mm-39
===
Be unhappy all you want, I don't care for your
nitpicking Maple bugreports. Why don't you submit some code to
solve these bugs, eh?If you search the archives of Basti's
postings from a year ago, you willfind he made statements like
: I am the leader of modern mathematics...Nobody but a crank
makes statements like these - I rest my case.Caesar Garcia>
Dear Caesar Garcia,While I have not read these papers yet,
and, thus, have none > idea on account of if Dr Basti is right
or wrong there, I must> admit that I am feeling fairly unhappy
with the way you were> expressing your opinion this time.I'd
say, I am hearing strong malevolence in your voice.> AFAIK,
torrent of emotion tends to break human reasoning.Publishing
or not publishing a paper not necessarily means> the paper is
wrong; for example, it simply can be written in> a difficult
to read fashion etc. As you most probably know,> the ultimate
example of publishers' blunder is Galois' papers:> nobody
published them over decades.http://www.galois-group.net/I was
wondering have you read all Dr Basti's papers yourself?> If
not which seems to be the case, then - no comment.CG> I wonder
if your new employers would have been so keen > CG> to hire you
if they knew you were such a nutcase.I am certain that if I
would ever hire a person like you I > would fall into a
serious error as such a person is obviously > not a team
player and would make constant attempts to break>
communication within the company. Speaking so I do not mean
that you are a bad or good > person, IMHO, such statements are
of no use; I also have> none idea what talents you are endowed
by. I just mean you> looks like an individual player; there
are and certainly> there will be always individual players of
superlative power,> for example, a Nobel prize winner
Frederick Soddy who once> worked with Ernest
Rutherfordhttp://www.nobel.se/chemistry/laureates/1921/
soddy-bio.html> Could I kindly ask you to report us rather
more facts about > Dr Basti's papers? I am very interested in
hearing from you> on this and other points.Best
wishes,Vladimir BondarenkoCo-founder, CEO, Mathematical
Director> Cyber Tester,
LLChttp://www.cybertester.com/................................
.............................
===
>>> So the strategy I am
using is to implement a user friendly syntax for>>
metamathematics plus axiomatic set theory. But I doubt it will
hold for>> any serious proof verification system. So on top
of that, I may add a>> system for user defined syntax. Then
this may in fact be asimplification>> for further
implementations.>>A very ambitious project. Good
luck!>> It is not as ambitious as it may sound, as I decided
to not work with> optimizations. But I have implemented things
like unification branching in> order to achieve an proof-engine
that is as general as possible. This way> I do not need Gentzen
sequents, it seems.>> One idea that comes to my mind is that
you might look at using the> semantic trees to write an
interface on top of a program like Qu-Prolog.> This might
saving you some time. :-)>Save me some time? As the subject
heading indicates, I have alreadyimplemented my system. If you
haven't already done so, please have a look atit and let me
know what you think. (System requirements: Windows 95 orlater,
and IE4 or later.) Try out the tutorial (click the Help button)
toget a general idea of the system's capabilities. Examples in
the tutorialinclude Russell's Paradox and what I called the
Paradox of the UniversalSet.DanVisit DC Proof Online at
http://www.dcproof.com -- FREE download
===
I posted this in
another group. But I wanted to get some feedbacksfrom you guys
as well.I was wondering. what are some criteria mathematicians
use in order tofigure out if there is (an) anlytical
solution(s) to a given ode orode system?if there are many,
then what books are available that shows suchmethods?what can
you suggest? any thoughts are welcome. thanks in
advancejohn
===
See for example the list of references
here:http://lie.uwaterloo.ca/odetools/references.htmlI posted
this in another group. But I wanted to get some feedbacks>
from you guys as well.I was wondering. what are some criteria
mathematicians use in order to> figure out if there is (an)
anlytical solution(s) to a given ode or> ode system?if there
are many, then what books are available that shows such>
methods?what can you suggest? any thoughts are welcome. thanks
in advancejohn
===
1. Given two arbitary symbolic expressions
involving only real algebraicnumbers of constant value (e.g.
1/6, Sqrt(37/6) are simple examples), is itpossible to
determine computationally if one expression is less than
orequal to the other? (Presumably this is at least as hard as
the zeroequivalence problem?).2. If it is possible, is it
well-understood and computationally tractible?3. If 2., then
is it also the sort of thing that one might reasonably expecta
computer algebra package to handle?TIA,James.
===
Download beta
1 - www.master-graph.com/mgraph20b1.exe (only 477KB).All who
will help me to improve this program will get a
freeregistration key.You can do the following:-find
bugs-feedback about you impression by the program-advice me to
change or add some new features-translate it to the other
language
(seewww.master-graph.com/instructions/interface.html)Feel free
to contact with me -
roman@master-graph.comSincerely,Roman.
===
Hoops 1-4 developed
Hoop division algebras, collapsed from Moufangloops with
r-fold symmetry and having additive elimination asgeneralized
subtraction. Sizes are functions that are conserved onhoop
multiplication; the sizes of a product are the products of
thecorresponding sizes of the multiplicands. I now explore
theconsequences of sizes becoming zero.(5a) Sizes can become
zero. New possibilities exist in non-degenerate algebras that
conservemore than one size. Sizes of vecs (generalized
vectors) can becomezero without the vec becoming a null vec.
C3 conserves a+b+c and((a-b)^2+ (b-c)^2+ (c-a)^2)/2 and so the
zeroes occur when eithera+b=-c or a=b=c. D3 conserves
a+b+c+d+e+f, a-b+c-d+e-f, & ((a-b)^2+(b-c)^2+ (c-a)^2
-(d-e)^2- (e-f)^2- (f-d)^2)/2, and so has 3non-trivial zeroes.
(5b) Zero sizes constrain calculations to a sub-algebra. A
multiplicand with a zero size gives a product with the same
sizeequal to zero. The result is projected onto a sub-algebra
(to whichthe multiplicand belongs) in which this size is
constrained to zero.The sub-algebra has lost a symmetry. (5c)
Operations with a zero size renormalize. Division by a vector
in the constrained algebra propagates the sameconstraint. This
is effected by the genInverse function; partialfractions are
ignored if the denominator is less than some prescribedh (i.e.
if the size approximates to zero). Conic sections provide
ananalogy. The bi-cone is highly 3D symmetrical.
Restrictingconsideration to a 2D plane gives various less
symmetrical 2D figures.The system is constrained to have zero
distance from the plane. This corresponds to renormalization,
the meta-mathematical trickused by mathematical physicists to
dispose of un-physical infinities.It also corresponds to sub-
& super-symmetry and the use of gradedalgebras. Roger
Beresford.Now you see it. Now you don't! (Magician's
patter.)
===
In the program Mathematica, one can factor an
equation Modulus a Primenumber. However, I am having a hard
time trying to understand how tointerpret the output. Could
someone offer a simple explanation ofFor example, the
following normally cannot be factored any further.Factor[5 +
x^2]5 + x^2However, if we factor this using the option Modulus
a Prime number, we geta different output.Factor[5 + x^2,
Modulus -> 3](1 + x)*(2 + x)..or2 + 3*x + x^2I have been
having a hard time understanding just what the output is
tryingto tell me.I understand how Mod[7, 3] returns 1, but I
do not see the relationship-- Dana
===
> In the program
Mathematica, one can factor an equation Modulus a Prime>
number. However, I am having a hard time trying to understand
how to> interpret the output. Could someone offer a simple
explanation of> For example, the following normally cannot be
factored any further.> Factor[5 + x^2]5 + x^2However, if we
factor this using the option Modulus a Prime number, we get> a
different output.> Factor[5 + x^2, Modulus -> 3](1 + x)*(2 +
x)> ..or> 2 + 3*x + x^2I have been having a hard time
understanding just what the output is trying> to tell me.> I
understand how Mod[7, 3] returns 1, but I do not see the
relationshipCalculating mod 3, Mathematica maps...,
-6,-3,0,3,6,9, .... to 0..., -5,-2,1,4,7,10, ... to 1...,
-4,-1,2,5,8,11, ... to 2so you asked for the factors of x^2+2,
when reduced mod 3.It gave you the factors 1+x and
2+x.multiplied together gives 2+3x+x^2, but note that 3 is the
same as 0.so the result is 2+x^2. That's what you asked to
factor.> X-Received: (from approve@localhost) by
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.9 primary) id i09NO2k28322;
===
I am trying to
solve PDEs in the following manner: setup the PDEsin Maple
(v.9), generate a C code of the corresponding set of ODEs,mex
them to make a .dll file and use MATLABs ODE45() to solve
thesystem of ODEs. I have tested an example problem
successfully consisting of 3ODEs. Here is the Maple code for
that.//// Start Code /////> restart;>
with(CodeGeneration):Warning, the protected name Matlab has
been redefined and unprotected> with(DEtools,convertsys):>
Lorenz := [ diff(x(t),t) = 1.0*(y(t)-x(t)),> diff(y(t),t) =
1.0*x(t)-y(t)-x(t)*z(t),> diff(z(t),t) = x(t)*y(t)-1.0*z(t)
]:> init := x(0)=1.0, y(0)=1.0, z(0)=1.0; init := x(0) = 1.0,
y(0) = 1.0, z(0) = 1.0> S := convertsys( Lorenz, [init],
[x(t),y(t),z(t)], t, y, yp );S := [[yp[1] = 1.0 y[2] - 1.0
y[1], yp[2] = 1.0 y[1] - y[2] - y[1]y[3], yp[3] = y[1] y[2] -
1.0 y[3]], [y[1] = x(t), y[2] = y(t), y[3] =z(t)], 0, [1.0,
1.0, 1.0]]> yp := array(map(rhs,S[1]));yp := [1.0 y[2] - 1.0
y[1], 1.0 y[1] - y[2] - y[1] y[3], y[1] y[2] -1.0 y[3]]>
example_3ode := codegen[makeproc](yp,
parameters=[yp,t,y]);example_3ode := proc(yp::array(1 .. 3),
t, y) yp[1] := 1.0*y[2] - 1.0*y[1]; yp[2] := 1.0*y[1] - y[2] -
y[1]*y[3];yp[3] := y[1]*y[2] - 1.0*y[3]; return ;end proc;>
C(example_3ode,output=example_3ode.c);//// End Code ////I
could mex the output file example_3ode.c and make it a .dll
fileusing a mexFunction and solve the ODEs using ODE45() of
MATLAB.I have also considered a sample PDE problem, x(r,t). I
converted thePDE into a set of ODEs. But I have not been able
to convert the systemof ODEs as done in the above case. I am
providing the correspondingcode below. Can somebody please
take a look at it and let me know howto go about the
problem.//// Start Code ////> restart;>
read`D:/madhu/FuelCells/PEMFCModeling/ModelingUsingMaple9/pde/
fdpack.mpl`:>
read`D:/madhu/FuelCells/PEMFCModeling/ModelingUsingMaple9/
utils/utils.mpl`:>
read`D:/madhu/FuelCells/PEMFCModeling/ModelingUsingMaple9/
plots/plots.mpl`:> read
`D:/madhu/FuelCells/PEMFCModeling/ModelingUsingMaple9/BESIRK`:
> with(DEtools,convertsys):> PDE1 := diff(x(r,t),t) =
nu*diff(x(r,t),r): PDE1;> IC1 := t=0, x(r,t) = 0.0: IC1; t =
0, x(r, t) = 0.> BC1 := r=0, x(r,t) = 1.0: BC1; r = 0, x(r, t)
= 1.0> BC2 := r=1.0, x(r,t) = 10.0: BC2; r = 1.0, x(r, t) =
10.0> n_x := 11; n_x := 11> rspec := h_r = 1.0/(n_x-1): rspec;
h_r = 0.1000000000> PDE1a
:=convert(PDE1,fddiff,order=[1,0],forward=[1,0],indexletters=[
j,none]):PDE1a; d nu (x[j + 1] - x[j]) -- x[j] =
-------------------- dt h[r] > PDE1b :=
subs(r[j]=(j-1)*h[r],h[r]=h_r,PDE1a): PDE1b; d nu (x[j + 1] -
x[j]) -- x[j] = -------------------- dt h_r > BC1a
:=convert(BC1[2],fddiff,order=[2,0],forward=[2,0],indexletters
=[1,none]):BC1a := subs(h[r]=h_r,BC1a): BC1a; x[1] = 1.0> BC2a
:=convert(BC2[2],fddiff,order=[2,0],forward=[2,0],indexletters=
[n_x,none]):BC2a := subs(h[r]=h_r,BC2a): BC2a; x[11] = 10.0>
params := {nu=0.05}: params; {nu = 0.05}> xeqns :=
[seq(PDE1b,j=2..n_x-1)];> whattype(xeqns); list> S :=
convertsys(xeqns, [], [seq(x[j],j=2..n_x-1)], t, x, xp
):Error, (in DEtools/convertsys) invalid system of
differentialequations//// End Code ////Not sure how do I go
about the above error message.madhu