mm-198
===
Subject: Re: Please enroll me in your group-
math-prizes> I am looking for a forum on unsolved problems. I
have several papers> to share on elementary number theory.>
The most important problem in mathematics is how to prevent
circle-squarers, angle trisectors, four-colour-map
counterexample producers, FermatOs Last Theorem provers*,
and
Wiles doesnt count.
===
Subject: Re: CombinationThe Ghost In The
Laborious, although one can write a small C program to do the>
bulk of the work, with some care.GUYS!!Come on, think just a
little. For odd prime P, you get(P-1)! =
product(/(i,i=1,(P-1)/2)/)*product(/(P-i,i=1,(P-1)/2)/) =
product(/(i,i=1,(P-1)/2)/)*product(/(-i,i=1,(P-1)/2)/) =
product(/(i,i=1,(P-1)/2)/)*product(/((-1)*i,i=1,(P-1)/2)/) =
product(/(i,i=1,(P-1)/2)/)**2*product(/((-1),i=1,(P-1)/2)/) =
((P-1)!)**2*(-1)**((P-1)/2)(all mod P)Therefore
(P-1)!/(((P-1)/2)!)**2 = (-1)**((P-1)/2) mod PSo that
(P-1)!/(((P-1)/2)!)**2-(-1)**((P-1)/2) = 0 mod PIn the case in
question, P = 73, (P-1)/2 = 36, (-1)**((P-1)/2) = 1,so
72!/(36!)**2-1 = 0 mod 73.It seems curious to me both that
number theory books 'ndthemselves next to numerical analysis
books on libraryshelves and that number theory questions are
often askedin s.m.n-a.-- write(*,*)
transfer((/17.392111325966148d0,6.5794487871554595D-85,
&6.0134700243160014d-154/),(/OxO/)); end
===
Subject: Re:
Combination by support1.mathforum.org (8.11.6/8.11.6/The Math
factors for 72!/(36!*36!).what you get is a*b*c*d*e*f*g... so
on. now group these numbers intosmall groups say (a*b*c) * (
d*e*f) * (f*.. so on. And then express the term (a*b*c) as
something say (x*73+y).And then express the term (d*e*f) as
something say (m*73+n).So on. There wonOt be too many terms.
Now multiply y*n*.. so on andtry dividing the sum by 73.
===
Subject: Re: Five Parameter Logistics> I would like to
state my 'nal 'ndings:> > The desired 5PL
(required in my
special case) is:> > A - D> y = D +
------------------------------------- > [ 1 + ( x / C )^B ]^E and IOm using 
the Levenberg-Marquardt algoritem/method to>
evaluate the parameters to 't the set of data points.> > Many
JoergYour function is linear in A and D but nonlinear in B, C,
and E.Therefore you could reformulate your problem as a
nonlinear leastsquares 't in B, C, and E -- for any set of
values of theseparameters, A and D can be computed using
linear least squares.
===
68.146.148.68Subject: Multivariate Statistical Process Control
with PCA (T2 and SPE charts)... IOve been looking all over
the
Net for equations regarding HotellingOsT2 and Squared
Prediction Error (SPE) calculations for a multivariate
SPCchart IOm trying to put together:While I did
('nally) 'nd
out how to calculate T2 and SPE, I still havenOtfound out:1)
How to determine the control limit for an SPE (Q) graph?2) How
to properly drill-down from an SPE graph to 'nd out which
pointers anyone can provide....-Jeff
===
Subject: Re: Intel
much,Paul> > While browsing ProgrammerOs Paradise, I saw
that
a student edition of> Intel Visual Fortran for Windows 8.0 is
available for $29. The link is>
http://www.programmersparadise.com/Product.pasp?txtCatalog=
Paradise&txtCategory=&txtProductID=I23+0D03 >> This product
should give Matlab a run for its money, and> run your problems
in seconds instead of days!> You mean people actually *pay*
for FORTRAN compilers??? Only the *smart* ones, the dumb ones
pay for a stripped (Fortran) subset>> stuffed under the Matlab
cover.> Take a look at http://www.openwatcom.org> >
Unfortunately, Windows, DOS, or OS/2 only.>
===
Subject: Re:
Kernel for cubic interpolation> ,> > IOve been getting
terribly confused with a simple problem... hope> someone can
put me out of my misery.> > I know linear interpolation has
the convolution kernal 1 - |dx|.> > So what is the convolution
kernel for (Lagrange) cubic interpolation?> > IOve been
looking
blankly at OA Note on Cubic Convolution>
InterpolationO which
IOm sure has the answer for about 2 hours with no>
realization
yet. Could be caffeine o/d? Someone help me... it hurts!> >
cited above, various kernels are stated and they areall
piecewise functions, eg.Catmull-Rom: 3/2.|x|^3 - 5/2.|x|^2 + 1
0<=x<=1 -1/2.|x|^3 + 5/2.|x|^2 - 4.|x| + 2 1<=x<=2 0 x>=2Keys
4th order: 4/3.|x|^3 - 7/3.|x|^2 + 1 0<=x<=1 -7/12.|x|^3 +
3.|x|^2 - 59/12.|x| + 5/2 1<=x<=2 0 x>=0IOm sure the last
one
is probably the best, since itOs a 4th orderrather than 3rd
order approximation, however IOd really like to knowwhat the
Lagrange formula is as well to compare them in my
===
Subject: Re: Kernel
for cubic interpolation> > ,> IOve been getting terribly
confused with a simple problem... hope> someone can put me out
of my misery.> I know linear interpolation has the convolution
kernal 1 - |dx|.> So what is the convolution kernel for
(Lagrange) cubic interpolation?> IOve been looking blankly
at
OA Note on Cubic Convolution> InterpolationO
which IOm sure
has the answer for about 2 hours with no> realization yet.
> [follow-up & addded comp.dsp to groups]> > In the paper I
cited above, various kernels are stated and they are> all
piecewise functions, eg.> > Catmull-Rom:> 3/2.|x|^3 -
5/2.|x|^2 + 1 0<=x<=1> -1/2.|x|^3 + 5/2.|x|^2 - 4.|x| + 2
1<=x<=2> 0 x>=2> > Keys 4th order:> 4/3.|x|^3 - 7/3.|x|^2 + 1
0<=x<=1> -7/12.|x|^3 + 3.|x|^2 - 59/12.|x| + 5/2 1<=x<=2> 0
x>=0> > IOm sure the last one is probably the best, since
itOs
a 4th order> rather than 3rd order approximation, however
IOd
really like to know> what the Lagrange formula is as well to
advice.You can 'nd the Lagrange interpolation formula in
Abramowitz & Stegun,Handbook of Mathematical Functions. It is
just a simple way to write apolynomial of degree N that goes
through N+1 points of a function.For example, suppose you know
f(x) at the points x0, x1 and x2. Callthese values f0, f1 and
f2. Then you write f0 * (x-x1)*(x-x2) f1 * (x-x0)*(x-x2) f2 *
(x-x0)*(x-x1) f(x) approx ------------------ +
------------------ + ------------------ (x0-x1)*(x0-x2)
(x1-x0)*(x1-x2) (x2-x0)*(x2-x1)You see this is quadratic in x.
gher-order polynomials are essentiallythe same. -- Julian V.
NobleProfessor Emeritus of
^^^^^^^^^^^^^^^^^^http://galileo.phys.virginia.edu/~jvn/ God
is not willing to do everything and thereby take away our free
will and that share of glory that rightfully belongs to us. --
N. Machiavelli, The Prince.
===
Subject: dividing by zero by
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
22:45:03 -0500
there, I just have a couple of more
questions please. 1. Explain why you cannot divide any nonzero
number by 0: a) as if you were explaining it to a small child
in the third grade. b) as if you were explaining it to a
fellow math major, who of courseis interested in the
mathematical reasoning behind your argument andnot a bunch of
baby talk. Feel free to use the following simple idea:a/b = c
is equavilanet to a=bc. 2. Which explanation do you prefer?
Which explanation do you think aMathmatician would prefer, and
why? Is one more or less correct thanthe other? I really
===
Subject: Re: dividing by
just have a couple of more questions please.> > 1. Explain why
you cannot divide any nonzero number by 0:> > a) as if you were
explaining it to a small child in the third grade.> Because
your teacher will give you a failing grade on your math
exam,which might cause your parents to withold certain
priviliges (such asyour allowance).> b) as if you were
explaining it to a fellow math major, who of course> is
interested in the mathematical reasoning behind your argument
and> not a bunch of baby talk. Feel free to use the following
simple idea:> a/b = c is equavilanet to a=bc.> x/0 is not
de'ned because any value of c will satisfy the equation
x=0*cEven more fundamentally, x/0 is not de'ned because that
is theDEFINITION of the division operation. The previous
explanation is agood reason WHY division was de'ned the way
it
is (i.e. to excludedivision by zero) but one COULD de'ne an
alternate division operatorthat would give any result you
liked, such as x/0=x or x/0=N (the setof natural numbers) or
x/0=What I had for breakfast this morning. Ofcourse, these
de'nitions would break all sorts of nice properties ofthe
division operator (such as a/b=c <=> a=bc for all but the
1stexample), but the de'nition could be made. > 2. Which
explanation do you prefer? Which explanation do you think a>
Mathmatician would prefer, and why? Is one more or less
correct than> the other?> I prefer the 'rst explanation, as
it
relates more directly totangible effects in the real world.> I
really appreciate this> -- Use of tools distinguishes Man from
Beast. And UNIX users from WINDOZE lusers.
===
Subject: Re:
1. Explain why you cannot divide any nonzero number by 0:> a)
as if you were explaining it to a small child in the third
grade.Because your teacher will give you a failing grade on
your math exam,> which might cause your parents to withold
certain priviliges (such as> your allowance).Seriously,
answering a) is harder than answering b). Young children
oftencome to the conclusion, on their own, that a nonzero
number divided by zeroshould give an in'nite result.
ThereOs
nothing wrong with that conclusion.The child should be
commended, not rebuked! And since you asked thequestion in
sci.math.num-analysis, IOll point out, for example, that
instandard ¤oating-point arithmetic, 1.0/0.0 yields
In'nity.The reason why you cannot divide any nonzero number
by
0 in the thirdgrade is simply that number systems (such as the
one-point extension ofthe reals) having in'nite elements are
never used in the third grade.> b) as if you were explaining
it to a fellow math major, who of course> is interested in the
mathematical reasoning behind your argument and> not a bunch of
baby talk. Feel free to use the following simple idea:> a/b = c
is equavilanet to a=bc.x/0 is not de'ned because any value of
c
will satisfy the equation x=0*cEh? Remembering that x is
nonzero, I must suppose that you actually meantto say:x/0 is
not de'ned because _no_ value of c will satisfy the equation
x=0*cDavid
===
Subject: Re: Jacobian calculation without
re-formulating thedescription in more mathematical terms.I
have found some matlab code, albeit poorly commented, from one
ofthe implementations I have had to look at and comparing the
two itseems they are doing quite a lot more than described in
your post andtheir paper although I am not sure exactly what
right now.Chris
===
Subject: 2D point pattern matching by
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
08:41:41 -0500
HIIOm looking for any help on point pattern
matching. I have 2 data setsof the same number of points
(100Os to 1000Os) IOm looking
for amethod (C code, detailed
algorithm etc?) which will allow me to 'ndthe best linear
transformation (scale rotate etc) of 1 set onto theother &
then obtain a goodness of match.I have found Match
http://spiff.rit.edu/match/ but this was designedfor
astronomical objects and requires a magnitude term as well as
thecoordinates also it requires O(N^6) operations which
===
Subject: Re: 2D
point pattern matching> HI> IOm looking for any help on
point
pattern matching. I have 2 data sets> of the same number of
points (100Os to 1000Os) IOm
looking for a> method (C code,
detailed algorithm etc?) which will allow me to 'nd> the best
linear transformation (scale rotate etc) of 1 set onto the>
other & then obtain a goodness of match.> > I have found Match
http://spiff.rit.edu/match/ but this was designed> for
astronomical objects and requires a magnitude term as well as
the> coordinates also it requires O(N^6) operations which
problem is called the assignment problem. The assignment
problem can be solved by the Munkres (optimal), JVC or Auction
algorithms. However, these algorithms do not perform any bias
removal or scaling.I think this problem is called the
registration problem by the image processing community.Good
luck,OUP
===
Subject: Re: 2D point pattern matching> >> HI>> IOm
looking for any help on point pattern matching. I have 2 data
sets>> of the same number of points (100Os to
1000Os) IOm
looking for a>> method (C code, detailed algorithm etc?) which
will allow me to 'nd>> the best linear transformation (scale
rotate etc) of 1 set onto the>> other & then obtain a goodness
of match. I have found Match http://spiff.rit.edu/match/ but
this was designed>> for astronomical objects and requires a
magnitude term as well as the>> coordinates also it requires
advance>> mark> > I think this problem is called the
registration problem by the image > processing community.Look
for OProcrustes methodO - this is a
well-studied
problem.Arnold Neumaier
===
Subject: approximation of cosh(x) or
sinh(x) for complex numbersI tried to use MATLABOs
Opoly'tO
command to relate two series ofcomplex numbers. But the result
is not satisfactory. Does anybody haveany ideas?
===
Subject: Re:
Advice on numerical libraries> Hello to Everyone in the NG,>
IOm developing a 'nite element code for various
academic
purposes.> Till now, IOve been working either with MatLab
developing my own code,> or adding elements and features to a
different academic program> written in Fortran 77.> Now I
would like to write my own complied program using an external>
library.> I would like to work with different type of matrices
(full sym|unsym,> skyline sym, sparse sym|unsym) and I need to
solve linear(ized)> systems, eigenproblems and SVD.> > Now my
request of advice to the NG concern both the programming>
language and the library (which should be free).The book
Programming the Finite Element Method, 3rd Edition, bySmith
and Grif'ths, published by Wiley in 1997, has Fortran 90
codefor FE. Until recently the code was available
athttp://people.man.ac.uk/~mbgasdk/dansoft/fe_book.1997/ .
There aresome F90 'nite element codes at John
BukardtOs web
site,http://www.csit.fsu.edu/~burkardt/f_src/f_src.html . He
also has somein C++ and Matlab.
===
Subject: Re: Advice on
numerical libraries, It would be easy for you to learn modern
Fortran 95 sinceyou know Fortran 77. Take a look at the free
FEM fortran 95libraries like
paramesh:http://ct.gsfc.nasa.gov/paramesh/Users_manual/
amr.htmlandhttp://www.math.u-psud.fr/%7Elaminie/F90_lib/vers-
IOm
developing a 'nite element code for various academic
purposes.>
Till now, IOve been working either with MatLab developing my
own code,> or adding elements and features to a different
academic program> written in Fortran 77.> Now I would like to
write my own complied program using an external> library.> I
would like to work with different type of matrices (full
sym|unsym,> skyline sym, sparse sym|unsym) and I need to solve
linear(ized)> systems, eigenproblems and SVD.> > Now my request
of advice to the NG concern both the programming> language and
the library (which should be free).> > I know the old trend
for scientist was to write in Fortran, as I told> I already
have experience of FE programming in F77, but I donOt have>
any knowledge of modern Fortran versions. > I donOt have lot
of sympathy for OOP (but this is probably due to a> lack of
guess that C++ could be a good solution for the need of
different> storage format (and also different algorithms for
sym/unsym systems).> IOve looked on netlib and sal and I got
lost, being unable to> understand which library 't my needs
(MV++ & Co., Blitz++, TNT).> Finally, my personal preference
as programmer goes to ANSI C, even> though the 0-referenced
array can be annoying.> > I apologize for any OT (or FAQ -
student
===
Subject: Re: Advice on numerical librariesLook at
some of the C++ libraries for 'nite elements (search for
FEMon
Seewhether they would be a good starting point. See what
matrixlibraries they are built around.I think it would be a
bad decision to use Fortran 77 or C. I thinkC++ can give you
the kind of simple code 'les you get withMatlab, but running
at compiled code speed and with ¤exibilityof a programming
language when you need it.If you are going to use someone
elseOs matrix library such as myC++ matrix library newmat11
I
think the knowledge of C++ youneed is not all that large
(newmat11 would be 'ne if you are goingto treat your big
matrices as dense band matrices - it does notprovide the
facilities to do your solves by Krylov type methods,search for
IML++ or sparselib++ for that).Robert>Hello to Everyone in the
NG,>IOm developing a 'nite element code for
various academic
purposes.>Till now, IOve been working either with MatLab
developing my own code,>or adding elements and features to a
different academic program>written in Fortran 77.>Now I would
like to write my own complied program using an
external>library.>I would like to work with different type of
matrices (full sym|unsym,>skyline sym, sparse sym|unsym) and I
need to solve linear(ized)>systems, eigenproblems and SVD.>>Now
my request of advice to the NG concern both the
programming>language and the library (which should be
free).>>I know the old trend for scientist was to write in
Fortran, as I told>I already have experience of FE programming
in F77, but I donOt have>any knowledge of modern Fortran
versions. >I donOt have lot of sympathy for OOP (but this is
probably due to a>lack of experience, since I never actually
solution for the need of different>storage format (and also
different algorithms for sym/unsym systems).>IOve looked on
netlib and sal and I got lost, being unable to>understand
which library 't my needs (MV++ & Co., Blitz++,
TNT).>Finally,
my personal preference as programmer goes to ANSI C,
even>though the 0-referenced array can be annoying.>>I
apologize for any OT (or FAQ - thought IOve not found much
===
Subject: Re: Advice on
numerical libraries> Hello to Everyone in the NG,> IOm
developing a 'nite element code for various academic
purposes.> Till now, IOve been working either with MatLab
developing my own code,> or adding elements and features to a
different academic program> written in Fortran 77.> Now I
would like to write my own complied program using an external>
library.> I would like to work with different type of matrices
(full sym|unsym,> skyline sym, sparse sym|unsym) and I need to
solve linear(ized)> systems, eigenproblems and SVD.> > Now my
request of advice to the NG concern both the programming>
language and the library (which should be free).,Please check
out the C++ 'nite element library which I help
develop,libmesh:libmesh.sourceforge.netA major feature of
libmesh is that it links with PETSc, and thereforecan be made
to use all of the great solvers in that package. It isfree and
open source, so if you donOt see something you need,
feelfree
to add it!Hope that helps,John
===
Subject: Re: Can anyone shed
any kind of light on this problem in number theory?>
everyone,> > Considering the following sequence of number
pairs.> > 1 2> 2 3> 3 4> 4 5> 5 6> 6 7> 7 8> 8 9> 9 10> 10 11
> 11 12> 12 13> 13 14> 14 15> 15 16> 16 17> > etc> > If I
extract any(all) pairs which include a number divisible by 3>
(including 3 itself) I get the following sequence of pairs:> >
1 2> 4 5> 7 8> 10 11 > etc> > I 'nd that the largest gap
between two sequential pairs is 3.> > If I continue and
extract further pairs which include any number> divisible by
5, then I 'nd the largest gap will become 6.> > What then if
I
extract any pair which includes a number divisible by> 7?> Only
'rst pair will survive which you can obviously prove.> Could
anyone answer these questions?> > What GENERALLY can I say
about the largest gap that will exist if I> continue onto 9,
11, 13 etc> > Is there ANY kind of predictablility in the
patterns of pairs left> after each extraction?> > Consider the
sequence of extractions 3,5,7,9,11; can one say that any>
predictability of the remaining pattern of pairs is linked to
13 (the> next number in the sequence)? Now the answers are
OBVIOUS!