mm-4399 === Subject: solution manual i was wondering do you have the solution manual for any of the fallowing text books fundemental of fluid mechanics by munson young odiishi fluid mechanics with engineering application by finnemore and franzini geotechnical engineering with principles and practices by Donald P. Coduto fundementals of structural analysis by Kenneth M.Leet Chia-Ming Uang Anne m Gilbert I really appriciate this === Subject: Re: ? vector of least common multiple or highest common factor <46d1bbad$0$31870$4c368faf@roadrunner.com > Given a set of natural numbers, one can find a nature > number as the highest common factor or the least common multiple. This can be seen as a lattice. Note sure what you meant, would you be more specific regarding to > extending these ideas to a set of vectors? > Are you familiar with lattices? Lattices don't extend to vector spaces. On the other hand, any vector space V with lineral ordered scalars, can be seen as a lattice over an orthogonal base for V. Was 'note' a typo? === Subject: Polynomial Root Finder Method. Here is a polynomial root finder. I have added some captions to the images so it's easier to follow. http://mypeoplepc.com/members/jon8338/polynomial/ === Subject: Re: Polynomial Root Finder Method. I can tell you that I'm tired of dicking around about this problem without finding a solution. There's going to be a way to solve it, and it's going to be the hard way. > Here is a polynomial root finder. I have added some captions to the > images so it's easier to follow. http://mypeoplepc.com/members/jon8338/polynomial/ > === Subject: Re: Test functions are dense in L^1 I'm trying to prove that space of test functions > D(R) is dense in L^1(R), > here is my argument: Take a mollifier f(x) and a mollifying sequence > f_n(x). For any compact > set K of R, let chi_K be a characteristic function > of K. Then it is known > that for any distribution u : u * f_n -> u in > D'(R). In particular, chi_K > * f_n -> chi_K in D'(R), and in particular in > L^1(R) norm. chi_K * f_n are > in infinitely differentiable and since chi_K is > compactly supported, chi_K > * f_n are also compactly supported, which implies > that chi_K * f_n in > D(R). chi_K for different compacts K being dense in > L^1(R) implies that L^1(R) > can be approximated by functions from D(R). Is that right? And does anybody know of any > other(maybe simpler) way. > L^1 functions are approximated by L^1 functions of > compact support. These are approximated by Schwartz functions. Use SW > to > approximate (1+x^2)f with f in C_c(R) by a function > of the form > (1+x^2) p(x)e^{-x^2/2}. This gives a simultaneous > approximation in all the L^p norms. Now just multiply by a suitably chosen bump function > to get a test > function. This is just one way. Another way is to convolve > the L^ 1 function of compact support with a series of > bump functions > with integral 1 and support in decreasing > neighbourhoods of 0. Why not look in Hormander OPD Vol I where many of > your > questions are answered? Unfortunately, i don't have it accessible. > rusty === Subject: solution manual hi i was wondering do you have the solution manual for any of the fallowing text books fundemental of fluid mechanics by munson young odiishi fluid mechanics with engineering application by finnemore and franzini geotechnical engineering with principles and practices by Donald P. Coduto fundementals of structural analysis by Kenneth M.Leet Chia-Ming Uang Anne m Gilbert I really appriciate this === Subject: theRat given any commutative ring A Spec(A) is an affine scheme and any affine scheme may be written as Spec(A) for some A the collection of all prime ideals of A is the collection of all the places p we can form localisations at every element a of A determines a subcollection of Spec(A) of prime ideals containing a and these extend to collections of A and can be used to define closed sets of a topology - this is the zariski topology on Spec(A) the construction of attaching to each place p of Spec(A) the quotient localisation Ap is a sheafification that provides the structure for the affine scheme call this quotient map local(p): Spec(A) -> A/Spec(A) all schemes are built up of affine schemes locally by classic decomposition theorems on sheafifications suddenly we are thrown out of our leisurely pace and elliptic curves start to pester the rat with all their questions take the neron model Escript of E/Qp at a point of good reduction this is an abelian scheme over Zp the multiplication maps [m]:Escript -> Escript turn out all to be rats the Escript[m] are affine and the [m] maps are finite and flat so what R are the schemes Escript[m] the spectrum of? they are from an elliptic curve embedded in P^2 so they are closed subscheme of P^2_{Zp} the closed fiber is finite over Fp so there is a homogeneous polynomial fbar e Fp[X, Y, Z] whose closure does not meet the closed fiber of Escript[m] so we can lift fbar to f e Zp[X, Y, Z] the scheme closure V of f in P^2_{Zp} does not interesct Escript[m] in P^2_{Zp} so Escript[m] is a closed subscheme of the affine scheme P^2_{Zp}V ( ie. in Spec(Zp[X,Y,Z]/(f)) ) and the closed subschemes of affine schemes are affine (by direct application of the zariski topology to produce the subspectrum correspondence) call this R (Escript[m] = Spec(R)) then Spec(R) -> Spec(Zp) is universally closed and so R is integral and finite over Zp the structure theorem for finite Zp modules then implies that since the dimensions of the closed fibers and generic fibers are identical Spec(R) is free and therefore flat any finite flat Spec(R)-schemes are also affine ~~~~~~~~~..^^^ return to http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/hida/hida-ps.pdf which galois representations are automorphic? lots of conjectures and a few major theorems artin L-functions can generally be attached to automorphic forms through the frobenius construction what are the motives of the rat? langlands reciprocity conjectures: if sigma : weilGroup(F) --> GL(2, C) then there exists an autorphic cuspidal representation pi with L(s, sigma) = L(s, pi) the goal is extending modularity to its most general representative setting so we have this relationship we are starting to develop between local information in galois representations lifted to ever elusive motives and some elusive local description of modularity lifted to automorphic forms connected through data in the L-functions vague because much of the structure is still conjectural artin's conjecture langlands' hodge... even which category things are defined over is not well understood the key tool used to transport properties over families of local data has been the use of deformations and the ability to construct deformations has been the crucial functorial property in wiles in langlands -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: theRat Spec(A) is an affine scheme > and any affine scheme may be written as Spec(A) for some A the collection of all prime ideals of A > is the collection of all the places p we can form localisations at every element a of A determines a subcollection of Spec(A) of prime ideals containing a > and these extend to collections of A and can be used to define closed sets of a topology > - this is the zariski topology on Spec(A) the construction of attaching to each place p of Spec(A) the quotient localisation Ap > is a sheafification that provides the structure for the affine scheme > call this quotient map local(p): Spec(A) -> A/Spec(A) all schemes are built up of affine schemes locally > by classic decomposition theorems on sheafifications suddenly we are thrown out of our leisurely pace > and elliptic curves start to pester the rat with > all > their > questions take the neron model Escript of E/Qp at a point of good reduction > this is an abelian scheme over Zp the multiplication maps [m]:Escript -> Escript turn out all to be rats > the Escript[m] are affine > and the [m] maps are finite and flat so what R are the schemes Escript[m] the spectrum of? they are from an elliptic curve embedded in P^2 > so they are closed subscheme of P^2_{Zp} the closed fiber is finite over Fp > so there is a homogeneous polynomial fbar e Fp[X, Y, Z] > whose closure does not meet the closed fiber of Escript[m] > so we can lift fbar to f e Zp[X, Y, Z] the scheme closure V of f in P^2_{Zp} does not interesct Escript[m] in P^2_{Zp} > so Escript[m] is a closed subscheme of the affine scheme P^2_{Zp}V > ( ie. in Spec(Zp[X,Y,Z]/(f)) ) > and the closed subschemes of affine schemes are affine > (by direct application of the zariski topology to produce the subspectrum correspondence) call this R (Escript[m] = Spec(R)) then Spec(R) -> Spec(Zp) is universally closed > and so R is integral and finite over Zp the structure theorem for finite Zp modules then implies that > since the dimensions of the closed fibers and generic fibers are identical > Spec(R) is free and therefore flat any finite flat Spec(R)-schemes are also affine ~~~~~~~~~..^^^ return tohttp://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/hida/hida-ps.pdf which galois representations are automorphic? lots of conjectures and a few major theorems artin L-functions can generally be attached to automorphic forms through the frobenius construction what are the motives of the rat? langlands reciprocity conjectures: > if sigma : weilGroup(F) --> GL(2, C) > then there exists an autorphic cuspidal representation pi > with L(s, sigma) = L(s, pi) the goal is extending modularity to its most general representative setting so we have this relationship we are starting to develop > between local information in galois representations lifted to ever elusive motives > and some elusive local description of modularity lifted to automorphic forms > connected through data in the L-functions vague because much of the structure is still conjectural > artin's conjecture > langlands' > hodge... even which category things are defined over is not well understood the key tool used to transport properties over families of local data > has been the use of deformations > and the ability to construct deformations has been the crucial functorial property in wiles > in langlands -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar What is the new subject theRat mean in connection with this thread and your last post? === Subject: Re: theRat > What is the new subject theRat mean in connection with this thread > and your last post? I introduced the term the Rat with a specific meaning: if rho0 is a representation of Gal(Qpbar/Qp) into GL(2,k), k being a finite field, then LeRat(rho) denotes the set of all Gal(Qpbar/Qp)-equivariant functions from k^2 to Zpbar. Galathaea seems to have decided to use the same terminology to refer to the finite flat group schemes one gets from points of order m on an elliptic curve over Zp. I would prefer that he find some other term, even though such finite flat group schemes are admittedly good experimental animals. Why not call E[m] a horse, like in the story in Fantasia Mathematica? Or if he thinks that what I call the rat is a subgroup scheme of what he calls the rat, maybe he should call E[m] a barrel, which would also fit with the Fantasia Mathematica story, and which also conveys the notion of containment. Also, thinking of points of order n on a torus suggests a kind of barrel, maybe a little twisted. I don't know why he decided to review the definition of affine schemes, but it might be consistent with other attempts he has made in this thread to make parts of this discussion more generally accessible to some readers. It may also have been intended to a partial reply to my question about whether a finite flat group scheme over an affine scheme is necessarily affine, without specifically assuming it to be so. When I posed the question, I also suggested a proof that it is always affine, but hadn't checked the proof for correctness. Galathaea hasn't addressed that question in his discussion of affine schemes, as nearly as I can tell, but it may be implicit in his discussion if, as it appears, he considers all finite flat group schemes to be sub-group-schemes of group schemes of the form E[m]. That result, if true, has not been proved nor supported by a citation in the literature. But if it is true, it does imply that finite flat group schemes over an affine scheme are affine provided this is so for the group schemes E[m]. The rest of Galathaea's posting seems to be aimed at my question about what objects in Wiles' proof might be what Langlands wants to fit in the lower right corner of his square diagram in his review of Hida's book. I'm not sure, but I think he is saying that he doesn't know and that Langlands doesn't know either, and may simply be paraphrasing Langlands to express this. Finally, I think Galathaea might be too busy at work to be more lucid and thorough (e.g. what about Proposition 1.1 of Wiles' paper), but doesn't want to drop out altogether. -- Ignorantly, Allan Adler * Disclaimer: I am a guest and *not* a member of the MIT CSAIL. My actions and * comments do not reflect in any way on MIT. Also, I am nowhere near Boston. === Subject: Re: Poor teaching of econ <18266811.1188077548020.JavaMail.jakarta@nitrogen.mathforum.org Once upon a time the economics profession knew that > the economy is a > consequence of the actions of individual human > beings; it was also > realised that such a problem was mathematically > intractable (this was > long before computers got on stage). Therefore nobody > bothered about > mathematics in economics; instead all focus was on > understanding the > principles that guide economic processes. intractable ??? Since the governing principles of economic behaviour comes down to the valuations of individual people, and there are rather a lot of those, the mathematics would be impossible to address with the tools of that day (and even of our day). > Some time later a lot of economists decided that they > WOULD force > mathematics into economics, whether it was tractable > or not. Their > solution was to assume that the economy behaves as > system governed by > mathematical equations prescribed from above (i.e. > they gave up on the > idea that the economy is a consequence of the actions > of individual > human beings). Since then they have been happily > fiddling with > differential equations to their hearts delight; and > this to the extent > that they have almost completely forgotten about the > fundamental > principles ruling economic processes. with all respect : bogus. fundamental economics are just the inclusion of political and social sciences , since they have influence on economics. does not debunk math in economics. I have absolutely not an inkling of an idea of what you are talking about. > Personally, I think the only kind of mathematics that > really belongs > in economics is non-linear dynamics, because this is > a mathematical > representation of economic reality, whereas the > differential equations > are not. ??? plz lookup universal differential equation. differential equations are non-linear. and non-lineair dynamics can be transformed in a differential equation, at least most of them. If you don't even know the math that governs the behaviour of the agents in the economy (people), then you do not stand a chance of rearranging it into a system wide equation. Clearly, any progress must begin with understanding the individual actions of the economic agents. Stefan W. Christensen === Subject: Re: Poor teaching of econ <46d06ee1$0$11009$4c368faf@roadrunner.com> On 25 Aug., 20:02, professorchaos Once upon a time the economics profession knew that the economy is a > consequence of the actions of individual human beings; it was also > realised that such a problem was mathematically intractable (this was > long before computers got on stage). Therefore nobody bothered about > mathematics in economics; instead all focus was on understanding the > principles that guide economic processes. Completely wrong. It is not mathematically intractable Never said it is; I specifically said it was. > and no one > bothered about math before the marginalist revolution because political > economy was in the realm of philosophy and the theorist had little > knowledge of math. I'm not going back that far; I was talking about economics around 100 years ago; during the time when the marginalist revolution was realised, but before Keynes and his grim followers came to do their evil bidding. > Some time later a lot of economists decided that they WOULD force > mathematics into economics, whether it was tractable or not. Wrong people like Stanley Jevons and Paul Samuelson showed how math was > useful and how it could enrich the study of behavior. Every science > needs proof So what's the value of proof in a science so complex that no theorems can be developed from the axioms, because there is only really one of them? (The axiom, by the way, is: Man acts.) > and you need measures and statistic to do that Try constructing a proof through statistics... >Their > solution was to assume that the economy behaves as system governed by > mathematical equations prescribed from above (i.e. they gave up on the > idea that the economy is a consequence of the actions of individual > human beings). Entirely wrong. Most that goes into the equations can be found in Smith, > Ricardo, and other pre-marginalist revolution writers. The rest comes > from the theory of marginal analysis that enriched the ability to use math. That's clearly an oversight; the main issue is that current economists work from the supposition that the economy can be described via system wide equations; the knowledge that it cannot, because the economy is controlled bottom-up via the actions of the individual agents (people) and therefore is a highly non-linear system to which system wide equations cannot apply, has in essense been lost. >Since then they have been happily fiddling with > differential equations to their hearts delight; and this to the extent > that they have almost completely forgotten about the fundamental > principles ruling economic processes. If that were true the psychic majors in graduate schools would have a > lot easier time. In graduate schools prior econ majors often trouble > with the math. Previous hard science majors have trouble with the > concepts. They can do the math in their sleep but struggling with > catching up with the principles. You have to know the principles to set > the model up. If you do not know them you have no idea how to write a > model to solve or why you are doing it. I'm not claiming that ALL principles are forgotten; the marginalist idea still is entertained by the main-streamers. Most principles have been forgotten, however (which is probabily primarily due to Keynes' ability to dupe politicians with pseudo-science). Personally, I think the only kind of mathematics that really belongs > in economics is non-linear dynamics, because this is a mathematical > representation of economic reality, whereas the differential equations > are not. Differential equations are not really only that common. The dynamics are > often not linear. Have you ever seen a growth model? Do you know > anything about the use of optimal control models for growth and for > renewable resource models? Have you seen a dynamic model in economics? The point is: a growth model is system wide and is fundamentally unable to capture the dynamics of the real economy. Stefan W. Christensen === Subject: Re: Poor teaching of econ > On Sat, 25 Aug 2007 13:17:35 -0500, professorchaos > Wrong. Politicians couldn't care less about the economic soundness of > policies. I would agree but I still have a little more faith and choose to believe it is because they are ignorant of economic principles. They just want money and power, and the way to get money > and power is to serve the interests of those who have money and power > to dispense. In the system we have you have to get money to get elected so yes lobbyist have disproportionate power. This is the whole basis of the public choice case some economist believe firmly in. You balance budgets yearly because tax increases are hard to pass. So it limit the money lobbyist can get. This lowers the payoff from lobbying and decreases lobbyist money into the system and their power. Still highly inefficient yet, it will happen until the US people decide they will not vote for anyone who does not support a law banning campaign contributions and public funds for elections where the money is divided equally among candidates. > Oh, garbage. Requiring economics would just ensure that everyone was > equally brainwashed with lies. Research by psychologists has shown > that economics students are the most amoral on campus, even beating > out law students. Research this is really funny. First of all a real psychologist doing real research would have to define amoral and be able to measure it. Good luck there. Garbage into the study garbage out. It was probably some hippy who defined amoral has meaning wanting a job that pays a decent amount is amoral. > It doesn't take a genius to infer that their > professors are likewise the most amoral on campus. Amorality is the > True Gospel of Economics, and economists are its disciples. Reponding > to incentives just like Pavlov's dogs, There is a huge difference between stimulus and incentive. Pavlov gave the dogs stimulus not incentives. Incentive gives a reason to want to do something. You don't have to do it. For example, allowing charitable contributions as a tax write off gives incentive to invest. It doesn't mean every does it. In Pavlov's experiment the stimulus created a response that the dogs had no choice over. You don't really even understand Pavlov much less economics if you can't understand what an incentive is. >economists lie to the public > about economics to serve the interests of the rich, because that is > what pays best. > Really? When I worked at a community college while finishing my doctoral degree were my students the rich? Could have fooled me. They responded a lot better to examples involving Top Ramen than examples involving Romeo and Juliet Cigars. They did pay a good portion of my salary then. Students at my own university paid at least 2/3 of graduate stipend. If you compare in state tuition to out of state tuition(note no state funding for out of state students). So I should burn all my AERs because all of those professors from Cambridge to small town Louisana colleges who have published in them are being paid by the man to lie? Do you stay up to 4 am listening to Alex Jones, David Eiche, and others who want to tell you the government is behind everything from UFOs to 9/11? Oh excuse me, the global government run by the Ilumanti or Masons depending on which psuedo-researcher is presenting the story. > The economist does no such thing. He most certainly does. Proof: the hundreds of economists who have > endorsed the execrable anti-scientific nonsense contained in the > FairTax proposal, a proposal whose economic rationale is laughable, > but that would massively shift the burden of taxation off the idle > rich and onto working people. > Personally, I have not even seen the proposal. Although I did get an email from the same people I think asking me to sign a petition to stop the oil taxes congress is proposing. That would not shift anything just prevent new taxes that are very bad. So I can not comment on what may or may not be in this proposal. My sense is you have no sense of science so if I have time I may look at it and evaluate for myself if it is unsound or not. My guess is Alex Jones said it was unsound over the radio and you believe him. > Although we > might be guilty of often writing with the audience of other economist in > mind. Garbage. Economists know very well they are lying for the purpose of > deceiving journalists and voters, not other economists who are also in > on the deceit. > Man, Alex Jones would love you. I bet he would get a spot on his radio show. Someone who believes certainly must believe that the government would have been stupid enough to waste a missile by shooting it into a building they were going to crash a plane into anyway. > In 1936 with John Maynard Keynes this may have been true. Today we stick > to testable hypothesis. _Liar_. When was any general equilibrium hypothesis ever tested, > hmmmm? > Over and over again. The empirical work supports it. Even some of my own research has dealt with general equilibrium models. Guess what the data said the model was pretty accurate. > Economics would more accurately be termed the deceitful science, not > the dismal one, and the absence of any measurable increase in > economics students' understanding is not a failure of economics > instruction at all, but its intended result. > Speaking like this could probably get on Coast to Coast. such as mine are never permitted in the mainstream media at all. > To call this analysis is a joke. I am surprised you do not know what Coast to Coast is. Art Bell or George Nory would put you on in a heart beat on that show. You just have to write a book that presents little fact and draws a conclusion like the Masons run everything to get on that show. I have had some bouts with insomina in graduate school and it was delightfully disengage to listen this type of psuedo-science in the early morning hours. It will helped to pull my head out of OX, modeling, and cutting edge econometrics. There are very few real scientist on that show and when they do come on they are on the outskirts talking about things like string theory and always stop the questioning when the host wants to pull that into alien abductions. > You really > should write a book this type of psuedo-science makes millions. Liar. No publisher will even print this sort of information, let > Look up David Eicke, Alex Jones, or Lynda Molten Howell on the internet. Publishers will publish anything. America is a great place where free speech is allowed. Alex Jones still hasn't been arrested for claiming the government was behind 9/11 nor even going further by claiming the government is controlled by the Masons. There are even books published saying George Bush is a reptilian alien and that people have seen him transform into an alien. I can not seriously believe with this claptrap attacking our government out there that a publisher wouldn't print a book bashing people politicians don't even listen to. The real problem is you make McCarthy statements and call it analysis. There is no analysis in your postings and you can't write more than a few paragraphs. You wouldn't have the faintest idea of how to put a book together. Although I wish you would. I would love to call into Coast to Coast and tear your psuedo-analysis apart while the incredulous lineup to buy the book. > I bet > you believe David Eicke when he tells you the illumanti and the masons > run the world. Wrong again. That's a perfect score: zero. David Icke gets lots of > press because he is safely and obviously a kook. > Well that is one thing we agree on. Maybe you are more the Alex Jones type. > How else do you explain disasters like the invasion of Iraq, which > benefit no one but certain narrow, wealthy interests who reap immense > profits from the immense suffering of others? Iraq hasn't benefited the wealthy. Gas prices are still soaring. Iraqi oil is not even fully online yet. The wealthy in the UN were in a much better position when the Oil for food scandals were going on and France and Russia were giving huge kickbacks to Saddam Hussein in exchange for contracts under OFF(Oil for Food) and buying Iraq oil at less than market rates and giving Saddam a cut. That war had nothing to do with wealthy people getting control of oil. It had everything to do with Saddam getting wealthy off a corrupt UN system that Kofi Annon and others were skimming off the top. All the while giving money back to Saddam so he could restart biological and nuclear programs. Read the Duefler report no massive stockpiles but those programs were in existence again with Oil for Food. The OFF debacle threatened Israel, our ally, and other allies in the region. As Saddam got back to his old tricks. Granted the stockpiles were not there and the programs were no where near 1991 levels. However, to keep Iraqi as a UN colony where certain security members were pillaging what they could will supporting a dangerous dictator who had no problems using biological weapons would have led to greater than 1991 levels eventually. George W. Bush did want Winston Churchill would have done during the Anschluss or the Munich conference had the pacifist not let him. Churchill would have gone done in history like Bush if he had been able to. He would been blamed for starting a small war with Germany and no one would have known the carnage he prevented if parliament would have listened him. Bush may have very prevented a huge amount of carnage that likely would have happened in 10-15 years time if Hussein had been left in power while corrupt UN policies fed him and corrupt Frenchmen, Russians, and UN members. Do you realize less than half of Iraqi oil sales went to Iraqi from 1994 to the invasion? Do you realize the UN got over 20% of Iraqi oil sales prior to the invasion? That Kuwait was still getting large reparations? That the UK/US tried price controls to stop the corruption? Iraq was all about stopping corrupt interest before it was true late. -- Roy L === Subject: Re: Poor teaching of econ <46cdb987.6203293@news.telus.net> <46d07264$0$31919$4c368faf@roadrunner.com> <46d0b87f.1988497@news.telus.net> <46d24e13$0$16512$4c368faf@roadrunner.com> On Aug 27, 12:07 am, professorchaos Oh, garbage. Requiring economics would just ensure that everyone was > equally brainwashed with lies. Research by psychologists has shown > that economics students are the most amoral on campus, even beating > out law students. > Research this is really funny. First of all a real psychologist doing > real research would have to define amoral and be able to measure it. > Good luck there. Garbage into the study garbage out. It was probably > some hippy who defined amoral has meaning wanting a job that pays a > decent amount is amoral. I don't know why this anonymous supposed professor wants to proclaim his more-than-ignorance. http://robertvienneau.blogspot.com/2006/09/does-studying-mainstream-economic s.html > In 1936 with John Maynard Keynes this may have been true. Today we stick > to testable hypothesis. > _Liar_. When was any general equilibrium hypothesis ever tested, > hmmmm? > Over and over again. The empirical work supports it. Even some of my own > research has dealt with general equilibrium models. Guess what the data > said the model was pretty accurate. Somehow I suspect this anonymous supposed professor is completely unaware of Alan Kirman's extensions and comments on the Sonnenschein- Mantel-Debreu results. Clearly the American Economic Association doesn't care if their members are liars and thieves. They have no sense of professional ethics. But I don't think most mainstream economists consciously lie all the time. Many, I suspect, are ignorant of their ignorance - ignorance squared as it has been called. === Subject: Re: Poor teaching of econ > On Sat, 25 Aug 2007 13:17:35 -0500, professorchaos > Wrong. Politicians couldn't care less about the economic soundness of > policies. I would agree but I still have a little more faith and choose to believe > it is because they are ignorant of economic principles. I would go farther to say that the more accurate description is that politicians are acting on misconceptions of economics. My basis for this argument is the Townsend Plan. Its basic idea was to support a trickle-down theory by giving money to senior citizens, not an all-together bad idea [*]. However, it promised approximately twice the average pre-retirement salary (this during the Great Depression) financed by a 2% value-added tax. Problem is, that wouldn't be near enough to actually finance the plan. IIRC, Townsend eventually admitted that he more-or-less made up the numbers. In short, though, my basic idea is that politicians try to do the right thing economically, but end up tripping over misconceptions of economics (e.g. the current China-bashing) and putting some interests over the economically right thing to do (e.g. Social Security). > They just want money and power, and the way to get money > and power is to serve the interests of those who have money and power > to dispense. In the system we have you have to get money to get elected so yes > lobbyist have disproportionate power. This is the whole basis of the > public choice case some economist believe firmly in. You balance budgets > yearly because tax increases are hard to pass. So it limit the money > lobbyist can get. This lowers the payoff from lobbying and decreases > lobbyist money into the system and their power. Still highly inefficient > yet, it will happen until the US people decide they will not vote for > anyone who does not support a law banning campaign contributions and > public funds for elections where the money is divided equally among > candidates. Democracies have some fundamental fatal flaws: the biggest one is that voters often act irrationally. I have heard a good review of The Myth of the Rational Voter from The Economist which is pertinent to this That brings up another point about politicians: they tend to cater more to their constituent core than to the good of the country. Given that voters are often irrational in their decisions (we want more but we don't want to pay more), politicians tend to put those concerns ahead of the right thing to do when given a choice. [*] Actually, I personally hold that schemes like Social Security are a bad thing, given that the middle- and upper-class are capable of creating saving schemes to comfortably live out the rest of their lives and do not need government intervention to do so. Any attempt by anyone else to dissuade me from this viewpoint would almost assuredly fail, so don't even bother trying to do so. === Subject: Re: Poor teaching of econ > [*] Actually, I personally hold that schemes like Social Security are a > bad thing, given that the middle- and upper-class are capable of > creating saving schemes to comfortably live out the rest of their lives > and do not need government intervention to do so. Any attempt by anyone > else to dissuade me from this viewpoint would almost assuredly fail, so > don't even bother trying to do so. You won't have any argument from me. I don't believe the Democrats when they say the middle class are too stupid to handle their own money so they need to give it to the government and that is exactly what they say and morons agree with it thinking the fathead was talking about everyone else but them. How many times have we heard liberals argue that people do not know how to invest and they lose money in the stock market? I think that is why politicians will never make economics part of the core curriculum in schools. It teaches kids to think and analyze. If thought right it teaches students to think about cost and weigh them against perceived or real benefits. That is the key to teaching economics not if they the student can remember what the marginal cost curve looks like. NB: I really wonder if part of the reason why students were failing the test 6 months after is because the course was taught right and students learned how to think like an economist then the test was a bunch of calculations like elasticity, marginal cost, and what is the shape of this curve rather how do we apply what we know. In the end, the thinking process being implanted is more important for principles than what supply and demand look like. Intermediate is a whole different story but for principles that is what most of colleagues and I want to achieve. If all students in the US were educated to do this the democrats and republicans would be screwed. People would realize minimum wages decrease employment. That supporting unions means you raise the union fat cat's salary and some people get a bit of a raise while many are left unemployed. They realize that those jobs they are supposed to protect by stopping trade with China actually decrease jobs in other areas because Chinese incomes do not grow as much and they do not import as much from us. They might actually start realize the logic in John C. Calhoun's exposition. They might realize that illegal immigration has kept housing and food prices down for a long time, even though it does hurt high school dropouts and manual laborers. They might start thinking about how it affects me rather than listening to propaganda. They might even realize they face higher prices when trade is limited and illegal immigration is stopped. They might realize the cost of stopping illegal immigration totally far outweighs the benefits. They might realize curtailing exports lowers prices here. They might realize investing in mutual funds is safe if you invest for the long haul and don't pull it out the first time prices drop. They might actually realize that politicians are calling them stupid on a daily basis and they can make decisions for themselves that are better than someone in Washington who knows nothing about them can make. That is just my opinion I could be wrong. Butters It is fortunate for rulers that people do not think. Adolf Hitler. === Subject: Re: Poor teaching of econ <46cdb987.6203293@news.telus.net> <46d07264$0$31919$4c368faf@roadrunner.com> <46d0b87f.1988497@news.telus.net> <46d24e13$0$16512$4c368faf@roadrunner.com> On Aug 27, 12:07 am, professorchaos George W. Bush did want Winston Churchill would have done during the > Anschluss or the Munich conference had the pacifist not let him. > Churchill would have gone done in history like Bush if he had been able > to. He would been blamed for starting a small war with Germany and no > one would have known the carnage he prevented if parliament would have > listened him. Bush may have very prevented a huge amount of carnage that > likely would have happened in 10-15 years time.... For a hard-nosed, fact-demanding scientist you are suddenly mighty imaginative. === Subject: Re: Poor teaching of econ <46cdb987.6203293@news.telus.net> <46d07264$0$31919$4c368faf@roadrunner.com> <46d0b87f.1988497@news.telus.net> <46d24e13$0$16512$4c368faf@roadrunner.com> On Aug 27, 12:07?am, professorchaos Anschluss or the Munich conference had the pacifist not let him. > Churchill would have gone done in history like Bush if he had been able > to. He would been blamed for starting a small war with Germany and no > one would have known the carnage he prevented if parliament would have > listened him. That's a stretch, as Neville Chamberlain was Prime Minister at that time. On the basic contention in this thread (mathematics in economics), one of the problems that I see is that the econ majors around here don't take enough mathematics to understand most of the models presented. Ours only take a baby business calculus and baby statistics course. As for fiat currency, I have serious concerns in the US and UK, especially given the tremendous dimunition of the actual reserves held in the poast 20 years. Off the top of my head, it's down to something like 0.4% === Subject: Re: Poor teaching of econ > On Aug 27, 12:07?am, professorchaos George W. Bush did want Winston Churchill would have done during the > Anschluss or the Munich conference had the pacifist not let him. > Churchill would have gone done in history like Bush if he had been able > to. He would been blamed for starting a small war with Germany and no > one would have known the carnage he prevented if parliament would have > listened him. That's a stretch, as Neville Chamberlain was Prime Minister at that > time. > Not a stretch at all. Churchill was speaking actively in parliament around this time about the German threat. He was warning parliament and the PM action was necessary. He was constantly reporting with alarm about the german build up of aircraft and aircraft engines that could be used as bombers and fighters. The UK didn't listen and was slow to even expand the RAF to meet the threat. There were few Hurricanes and no spitfires at the time and parliament thought pacifying Hitler would work. They believed D0-17z bombers were really postal planes and that the aircraft engines were for civilian use. Read the Dulfer report then read Gather Storm. The similarities are way too much. All of those dual purpose chemicals sitting around Iraq that liberals claim were for industrial use sound a lot like the Do-17Z postal plane, uhmm bomber, to me. > On the basic contention in this thread (mathematics in economics), one > of the problems that I see is that the econ majors around here don't > take enough mathematics to understand most of the models presented. > Ours only take a baby business calculus and baby statistics course. > Granted. Some institutions do not even put an algebra requirement before students take economics. Those institutions are really fun to teach in why 90% of the students miss a question like say what is the temperature and time at the origin of this graph. That is the pre-test to let them know what they need to work on math skills wise to be ready for the course. === Subject: Re: Poor teaching of econ > On Aug 25, 11:07 am, professorchaos Now if you are referring to credit as bank money that may be different > but then you miss the point that bank money, money that exist only on > bank books (not currency not credit just numbers representing currency) > then miss the whole point of what a fiat system of money is. > Right-on Professor! I hope you are really a professor, teaching our > kids. Maybe you could add a little for me regarding bank money. It > is not currency and it is not credit, it is....it is...What is it? > How'd it get there? > Who put it there? > Essentially in a fiat system bank move is just like currency but the definition of currency means it something that be held. Bank is created by the fractional reserve system. Lets say I deposit $100 in my bank. The bank keeps a fraction on hand in case I want to withdraw. Some people withdraw more than others so they have a percentage of total outflows they can expect on a day to day basis. Lets say it is 10% they put in the vault. Ok, then what do they do with the other $90. They loan it. So they keep $10 to meet expected withdrawals and give out $90 dollars of the deposit in a loan. They have created bank money. I still have access to my $100 but the person who gets the loan has $90 of the money I deposited. Although there is no currency to back up my $100 deposit merchants will take a check or a debit card as payment. So my $100 is money in circulation but so is the $90 loan. That is how bank money is created. In reality all cash goes in the vault and the $100 dollar deposit becomes bank money and so does the $90 loan. The other $10 is also bank money listed as reserves. === Subject: Re: Poor teaching of econ <46d0700a$0$11009$4c368faf@roadrunner.com> <46d244c6$0$15419$4c368faf@roadrunner.com> On Aug 25, 11:07 am, professorchaos Bank (money) is created by the fractional reserve system. > reserve system is. Your bank money sounds like it is bank deposits that are available for loans. Bank money is available for credit (with the multiplier). Bank money becomes credit when it is actually lent out. How am I doing so far ? :) === Subject: Re: Poor teaching of econ > On Aug 25, 11:07 am, professorchaos Bank (money) is created by the fractional reserve system. reserve system is. Your bank money sounds like it is bank deposits > that are available for loans. Bank money is available for credit (with > the multiplier). Bank money becomes credit when it is actually lent > out. How am I doing so far ? :) > Bank money is what happens to your money when you deposit. The loan is turned into money when it is used and deposited into a checking or savings account. This might occur from the check going straight to a dealership for a car. The dealership then deposits the check and the bank balance goes up. The money available for loans is excess reserves. This is money the bank is holding in reserve until it is lent and this not counted as part of the money because it is not available to be used until the bank approves loans so people can use it. In the car loan example the lending bank transfers from reserves to the dealership's account. It becomes part of the money supply then because it can now be circulated. === Subject: Re: Prime Spectrum and Axiom of Choice > Also, here's one more equivalence, stated for the reduced case ... For this discussion, the term ring means commutative ring with 1. Let R be a reduced ring, but not a field. > The following statements are equivalent: (1) Spec(R) has a clopen point. (4) R is isomorphic to the direct sum of a field and a reduced ring. Note -- the proof uses the previous proved equivalences (1) <=> (2) > <=> (3). > This generalizes to the non-reduced case, too: > For a unitary commutative ring R the following statements are equivalent: > (1) Spec(R) has a clopen point. > (4') R is the direct product A x B where A is a 0-dimensional local ring. > Crucial for this amendment is that the proof does not step back to > induced closed subschemes, but considers the same subsets as open > subschemes. Ok, here is one more generalization of what is going on here. I think > everything else which was proved here can be derived from the following > proposition. Prop.: Let X be an affine scheme and U1 u U2 a *disjoint* open covering > of X. Then U1 and U2 are standard affine open subsets. In particular U1 > and U2 are affine. Cor.: If a clopen subset U is removed form an affine spectrum X, then > XU is a standard affine subset of X. In particular XU is affine. Correction to make it a bit clearer: ... then XU is a standard affine *open* subset of X. > Proof of Prop.: Let X be Spec(R). Since the covering U1 u U2 is > disjoint, the open set U1 and U2 are closed, hence of the form V(Ii) for > ideals I1, I2 of R. Then I1 and I2 are copime (U1, U2 is a covering) > such that the natural ring homomorphism pi: R -> R/I1 x R/I2 is > surjective (Chinese remainder theorem). Take s1 in R with pi(s1)=(1,0) > and set s2:= 1 - s1. Then U1 and U2 is the open covering subordinated to > the decomposition of unity 1 = s1 + s2, i.e. Ui = D(si). qed Best wishes, > J. === Subject: Re: Prime Spectrum and Axiom of Choice <46CDC6AF.3010802@web.de> <46CF23A5.1090205@web.de> <46D0B4F5.20102@web.de> <46D14EB5.6060507@web.de> <46D185B0.7010302@web.de Ok, here is one more generalization of what is going on here. I think > everything else which was proved here can be derived from the following > proposition. Prop.: Let X be an affine scheme and U1 u U2 a *disjoint* open covering > of X. Then U1 and U2 are standard affine open subsets. In particular U1 > and U2 are affine. X is a reducible affine scheme.. isn't this a standard result in algebraic geometry? Zariski closed subspaces of an affine scheme is again affine =) , U1 and U2 are clopen in your case :) Cor.: If a clopen subset U is removed form an affine spectrum X, then > XU is a standard affine subset of X. In particular XU is affine. as above XU is Zariski closed :) .. I think one can also explicitly name the ring that associates to XU.. namely if Spec A=X, then Spec (A/I(XU)) is homeomorphic to XU (I didnt checked this, but I think its nothing to worry about). Where I(XU) is the intersection of all primes of XU .. === Subject: Re: Prime Spectrum and Axiom of Choice > Ok, here is one more generalization of what is going on here. I think > everything else which was proved here can be derived from the following > proposition. > Prop.: Let X be an affine scheme and U1 u U2 a *disjoint* open covering > of X. Then U1 and U2 are standard affine open subsets. In particular U1 > and U2 are affine. X is a reducible affine scheme.. isn't this a standard result in > algebraic geometry? > Zariski closed subspaces of an affine scheme is again affine =) , U1 > and U2 are clopen in your case :) Of course it is. But it is meant that the closed subset is equipped with the structure of a closed subscheme. But I am talking of the closed subset which is open as well and it is equipped with the structure of an *open* subscheme. That *is* a big difference here. It is by far not true in general that any open subset of an affine scheme (equipped the in induced open subscheme structure) is affine again. > Cor.: If a clopen subset U is removed form an affine spectrum X, then > XU is a standard affine subset of X. In particular XU is affine. as above XU is Zariski closed :) .. I think one can also explicitly > name the ring that associates to XU.. namely if Spec A=X, then Spec > (A/I(XU)) is homeomorphic to XU (I didnt checked this, but I think > its nothing to worry about). Where I(XU) is the intersection of all > primes of XU .. Yes of course. But as already mentioned above: This does not apply here since XU is not considered as closed subscheme but as open subscheme. Note that the structure of an open subscheme is unique, whereas for a closed subscheme it is not. Among these there is a extremal, called the induced reduced structure of a closed subscheme. When it was not important, why do you look at clopen points and not at closed point only? ;) J. === Subject: Re: Prime Spectrum and Axiom of Choice <3ehqc35h4jcamgbshrm5u8v7b6si4okjan@4ax.com> <46CDC6AF.3010802@web.de> <46CF23A5.1090205@web.de> of R. Minor correction (to avoid a degenerate case): Let R be a reduced commutative ring with 1, but not a field, and let P > be a prime ideal of R. > Well.. if you use strict set theory I think the statement does no harm even with fields. When on says the intersection and when the index is empty, then we would (in the category of rings) assume it to be the field itself. === Subject: Re: Prime Spectrum and Axiom of Choice <3ehqc35h4jcamgbshrm5u8v7b6si4okjan@4ax.com> <46CDC6AF.3010802@web.de> <46CF23A5.1090205@web.de> of R. The following statements are equivalent: (1) {P} is clopen in Spec(R). (2) P is a maximal ideal of R and the intersection of Spec(R){P} is > nonzero. These results are almost straightforward. (2) just says that Spec(R) {P} is not dense and {P} is closed, and this statement is equivalent to {P} being clopen. === Subject: Re: Electronic Solution Manuals in .pdf/doc - Get it Within 30 Minutes Physics 6th ed, Giancoli Physics 5th ed, Giancoli. === Subject: Re: Electronic Solution Manuals in .pdf/doc - Get it Within 30 Minutes > I have the comprehensive solution manual, solutions manual, solutions > manuals, in electronic format for the following textbooks. They > include complete solutions to all the problems in the text, except > where noted below in the listing. Payment is through Paypal. Email me > bookstoday777[at]gmail.com but please DO NOT POST HERE because I will > not be able to help you, but instead email and ask me for the solution > that you need. Downloads emailed immediately - within 30 minutes! A Course in Game Theory by Osborne, Rubinstein > A Course in Algebraic Number Theory by Cohen > Adaptive Filter Theory, 4th Edition, by Haykin > Adaptive Control, 2nd. 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Burden > (Selected Solutions) Operating Systems: Internals and Design Principles, 4th Edition, by > Stallings > Operating System Concepts, 7th Ed., Silberschatz, Galvin, Gagne > Options, Futures and Other Derivatives, 4th Ed., by John Hull > Options, Futures and Other Derivatives, 5th Ed., by John Hull > (Chapters 1 thru 18 ONLY) > Orbital Mechanics: For Engineering Students by Howard Curtis (includes > matlab scripts) > Organic Chemistry, 4th Ed., by Carey, Atkins (Student Study Guide and > Sol. Man.) 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Giancoli > Physics for Scientist and Engineers, 5th Edition, by Tipler, Mosca > Physics: Principles with Applications, 6th Ed. by Giancoli > Power System Analysis and Design, 3rd Ed., by Glover, Sarma > Principles and Applications of Electrical Engineering 4th (Revised) > Edition by Rizzoni > Principles and Practices of Automatic Process Control, 3rd Edition by > Smith, Corripio [ISBN: 0471431907] > Principles of Communication: Systems, Modulation Noise, 5th Ed., > Ziemer > Principles of Physics, 3rd Edition, by Serway > Principles of Physics, 4th Edition, by Serway > Principles of Statics, 10th Ed., by Russell C. Hibbeler [ISBN: > 0131866745] > Probability and Statistics for Engineers and Scientists, 3rd Edition, > Hayter > Probability and Statistics for Engineering and the Sciences, 6th Ed., > by Jay L. Devore > Probability Random Variables, and Stochastic Processes, 4th Ed., by > Papoulis, Pillai > Quantum Mechanics: An Accessible Introduction, 1st Ed., by Robert > Scherrer Recursive Macroeconomic Theory, 1st Ed., by Ljungqvist, Sargent > Recursive Methods in Economic Dynamics, (2002) by Irigoyen, Rossi- > Hansberg, Wright > RF Circuit Design: Theory & Applications, by Bretchko, Ludwig Sears and Zemansky's University Physics 11th Edition by Young.. > Semiconductor Device Fundamentals by Pierret > Semiconductor Devices: Physics and Technology, 2nd Ed., S.M. Sze > Semiconductor Physics And Devices -3rd Ed. by D. Neamen > Separation Process Principles, 2nd Ed., Seader, Henley > Signal Processing and Linear Systems by Lathi > Signals and Systems, 2nd Edition, by Haykin, Van Veen > Signals and Systems, 2nd Edition, Oppenheim, Willsky, Hamid, Nawab > Signals and Systems: Analysis Using Transform Methods and MATLAB, 1st > Ed., by M. J. Roberts > Signals, Systems, and Transforms, 3rd Ed., by Charles L. Phillips, Eve > A. Riskin, John M. Parr > Shigley's Mechanical Engineering Design, 8th Ed. by Budynas, Nisbett > (No Sol. for Chapt 18 & 19) > Simply C#: An Application-Driven Tutorial Approach, by Deitel, Hoey > (Chapters 1-32) > Soil Mechanics: Concepts and Applications, 2nd Ed., by Powrie > Solid State Electronic Devices - 5th Ed by Streetman > Solid State Electronic Devices - 6th Ed by Streetman > Statics and Mechanics of Materials: An Integrated Approach, 2nd Ed., > by Riley, Sturges, Morris > Structural Analysis, 5th Edition, by Hibbeler Theory and Design for Mechanical Measurements, 4th Ed., Beasley, > Figliola > Thermal Physics, 2nd Edition, by Charles Kittel > Thermal Physics, by Ralph Baierlein > Thermodynamics: An Engineering Approach, 5th Ed., by Cengel, Boles > (Missing solutions #118-149 of Chapter 7) > Thermodynamics: An Engineering Approach, 6th Ed., by Cengel, Boles > The Science and Engineering of Materials, 4th Ed., by Donald R. > Askeland, Pradeep P. Phule > Thomas' Calculus, Early Trans., Part 1, 10th Ed. by Thomas, Weir, > Hass, Giordano > Thomas' Calculus: Part 2, 10th Ed. (Multivariable, chs. 8-13), by > Thomas, Weir, Hass, Giordano > Thomas' Calculus, Early Trans., Part 1, 11th Ed. by Thomas, Weir, > Hass, Giordano > Thomas' Calculus: Part 2, 11th Ed. (Multivariable, chs. 11-16), by > Thomas, Weir, Hass, Giordano > Transport Phenomena, 1st Edition, by R. Byron Bird > Transport Phenomena, 2nd Ed., by Bird University Physics 11th Edition by Young.. Vector Mechanics: Statics 7th Edition by Beer > Vector Mechanics: Dynamics, 7th Ed., by Beer, Johnston, Staab, Clausen > Vibrations and Stability: Advanced Theory, Analysis, and Tools, 7th > Ed., by Thomsen Wireless Communications: Principles and Practice, 2nd Ed, by Rappaport Hi! I need this now Managerial Accounting, 11th Ed., by Noreen, Brewer, Garrison....because i have homework for tomorow Cristina === Subject: Many Solutions Manuals and Ebooks in Electronic (PDF)Format! Many Solutions Manuals and Ebooks in Electronic (PDF)Format! PS: These are part of my solutions, if the solution you want isnOt on the list, do not give up, just contact with me: My email is solutionpay(at)hotmail.com( please replace the (at) with @ ) Solution Manual for ADVANCED ENGINEERING MATHEMATICS.81i9/e.81j by ERWIN KREYSZIG Solution Manual for ADVANCED ENGINEERING MATHEMATICS.81i8/e.81j by ERWIN KREYSZIG Solution Manual for Calculus, 4th edition by James Stewart Solution Manual for Design of Analog CMOS Integrated Circuit by B. Razavi Solution Manual for DISCRETE-TIME SIGNAL PROCESSING/2e by Oppenheim.81ASchafer Solution Manual for Electrical Circuits (7/e) by James W. Nilsson, and Susan A. Riedel,Prentice Hall Solution Manual for Elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Solution Manual for Engineering electromagnetics (7/e) by HAYT Solution Manual for Engineering electromagnetics (6/e) by HAYT Solution Manual for Fundamentals of Logic Design 5Ed by CharlesRoth Solution Manual for field and wave electromagnetics (2/e) by David Cheng Solution Manual for Introduction to Electrodynamics(3/e) by David J. Griffiths Solution Manual for Introduction to Solid State Physics (8 ED) by Charles.Kittel__ Solution Manual for MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Solution Manual for Modern Control Engineering/ 4E by K.OGATA Solution Manual for Physical Chemistry (7th) by P.W.Atkins Solution Manual for Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Solution Manual for Thomas' Calculus (11th Edition) by George B Thomas Solution Manual for Thermodynamics: An Engineering Approach,5th Ed. by Cengel Solution Manual for Thermodynamics: An Engineering Approach,6th Ed. by Cengel http://pdfsolutionpay.space.live.com === Subject: Saying Goodbye to an Old Friend Now I have solved the original problem that inspired all of this madness in the first place. The object was to find a non-iterative solution for the angle subtending a known arc and chord on a circle. I just couldn't let go of this problem until I got it. Even with what I've come up with now, I still haven't got it. This concludes my arclength solution for the weekend. Maybe one or two of you might profit from my fixation on this problem, which has gone on for at least 6 years. .... but I can think of some more unhealthy fixations than math... and others more healthy, like mowing the yard... you may be amazed to discover that I actually did mow it yesterday. http://mypeoplepc.com/members/jon8338/polynomial/ === Subject: Re: Saying Goodbye to an Old Friend Am 27.08.2007 10:09 schrieb Jon G.: > Now I have solved the original problem that inspired all of this madness in > the first place. The object was to find a non-iterative solution for the angle subtending a > known arc and chord on a circle. I just couldn't let go of this problem until I got it. Even with what I've come up with now, I still haven't got it. This concludes my arclength solution for the weekend. Maybe one or two of > you might profit from my fixation on this problem, which has gone on for at > least 6 years. > I wish for you, it comes out to be right. Then: congratulations! The point of getting free of an obsession, when the solution is found may be a bit melancholic, but most time the intense struggle has moved something in the brain to a new level of understanding and to the ability of inner imagination of more general problems too. So I wish you a good walk and a good mental rest... ehm... until next time... ;-) See you then - Gottfried -- --- Gottfried Helms, Kassel === Subject: Re: Comprehensive Solution Manual for Textbooks === Subject: Distribution of an infinite order Could you give an example of a distribution of an infinite order defined on some subset of reals. === Subject: Re: Distribution of an infinite order >Could you give an example of a distribution of an infinite order defined on some subset of reals. Perhaps. Exactly what do we mean by the order of a distribution? I'm not sure I understand the question, but I suspect that the distribution u defined by u(f) = sum_1^infinity D^n f(n) is an example. ************************ David C. Ullrich === Subject: Re: Distribution of an infinite order > On Mon, 27 Aug 2007 04:25:56 EDT, jane Could you give an example of a distribution of an > infinite order defined on some subset of reals. Perhaps. Exactly what do we mean by the order of a > distribution? We say that u has order N if for this N there exists a compact K s.t. | u(f) | <= C sup_{|a|<=N ,x in K} |D^a f| for every test function f with compact support in K. This constant C > 0 may vary for different functions f, but this N must work for all f in D_K with this chosen K= K(N). > I'm not sure I understand the question, but I suspect > that the > distribution u defined by u(f) = sum_1^infinity D^n f(n) I actually found almost the same example, shortly we can take some domain U and x_n accumulating not in U (as far as i understand we do want our series converge), u(f) = sum c_n D^n f (x_n) must work, but i afraid i don't have any more or less rigorous proof of this. I would be grateful for you suggestion of a rigorous proof. > is an example. > ************************ David C. Ullrich === Subject: Re: Distribution of an infinite order > On Mon, 27 Aug 2007 04:25:56 EDT, jane Could you give an example of a distribution of an > infinite order defined on some subset of reals. Perhaps. Exactly what do we mean by the order of a > distribution? We say that u has order N if for this N there exists a compact K s.t. | > u(f) | <= C sup_{|a|<=N ,x in K} |D^a f| > for every test function f with compact support in K. This constant C > 0 may vary for different functions f, but this N must > work for all f in D_K with this chosen K= K(N). Surely this is not quite what you mean. Otherwise you could take K to be a single point. Since the only test function with support in K is 0, every distribution would have order N. Instead, I think you want your condition to be true for all compact K. Also, this condition should be a definition of order <= N. u has order exactly N your condition is true for N but not for N-1. Infinite order would mean that there is no N for which it has order <= N. > I'm not sure I understand the question, but I suspect > that the > distribution u defined by u(f) = sum_1^infinity D^n f(n) I actually found almost the same example, shortly we can take some domain U > and x_n accumulating not in U (as far as i understand we do want our series > converge), > u(f) = sum c_n D^n f (x_n) must work, but i afraid i don't have any more or > less rigorous proof of this. I would be grateful for you suggestion of a rigorous proof. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Distribution of an infinite order On Mon, 27 Aug 2007 04:25:56 EDT, jane Could you give an example of a distribution of > an > infinite order defined on some subset of reals. Perhaps. Exactly what do we mean by the order > of a > distribution? We say that u has order N if for this N there > exists a compact K s.t. | > u(f) | <= C sup_{|a|<=N ,x in K} |D^a f| > for every test function f with compact support in > K. This constant C > 0 may vary for different > functions f, but this N must > work for all f in D_K with this chosen K= K(N). Surely this is not quite what you mean. Otherwise > you could take K to be a > single point. Since the only test function with > support in K is 0, every > distribution would have order N. Instead, I think > you want your condition > to be true for all compact K. Oops, sorry - i indeed mixed this definition up. Here is what i meant: Suppose there exists N such that }u(f) | <= C sup_{|a|<=N ,x in K} |D^a f| for all f in D_K(U) - test function with supoort in K, for _every_ K. Note, that, indeed , this N must work for all compacts altogether, probabbly with different constants C. The minimal N among those is called the order of u. And in case, there is no such an N, we say that u is of infinite order. > Also, this condition should be a definition of order > <= N. u has order > exactly N your condition is true for N but not for > N-1. Infinite order > would mean that there is no N for which it has order > <= N. I'm not sure I understand the question, but I > suspect > that the > distribution u defined by u(f) = sum_1^infinity D^n f(n) I actually found almost the same example, shortly > we can take some domain U > and x_n accumulating not in U (as far as i > understand we do want our series > converge), > u(f) = sum c_n D^n f (x_n) must work, but i afraid > i don't have any more or > less rigorous proof of this. I would be grateful for you suggestion of a > rigorous proof. > -- > Robert Israel > israel@math.MyUniversitysInitials.ca > Department of Mathematics > http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, > BC, Canada === === Subject: Re: Distribution of an infinite order 1. Potential 2. Actual === Subject: Rocket scientist is looking for intelligent woman! Hello! My name is Vitaly. I'm 30 years old, handsome, attractive, romantic, passionate white man. I am financially and emotionally stable and have a good job - chief programmer. 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Vitaly Please, visit my web site: http://www.geocities.com/isonmark/about.html Please write me a letter: email: vitalyolegovich@msn.com === Subject: Re: Finding the equation that travels through a given set of 2d points > Hi all, > I hope someone on this list can help me with a problem I have. Since I > am a math novice I'm not sure if this is a simple question or even > doable. The short question > --------------------------- > Is there a way to create an equation that, when plotted in a 2d > coordiante system, creates a graph that goes through (or close to) a > set of predefined 2d-points? For example, f(0)=0.0, f(10)=14.2, f(20)=45.5, f(30)=72.0 ... > f(100)=240.1. This series is non-linear (I think that is the correct term). Does anyone know of a website or program that can help in finding this > kind of equations? (preferably a free resource since I'm doing this > for my master's thesis, and I'm on a limited budget). The slighly longer question > --------------------------- > The reason I ask these questions is that I'm working on a color tool > that is supposed to be able to translate colors between different > color models that relate to eachother in a non-linear fashion. In my dreams I would like to make one function for each of the three > RGB-channels and each of those functions takes 3 different values as > input and returns an integer between 0-255. I have a lot of cross-reference values to match a color in one model > to the corresponding in another model. Could I use this data to > train an equation to behave in a certain way? That is, by inserting > the black, chroma and hue and the value the functions should > return into a program. The functions could look like f_r(black, chroma, hue) = [0-255] > f_g(black, chroma, hue) = [0-255] > f_b(black, chroma, hue) = [0-255] Is it possible to have as many as three variables as input? Is there a smarter way to do this? If I have done my research right a function with one variable creates > a 2d curve, two variables creates a plane in space and three variables > creates a volume in space - is this correct? Any comments are very welcome! > Robert Karlsson > architecture student, Sweden > may get some ideas from here http://www.easyrgb.com/calculator.php === Subject: Re: Finding the equation that travels through a given set of 2d points you said and will post a new question based on this. Robert === Subject: Re: Finding the equation that travels through a given set of 2d points Actually you want to use an interpolating polynomial instead of least squares. An interpolating polynomial (See Wiki) will always go right through all of the points specified. Not just close. Say you have a n points, it will require solving and n x n matrix of equations. On my system it still seems instantaneous up to a few hundred points. You can setup the matrix as below and then all you have to do is call any matrix solver, probably Gauss or Gauss-Jordon. Just remember that this is an nth degree polynomial, so any values outside of the specified points can vary radically and give unexpected values. It is useless for predicting or extrapolating. T1 = Degree + 1 'the degree is usually set to the number of points that you want to fit T2 = T1 + 1 then dimension a matrix to Mat(T2 + 1, T2 + 1) I think that I used i-1 because my matrix started at 0,0 For i = 1 To T1 T5 = X(i - 1) T6 = T5 For j = 2 To i Mat(i, j) = T6 T6 = T6 * T5 Next j Mat(i, 1) = 1 Mat(i, j) = Y(i - 1) Next i Have fun! === Subject: Topology with normal and regular. Hello sir~ T = {empty, R} U {(a, 00) | a in R}. This is a normal space. Because, closed sets : {R, empty}U {(-00, a] | a in R}. so, I can not choose two disjoint closed set except empty. and This is not a regular space. For b (b>a), closed set (-00, a], I can not choose disjoint open sets containing b and (-00, a], respectively. If T_1 (one-point sets are closed in R) contained in the definition of normal space, (R, T) is not a normal. Becasue, {a} is not closed in (R, T). Similary, (R, T) is not a regular. If my thinking is right, What's perfect example ? (normal , not regular) === Subject: Re: Topology with normal and regular. > Hello sir~ > Good day, m'dam. > T = {empty, R} U {(a, 00) | a in R}. This is a normal space. > Because, closed sets : {R, empty}U {(-00, a] | a in R}. > so, I can not choose two disjoint closed set except empty. > It is vacuously normal. For nulset and any closed set, nulset and R are the required disjoint open sets. > and > This is not a regular space. > For b (b>a), closed set (-00, a], > I can not choose disjoint open sets containing b and (-00, a], respectively. > Correct. A space like this is call hyper-connected, ie no two open nonnul subsets can be disjoint. > If T_1 (one-point sets are closed in R) contained in the definition of > normal space, > (R, T) is not a normal. > Becasue, {a} is not closed in (R, T). > That is correct. As usage varies from author to author, I try to be unambiguous by distinguishing 'normal' and 'normal T1'. Exercise: normal T1 ==> Hausdorff. > Similary, (R, T) is not a regular. > It's already not regular even without requiring T1. Again I prefer to use 'regular' and 'regular T0'. Exercise: regular T0 ==> Hausdorff. > If my thinking is right, What's perfect example ? (normal , not regular) > What do you mean? Normal T1 ==> regular T0 and you just gave an example of a normal, not regular space. Do you want a regular, not normal space? The double origin line is an example. It's also not Hausdorff. Add O to R and use { (-1/n, 1/n)0 | n in N } as a nhood base for O. This is the same space that is gotten from two parallel lines Rx{0} and Rx{1}, by identifying (r,0) with (r,1) for all r /= 0. For a regular Hausdorff, not normal space, I suggest you look up Niemytzki's tangent disk topology (space 82, Steen's Counterexamples in Topology). === Subject: Re: Topology with normal and regular. > Hello sir~ > Good day, m'dam. > T = {empty, R} U {(a, 00) | a in R}. > This is a normal space. > Because, closed sets : {R, empty}U {(-00, a] | a in R}. > so, I can not choose two disjoint closed set except empty. > It is vacuously normal. For nulset and any closed set, nulset and R are > the required disjoint open sets. > and > This is not a regular space. > For b (b>a), closed set (-00, a], > I can not choose disjoint open sets containing b and (-00, a], > respectively. > Correct. A space like this is call hyper-connected, ie no two open nonnul > subsets can be disjoint. > If T_1 (one-point sets are closed in R) contained in the definition of > normal space, > (R, T) is not a normal. > Becasue, {a} is not closed in (R, T). > That is correct. As usage varies from author to author, I try to be > unambiguous by distinguishing 'normal' and 'normal T1'. Exercise: normal T1 ==> Hausdorff. You assign me too much homework. Anyway, It's very easy by definition of normal T1. > Similary, (R, T) is not a regular. > It's already not regular even without requiring T1. Again I prefer to use 'regular' and 'regular T0'. Exercise: regular T0 ==> Hausdorff. For distinct points x, y, y in U for some x not in U.(T0) x in U^c is closed. so, x in U^c subset V_1 and y in V_2 for some open sets V_1, V_2.(regular) so, Hausdorff. > If my thinking is right, What's perfect example ? (normal , not regular) > What do you mean? Normal T1 ==> regular T0 and you just gave an example > of a normal, not regular space. Do you want a regular, not normal space? > The double origin line is an example. It's also not Hausdorff. Add O to R and use { (-1/n, 1/n)0 | n in N } as a nhood base for O. > This is the same space that is gotten from two parallel lines > Rx{0} and Rx{1}, by identifying (r,0) with (r,1) for all r /= 0. For a regular Hausdorff, not normal space, I suggest you look up > Niemytzki's tangent disk topology (space 82, Steen's Counterexamples in > Topology). It looks like high example. and I know the 84. Sorgenfrey's Half-open square topology. === === Subject: Re: Topology with normal and regular. > T = {empty, R} U {(a, 00) | a in R}. This is a normal space. > Because, closed sets : {R, empty}U {(-00, a] | a in R}. > so, I can not choose two disjoint closed set except empty. and > This is not a regular space. > For b (b>a), closed set (-00, a], > I can not choose disjoint open sets containing b and (-00, a], respectively. If T_1 (one-point sets are closed in R) contained in the definition of > normal space, > (R, T) is not a normal. > Becasue, {a} is not closed in (R, T). Similary, (R, T) is not a regular. If my thinking is right, What's perfect example ? (normal , not regular) There aren't, of course. If it is normal and, furthermore, if one-point sets are closed, then, given a closed set C and a point _p_, such that _p_ is not in C, then, because the space is normal, there are open sets A_C and A_p such that A_C contains C, A_p contains {p} and whose intersection is empty. Jose Carlos Santos === Subject: Re: Topology with normal and regular. > T = {empty, R} U {(a, 00) | a in R}. > This is a normal space. > Because, closed sets : {R, empty}U {(-00, a] | a in R}. > so, I can not choose two disjoint closed set except empty. > and > This is not a regular space. > For b (b>a), closed set (-00, a], > I can not choose disjoint open sets containing b and (-00, a], > respectively. > If T_1 (one-point sets are closed in R) contained in the definition of > normal space, > (R, T) is not a normal. > Becasue, {a} is not closed in (R, T). > Similary, (R, T) is not a regular. > If my thinking is right, What's perfect example ? (normal , not regular) There aren't, of course. If it is normal and, furthermore, if one-point > sets are closed, then, given a closed set C and a point _p_, such that > _p_ is not in C, then, because the space is normal, there are open sets > A_C and A_p such that A_C contains C, A_p contains {p} and whose > intersection is empty. Oh, very sorry. stupid question... I know that T_1 + normal ==> T_1 + regular. My first example is a counter-example that normal ==> regular except T_1. If there is T_1 condition, T_1 + normal ==> T_1 + regular is trivial. === Subject: Re: INTERESTING EQUATION > even simpler: Simpler than a substitution? I don't think so. Kiuhnm === Subject: Re: INTERESTING EQUATION <7063354.1188145028491.JavaMail.jakarta@nitrogen.mathforum.org > On Aug 25, 6:01 pm, tommy1729 even simpler: n^3 cannot be prime, therefore must be of the > form a^2-b^2. Why? and neilist didnt understand :-) a^2-b^2 = (a-b)(a+b). > So anything that can be written as x y where x == y > mod 2 can > be written as a^2-b^2 where a = (x+y)/2 and b = > (x-y)/2. The > composites that are not of the form a^2 - b^2 are > congruent to > 2 mod 4 (and none of these are cubes). > -- > Robert Israel > isr...@math.MyUniversitysInitials.ca > Department of Mathematics > http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, > BC, Canada exactly quite trivial, but well explained. neilist has been beaten :-) tommy1729- Hide quoted text - - Show quoted text - Why did you limit N to integers? It was totally unnecessary. === Subject: Re: INTERESTING EQUATION <536393.1188079300579.JavaMail.jakarta@nitrogen.mathforum.org> On Aug 26, 2:05 am, Robert Israel > even simpler: n^3 cannot be prime, therefore must be of the form a^2-b^2. Why? a^2-b^2 = (a-b)(a+b). > So anything that can be written as x y where x == y mod 2 can > be written as a^2-b^2 where a = (x+y)/2 and b = (x-y)/2. The > composites that are not of the form a^2 - b^2 are congruent to > 2 mod 4 (and none of these are cubes). > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada You also mean to say a and b and x and y are integers. The original poster didn't need to limit to limit N or X to integers, since the original poster's equations did not depend on any properties of integers or primes. Tommy mistakenly assumed that N had to be an integer based on the original poster's overly limiting statement. === Subject: Re: What if I succeed? For years I've been talking about using the factoring problem to force > acceptance of my other mathematical research as I figured that if I > demonstrate my problem solving ability with a practical math problem > away from pure math then I can get people to pay attention to my > other decried research. My take on responses from this newsgroup at least has been a > contemptuous dismissal of any possibility of my success. Note that for years professors here have refuted your arguments > line-by-line, not by being contemptuous. If there was any contempt, > you have generated much of it by being contemptuous first. No, they'd say they refuted and people like you would say the same > thing even when it wasn't true. So you'd simply make a group claim and refuse to be swayed by facts. A group process of denial. Maybe to see if you were being discriminated against, you copied > Meisel's algorithm, which was revealed for what it was. Repeating something false over and over again does not make it true. There are similarities, that's all. ANY prime counting method will give certain equations because they all > count the same thing. Even the Lagarias-Odlyzko prime counting method will give the same > equation as Legendre's if you take away all its prime tables and force > it to an explicit equation. The same argument used against my research can be used to say that all > other exact prime counting functions known are just Meissel's. Sci.math is an equal opportunity forum, and you know it. > That's one reason you cannot leave. I tried to leave and you people mounted an email assault against a > published paper of mine, convincing naive editors--people who should > not have listened to newsgroup posters--to yank it, and the journal > later quietly folded. You people destroyed a math journal with no conscience. You don't just hate people you call cranks, you hate mathematics > itself. Demonstrably you hate the discipline as you lie about details, like in > claims against my research, and destroy the foundations of the field, > like how posters beat the formal peer review system, and then just > walked away, claiming it was not their fault. James Harris You never once answered the question: 'How do you know your paper was reviewed?' I can give you a clue as to how I know it wasn't: It was full of errors and even you accept it was flawed, so the most likely reason for publication is that the editor was sloppy. === Subject: Re: What if I succeed? For years I've been talking about using the factoring problem to force > acceptance of my other mathematical research as I figured that if I > demonstrate my problem solving ability with a practical math problem > away from pure math then I can get people to pay attention to my > other decried research. My take on responses from this newsgroup at least has been a > contemptuous dismissal of any possibility of my success. Note that for years professors here have refuted your arguments > line-by-line, not by being contemptuous. If there was any contempt, > you have generated much of it by being contemptuous first. No, they'd say they refuted and people like you would say the same > thing even when it wasn't true. So you'd simply make a group claim and refuse to be swayed by facts. A group process of denial. Maybe to see if you were being discriminated against, you copied > Meisel's algorithm, which was revealed for what it was. Repeating something false over and over again does not make it true. There are similarities, that's all. ANY prime counting method will give certain equations because they all > count the same thing. Even the Lagarias-Odlyzko prime counting method will give the same > equation as Legendre's if you take away all its prime tables and force > it to an explicit equation. The same argument used against my research can be used to say that all > other exact prime counting functions known are just Meissel's. Sci.math is an equal opportunity forum, and you know it. > That's one reason you cannot leave. I tried to leave and you people mounted an email assault against a > published paper of mine, convincing naive editors--people who should > not have listened to newsgroup posters--to yank it, and the journal > later quietly folded. You people destroyed a math journal with no conscience. You don't just hate people you call cranks, you hate mathematics > itself. Demonstrably you hate the discipline as you lie about details, like in > claims against my research, and destroy the foundations of the field, > like how posters beat the formal peer review system, and then just > walked away, claiming it was not their fault. James Harris The fact that you can do nothing but resort to personal attacks and slams on the math community demonstrates you have no point left at all. ANYONE who uses personal attacks has lost the debate. ANYONE. Personal attacks = concession of defeat. Period. End of story. === Subject: log 2 = 0 ??? Hello sir~ I showed log 2 = 0 in some web-site. log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... = {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + ....} = [{1 + (1/3) + (1/5) + (1/7) + ....} + {(1/2) + (1/4) + (1/6) + (1/8) + ....}] - 2*{(1/2) + (!/4) + (1/6) + (1/8) +....} = {1 + (1/2) + (1/3) + (1/4) +.....} - {1 + (1/2) + (1/3) + (1/4) +....} = 0. I can not find the error well. Can you find the error ? === Subject: Re: log 2 = 0 ??? > Hello sir~ I showed log 2 = 0 in some web-site. log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... = {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + > ....} Are you sure that the {}-brackets are convergent? === Subject: Re: log 2 = 0 ??? > Hello sir~ > I showed log 2 = 0 in some web-site. > log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... > = {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + > ....} Are you sure that the {}-brackets are convergent? I think..... If I want to find a error, I must show that 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... =/= {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + ...}. If {}-brackets are not convergent, what happens ? But we can write similary. (1 + 2 + 3 + 4 + .....) - (2 + 3 + 4 + ....) = 1 === Subject: Re: log 2 = 0 ??? > Hello sir~ I showed log 2 = 0 in some web-site. log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... = {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + > ....} > Are you sure that the {}-brackets are convergent? > I think..... > If I want to find a error, > I must show that > 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... >=/= {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + > ...}. Actually, you don't need to show that much. It's enough to show that the series is not absolutely convergent, because this implies that rearranging terms is unjustified. Whether it just happens to give the same answer is irrelevant. > If {}-brackets are not convergent, what happens ? > But we can write similary. > (1 + 2 + 3 + 4 + .....) - (2 + 3 + 4 + ....) = 1 No, because a necessary condition for a series to converge is that the terms must go to zero. -- Dave Seaman Oral Arguments in Mumia Abu-Jamal Case heard May 17 U.S. Court of Appeals, Third Circuit === === Subject: Re: log 2 = 0 ??? > Hello sir~ I showed log 2 = 0 in some web-site. log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... = {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + > ....} = [{1 + (1/3) + (1/5) + (1/7) + ....} + {(1/2) + (1/4) + (1/6) + (1/8) + > ....}] > - 2*{(1/2) + (!/4) + (1/6) + (1/8) +....} = {1 + (1/2) + (1/3) + (1/4) +.....} - {1 + (1/2) + (1/3) + (1/4) +....} = 0. I can not find the error well. > Can you find the error ? Hint: Rearranging allowed? === Subject: Re: log 2 = 0 ??? > Hello sir~ > I showed log 2 = 0 in some web-site. > log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... > = {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + > ....} > = [{1 + (1/3) + (1/5) + (1/7) + ....} + {(1/2) + (1/4) + (1/6) + (1/8) + > ....}] > - 2*{(1/2) + (!/4) + (1/6) + (1/8) +....} > = {1 + (1/2) + (1/3) + (1/4) +.....} - {1 + (1/2) + (1/3) + (1/4) +....} > = 0. > I can not find the error well. > Can you find the error ? Hint: Rearranging allowed? But absolute convergence is sufficient condition to rearragement(same limit). NO ? === Subject: Re: log 2 = 0 ??? > Hello sir~ I showed log 2 = 0 in some web-site. log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... Is this sequence absolutely convergent? > = {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + > ....} = [{1 + (1/3) + (1/5) + (1/7) + ....} + {(1/2) + (1/4) + (1/6) + (1/8) + > ....}] > - 2*{(1/2) + (!/4) + (1/6) + (1/8) +....} = {1 + (1/2) + (1/3) + (1/4) +.....} - {1 + (1/2) + (1/3) + (1/4) +....} = 0. I can not find the error well. > Can you find the error ? > Hint: Rearranging allowed? But absolute convergence is sufficient condition to rearragement(same > limit). > NO ? === Subject: Re: log 2 = 0 ??? <46D2A632.30000@web.de I showed log 2 = 0 in some web-site. log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... Is this sequence absolutely convergent? > No. > = {1 + (1/3) + (1/5) + (1/7) + ....} - {(1/2) + (1/4) + (1/6) + (1/8) + > ....} = [{1 + (1/3) + (1/5) + (1/7) + ....} + {(1/2) + (1/4) + (1/6) + (1/8) + > ....}] > - 2*{(1/2) + (!/4) + (1/6) + (1/8) +....} = {1 + (1/2) + (1/3) + (1/4) +.....} - {1 + (1/2) + (1/3) + (1/4) +....} = 0. I can not find the error well. > Can you find the error ? > Hint: Rearranging allowed? But absolute convergence is sufficient condition to rearragement(same > limit). > NO ? > You've shown that absolute convergence is necessary. IIRC, a conditionally convergent sequence can be rearranged to have any limit. === Subject: Re: log 2 = 0 ??? > Hello sir~ > I showed log 2 = 0 in some web-site. > log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... Is this sequence absolutely convergent? Of course, NO. If a sequence is not absolutely convergent, Rearrange(with same limit value) is impossible ?? === Subject: Re: log 2 = 0 ??? Am 27.08.2007 12:33 schrieb mina_world: > Hello sir~ I showed log 2 = 0 in some web-site. log 2 = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + .... > Is this sequence absolutely convergent? Of course, NO. If a sequence is not absolutely convergent, > Rearrange(with same limit value) is impossible ?? Well, it may be, that finite rearrangements lead to the same limit. But I found that problem counterintuitve, too, when I first came across it. William already said: rearranging *can* lead to any arbitrary limit-value - may be they are some of which lead to the same value as the un-rearranged series. It is best to see some examples, which make this obvious. The nicest reference for me with many examples is here the monography of Konrad Knopp unendliche Reihen, but unfortunately I know of it in German only. Another, may be even more fundamental, but also with lots of examples is the monography of G.H. Hardy Infinite Series, may be this book is even the definite reference. Both books discuss the problem of reordering in detail and develop the criteria, when and when not this can be allowed, to keep the attributed results consistent with the rest of math. Gottfried -- --- Gottfried Helms, Kassel === Subject: Re: log 2 = 0 ??? > If a sequence is not absolutely convergent, > Rearrange(with same limit value) is impossible ?? Note that a sum (not a sequence) is absolutely convergent to S iff, for every permutation of the index set, the permuted sum is convergent with limit S. === Subject: Re: Another Inconvenient Truth > William Hughes replied: >Does experimental physics lead theoretical >physics by discovering new phenomena that >require explanation, or does theroretical >physics lead experimental physics, suggesting >new experiments to be tried? >Yes Demonstrably, both. Special and general relativity > came to us as mathematically complete theories, > to be tested against phenomena. Quantum mechanics > began as a theory to explain (and still is such a > theory to some extent) the results of Thomas Young's > 2-slit experiment. Regardless of which comes first chronologically, however, > theory is primary. That is, scientific results are > interpreted by (deduced from) theory and by no other > means. Therein the flaw in Han deBruin's reasoning, > which leaps to inductive conclusions about what is real. Some writers are truly flabbergasted about how they are interpreted. > Objective science assumes no reality, or in Newton's > immortal words, I make no hypothesis. (Hypotheses non > fingo.) Did you actually read Philosophiae Naturalis Principia Mathematica, or at least skip through it? I think not. http://en.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica > Just as the kinetic theory of matter still > survives without an explanation for the mechanism of > gravity, our mathematical theories today stand on their > own without imposing one's personal philosophy on them. Sorry. What is the kinetic theory of matter and what has it to do with the mechanism of gravity? === Subject: Re: Another Inconvenient Truth William Hughes replied: >Does experimental physics lead theoretical >physics by discovering new phenomena that >require explanation, or does theroretical >physics lead experimental physics, suggesting >new experiments to be tried? >Yes Demonstrably, both. Special and general relativity > came to us as mathematically complete theories, > to be tested against phenomena. Quantum mechanics > began as a theory to explain (and still is such a > theory to some extent) the results of Thomas > Young's > 2-slit experiment. Regardless of which comes first chronologically, > however, > theory is primary. That is, scientific results are > interpreted by (deduced from) theory and by no > other > means. Therein the flaw in Han deBruin's > reasoning, > which leaps to inductive conclusions about what is > real. Some writers are truly flabbergasted about how they > are interpreted. Objective science assumes no reality, or in > Newton's > immortal words, I make no hypothesis. (Hypotheses > non > fingo.) Did you actually read Philosophiae Naturalis > Principia Mathematica, > or at least skip through it? I think not. http://en.wikipedia.org/wiki/Philosophiae_Naturalis_Pr > incipia_Mathematica Just as the kinetic theory of matter still > survives without an explanation for the mechanism > of > gravity, our mathematical theories today stand on > their > own without imposing one's personal philosophy on > them. Sorry. What is the kinetic theory of matter and > what has it to do with > the mechanism of gravity? > Excuse me? And you're linking ME to Wikipedia it may take a little more than an encyclopedia reference, however. That the kinetic theory of matter survives WITHOUT an explanation of the mechanism of gravity was the point. Tom === Subject: Re: Another Inconvenient Truth > That the kinetic theory of matter survives WITHOUT > an explanation of the mechanism of gravity was > the point. I beg you again to explain what the kinetic theory of matter has to do with the mechanism of gravity. I really don't get the point. Han de Bruijn === Subject: Re: Another Inconvenient Truth That the kinetic theory of matter survives WITHOUT > an explanation of the mechanism of gravity was > the point. I beg you again to explain what the kinetic theory of matter has to do > with the mechanism of gravity. I really don't get the point. Han de Bruijn Ray's point seems to be that the kinetic theory of matter has NOTHING to do with the mechanism of gravity. As seems obvious enough to anyone who reads what he says. === Subject: Re: Another Inconvenient Truth > It's ugly. >Truth is not elegant. Truth is ugly. Better get >used to it. How absurd. >But first define ugly. >Han de Bruijn Abusing mathematics for the sake of making it > fit into one's procrustean bed of limited experience. http://hdebruijn.soo.dto.tudelft.nl/www/programs/index.htm Han de Bruijn === Subject: Re: Another Inconvenient Truth It's ugly. >Truth is not elegant. Truth is ugly. Better get >used to it. How absurd. >But first define ugly. >Han de Bruijn Abusing mathematics for the sake of making it > fit into one's procrustean bed of limited > experience. http://hdebruijn.soo.dto.tudelft.nl/www/programs/index > .htm Han de Bruijn > So I take it you believe computation is identical to mathematics. Procrustean bed, indeed. Tom === Subject: Re: Another Inconvenient Truth >It's ugly. >Truth is not elegant. Truth is ugly. Better get >used to it. How absurd. >But first define ugly. >Han de Bruijn Abusing mathematics for the sake of making it >fit into one's procrustean bed of limited >experience. >http://hdebruijn.soo.dto.tudelft.nl/www/programs/index >.htm So I take it you believe computation is identical > to mathematics. Procrustean bed, indeed. No. But computation is where mathematics begins. And where it ends: http://hdebruijn.soo.dto.tudelft.nl/QED/klassiek.htm Han de Bruijn === Subject: Re: Another Inconvenient Truth So I take it you believe computation is identical > to mathematics. Procrustean bed, indeed. No. But computation is where mathematics begins. And where it ends Only for non-mathematicians. === Subject: Re: Another Inconvenient Truth You conclude that N cannot exist at all, because it must >be an infinite set. Which of course begs the question, if all >sets are finite, is there a largest set? >If all naturals are finite, is there a largest natural? >Apparently _not_. There is no largest set in my toy theory. >If so, how large is it? >Not so. >If not, is the number of possible sets therefore infinite? >Yes. In the sense that you can always form another set, which hithereto >has not been in my universe. (Potential infinite) >But another question is: can this infinite number of possible sets form >a (completed) set? Well, maybe somewhere else, but _not_ in my universe. So your mental universe, unlike your supposed physical one, must be open > ended? Open ended. Very good, Virgil! Han de Bruijn === Subject: Re: Another Inconvenient Truth >You conclude that N cannot exist at all, because it must >be an infinite set. Which of course begs the question, if all >sets are finite, is there a largest set? >If all naturals are finite, is there a largest natural? >Apparently _not_. There is no largest set in my toy theory. >If so, how large is it? >Not so. >If not, is the number of possible sets therefore infinite? >Yes. In the sense that you can always form another set, which hithereto >has not been in my universe. (Potential infinite) >But another question is: can this infinite number of possible sets form >a (completed) set? Well, maybe somewhere else, but _not_ in my universe. So your mental universe, unlike your supposed physical one, must be open > ended? Open ended. Very good, Virgil! Your requiring an open ended universe within a closed one, suggests more contradictions than anything in mathematics. === Subject: Re: Another Inconvenient Truth Considering the discontinuities before noon, that is hardly justifiable. >http://hdebruijn.soo.dto.tudelft.nl/jaar2006/ballen.jpg >A picture says more than a thousand words .. You claim that noon does not exist, but the graph has to be continuous >at noon. Have you moved to Orlovia? >No, but the universe _explodes_ near noon. And explosions are not zero. HdB also graphs a notably discontinuous function as being continuous, >indeed, even apparently differentiable, for negative arguments. >You must even learn to read a picture. I've just drawn a continuous line >through the discontinuities. AS the appropriate graph through those points is a step function, and is > clearly constant between points and only discontinuous at them, your > graph is deliberately misleading. Deliberately suggesting, yes. > A valid picture would look more like y = the integer part of (-1/x), > for x < 0. Han de Bruijn === Subject: Re: Another Inconvenient Truth >HdB also graphs a notably discontinuous function as being continuous, >indeed, even apparently differentiable, for negative arguments. >You must even learn to read a picture. I've just drawn a continuous line >through the discontinuities. AS the appropriate graph through those points is a step function, and is > clearly constant between points and only discontinuous at them, your > graph is deliberately misleading. Deliberately suggesting, yes. It is deliberately suggesting conditions contrary to those specified by the gedankenexperiment. So while it may be relevant to a different problem, it is irrelevant to the one at issue. A valid picture would look more like y = the integer part of (-1/x), > for x < 0. === Subject: Re: cantorian algebra >if you read for instance the work of Riemann or even better >prof. Andrew Wiles , you will notice an enormous amounts of >connections between different branches. It might amuse you to know that Wiles's proof of Fermat's last theorem > is highly infinitary, and in particular in its current form relies on > the existence of two inaccessible cardinals -- though I have been > assured by experts that removing these, so that the proof goes through > in ZFC, would be routine (for some values of routine). What ?! Relies on the existence of two inaccessible cardinals ?! How about the idea then that Wiles's proof might simply be wrong ! Han de Bruijn === Subject: Re: cantorian algebra >if you read for instance the work of Riemann or even better >prof. Andrew Wiles , you will notice an enormous amounts of >connections between different branches. It might amuse you to know that Wiles's proof of Fermat's last theorem > is highly infinitary, and in particular in its current form relies on > the existence of two inaccessible cardinals -- though I have been > assured by experts that removing these, so that the proof goes through > in ZFC, would be routine (for some values of routine). What ?! Relies on the existence of two inaccessible cardinals ?! > How about the idea then that Wiles's proof might simply be wrong ! Han de Bruijn Wiles proof has been vetted by mathematicians much more competent at mathematics than HdB will ever be, so if he has doubts about that proof, he will have to search for his alleged errors himsmelf. === Subject: Re: cantorian algebra <7273219.1187822604039.JavaMail.jakarta@nitrogen.mathforum.org> |What's non-commutative geometry? It's a rather important area in contemporary mathematics. The properties of an ordinary space (manifold, algebraic variety, general topological space, what have you) tend to be closely related to properties of an associated ring of functions. The ring is of course a commutative ring (the multiplication is commutative). Non-commutative algebra studies certain kinds of non-commutative algebras in an analogous way, as if they were rings of functions on some kind of non-commutative space. The adjective quantum is used a lot by some people. Alain Connes has done a lot of important work in the area. Keith Ramsay === Subject: New mathematics / physical sciences positions at http://jobs.phds.org, Aug 27, 2007 There are new job listings at http://jobs.phds.org -------------------------------------------------------------------- Title: Physicist Employer: Advanced Design Consulting USA, Inc. 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Full details: -------------------------------------------------------------------- Post your job (free!): http://jobs.phds.org/jobs/post PhDs.org: Science, Math, and Engineering Career Resources --------------------------------------------------------- * Job Listings: http://jobs.phds.org/ - Job board with hundreds of listings for Ph.D.s - Reach tens of thousands of Ph.D.s each month * Graduate School Rankings: http://graduate-school.phds.org/ - Comprehensive, customizable rankings of graduate programs * Career Resources: http://www.phds.org/ - Pointers to the best resources on the web for: + getting into graduate school + writing your dissertation + jobs for Ph.D.s in academia and industry * Engineering Science Weblog: http://blog.phds.org/ - Building better scientists and engineers === Subject: Antique 1912-1949 Porcelain teapot 528 chinaware 400 Website invitation visit Antique 1912-1949 Porcelain teapot 528 chinaware 400 Website invitation visit http://www.xjx588.com http://www.xjx588.com/more.asp?name=xjx588&id=14 E-mail xjx_588@tom.com xjx_588@126.com City Shengzhou Zhejiang China Jianxiong Xu === Subject: Re: open maps (et alii) > Then _f_ may not be a homeomorphism. See S as the set of those complex > number _z_ such that |z| = 1 and take f(z) = z^2. Kiuhnm === Subject: Re: open maps (et alii) > e) If f:R->R is a continuous, open surjection, must it be a homeomorphism? > Yes. > f) What happens in (e) if R is replaced by the unit circle S? f is closed. === Subject: Re: open maps (et alii) > Is f injective? Who knows... Kiuhnm === Subject: Re: open maps (et alii) >I need some help with the last point of the following exercise, which I >report entirely for the sake of completeness. Let f be a function from M to N, two metric spaces. >a) If f is open, is it continuous? > Not always. >b) If f is a homeomorphism, is it open? > Yes. >c) If f is an open, continuous bijection, is it a homeomorphism? > Yes. >d) If f:R->R is a continuous surjection, must it be open? > No. >e) If f:R->R is a continuous, open surjection, must it be a homeomorphism? > Yes. >f) What happens in (e) if R is replaced by the unit circle S? Right... what happens? Kiuhnm I am struck by part (e) as it is analagous to a famous algebra result known as Fitting's Lemma - actually it's the dual of Fitting's Lemma. Fitting's Lemma If M is an Aritinian Module and f: M --> M is an injective homomorphism, then f is onto. Dual to Fitting's Lemma If M is a Noetherian module, and f: M --> M is a surjective homomorphism, then f is one-to-one. Both of these results are because the module M has certain properties (well f is allmost an isomorphism in each case, but M completes it). I'm looking at e) and see that the space is R. Does that result generalize to more general spaces - outside of metric spaces perhaps? Brian === Subject: Re: open maps (et alii) > I'm looking at e) and see that the space is R. Does that result > generalize to more general spaces - outside of metric spaces perhaps? What a beautiful exercise! Let's see. Let U and V be two topological spaces (U, T(U)), (V, T(V)). Let f be a continuous open surjection from U onto V. Because f is continuous and open, X in T(U) <=> f(X) in T(V), i.e. there is a bijection between the open sets of U and V. Now let's suppose f is not injective. There are two open sets A, B s.t. f(A) = B and s.t. there are two points x,y in A s.t. f(x) = f(y) = z in B. Let g be f^{-1}. We can have g(z) = x or g(z) = y or g(z) not in {x,y}. Let assume, with no loss of generality, that g(z) <> y. Then there is a point u in B s.t. g(u) = y. Schematically: A f B x -----> z y -----> z y <----- u Now, if B is hausdorff, then there are two disjoint neighborhoods B_z and B_u of z and u respectively. But then f|A is a bijection A->B_z and A->B_u. That's clearly absurd. I suspect that the hausdorff condition on B is also *necessary*. Kiuhnm === Subject: Re: open maps (et alii) > Now, if B is hausdorff, then there are two disjoint neighborhoods B_z > and B_u of z and u respectively. But then f|A is a bijection A->B_z and > A->B_u. That's clearly absurd. No, there must be some error... otherwise it would be true even for f:S->S, no? Kiuhnm