mm-459
===
Subject:
: Re: I can't stand it anymore>
I was referring to people mentioning IQ tests in discussion
about> determinging intelligence of different race in all
these 3 groups.> But, how could you possibly realized that?
After all, you got F in> all these 3 subjects.Seems to me that
*you're* the one that brought it up.So are you a Troll or just
clueless?===
Subject:
: Re: Those Tricky Natural Numbers . . .>In
Set Theory, is an element of N also a proper subset of N?It is
in the von Neumann representation of the ordinals, orin any
representation in which an ordinal number is preciselythe set
of all smaller ordinal numbers. However, one can give other
representations.>For example, I want to prove that a cardinal
k belonging to N is less>than the cardinal of N itself, aleph
null. If an element of the>natural numbers also a proper
subset of N, then I can show k < aleph>null by showing that a
set A with cardinal k is a proper subset of the>natural
numbers. Since a natural number n can't be mapped onto
a>proper subset of itself,This takes proof; what is the
formulation of natural number? I think I can say that aleph
null can't be>mapped onto a proper subset of itself.This is
CLEARLY false. The mapping n -> n+1 does this.-- This address
is for information only. I do not claim that these viewsare
those of the Statistics Department or of Purdue
University.Herman Rubin, Department of Statistics, Purdue
Universityhrubin@stat.purdue.edu Phone: (765)494-6054 FAX:
(765)494-0558===
Subject:
: Re: Uncle Al is Sadistic .> 3
Africans I met in Computer science department in the last 4
years>were way above average in thier programming skills in
the midst of>Chinese and Indian grad students who are the
overwhelming majority in>that department. One was so good that
he even got a parttime teachign>position to teach an undergrad
programming course, while he's still a>student himself.> You
will always find bright smart people in just about any
naturally > occuring group of humans. Race is nothing. Culture
is everything.That's my point.> Bob Kolker===
Subject:
: Re:
B-Spline Extension> I have quickly looked up what you
suggested. However, where I was looking> all they were talking
about was the interpolating curve that is created.> How do I go
about explorating this, or what other 3d curve fitting method>
do you suggest. The need to explorate is crutically important
to what I am> trying to achieve.When you explorate a B-Spline
curve (which is a collection of B-Splinesegments that flow
neatly into each other), you can only take the firstand last
B-Spline of the curve and stretch them. Suppose you work
withthird degree B-Spline curves, then you have two
three-degree polynomialsthat you want to draw over a bigger
domain than just from begin-to enddatapoint. That is why I
suggested to look up this information since youdon't seem to
knwo what a B-Spline really is.B-splines also have little or
nothing to do with data-points, you build themusing *control*
points.Data-points are things only used in Lagrange
curves.However, there are also n'th order B-Spline curves, for
n datapoints. Thismeans that for each control point you add,
you get another degree to yourpolynomial. So you work with
*one* n-th degree polynomial. (as opposed tostickign with
third degree polynomials and then just adding anotherB-spline
segment to the curve for each new control point) They are
called'Bezier' curves, and you can stretch them too of course,
they arepolynomial in nature (the functions x(t), y(t) and z(t)
are anyway)There is a simple equivalence between Lagrange and
Bezier curves using amatrix that is filled with coefficients
created by the algoritm ofCasteljau.Lagrange curves are, as
said, the curves you make to fit data-points.As for NURBS or
anything, they're not what you need, they are
basicallyB-splines with the added quality that you can perform
non-affinetransformations on their control-points and then the
shape of the curvewill change in the same manner.Well there's
a lot of theory you have to go through I think,
becausestretching a curve, what you want to do, is very
starightforward if you'dunderstand the theory, and there's
more than I can type here. I do knowsomething about curves,
but perhaps someone with a clearer pen might helpyou better
here.-- Quaternion===
Subject:
: Re: A NOTy problem.> G'day G'day
Folks, > I have been puzzling over what ought to be a simple
logic problem> but am at a loss to come up with a method. > A
crime is committed by one of the following; , Bob, Chris or>
Dave. > Each makes a statement to the police but three of them
lie. > says, I didn't do it.> Bob says, is lying.> Chris
says,Bob is lying.> Dave says, Bob did it.> Usually one can
solve such problems with a grid I find such grids helpful, but
not perfect. It's hard totrack some statements with them, and
to keep track ofwhat ifs.> Where A. B. C. D represent their
names and > L. = lying,> N. = not_lying,> I. = innocent,> G. =
guilty. > Somehow that doesn't seem to get anywhere is this
case. > Maybe it is because N = NOT(lying) and G =
NOT(innocent)Well because of that, an easier grid to use would
be T GABCD(T for telling truth)Then you just need a method to
indicate whether thestatement is true or false for each one.
For instance,an X means its false and a dot means it's
true.Thus, each column will have one dot and three X'swhen
you're done. If you put a dot, you have to putthree
corresponding X's.> I am less interested in knowing the answer
to the puzzle than> understanding why it is different from the
routine logic puzzles.It's not. But you do need to be able to
backtrack andreset your grid after a false hypothesis.For
instance, let's start with the first statement. > says, I
didn't do it.Suppose that's true. Then gets an O in columnone
(he's telling the truth) and an X in columntwo (he's not
guilty). T GA O XB XC XD XOnce we put an O, everybody else
gets an X.Now Bob says is lying. We assumed is atruth teller,
so Bob is lying. We already marked that.Chris says Bob is
lying. This is true. But we alreadymarked Chris as a liar.
Inconsistency. is notthe truth teller. Restart the grid with
somebodyelse as truth teller and X under for column one.Of
course, if is lying, then this statementis false: says, I
didn't do it.So no matter who the truth teller is, did it. T
GA X OB XC XD XNow we just have to see if putting an O underB,
C, or D works out consistently.But actually, I see that Bob's
statement is nowtrue. T GA X OB O XC X XD X XIs this
consistent with the other two statements? Bettercheck (if not,
there is no solution).> Chris says,Bob is lying.If Chris is a
liar, then this statement is wrong. Whichit is. It checks.>
Dave says, Bob did it.If Dave is a liar, then Bob didn't do
it. And he didn't.The grid system works fine, you just set up
an improper grid. - Randy===
Subject:
: Re: One algebra question>
Hi I am learning algebra by myself> I am trying to do some
problems > but I can't solve this one> could you please do me
a favor to give me some help> here is the question:> Let f be
a homomorphism defined on a finite group G and let> H subset
G> a) show that |f(G):f(H)| divides |G:H|> b) show that |f(H)|
divides |H|The claims are false unless H is actually a
subgroup. If that is thecase, let N be the kernel of f. Then
|f(G)| = |G:N| and |f(H)| =|H:Ncap H| so that|f(G):f(H)| =
|G:N|/|H:Ncap H| = |G:H|/|N:Ncap H| which the makes a)obvious
and b) already is.===
Subject:
: A 3rd Grade Word
Problem---HELP>I don't see 127 either. It should be 31. If you
keep telling the story up>till and including Saturday, then you
would have 127.> 30 if you don't count yourself.> /DavidSurely
31 is the number not including yourself ?===
Subject:
: Re:
Magnetism: compare magnetic fields>Looking for a direct
mathmatical comparison between the magnetic field>produced by
an electronic current (i) and that of a fixed magnet of
a>given strength.> See:
http://scienceworld.wolfram.com/physics/Magnetism.html> Note
the differences in> o diamagnetism> o ferromagnetism <===> o
Paramagnetism> Ferromagnetism>
http://scienceworld.wolfram.com/physics/Ferromagnetism.html>
The development of extremely strong magnetic properties in
certain> materials which occurs when magnetic domains (regions
at most 1 mm in> dimension) become aligned in the absence of an
applied field, below a> temperature known as the Curie
temperature. The net magnetization> depends on the magnetic
history (the hysteresis effect). Above the> Curie temperature,
these materials become paramagnetic. Iron, nickel,> cobalt, and
gadolinium are ferromagnetic at room temperature.>
Ferromagnetism is believed to be caused by magnetic fields
generated> by the electrons' spins in combination with a
mechanism known as> exchange coupling, which aligns all the
spins in each magnetic> domain.===
Subject:
: Re: A 3rd Grade
Word Problem---HELP> Surely 31 is the number not including
yourself ?Oh, sorry, I overlooked that it starts on sunday
with one person. My weeks start on mondays :)/David===
Subject:
:
Re: Uncle Al is Sadistic .> 3 Africans I met in Computer
science department in the last 4 years> were way above average
in thier programming skills in the midst of> Chinese and Indian
grad students who are the overwhelming majority in> that
department. One was so good that he even got a parttime
teachign> position to teach an undergrad programming course,
while he's still a> student himself.>You will always find
bright smart people in just about any naturally >occuring
group of humans. Race is nothing. Culture is everything.> She
said Africa. I would have asked what country? Ethiopia> used
to send their brightest to the States for grad study. It>
would be interesting which countries are starting to get
their> act together.> /BAH> Subtract a hundred and four for
e-mail.None of them Ethiopians.===
Subject:
: Re: [JSH] On the
Rewriting of a PolynomialIn sci.math,
Phil<none@all.org<H1Zpb.178973$bo1.154862@
news-server.bigpond.net.au>:> To reprise ' proof, or at least
the first two steps> (I've included '*' so that GP/Pari
works):> [begin excerpt]> 1. Let P(x) = 14706125 * x^3 -
900375 * x^2 - 17640 * x + 1078, where x> is> in the ring of
algebraic integers, notice that P(x) has a constant> term
that is 1078.> 2. It can be shown that> P(x)= 7^2*(2401*x^3
- 147*x^2 + 3*x)*(5^3) - 3*(-1 + 49*x)*(5)*(7^2)+7^3> where
the *same* polynomial has been put in a form which allows a>
factorization into non-polynomial factors so that I have>
P(x) = (5*a_1(x) + 7)(5*a_2(x)+ 7)(5*a_3(x) + 7)> where the
a's are roots of> Q(a) = a^3 + 3*(-1 + 49*x)*a^2 -
49*(2401*x^3 - 147*x^2 + 3*x).> [end excerpt]> Now, here's
where I have a problem. How did Mr. Harris get to> this
point?> <snippage> You can get there quickly by noticing that
if you let a = -7/5 then> -5^3Q(a=-7/5) = P(x)> Similarly in
the factored from Q(a)=(a-a_1)(a-a_2)(a-a_3)> let a = -7/5
then> -5^3Q(a) = (5a_1 + 7)(5a_2 + 7)(5a_3 + 7) =
P(x)Hm...yes, that looks fairly simple. :-) I'll admit what
confusedme was the requirement that Q(a,x) have two
independent variables.> This confirms that the P(x) is a
correct expression for the a_1, a_2 and a_3> and that they>
are indeed algebraic integers.> The problem starts when James
divides them by 7 and declares that because> a_1/7 and a_2/7
are not necessarily algebraic integers, something is wrong.> I
can't work out what he means.Join the club. :-/> For example>
P(x) = x(x + 1) is a multiple of 2 for all x integer>
therefore P(x)/2 is integer for all x integer> P(x)/2 = x/2*(x
+ 1) (the only way it can go when you set x = 0, or>
something)> But x/2 is not an integer for all x integer.>
Presumably there is something wrong with integers as
well.Well, James has also tried to argue that Z[1/2] contains
all reals. :-)(It doesn't even contain 1/3.)> HTH, Phil.--
#191, ewill3@earthlink.netIt's still legal to go
.sigless.===
Subject:
: Re: Riemann's Zeta Function by H. M.
Edwards> I presume you are using the contour integral argument
for continuing> Gamma(s)zeta(s). One introduces a countour C_e
in three parts:> imaginary axis from -infinity to -e, circle
radius e about origin,> imaginary axis from -e to -infinity
and take the integral> of z^{s-1} e^z on C_e (with branch cut
on negative real axis).> Thse integral f(s) is independent of
e by Cauchy's theorem.> It is also an entire function of s:
convegence is nice since e^t -> 0> rapidly as t ->
-infinity.>Really dumb question. is e in the contour integral
an epsilon, or the>basis>of the natural logarithm. (I am
getting confused by both uses of e.)> No Real Mathematician
thinks of the logarithm having a basis:-)Oops I meant base
:-(> If you want to use epsilon instead of e you're welcome:
using e> does save typing.True. :-)> The integral of z^{s-1}
e^z on the first part of the contour is> integral_e^infinity
t^{s-1} exp(-pi i(s-1)) e^{-t} dt> = - integral_e^infinity
t^{s-1} exp(-pi is) e^{-t} dt.> Similarly on the third part of
the contour it is> integral_e^infinity t^{s-1} exp(pi is)
e^{-t} dt.> These add to> 2i integral_e^infinity t^{s-1}
sin(pi s) e^{-t} dt.> If Re(s) > 0 the integral over the
circle of radius e is> O(e^Re(s)). Letting e -> 0 we get
that>What is this O Is this Big-O notation?> Yes. Very
useful!Consider> G_N(s) = integral_{C_{(2N+1)pi}} z^{s-1}
e^z/(1-e^z) dz.> By Cauchy's theorem the difference G_N(s) -
g_e(s) is 2pi i times> the sum of the residues of the poles of
the integrand> at +-2pi i, +- 4pi i, ..., +- 2Npi i, that is>
2pi i sum_{n=1}^N [-(2pi ni)^{s-1} - (-2pi ni)^{s-1}]> = 2pi i
(2pi)^{1-s} sum_{n=1} (-2) cos(pi(s-1)/2)/n^{1-s}> = something
nasty times sum_{n=1}^N 1/n^{1-s}>Hmm. Edwards gets sin(s
pi/2).> How does sin(s pi/2) relate to cos((s-1)pi/2)?Oh yeah.
They're equal! I think I am going to look at the Davenport
book, Chapter 8. If I canfind it for less than $58.00! This
Edwards book is over my head. :-o===
Subject:
: Re: I can't stand
it anymore>But, how could you possibly realized that? After
all, you got F in>all these 3 subjects.Oh, I see. You're
trolling - why didn't you just say that?Doug===
Subject:
: Re:
The need of geodesics in physics>That's a bit confusing, one
can set the Lorentz >Force to generally vanish ie. >f_u =
q*F_uv *U^v =0>and in effect decribe EM geodesics, then
put>q*F_uv in the metric forming a non-symmetrical
>metric.>The problem with that is that both sides of that
equation are tensors.>If they vanish in one frame, then they
must vanish in all frames.>Geodesics are based on affine
connections, which are not tensors, so>they have
non-homogeneous transformation properties. >Ah, but the
geodesic equation is the absolute derivative>of the 4
velocity U^u = dx^u/ds, ie>DU^u/ds = U^u;v * U^v =0.> True,
but how does that relate to the LF?>Well multiply by mass
(scalar invariant) then, >m*DU^u/ds =0 >but QT requires m to
change discretely, and >since dm >0 requires a continuous
change in m, >dm=0, therefore set P^u = m*U^u (the
4->momentum) and find >DP^u/ds =0 (P^u = m*U^u, dm=0).>I
don't know where you got that notion from. QT says nothing
about m>changing discretely. In fact, the rules of QT maintain
continuous>change of mechanical variables (of course under the
restrictions of>the operator algebra). What is discrete in QT
are the quantized>values of the so-called stationary states,
but these tend to be the>exception rather than the rule.
Continuous fluctuation tends to occur>everywhere in the
quantum world.We should make sure we're talking about the same
thing. It is *invariant* energy which canonly vary discretely
and NOT continuously.A simple atom emits and absorbs energyby
photons. >Is true generally, and applies to LF, so
>f^u=DP^u/ds =0.>Moreover,>geodesic acceleration should
be independent of mass, which applies to>forces such as
centrifugal, coriolis, and of course, gravitation.>True for
acceleration of point masses, (but not true>for relatively
large masses, that's why acceleration>is a better term than
force in GR, otherwise you'll>need to include the term k*t_uv
>0 we figuring G_uv).>Acceleration due to Lorentz force will
be inversely dependent on mass,>making it a no go.>motion
must respect Quantum Theory, Lorentz force does>not, so the
stated objection evaporates.>But why are you making that
assumption? I can make that statement>certainly, but I'm
excluding a large variety of systems by doing it.>So I don't
think it is very realistic.>Consider, for example f_0 =
q*F_0i*U^i,>which in vectors is approximately >f_0 = q*E_i
(dot) V_i.>If q moves in direction of E_i then
it's>potential energy will vary continuously and>this is
prohibited by QT, therefore >E_i (dot) V_i =0 and thus f_0
=0.>Simply stated, charge q's V_i is always >perpendicular
to E_i. >But potential still varies continuously in QT and its
changes are very>easily tracked in the position representation.
We're talking about Lorentz force not potential.>I don't know
how you came to that conclusion.Fair enough. Just to make
clear definitions, define invariant energy P by P*P = P_u*P^u
ok?An invariant force would be f = dP/ds, and dP = f*ds ok?The
Lorentz force f_u *dx^u = f*ds, ok?f_u*dx^u = q*F_uv
*(dx^v/ds)* dx^u ok?Since dx^u*dx^v is symmetrical and F_uv is
antisymmetrical F_uv*dx^u*dx^v =0 whensummed ok?Then f*ds = 0 =
dP ok?That's it! To summarize: The Lorentz Force
Equationpredicts dP=0. But we know P is not a
constant,therefore P varies discretely, ie by quanta. Ken S.
TuckerPS: Snippable comment - That LF predicts and is
compatible with QT is excellent. It forms a great bridge
between GR and QT embodied inDP^u/ds = 0 (absolute
derivative).This equation is derived w.r.t LF, QT
(thereforeEM) and GR, without any added assumptions,
iestraight from working in the system.It can be called a
*generalized geodesic*, (I'd hestitate to call it THE
*universal geodesic*).One thing that is of interest : since
P<>0 the Limited Einstein Field Equation G_uv =0 is
notapplicable (as it applies to massless points) sothe EFE
G_uv = k*T_uv would be required.L8RKST===
Subject:
: Re:
c-numberOriginator: grubb@lola> I'm reading Peskin and
Schroeder's Intro to QFT and in this> book the author
constantly refers to c-numbers... without> saying what a
c-number is. I couldn't find c-number> on
mathworld.wolfram.com or physicsworld.wolfram.com.> Can
someone please tell me what the hell a c-number is?>
adam>I haven't read Peskin and Schroeder but if their usage
of the term c-number is the same as everyone else's usage then
they are referring >to commuting variables. For example, Bryce
DeWitt introduces the >concepts of c-numbers (commuting
variables) and a-numbers (anticommuting >variables) in his
book Supermanifolds. If a,b are c-numbers then>a*b = b*aThis
is correct. The problem is that Peskin and Schroeder don't
gointo 'grassman numbers' in any detail at all. DeWitt's book
is a goodintro.--Dan Grubb===
Subject:
: Re: how to identify data
from different distributions?>Hi sorry to bother you guys.>This
problem suddently comes into my mind.>Given two data sets from
two different distributions, >if I mixed them together, i.e.,
you don't know which point comes from>which>distribution. Is
it possible to use some learning or statistical>algorithms to
separate the two data set out?>For example,>X=(x1,x2,...,xn) ~
Gaussia>Y=(y1,y2,...,yn) ~ Uniform>Given (x1, y1,
x2,x3,y2,x4,y3,...), can you separate out X and Y?It can be
partially used to separate them. The most thatone can get by
learning or statistical algorithms is thenumber from each
group, and the precise distributions.If an individual has a
prior probability h of coming fromthe first group, the
posterior probability is given byBayes' Theorem. More than
this cannot be done for oneindividual. If it is known exactly
how many are from eachgroup, one can get the posterior
probability that a particular partition is the correct
partition.-- This address is for information only. I do not
claim that these viewsare those of the Statistics Department
or of Purdue University.Herman Rubin, Department of
Statistics, Purdue Universityhrubin@stat.purdue.edu Phone:
(765)494-6054 FAX: (765)494-0558===
Subject:
: Smallest
Eigenvalue in a Potential ProblemGiven an open subset A of the
unit square [0,1]x[0,1] with fixed area a:=area(A), it is known
that the lowest eigenvalue of the operator u |-> - u_xx - u_yy
+ chi_A * u i.e. Laplacian of u + [characteristic function of
A] times u on the space of functions u on [0,1] x [0,1] with
periodic boundary conditions will be positive. But does there
exist a positive lower bound for this eigenvalue which is
independent of the choice of open subset A as long as we keep
the area a=area(A) fixed? Does anyone have an idea? Many
thanks in advance ===
Subject:
: Re: Bible 1, Darwin 0! And we
are talking pure archeology?Forbidden archeology by Cremo,
Thompson!> Like the name says: Forbidden> I urge you not to
read it!If it is about Bible and Darwin, it is not physics,
not math and notarchaeology.You are posting in wrong
newsgroups.Mikko===
Subject:
: Re: A 3rd Grade Word
Problem---HELP> I don't see 127 either. It should be 31. If
you keep telling the > story up till and including Saturday,
then you would have 127.> 30 if you don't count yourself.Nope.
31 not counting yourself.Remember that the first day you tell
it to *one* person.1(Sun) + 2(Mon) + 4(Tue) + 8(Wed) +
16(Thu)That is 31, and is the number of people you have told
thestory -- not the number of people that know the story
(whichwould be 32, including yourself)--===
Subject:
: Re:
Conversion of red phosphorus to white phosphorushanson
<hanson@quick.net> spewed:> Nice, but quasi green bob
<thanatos@coldmail.nu> suffers from> Plumbum paranoia of
legendary dimensions which forced him> to hallucinate that his
NG comments will enhance mankind's> survival I'm betting on
marsupials.> against the doomsday prospects of lead in
message> which he delivered under great inner torment and
psychotic fear,> because he says...>I wonder if you are a
danger to others at times.Well, are you? Do you take
antipsychotics? If not, has a doctor eversuggested that you
take them?> His comment here is embedded in a master piece of
a post,> that teeters on the intellectual niveau of a petrock,
the belletristic> values of an ameba and his understanding of
the field with> the depth comparable to that of a
flatlander's. That didn't flow very well Hanson. You get a
C-.> His efforts> nevertheless elicit a faint chuckle, at
best, but, me being> magnanimous will bless him with a
roaring> AHAhahahhaha.......ahahahahansonA twitter when you
say it aloud.===
Subject:
: Re: Graduate algebra book>Well, I
think the U.S. and other countries are wildly different
in>their structure of an undergraduate curriculum. I don't
have a>problem admitting that my university is not so
terrific. We have 2>algebra courses which are available to
undergraduates at my>university, the more advanced of which is
almost identical to the>introductory course, albeit slightly
more fast paced. It so happens>that I _am_ an undergraduate
and I am trying to get a better education>than what my
university offers to the typical student. > Good for you.> So
you really want a decent undergraduate text, rather than> a
postgrad text, to compensate for the impoverished curriculum>
at your university.>What I have a>problem with, is listening
to the egos of those people who feel like>they are superior to
everyone else for no particular reason. > Who's that then?>All
Mr.>Chapman had to say was generally those topics are covered
at the>undergraduate level, instead of the snide remark 'thats
graduate>algebra?'> Aaaaaaaah!>Actually, upon checking a few of
the top universities' websites, I>find that while the
undergraduate curriculum generally does offer>algebra courses
which talk about galois theory and the topics I>mentioned,
they are generally at the near-graduate level. Thus, for>any
AVERAGE university, they will not be offered until the
graduate>level. > What is an AVERAGE university?>And even at
these better universities, not everyone takes>every single
course, and I imagine not everyone takes 5 or 6 semesters>of
algebra as an undergraduate. Should they take 5 semesters
of>analysis and 5 more of topology as well? how is anyone ever
supposed>to graduate?> It's quite possible to study a
reasonable amount of algebra,> a reasonable amount of analysis
and a reasonable amount of topology> all in three years. (And
also a reasonable amount of applied maths> and statistics if
that's your thing.) I'm a bit baffled about your reference> to
semesters of algebra --- do you only study one topic per
semester> at your university?No, but at my university (and in
the United States in general) wedon't usually take more than
one course of the same discipline persemester. If you go to a
university's website and find that they have5 algebra courses,
each of them is a semester long, usually with onebeing a
prerequisite for the next (but not always). But when I
saysemesters of algebra i mean algebra courses, since each
course isone semester long. So, for example, if there are 5
algebra courses,the only people who actually end up taking all
of them are thosepeople who have a pretty good idea that they
are going to specializein algebra. Because there simply isn't
enough time to take so manycourses and they aren't generally
required anyway. Remember that inthe states we have to take
lots of courses which are completelyirrelevant to anything we
plan to do in the future, such as 2political science courses,
2 history courses, 3 or 4 english courses,some other courses
such as psychology, art history, economics, etc,PLUS get a
minor in another subject. I realize this is not the casein
most european countries, so there is more time to focus on
studyingmath and it's only natural that your undergraduate
education will takeyou farther.===
Subject:
: Re: Pyrazine amide
charset=iso-8859-1>A classical route to 1,4
pyrazine-2-amide,>a simple 6 ring* , *=N-CH=CH-N=CH-C(CONH2)=*
molecule>starts with o-phenylene diamine + Glyoxal ring
condensation to>!,4 Benzo diazine (A). -- (A) being oxidized
by fracturing the C ring side>with KMnO4/H2O to pyrazine-1,2
carboxylic acid (B). --- (B) being>decarboxylated in hot conc.
H2SO4 to 1,4 pyrazine-2-carboxylic acid,>then esterification
and ammination to the final 1,4 pyrazine-2-amide.>Question:
Has anybody done or does anybody know which/what>catalysts &
conditions are beneficial to get the same product via:>1)
Dicyan (Cyanogen) and Acrylamide per>NC-CN + CH2=CH-CONH2 -->
*=N-CH=CH-N=CH-C(CONH2)=*>or>2) 1,2 Dinitrosoethan and
Acrylamide per>O=N-CH2-CH2-N=O + CH2=CH-CONH2 -->
*=N-CH=CH-N=CH-C(CONH2)=* + 2 H2O[Mark]> Is this [from]
hanson, hahahanson, or hahahahanson?Yes, these are different
quantum states of nuclear excitement in/of the same entity,
where [h] = Planck's constant and [a] refersto Sommerfeld's
Finestructure constant. The first quantum levelof ha =
2pi*e^2/c yields an action quantum of atomic emotions.Since
symbolism in science seldom produces only one
singularinterpretation but does ususally cause different
strokes for differentfolks, this particular event is no
exception. As can be seen, it doesevoke in Tom-Tom Crack
Potter subconscious, archetypical fears of the hyenas which
have terrified Tom's ancestors on the savannasin Africa, which
is why he calls me Harry Hyena Hanson. Wherehe got the Harry
from is still a mystery, but it has probably something to do
with his personal instigations for/against Bolsheviks.[Mark]>
Are we talking organic chemistry here? If so,> you might want
to cross-post to sci.physics,> as I have so thoughtfully done
:-)[hanson]Your motion is acknowledged as a fait-accompli. It
had howeversome unexpected effects in that some of the 5.5
times smarterweb lice and net flees that infest these cyber
parties grievouslyobjected to the word Pyrazinamide,
Pyr-Azin-Amid, insisting that it referred to you, Mark, as
being a Beer-Nazi-amidst, in the code lingo used by Odessa.
So, see Mark, one man's thoughtfulness (yours) can easily
become other folks' nightmares.[Mark]> Seriously tho...there's
a lot being done with> metal-mediated chemistry that is
cutting-> edge stuff (some of it is even reproducible).>
Checked the patent office? Tetrahedron Lett.?> Overall, you
sound like you're in a position> to be on top of it. That
said, if I find> something in the trash can, I'll pass it on
:-)[hanson]sentence. A high yield solution will most probably
come from/via some totally unusual or trashy source. So,
yeahyeah, if you find something off beat, while rummaging thru
trash cans do let me know.Ansaetze thus far are not too
impressive as the polymerization speed of the 2 educts is
still much faster then the desired ring closure or
condensation rates. The most promising results that came
across my desk were reaction initiations induced by laser
radiation with distinct wave lengths using fine, reflective
metal flakes and colored pigments suspended in the solvent for
delivering the bestactivation energy level and intensity to the
compounds in sol.[hanson]>PS: This Pyrazin compound is gaining
attention again in >the treatment against new tuberculosis
strains, >resistant to the latest antibiotics.>hanson[Mark]>
What've you got for terminally stupid people resistant> to
common sense (now I didn't say current administration> so
don't go imputing motives to me where there are none> that can
be proven beyond a reasonable doubt in a non-biased> competent
court of law or public opinion, both of which> should be on
the endangered species list, eh)?[hanson]Your non- or quasi
chemical response in your above parawent completely over my
head in both modes, FIFO or LAFI.hanson> Mark > (Harassment is
out. Groping is out. Oogling> is out. So, let's talk about the
weather :-)[hanson]Wait, I'd go for a try with unbridled and
unabashed Goosing.ahahahhaha.......ahahahanson===
Subject:
: Re:
Graduate algebra book> What's a good book for a first year
graduate algebra course? > Something with alot of emphasis on
factorization, polynomial rings,> fields, PIDs, Galois Theory,
and of course all the more basic topics> of algebra as well
like groups, ideals, integral domains, etc. > Something that
has lots and lots of _good_ exercises? Hungerford is> good,
but I'll have finished most of the exercises by the time I
want> to start doin the exercises in this new book. Lang is
probably good,> but there don't seem to be very many
exercises.A severely critical opinion of Hungerford may be
found athttp://www.math.hawaii.edu/~lee/algebra together with
someprofessional remarks as to what sort of algebra is
commendable at thegraduate level.An on-line book of first-year
graduate mathematics may be found
athttp://www.math.uiuc.edu/~r-ash/and this may be a direct
answer to your question.Both these references may be seen
athttp://hilbert.dartmouth.edu/~leejstem/freebook.html#al===

===
Subject:
: Re: Jaynes' book on probability - thoughts?>As a
matter of interest, didn't Jayne's book used to be available
on-line?>Is it still? Or am I
mistaken?http://omega.albany.edu:8008/JaynesBook
Baileyhttp://home.rochester.rr.com/jbxroads/mailto.html===

===
Subject:
: Re: B-Spline ExtensionI understand what you have
said, and I did know most of this.But you did not answer my
question from my last post.How do I go about explorating
Lagrange curves, or what other 3d curvefitting method domyou
suggest. My initial research into the Lagrange curve,keeps
saying they are for interpolation.If you could suggest a web
link to somewhere that would explain them betterthat would be
great.Adam>I have quickly looked up what you suggested.
However, where I waslooking>all they were talking about was
the interpolating curve that is created.>How do I go about
explorating this, or what other 3d curve fittingmethod>do you
suggest. The need to explorate is crutically important to what
Iam>trying to achieve.> When you explorate a B-Spline curve
(which is a collection of B-Spline> segments that flow neatly
into each other), you can only take the first> and last
B-Spline of the curve and stretch them. Suppose you work with>
third degree B-Spline curves, then you have two three-degree
polynomials> that you want to draw over a bigger domain than
just from begin-to end> datapoint. That is why I suggested to
look up this information since you> don't seem to knwo what a
B-Spline really is.> B-splines also have little or nothing to
do with data-points, you buildthem> using *control* points.>
Data-points are things only used in Lagrange curves.> However,
there are also n'th order B-Spline curves, for n datapoints.
This> means that for each control point you add, you get
another degree to your> polynomial. So you work with *one*
n-th degree polynomial. (as opposed to> stickign with third
degree polynomials and then just adding another> B-spline
segment to the curve for each new control point) They are
called> 'Bezier' curves, and you can stretch them too of
course, they are> polynomial in nature (the functions x(t),
y(t) and z(t) are anyway)> There is a simple equivalence
between Lagrange and Bezier curves using a> matrix that is
filled with coefficients created by the algoritm of>
Casteljau.> Lagrange curves are, as said, the curves you make
to fit data-points.> As for NURBS or anything, they're not
what you need, they are basically> B-splines with the added
quality that you can perform non-affine> transformations on
their control-points and then the shape of the curve> will
change in the same manner.> Well there's a lot of theory you
have to go through I think, becausestretching a curve, what
you want to do, is very starightforward ifyou'd> understand
the theory, and there's more than I can type here. I do know>
something about curves, but perhaps someone with a clearer pen
might help> you better here.> --> Quaternion===
Subject:
: Re:
Uncle Al is Sadistic . charset=iso-8859-1> 3 Africans I met in
Computer science department in the last 4>years were way above
average in thier programming skills in>the midst of Chinese
and Indian grad students who are the>overwhelming majority in
that department.>You will always find bright smart people in
just about any naturally>occuring group of humans. Race is
nothing. Culture is everything.>Bob Kolker> That's my
point.What point? Culture Shmulture....that is simplistic
politically correctheurist bull of the first kind. If it were
that simple then theproblem would have been solved a long time
ago. Painlessly.But one can easily see the problem being
enhanced and aggravatedat every step of its emergence and
development because, basically...What was thoughtless came by
easy.What was easy became habit.What were habits became
tradition.What were traditions became culture.What was culture
became religion.What is religion becomes
thoughtless.ahahahaha...........ahahahahanson===
Subject:
: Re:
Graduate algebra bookRemember that in> the states we have to
take lots of courses which are completely> irrelevant to
anything we plan to do in the future, such as 2> political
science courses, 2 history courses, 3 or 4 english courses,>
some other courses such as psychology, art history, economics,
etc,> PLUS get a minor in another subject. I realize this is
not the case> in most european countries, so there is more
time to focus on studying> math and it's only natural that
your undergraduate education will take> you farther.In France
undergraduate students (who plan to graduate in mathematics
orphysics) study maths (eheh), physics (electronics,
mechanics,thermodynamics), chemy, computer sciences, and (a
little) English. We don'thave to minor in anything, but we can
chose either maths or physics as aprevalent subject for our two
first years. That means you'll have moremaths, or more physics,
depending on what you'll do later.Moreover, we have only two
years of undergraduate school (ie your BchS isone year more
than ours) so we can specialize earlier (this system is
goingto change in two years in order to follow other european
and americansystems).===
Subject:
: Re: Uncle Al is Sadistic
.X-SessionID: L5bqb-1314-_4-3464@news.uchicago.eduX-Hash-Info:
post-filter,v:1.4X-Hash: 4b2396d3 2b1e64bd 9e6380c8 7388cc04
cf5cf234>I think part of the problem is that we have such poor
measures of what>it is to be educated. The College Board only
claims that the SAT is>a very good predictor of first-year
college grades; the average>correlation between SAT scores and
_freshman_ grades is +0.52; the>correlation to being educated
and smart is almost certainly quite a>bit smaller.>Aha. The
only problem is, we've (currently) no measure which gives a
>of deciding (in this field as in any other) that you won't
use any >measure until you've one which is perfect.>I'm not
arguing that we need a perfect measure. My point is
that>whether the measures used today are good enough is open
to debate.Sure.>We base a very large proportion of our
judgments of who is smart and>capable of being educated on the
results of multiple choice>examinations. There is at the very
least a significant body of>anecdotal evidence that the skills
required to do well on such tests>are different from those we
would otherwise consider desirable in>students.No doubt.
Nevertheless, there is a significant correlation between
aptitude exam scores and college performance (don't recall
exact numbers but it is in the 0.5-0.6 range). Far from
perfect, indeed, and that's why you do get anecdotal evidence
for cases where it fails. But far from irrelevant as well.
Note further that, as with any positive correlation measure of
this sort, the value improves when applied to a larger
population. Thus, while a difference of, say, 50 points on SAT
score between two individuals is not terribly meaningful, a
similar difference between the averages of graduating classes
of two different high schools is much more meaningful.>My
personal experience with standardized testing is somewhat
mixed. On>the one hand, I did well enough on standardized
tests to end up>admitted to graduate school in chemistry (and
yes, I did graduate). On>the other hand, I'm fond of using a
personal story as a cautionary>tale; my junior high school
guidance counselor advised me not to take>algebra as a high
school freshman because I didn't have the necessary>aptitude.
(To this day, I'm still not sure how he arrived at
that>judgment, although I'm pretty sure it had something to do
with test>scores; I wonder if he knows that I actually enjoyed
P Chem). My>experience on a university faculty graduate
admissions committee also>indicated that standardized test
scores are a highly imperfect>measure.I didn't encounter
anybody claiming that they're perfect. But imperfect does not
mean meaningless and, as I said, the value of the score grows
with the size of the population it is applied to.All tests are
fallible, on the individual level. Even performance tests are
fallible. Aptitude tests, much more so. Still, they do carry
information.>[snip discussion on the Washington DC school
district]>I don't have actual budget figures. I was not
looking to defend the>performance of DC schools; my first
statement acknowledged that they>are a mess. My point was that
there are a lot of confounding factors>that don't get
controlled in the SAT points per dollar metric. Also,>DC will
always be an outlier in such comparisons because
their>statistics often end up being the orange in a barrel of
apples. Their>finances are not exactly comparable to other
states because they have>all the difficulties of an urban
school system without the>less-expensive suburban and rural
systems that get factored into the>performance of every other
state. Their finances aren't exactly>comparable to other big
city systems because the DC school board>handles some
functions that are paid for at the state level in
other>jurisdictions.For sure. That's why a better comparison
would be obtained keeping DC out of it and comparing various
states. You'll still find little if any correlation between
spending levels and performance. Meaningful? I don't know. All
states are not the same either.>[Mr. Meron continues:]>.>For
sure. But they are not going to be solved by hiding behind
ohh, >it is so complicated, we can't really measure what
we're doing, so >lets just keep spending and hope for the
best. Anything that is >fundamentally sound can only benefit
from some serious questioning.>I agree that serious
questioning is beneficial. Nevertheless, I'm not>hiding behind
that particular straw man; I would observe that>unintended
consequences can be particularly surprising when one
uses>simple and perhaps inadequate measures to solve a complex
problem.For sure.>Urging caution so that we better understand
the nature of the problem>before we fix it is not the same as
saying keep on spending and>hope for the best.That's all fine.
But, the ongoing process on these issues seems to be the fact
that what we did appears to yield no results, indicates that
we didn't try hard enough. That's a questionable attitude.Mati
Meron | When you argue with a fool,meron@cars.uchicago.edu |
chances are he is doing just the same===
Subject:
: downloads
about philosophy, religion, natural sciences, mathematics and
justiceHello!I'm working on a website right now. You can find
free downloads aboutphilosophy, religion, natural sciences,
mathematics and justice at mywebsite. The archive is already
quiet large. I would be happy aboutyour visit and your comment
in my guestbook. The internet address
is:www.philosophieren.comAt the bottom of this message you can
find a list of the downloadabletexts available. If you're a
webmaster, I would be happy if you put alink to my site on
your site.Sincerely,Rainer
Ebert-------------------------------> Philosophy and
ReligionAltgyptische WeisheitslehrenEthical texts from the
Bible (M. Luthers)Codex Hammurapi (Babylonian laws from the
18th century before Christ)Recht und RechtschaffenheitDer
hippokratische EidParmenidesApologyThe RepublicDas
Liniengleichnis.Das Hhlengleichnis von der Natur des
Menschen.Der SophistDas Gastmahl (Symposion)Thrasymachos' Rede
ber Nutzen und Vorteil der Ungerechtigkeit.Tugend ist das
Finden des rechten MaesDer Tod ist fr uns ein NichtsHoly Bible
(King James)Meditationen ber die Grundlagen der Philosophie in
denen das DaseinGottes und die Verschiedenheit der
menschlichen Seele vom Krperbewiesen werdenWas ist Aufklrung?
The AntichristAlso sprach Zarathustra. Quotations: Fried
NietzscheQuotations: AtheismThe world as I see itLexicon: Sein
und Zeit - Martin HeideggerWas ist Philosophie?Intro to
Philosophy Part 1: BasicsIntro to Philosophy Part 2:
SemanticsIntro to Philosophy Part 3: MetaphysicsTheory of
ScienceTheory of ScienceLogicInterview with Tom Regan: Tiere
gehren nicht zwischen zwei ScheibenBrot.Interview with Tom
Regan: Auf das junge Gemse kommt es an.Die Philosophie der
TierrechteMaterialismus und MetaphysikSelbstbewusstsein: Ein
metaphysisches Relikt?Mythen des MaterialismusPlato-> Natural
SciencesCosmologyThe Big BangQuantum Mechanics TextbookA Brief
History of TimeVibrations and WavesThe modern revolution in
PhysicsQuantum Mechanics-> MathematicsMathematik IILineare
Algebra ILinear AlgebraTrigonometry-> LawBrgerliches
Gesetzbuch (BGB)Strafgesetzbuch (StGB)Strafvollzugsgesetz
(StVollzG)Bundesverfassungsgetsgesetz (BVerfGG)===
Subject:
: Re:
c-number> Howdy everybody,> I'm reading Peskin and
Schroeder's Intro to QFT and in this> book the author
constantly refers to c-numbers... without> saying what a
c-number is. I couldn't find c-number> on
mathworld.wolfram.com or physicsworld.wolfram.com.> Can
someone please tell me what the hell a c-number is?>
adam>I haven't read Peskin and Schroeder but if their usage
of the term c-number is the same as everyone else's usage then
they are referring >to commuting variables. For example, Bryce
DeWitt introduces the >concepts of c-numbers (commuting
variables) and a-numbers (anticommuting >variables) in his
book Supermanifolds. If a,b are c-numbers thenEh? I thought it
was just a complex number.-- Let us learn to dream, gentlemen,
then perhaps we shall find the truth... But let us beware of
publishing our dreams before they have been put to the proof
by the waking understanding. -- Fried August Kekul===
Subject:
:
Re: Unit interval homemorphic to Circle help>If I = [0,1],
and I / ~ is the quotient space of I obtained by> identifying
0>and 1, then the circle S^1 is homeomorphic to I / ~.>This
is intuitively clear, but how can I prove this?>I think I want
to show that p : I ---> S^1 given by p(x) = e^(2ix*pi) is>
a>quotient map.>That's exactly what you must show.>In this
case it is quite easy (fortunately).>The map p is already
continuous, as I and S^1 are compact metric the map>p
is>automatically closed (i.e., if A is closed then so is
p[A]).> Why does a continuous map from a compact space to a
compact space> necessarily> have to be a closed map? Is this
what you are implying? If X is a compact space and Y is a
Hausdorff space, then any continuous map f: X --> Y is closed.
This follows from: (1) If X is compact and A subset X is
closed, then A is compact. (2) If Y is Hausdorff and C subset
Y is compact, then C is closed since continuous maps preserve
compactness.>This implies that p is a quotient map.>KP>--
>E-MAIL: K.P.Hart@EWI.TUDelft.NL PAPER: Faculty EWI>PHONE:
+31-15-2784572 TU Delft>FAX: +31-15-2786178 Postbus 5031>URL:
http://aw.twi.tudelft.nl/~hart 2600 GA Delft> the
Netherlands===
Subject:
: Re: A NOTy problem.This post not CC'd
by email> G'day G'day Folks, > I have been puzzling over
what ought to be a simple logic problem> but am at a loss to
come up with a method. > A crime is committed by one of
the following; , Bob, Chris or> Dave. > Each makes a
statement to the police but three of them lie. > says, I
didn't do it.> Bob says, is lying.> Chris says,Bob is
lying.> Dave says, Bob did it.> Usually one can solve
such problems with a grid >I find such grids helpful, but not
perfect. It's hard to>track some statements with them, and to
keep track ofwhat ifs.> Where A. B. C. D represent their
names and > L. = lying,> N. = not_lying,> I. = innocent,>
G. = guilty. > Somehow that doesn't seem to get anywhere
is this case. > Maybe it is because N = NOT(lying) and G =
NOT(innocent)>Well because of that, an easier grid to use
would be> T G>A>B>C>D>(T for telling truth)G'day G'day Randy,
That is much simpler and it handles the negation aspect. >Then
you just need a method to indicate whether the>statement is
true or false for each one. For instance,>an X means its false
and a dot means it's true.>Thus, each column will have one dot
and three X's>when you're done. If you put a dot, you have to
put>three corresponding X's.> I am less interested in knowing
the answer to the puzzle than> understanding why it is
different from the routine logic puzzles.>It's not. But you do
need to be able to backtrack and>reset your grid after a false
hypothesis.I thought there had to be a way to avoid
backtracking ie a method ofdoing the grid WITHOUT using an
eraser. I imagined solving a Booleanmust arrive at the answer
using reductio absurdum ie it can't be thisanswer or that one
so it must be whatever is left. >For instance, let's start
with the first statement.> says, I didn't do it.>Suppose
that's true. Then gets an O in column>one (he's telling the
truth) and an X in column>two (he's not guilty).> T G>A O X>B
X>C X>D X>Once we put an O, everybody else gets an X.>Now Bob
says is lying. We assumed is a>truth teller, so Bob is lying.
We already marked that.>Chris says Bob is lying. This is true.
But we already>marked Chris as a liar. Inconsistency. is
not>the truth teller. Restart the grid with somebody>else as
truth teller and X under for column one.>Of course, if is
lying, then this statement>is false:> says, I didn't do it.>So
no matter who the truth teller is, did it.> T G>A X O>B X>C X>D
X>Now we just have to see if putting an O under>B, C, or D
works out consistently.>But actually, I see that Bob's
statement is now>true.> T G>A X O>B O X>C X X>D X X>Is this
consistent with the other two statements? Better>check (if
not, there is no solution).> Chris says,Bob is lying.>If
Chris is a liar, then this statement is wrong. Which>it is. It
checks.> Dave says, Bob did it.>If Dave is a liar, then Bob
didn't do it. And he didn't.>The grid system works fine, you
just set up an improper grid.I love it. Personally I find I
need a visual grid of some sort totrack the possibilities and
see the inconsistencies. Thank you verymuch. > - Randy--
Quentin Grady ^ ^ /New Zed, >#,#< [ / / ... and the blind dog
was
leading.http://homepages.paradise.net.nz/quentin===
Subject:
:
Re: A NOTy problem.This post not CC'd by email> I am less
interested in knowing the answer to the puzzle than>
understanding why it is different from the routine logic
puzzles. >I am not familiar with the routine logic puzzles,>so
I don't know why its solution would be different.>However, it
seems to be straigtforward to solve.>You did not make use of
the information that exactly three are lying.>I would guess
that the routine puzzle would be that exactly>three are
telling the truth.G'day G'day William, In the routine logic
puzzles the person setting the puzzles providesthe grid. This
was my inexpert attempt at creating a grid and solvinga logic
puzzle. >The same method can be used to solved both types of
problems.>This method must be a routine method to solve
puzzles like this.>-- Hale-- Quentin Grady ^ ^ /New Zed, >#,#<
[ / / ... and the blind dog was
leading.http://homepages.paradise.net.nz/quentin===
Subject:
:
Re: Asymtotic normal distribution>Hello everybody,>I'm working
on a project and I want to prove the following.>Let>Ggr ~ BIN(
m/2 , pgr)>Gro ~ BIN( m/2 , pro)>Zgr ~ BIN( n/2 , pgr)>Zro ~
BIN( n/2 , pro)>I've already proved that S is a unbiased
estimator for the ratio n/m is:> S = Sqrt{ (Zgr Zro)( Ggr Gro)
}> What I want to prove now is that LOG(S) ~ Normal
distributed.>I already have:> LOG(S)=1/2LOG(Zgr) +1/2LOG(Zro)
- 1/2LOG(Ggr) - 1/2LOG(Gro) = ..> Can somebody help me with
this prove?I do not see how one can say that S (or LOG(S))
isunbiased, as the numerator or denominator in thesquare root
can be 0.That said, the variable Ggr/(m/2) is
asymptotically(as m goes to infinity) normally distributed
withmean pgr and variance 2/(m*pgr*(1-pgr)), etc., andas
LOG(S) is a differentiable function of its arguments,it is
asymptotically (for m and n large) normallydistributed with
mean LOG(n/m) and variance givenby linearizing the logarithms.
This is the usualdelta-method.-- This address is for
information only. I do not claim that these viewsare those of
the Statistics Department or of Purdue University.Herman
Rubin, Department of Statistics, Purdue
Universityhrubin@stat.purdue.edu Phone: (765)494-6054 FAX:
(765)494-0558===
Subject:
: Re: Naive Q: Set theory, logic -
which comes first?>Two questions whose answers I am seeking
are:>1) What exactly might we mean by representation?>2) How
do we define a mathematical object if we do not want
to>identify it with some representation of it?> This is done
quite often. The Peano Postulates CHARACTERIZE> the positive
(or non-negative) integers. There are many other> ways to
characterize them. >So we say that 0 is a natural number, that
the successor operation>takes us from a natural number to
another natural number, and then>list properties that natural
numbers satisfy. But what we say is>consistent with their
being sets, functions in lamda calculus, or>something else. We
need to exclude such interpretations, but how?Why? We only
characterize what it means for a particular object to be
considered as a model for the integers. Itis a mistake to
attempt to say what an integer is.-- This address is for
information only. I do not claim that these viewsare those of
the Statistics Department or of Purdue University.Herman
Rubin, Department of Statistics, Purdue
Universityhrubin@stat.purdue.edu Phone: (765)494-6054 FAX:
(765)494-0558===
Subject:
: Re: A NOTy problem.This post not CC'd
by email>Hello> I have been puzzling over what ought to be a
simple logic problem> but am at a loss to come up with a
method.> A crime is committed by one of the following; , Bob,
Chris or> Dave.> Each makes a statement to the police but
three of them lie.> says, I didn't do it.> Bob says, is
lying.> Chris says,Bob is lying.> Dave says, Bob did
it.>Sounds like Dave plays no role here.G'day G'day Julian, I
like the approach. Reducing a four possibility problem to a
threepossibility problem. My question is how did you do that?
Are you working that out from what Dave said or because of
thestatements that follow? >Either Bob or is telling the truth
(if not, than Bob lies and is>not lieing, which is
absurd).>Either Chris or Bob is telling the truth (same
proof)>But there is only one truth-teller, hence Bob tells the
truth.That is fantastic. As I see it you aren't forced to do an
eventualback track. Your description fits finding the
intersection of twosets. The reductio absurdum is confined to
establishing the _initial_is that the backtracks are confined
to a single stage and not tomultiple stages in the logic.
(Hey, it saves on erasers.) > did commit the crime!
-hopefully, he's living in New Zed so he>won't be grilled like
chicken-.Indeed. Best wishes, -- Quentin Grady ^ ^ /New Zed,
>#,#< [ / / ... and the blind dog was
leading.http://homepages.paradise.net.nz/quentin===
Subject:
:
Re: A NOTy problem.This post not CC'd by email===>
===
Subject:
: A
NOTy problem.>I have been puzzling over what ought to be a
simple logic problem>A crime is committed by one of the
following;>, Bob, Chris or Dave.>Each makes a statement to the
police but three of them lie.> says, I didn't do it.>Bob says,
is lying.>Chris says,Bob is lying.>Dave says, Bob did it.>If
Chris told truth: told truth; two soothe sayers.>Thus Chris
lied; Bob told truth; did it.> lied; Dave is wrongG'day G'day
, Well that is brilliant but I am not. Somehow you must
haveeliminated other entry points to the problem. That is
quite a skillbacktrack because of further reductio absurdum.
Best wishes, -- Quentin Grady ^ ^ /New Zed, >#,#< [ / / ...
and the blind dog was
leading.http://homepages.paradise.net.nz/quentin===
Subject:
:
Re: Why is math so difficult for some people?> Many of the
so-called elegant proofs completely hide the> concepts.
Proving the Central Limit Theorem for sums of> independent
identical distributions is certainly the most> elegant, but it
hides virtually everything; it has no> probability in it at
all. This is also the case when the> distributions are not
identical.But it shows the power of the Fourier transform.>
However, the somewhat clumsy Lindeberg proof extends to> the
martingale case, and gives an idea of what is happening.> I
can give lots of somewhat unrelated proofs, but does anyone>
really understand the theorem?> Similarly, Cramer's proof of
the Levy-Cramer theorem that> the sum of two independent
random variables is not normal> unless they both are is
probably the only easy proof, but> it likewise obscures the
ideas. Any time characteristic> functions are used to prove a
probability theorem, the> concepts are not even present.Would
you say that the elementary proofs of say the prime
numbertheorem due to Selberg-Erdos etc, give more insight than
methodsusing complex analysis and Fourier analysis as done by
Wiener,Ikehara and Newman?-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Partridge, _Bouncing Back_ (14 times)===
Subject:
:
Re: Key core error argument, stepped out>For crying out loud.
You should stop cutting and pasting incorrect>stuff. In fact,
you should stop cutting and pasting, period. Why not>post a
link to your original post, instead, if all you are going to
do>is repeat it verbatim, ERRORS INCLUDED?> [.snip.]>Why
don't you off Arturo Magidin?>Three times I offered to do so
if you told me to stop posting>replies. You declined to do
so.>Are you doing so now, in your oh-so-courteous way?>Just
say so: Do you want me to stop posting with comments about
your>statements? Yes or no?> You're ing kidding me!!! You
mean you're asking *me* whether or> not I want you to stop
posting in my threads?> Quit posting in my threads Arturo
Magidin.> off.I'm amazed you finally said that. He made the
same offer about a month ago, and you didn't answer.--
===
Subject:
: Re: Usenet Posting Guide?> I am still using 'rn'.
An improvement over 'readnews', but until now I> have seen
nothing better. (And, no, no graphical interfaces for me,>
please. I have problems when I use the mouse too much.)I
prefer 'tin' but remember 'rn' (and 'readnews') fondly and
could use itif necessary. Graphical interfaces do have their
uses; for instance, theX Window System lets me open multiple
xterm windows to run command-lineclients like tin (or rn).--
Wayne Brown (HPCC #1104) | When your tail's in a crack, you
improvisefwbrown@bellsouth.net | if you're good enough.
Otherwise you give | your pelt to the trapper.e^(i*pi) = -1 --
Euler | -- Myers Myers, Silverlock===
Subject:
: Re: Usenet
Posting Guide?>I prefer 'tin' but remember 'rn' (and
'readnews') fondly and could use it>if necessary. Graphical
interfaces do have their uses; for instance, the>X Window
System lets me open multiple xterm windows to run
command-line>clients like tin (or rn).What benefit do you get
by having two newsreader windows open at once?===
Subject:
: Re:
A 3rd Grade Word Problem---HELP> The Problem:> You know a very
good story. On Sunday you tell the story to a friend.> On
Monday you tell it to two new people. (So far, a total of
three> people have heard the story). Each day after Monday,
you double the> number of new people you tell the story to.
What will be the total> number of people that will have heard
your story after you tell it on> Thursday? If I have a few
beers, I might solve the problem like this (Istill don't get
127, but I get closer.)On Sunday I tell one person. On Monday,
I want to double thenumber of people told, so I tell 2 new
people, for a total of 3.On Tuesday, having told 3 people, I
want to tell double thatnumber of new people, so I tell 6
more. Now 9 people have heard.On Wednesday, 9 people have
heard, and I want to tell doublethat number of new people, so
I tell 18 more. On Thursday, 27 people have heard, so,
doubling that I tell54 more. Now 81 people have heard me tell
my story. So 81 seems to be the answer. But wait. The problem
tells onlyabout new people I tell the story to, but asks,
finally onlyabout people who've heard the story. No qualifying
new. It turns out that while you were telling your story to
newpeople, a few old people were standing around, caught in
thecrossfire, and heard the story also. Obviously, from the
story,there were 46 of these old people standing around and
theymust be added in, getting 81+46 = 127.Beer, now THERE'S a
temporary solution. --Homer.Bart===
Subject:
: Re: Key core error
argument, stepped out> Three times I offered to do so if
you told me to stop posting> replies. You declined to do
so.> Are you doing so now, in your oh-so-courteous way?> Just say so: Do you want me to stop posting with comments
about your> statements? Yes or no?> You're ******* kidding
me!!! You mean you're asking *me* whether or> not I want you
to stop posting in my threads?We've all seen him asking you if
you wanted him to stop replying to you.(Actually, I thought it
was more than three times, but I haven't reallybeen counting.)
I've always assumed that you ignored the offer becausethe
attention you get from him (and others like him) is the only
thingthat lends you even the *appearance* of any credibility.>
Quit posting in my threads Arturo Magidin.So you've decided to
accept the offer. Either you've finally learnedto read, or
else you've finally realized you can't stay backed into
thisparticular corner forever. (I'd bet on the latter.)> ****
off.Please try at least to *pretend* that you are fit for
decent company.-- Wayne Brown (HPCC #1104) | When your tail's
in a crack, you improvisefwbrown@bellsouth.net | if you're
good enough. Otherwise you give | your pelt to the
trapper.e^(i*pi) = -1 -- Euler | -- Myers Myers,
Silverlock===
Subject:
: Re: Two coin flip/ clarification for C
Bond>As I said, end of conversation. Bye bye.> Randy,> I'll
write this slowly. (I know, that like Ull, you think
slowly)Getting bored? Trolling for 2-week-old posts to try
tokick up old dust? Finding nobody will play with youany
more?I walked out of this conversation with that post onOct 23
and have no interest in returning. - Randy===
Subject:
: Re: Key
core error argument, stepped out> Using Dot's proof that the
values of a polynomial with algebraic> integer coefficients
are always divisible by an integer if and only if> each
coefficient is a multiple of that integer (in the algebraic>
integers) gives you that the statement is correct for
polynomials in> A[x]. > I had not noticed Dot's theorem.
The x^2 + x example seems to belie> it: for any integer x,
x^2 + x is divisible by 2, but the coefficients > are not
multiples of 2, and both of the coefficients are algebraic>
integers. You must therefore be thinking that the domain is
algebraic> integers as well.>I think you are reasoning on
cross-purposes. As I remember, Dot's theorem>was about
polynomials over the algebraic integers. As a polynomial
over>the integers, x^2 + x is always divisible by 2, but not
as a polynomial>over the algebraic integers.> Oh yeah, I
finally realized where you were cheating Dik Winter, as> using
v=-1+49x my polynomial is simply enough> P(x) = (v^3+1)5^3 -
3v(5)7^2 + 7^3When you started this thread you said:1. Let
P(x) = 14706125 x3 - 900375 x2 - 17640 x + 1078, where x isin
the ring of algebraic integers, notice that P(x) has a
constantterm that is 1078.Where did the v's come frome?> which
I'm sure you conveniently forgot when you came up with your>
examples.Why would he think it's there?> Nevertheless my
explanations before were correct, but maybe now you> can start
to see more of the particulars of why your hacks put you in> a
field.Or not.-- ===
Subject:
: Re: Graduate algebra book> It's
quite possible to study a reasonable amount of algebra,> a
reasonable amount of analysis and a reasonable amount of
topology> all in three years. (And also a reasonable amount
of applied maths> and statistics if that's your thing.) I'm a
bit baffled about your reference> to semesters of algebra ---
do you only study one topic per semester> at your
university?>No, but at my university (and in the United States
in general) we>don't usually take more than one course of the
same discipline per>semester.Oh dear, oh dear. I do hope by
discipline you mean, forinstance, subfield of a subject. If
you mean to imply that taking more than one course per
semester in all ofmathematics is unusual (for someone studying
mathematicsseriously, e.g., majoring--or even minoring--in
it),then either you're wildly wrong or I am living in a
dreamworld.How could someone graduate from university with a
degree inmathematics having taken only eight courses in
mathematics?Lee Rudolph===
Subject:
: Re: Your Attention Please,
Sci.* NG <1068060341.6117.0@ersa.uk.clara.net>Abhi:>This is
very serious attempt indeed. My life is at stake...> But one
thing is certain. You people change my emotions from sadness>
to flames whenever I came here. It really makes me forget
problems in> my personal life. Sometime bad things turn out to
be good.Perhaps you should spend the effort on solving
thoseproblems instead. Some ideas work, some don't butwhether
this one does or not, it won't change whateverhas upset you.
Your life will be what you make of it,the same it true for all
of us.Good luck.George===
Subject:
: Re: Integral of e^x^2 dx> I
was evaluating the integral of e^(x^2) from 2 to 3 and got
something> around 12, which I know cannot be right (and I
verified it on my TI-83).> David Moran Whoa ... that can't
possibly be anywhere _close_ to being correct. After all, the
integrand is increasing and exp(2^2) = 54.59815003314423907811
so the integral has to be greater than 54. In fact, I think
that a reasonably accurate estimate for the value of your
integral is 1428.052253 ...===
Subject:
: NOVA on strings and
branes & bogus free energy claims you are absolutely right
that there is a cult that has grown up aroundvarious FE
claims. They fit into 3 general classifications: kooks,
consand idiots. The people in the Bearden cult have tried
legal threats toshut down email lists that challenge their
claims. they won't respondto errors in their instrumentation -
like at:www.phact.org/e/z/beardenreview.htmNew free energy
people spring up all the time. There is a lot of
crosspollenation between FE people and UFO nuts - they both
expectundeniable vindicating evidence to arrive very soon -
they both thinkthat a lot of poor evidence adds up to good
evidence, and they willreport glowingly on a claimant with out
mention things like a priorhistory of frauds.Eric
Kriegwww.phact.org/e/dennis4.htmlYes, I also know what you say
to be true from first-hand experience.This is what makes
legitimate work so difficult. The Skeptical Inquirer lobbydoes
not help by garbling important differences. Perhaps 90% of
theFE claims are nonsense, perhaps 99% or even more. In fact
so farI am confident that 100% of over-unity FE claims are
bogus.ThatThe UFO data is another matteralthough there too the
noise swamps the signal and one must bevery careful. It is
obvious from NOVA's Elegant Universe lastnight that the
Universe is a lot stranger than anyone
imagined.http://www.pbs.org/wgbh/nova/elegant/My main themes
in my two books Destiny Matrix and Space-Timeand Beyond II
published in 2002 were there last night in NOVA i.e.Star Gate
space and time travel, contact with UFO alien intelligence
inthe Universe Next Door. Yes they were done in a humorous
way, but themain point of the NOVA was that such science
fiction may not betotally fiction.Just in:Sorry Jack it is not
nonsense. Hal knows dam well who I am speaking of and it is
time he comes clean. Again are you part of the solution or
part of the cover up and censorship. Z Energy was involved in
this as well. Puthoff has to search his own soul on this one,
regain his own integrity. My integrity and the scientist are
not in question. I find it interesting how quick you dismiss
all of this without any investigation not even asking who the
scientist is. All it takes is Puthoff to say this is nonsense
and you drop everything. Do you have a mind of your own? Or do
you just ask the government boys what is the truth. Don't you
find it hard to consider yourself an authority in these
matters when all you know is what you are told by those with a
track record of not telling the truth. Sorry Jack you and
Puthoff seem to be bedfellows and he has already established
his character.Sarfatti's reply: Hal and I have our specific
disagreements on matters of zero point energy induced gravity
metric engineering theory, which is part of normal scientific
method. Hal tells me my refutations of his theory is nonsense
all the time. I do not believe him. However, I do believe him
on this because that is one of his fields of expertise.
However, I do not rely only on Hal in these matters. Hal
worked with Creon Levit at ISSO on many of these bogus free
energy claims in our ISSO laboratory. Creon did his work with
complete integrity and an open mind. There is no coverup,
there is no censorship. The fact is that ALL the current
over-unity free energy claims that are for example described
by Nick Cook are bogus or bad physics and engineering, I asked
you what your scientific credentials were and you have not
answered. The government boys sometimes ask me what is the
truth in these matters. You got it wrong way round. :-)I
suggest you carefully study
http://qedcorp.com/APS/StarGate1.movWhat were the specific
technical details in the case you described? Whose lab was
blown up BTW?In a message dated 11/4/03 8:56:10 PM,
sarfatti@pacbell.net quotes a statement by: >Statement: It was
so far over unity it scared them. He (Puthoff) refused to come
up with > the money they boast to have for anyone who
demonstrates such a > device. Several other top scientists
were there. This same device was > demonstrated to other top
scientists in the field. Shortly afterwards > demands were
made for the device, threats to family etc. His lab was >
blown up and these idiots keep saying no such device
exists.Jack: This sounds like fiction to me. ;-)Puthoff:
Definitely fiction!Hal PuthoffThis is nonsense. Putoff had a
demonstration of a zero point freeenergy device that put out
phenomenal energy.Oh really? What are your credentials in
physics? It was so far over unity it scared them. He refused
to come upwiththe money they boast to have for anyone who
demonstrates suchadevice. Several other top scientists were
there. This same devicewasdemonstrated to other top scientists
in the field. Shortlyafterwardsdemands were made for the
device, threats to family etc. His labwasblown up and these
idiots keep saying no such device exists.This sounds like
fiction to me. ;-)With friends like you, Hal does not need
enemies. :-)I have told Hal of my concern that a cult has
grown up around thesemindless free energy claims using his
name in the most outlandishfabrications like yours here.The
next thing you will ask is prove it. Show us the device or
itdoesnot exist. Been there done that, will not expose the
scientistagainto the so called free energy zero point
community. Most are theretosuppress it, some are there to
control and capitalize on it, mostwantto steal it. When the
integrity returns, the devices will come. notbefore. Do you
really think the US government the top of which isnowgoverned
by the oil companies want such a device to get out?Then
whydoes everyone look to government officials as an authority
onwhetheror not zero point devices exist. It is like asking
the wolf to guardyour chickens and trusting him to give you an
accurate head count.Might want to ask these retired government
officials if they areafraid of loosing their pensions, doing a
little jail time, maybeloosing their lives or the lives of
their families. Might want to askthem if they would stand up
for the truth, the right of theAmericanpublic which they were
sworn to serve to know the truth? Ask themifthey new any of
the people on the shuttles that died needlessly tokeep a lie
going?Might want to ask them how it feels in their soultolie?
Sending people up on giant firecrackers hoping they can
droplikea rock and land is ridiculous with the hidden
technologies at area52etc. Hey ask them about the other areas
from 1 to 52 andbeyond. Whatis being done there? How about
hunt for integrity as a new book?----- Original Message
-----===
Subject:
: Nazi Saucers?re: Nick Cook's Hunt for the
Zero
Pointhttp://www.salon.com/books/review/2002/08/05/zero_gravity
/--- In ItalianPhysicsCenter@yahoogroups.com, Jack SarfattiHow
about this from a PhD physicist, in the minority, who
hasstudied the UFO subject:I did some investigating and
interviewed retired senior USGexecutiveswho laid the Nazi
flying saucer (disguised as UFOs) claim (a laCook's book) to
rest - it didn't exist and it didn't fly.Which is pretty much
what I have also been saying about Cook'sbook BTW.I'm
interested in any debunkery of Cook's book. What did
thisPh.D.fellow discover precisely?You need to ask him. I have
bcc'd him on this. He can reveal hisID ifhe wishes. He has USG
Intelligence connections for information.The point is that we
at ISSO 1999-2000 checked out many of thebogusclaims on zero
point energy by fringe people and found them tobeessentially
worthless.Creon Levit on leave from NASA Ames did a very
thorough job onseveralof the claims. More information on this
is in my two books from2002Destiny Matrix and Space-Time and
Beyond II and in my semi-popularto theSociety for Literature
and Science online athttp://qedcorp.com/APS/StarGate1.movNote
of clarification I do not include the Haisch-Puthoff zero
pointenergy program nor Puthoff's PV gravity program in the
samecrackpotcategory as ALL the other work mentioned by Nick
Cook in hisbook. Myobjections to the HRP program are that they
do not ask the rightquestions, are basically superficial in
their formulations, makesomeerrors of interpretation of their
formalisms and most importantlyhavenot led to any testable
predictions nor any clarifying explanationsofsignificant
problems and mysteries, e.g the UFO. They arenot bogusphysics
simply wrong physics in my humble opinion.A few specifics:1.
On the zero point origin of inertia - it is a mistake to look
onlyat the virtual photons. It is the virtual
electron-positrons that ismost important.2. There is no vacuum
coherence in their idea set. That throwsthebaby out with the
bathwater because guv Einstein's metric field forcurved
spacetime emerges from that non-perturbative vacuumcoherenceof
the virtual electron-positron pairs primarily. So does the
darkenergy/matter that is 96% of the universe that does not
appearanywhere in their models. They have been working on this
foralmost 20years with little to show really.3. There is no PV
(i.e. no quantum polarized fluctuations) inPuthoff's PV
math.4. Puthoff and Ibison mis-interpret the physical meaning
of theirisotropic radial r coordinate in their toy model K =
e^2GM/c^rPuthoff is very interested in UFOs and that is a
primary motivationfor this zero point gravity work. Nowhere do
Puthoff and Haisch et-alsquarely face the numberString Tension
= c^4/8piG = 10^19 Gev per 10^-33 cm whichprevents
anyplausible explanation of UFO metric engineering with their
bruteforce approach. Space-time geometry is simply too stiff
to bendwiththe energy schemes they have in their paradigm.
They aremissing somevery essential new concepts.Cook is a very
approachable fellow; haveyou cross-checked with him
also?-AndrewItold him about the flaky stuff he was pushing so
he erased mefrom hisbook. That told me he was not
intellectually honest, but hadsomehidden non-scientific
agenda. I find this disturbing since he isassociated with
Jane's Defence Weekly in UK.-------------------------Caveat
from Jack SarfattiTorsion fields may well exist. Orthodox
studies suggest that the coupling of electron spins to
hypothetical torsion fields are too weak to be of biological
importance. However, not enough work has really been done. It
is remotely conceivable that there could be bio-torsion
effects. However, the theory of the Russian claims below is
not at all clear to me nor how torsion waves would be
generated and in what strength.Brief explanation of torsion
field.Physics today is based on invariants of groups of
symmetry transformations.The invariant is what does not change
when the perspective or frame of reference of the detectors
changes.Symmetries are first introduced globally i.e. same
everywhere-when then they are made local. This localization of
symmetry explains ALL the well-established fundamental forces
of nature i.e. gravity, electromagnetism, weak radio-active
and strong sub-nuclear.The global symmetry group of
flat-torsionless 4Dim space-time is the 15 parameter conformal
group of massless null geodesics or light rays.The conformal
group splits into 4 pieces or subgroups.1 parameter dilation
group.4 parameter nonlinear special conformal translations4
parameter linear translations6 parameter space-time rotations
i.e. O(1,3) Lorentz group.Rest masses of electrons etc.
require a breaking of symmetry of the dilation group at
least.Utiyama showed how to derive Einstein's gravity that is
torsion free from locally gauging the 4-parameter linear
translation group which, in turn, is locally generated by the
special relativity total four-momentum Pu.Einstein's curved
space-time gravity metric field guv is the compensating field
whose new dynamical degrees of freedom restore the
translational invariance.Similarly, the torsion field would be
the compensating gauge force field from locally gauging the
6-parameter space-time rotation group.There are then also
compensating gauge force fields from the one-parameter
dilation group and the 4-parameter special conformal
transformations.The compensating field for the 1-parameter
dilatation group seems to be the inflation complex scalar
field in the large-scale limit.i.e. spin 0 Vacuum Coherence
Field = (Higgs Amplitude Field)e^i(Goldstone Phase Field) from
locally gauging the dilation subgroup.The compensating field
for the 4-parameter nonlinear special conformal group seems to
be the exotic vacuum unified dark energy/matter w = -1
fieldmodulations around / = 0 where /zpf > 0 is negative zero
point pressure anti-gravity dark energy and /zpf < 0 is
gravitating positive zero point pressure dark matter.
Lepto-quarks are quantized gauge force flux vibrating strings
like vortex strings in Type II superconductors where in the
core the Vacuum Coherence Field = 0. The ends of the spin 1/2
lepto-quark vortex core strings and spin 1 strings may be
stuck to the 3D branes as shown last night on NOVA with
off-brane spin 2 gravitons as closed vibrating strings.
However these strings are ~ 1 fermi not 10^-33 cm which is why
the hadronic alpha' Regge slope is (1 Gev)^-2 i.e.hadronic
gravity G* ~ 10^40G(Newton).Einstein's gravity is from
modulating the Goldstone phase of the Vacuum Coherence Field
in the local gauging of the linear 4-parameter translation
group. When there is local restoration of translational
invariance is simply Einstein's field equation for the total
local stress-energy density Diff(4) tensortuv(geometry) +
Tuv(matter) = 0where trivially there is local total current
conservationtuv(geometry)^;v + Tuv(matter)^;v =
0wheretuv(geometry) = (c^4/8piG)GuvGuv = Ruv - (1/2)RguvWhen
there is NO TORSION we also havetuv(geometry)^;v = 0All of the
above is for non-exotic vacuum where /zpf = 0.In the exotic
vacuum dark energy/matter case we have local stress-energy
density current conr all A.)> That's a different question. Are
you also requiring f to be> monotone?>I'd say that you've got
C(a,x) sets or card x in A. For each of those>sets, your
function can take 2^x values. Therefore, you must
have>Sum(x=0,a) 2^x C(a,x) = 3^a.>Am I right ?> Yes, for the
second question (if f is not required to be monotone).Oops
again! You want Product_{A in 2^X} 2^|A| = 2^(Sum_{A in 2^X}
|A|) = 2^(|X| 2^(|X|-1))Department of Mathematics
http://www.math.ubc.ca/~israel University of British Columbia
Vancouver, BC, Canada V6T 1Z2