. So there is no contradiction between the incorrect conclusion that P is uniform and the fact that P is not uniform. I just get that under my precondition, I use the probability under imperfect conditions to compromise. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > i consider C fixed, k uniform, regardless P prior This assumption is only correct if > P is uniform. So any conclusion you draw from this > assumption will be correct only if > P is uniform. If P is not unform, the conclusion that > P is uniform is incorrect. So there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. - William Hughes i consider C fixed, k uniform, regardless P prior > This assumption is only correct if > P is uniform. > P is uniform. > An assumption that get[s] the result that P is uniform is only correct if P is uniform. If P is not uniform the assumption is incorrect. > So any conclusion you draw from this > assumption will be correct only if > P is uniform. > ==i just get P is uniform And this is only correct if P is uniform. If P is not unform, the conclusion that > P is uniform is incorrect. > So there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. > No An *incorrect* conclusion that P is uniform does not contradict the fact the P is not uniform. - William Hughes > === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad i consider C fixed, k uniform, regardless P prior This assumption is only correct if > P is uniform. So any conclusion you draw from this > assumption will be correct only if > P is uniform. If P is not unform, the conclusion that > P is uniform is incorrect. So there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. - William Hughes i consider C fixed, k uniform, regardless P prior > This assumption is only correct if > P is uniform. > P is uniform. An assumption that get[s] the result that > P is uniform is only correct if P is uniform. > If P is not uniform the assumption is incorrect. So any conclusion you draw from this > assumption will be correct only if > P is uniform. > ==i just get P is uniform And this is only correct if P is uniform. If P is not unform, the conclusion that > P is uniform is incorrect. > So there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. > No An *incorrect* conclusion that P is uniform > does not contradict the fact the P is not uniform. - William Hughes - - - -- - - - what i say is results get from imperfect conditions are inconsistant, then the perfect result under perfect condition should be a compromise of the results get from imperfect conditions . that is also to say, it is not proper to insist posterior pribability of P = prior. just like you insist K is uniform. you can see detail in my paper relavity of probability t === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > i consider C fixed, k uniform, regardless P prior This assumption is only correct if > P is uniform. So any conclusion you draw from this > assumption will be correct only if > P is uniform. If P is not unform, the conclusion that > P is uniform is incorrect. So there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. - William Hughes i consider C fixed, k uniform, regardless P prior > This assumption is only correct if > P is uniform. > P is uniform. An assumption that get[s] the result that > P is uniform is only correct if P is uniform. > If P is not uniform the assumption is incorrect. So any conclusion you draw from this > assumption will be correct only if > P is uniform. > ==i just get P is uniform And this is only correct if P is uniform. If P is not unform, the conclusion that > P is uniform is incorrect. > So there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. > No An *incorrect* conclusion that P is uniform > does not contradict the fact the P is not uniform. - William Hughes - - - -- - - - > My comment was that there is no contradiction between the incorrect conclusion that P is uniform and the fact that P is not uniform. Your reply was they are obvious contradiction Do you continue to maintain this position? - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > i consider C fixed, k uniform, regardless P prior > This assumption is only correct if > P is uniform. > So any conclusion you draw from this > assumption will be correct only if > P is uniform. > If P is not unform, the conclusion that > P is uniform is incorrect. > So there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. > - William Hughes i consider C fixed, k uniform, regardless P prior > This assumption is only correct if > P is uniform. > P is uniform. An assumption that get[s] the result that > P is uniform is only correct if P is uniform. > If P is not uniform the assumption is incorrect. > So any conclusion you draw from this > assumption will be correct only if > P is uniform. > ==i just get P is uniform And this is only correct if P is uniform. > If P is not unform, the conclusion that > P is uniform is incorrect. > So there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. > No An *incorrect* conclusion that P is uniform > does not contradict the fact the P is not uniform. - William Hughes - - - -- - - - My comment was that there is no contradiction between > the incorrect conclusion that P > is uniform and the fact that P > is not uniform. Your reply was they are obvious contradiction Do you continue to maintain this position? - William Hughes- - - - do not say any of them are correct, just to say they are contradiction and do not coexist, then the compromise. just like the four feet of a table. YOu just insist one is correct and one is incorrect. you just insist key uniform incorrect, but P Prior correct. but the latter is also incorrect. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > how you get the probability??? when c fixed, we can compute the probability distribution > of M from the known joint probability distribution > of M, and C. (there is only one joint probability > distribution, there is no such thing as the joint > probability distribution of M and C when C is fixed) > We find that the probability distribution > of M is not uniform. if we soppose k uniform, then m uniform and as we know that M is not uniform we conclude that > the assumption that K is uniform when C is fixed > is incorrect. - William Hughes we can compute the probability distribution > of M from the known joint probability distribution > of M, and C. (there is only one joint probability > distribution, there is no such thing as the joint > probability distribution of M and C when C is fixed) > We find that the probability distribution > of M is not uniform. fixed is considered is not the same as when c not fixed, but you just > use when c not fixed, if we soppose k uniform, then m uniform and as we know that M is not uniform we conclude that > the assumption that K is uniform when C is fixed > is incorrect. > - - I just regardless one of the conditions such as M prior and K uniform to make show there need a compromise . === Subject: Finding the derivative I need to find the first derivative for f(x) = (2x^3-4x^2+3)/(x^2) I know the answer, f'(x) = (2x^3-3)/(x^3), but the steps to get it is what I am having trouble with. This is the only type of problem I am having trouble with on a section I am going to be tested on later this === Subject: Re: Finding the derivative >I need to find the first derivative for f(x) = (2x^3-4x^2+3)/(x^2) >I know the answer, f'(x) = (2x^3-3)/(x^3), but the steps to get it is >what I am having trouble with. This is the only type of problem I am >having trouble with on a section I am going to be tested on later this First divide through by x^2, writing each term as a constant times a power of x (allow negative powers). quasi === Subject: Re: Finding the derivative what I am having trouble with. This is the only type of problem I am >having trouble with on a section I am going to be tested on later this First divide through by x^2, writing each term as a constant times a > power of x (allow negative powers). quasi Yes I am using the power rule, I can find the answer to other problems with no problem, it is only these bigger types of fractions I cannot === Subject: Re: Finding the derivative >I need to find the first derivative for >f(x) = (2x^3-4x^2+3)/(x^2) >I know the answer, f'(x) = (2x^3-3)/(x^3), Note -- your answer is wrong. >but the steps to get it is >what I am having trouble with. This is the only type of problem I am >having trouble with on a section I am going to be tested on later this > First divide through by x^2, writing each term as a constant times a > power of x (allow negative powers). > quasi >Yes I am using the power rule, I can find the answer to other problems >with no problem, it is only these bigger types of fractions I cannot How did you use the power rule without first dividing each term of the numerator by x^2? quasi === Subject: Re: Finding the derivative On 2007-11-06 19:58:59 -0500, theglovegp@aol.com said: > I need to find the first derivative for f(x) = (2x^3-4x^2+3)/(x^2) > I know the answer, f'(x) = (2x^3-3)/(x^3), Are you sure that is the answer? > but the steps to get it is > what I am having trouble with. What methods have you learned so far? Do you know the power rule? > This is the only type of problem I am > having trouble with on a section I am going to be tested on later this If you can show us what you can do so far, we can help you in where you got stuck. But if you show us nothing, are we to assume you have no knowledge at all about finding derivatives? -- -kira === Subject: =?windows-1256?B?TmV3INHT3Nzcx8bc3NzhIObT3Nzc3MfG3Nzc2CAyMDA3IE5ldw==?=