mm-254
===
Subject: Re: Covering number by support1.mathforum.org
(8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id
i2C1JWx04056;i think you are looking for something like
Ininuga. Go tohttp://www2.arnes.si/~ubolti/ininuga.nina>A
Covering Design c(v,k,t,m,b) is a pair (V,B), where V is a set
of v>elements (called points)>and B is a collection of b
k-subsets of V (called blocks) such that >every m-subset of
V>intersects at least one member of B in at least t points.>It
is required that v >= k >= t and v >= m >= t.>Given some
parameters of a design and some subsets,>how can you determine
fast the number of Covered/Uncoverd blocks>within these
parameters?>I'm looking for an algorithm or pseudocode to
count the number>of blocks that are covered/uncovered, with a
method other than bruteforce.>Some examples of partially
covered designs below:>Example #1,>Parameters: v=12 k=5 t=4
m=6 b=9> 1 3 5 6 12> 1 4 7 9 12> 1 8 9 10 11> 2 3 4 7 8> 2 3 8
9 12> 2 4 5 6 9> 2 7 10 11 12> 3 4 5 10 11> 5 6 7 8 10>The
above design covers 770 blocks of the possible 924.>It leaves
uncovered 154 blocks.>My question again is as of
methods/algorithms to count the number of>covered/uncoverd
blocks as fast as possible.>Example #2,>Parameters: v=18 k=7
t=4 m=7 b=11> 1 2 3 4 9 14 18> 1 2 3 4 11 12 13> 1 2 5 6 7 8
9> 1 2 8 15 16 17 18> 1 7 8 10 11 15 16> 2 10 12 13 14 15 16>
3 4 5 6 7 14 17> 3 4 5 6 8 10 18> 3 4 9 10 15 16 17> 5 6 7 11
12 13 18> 8 9 11 12 13 14 17>Covered blocks=31,692 of the
possible 31,824.>Uncovred blocks=132>Example #3,>Parameters:
v=15 k=6 t=3 m=4 b=14> 1 2 3 4 5 6> 1 2 3 7 10 13> 1 3 6 8 12
13> 1 4 7 8 10 14> 1 5 9 12 13 14> 1 6 7 9 11 13> 2 4 10 11 12
15> 2 5 6 7 12 14> 2 8 9 11 14 15> 3 4 7 9 12 15> 3 5 10 11 14
15> 4 5 7 8 11 13> 4 6 9 13 14 15> 5 6 8 9 10 15>Covered
blocks=1363 of the possible 1365.>Uncovred blocks=2>Your ideas
===
or comments are welcome.Subject: Modelling dynamics of linked
membersI'm looking at a problem of modelling a mechanical
system that can be approximated by a number (say 20) of rigid
members (rods), linked to each other endwise to form a chain.
Imagine that the chain of members is strung between two fixed
points, and that the members are acted on by varying external
forces + gravity + damping.I am (currently) ignoring
rotational effects, so a member is treated as having mass but
no moment of inertia about its axis. In other words, I'm
assuming that the state of the system is defined completely by
the positions and velocities of the junctions. A junction is
like a universal joint, fully flexible in all directions, i.e.
zero (or small) bending stiffness. Members and joints are
considered to be very stiff in tension/compression.What is the
best approach to modelling this system? So far I have been
looking at the static case, and solving for the steady-state
shape with constant external loading. I have adopted the quick
and dirty approach of treating the members like springs, with a
stiffness that I increase as the equilibrium is approached, and
with artificially high damping. This allows me to use the ODE
solvers in Matlab without much sweat.I may want to solve for
the true dynamics, and it seems to me that this could be quite
a hard problem, since in some sense it is very stiff. Is this a
===
well-known problem?GibSubject: Re: Modelling dynamics of linked
members> I'm looking at a problem of modelling a mechanical
system that can be > approximated by a number (say 20) of
rigid members (rods), linked to > each other endwise to form a
chain. Imagine that the chain of members > is strung between
two fixed points, and that the members are acted on by >
varying external forces + gravity + damping.> I am (currently)
ignoring rotational effects, so a member is treated as > having
mass but no moment of inertia about its axis. In other words, >
I'm assuming that the state of the system is defined completely
by the > positions and velocities of the junctions. A junction
is like a > universal joint, fully flexible in all directions,
i.e. zero (or small) > bending stiffness. Members and joints
are considered to be very stiff > in tension/compression.>
What is the best approach to modelling this system? So far I
have been > looking at the static case, and solving for the
steady-state shape with > constant external loading. I have
adopted the quick and dirty approach > of treating the members
like springs, with a stiffness that I increase > as the
equilibrium is approached, and with artificially high damping.
> This allows me to use the ODE solvers in Matlab without much
sweat.> I may want to solve for the true dynamics, and it
seems to me that this > could be quite a hard problem, since
in some sense it is very stiff. Is > this a well-known
problem?> GibGo to http://www3.addall.com/ type mechanism
linkage Formore hits, go to Used Books there. Then visit your
===
university library.Subject: Re: Modelling dynamics of linked
members> Go to http://www3.addall.com/ type mechanism linkage
For> more hits, go to Used Books there. Then visit your
university library.I think what makes the problem I'm
interested in rather different from the problems treated in
robotics and mechanical machinery etc. is that all rotational
degrees of freedom exist at the junctions. Effectively my
linked chain of members is more like a string with attached
weights than a mechanical linkage system. I can't think of a
mechanical system with this character. I'm guessing that it
might have chaotic behaviour.I'm looking for suggestions on
===
appropriate mathematical simulation methods.GibSubject: Re:
Modelling dynamics of linked members> I'm looking at a problem
of modelling a mechanical system that can be > approximated by
a number (say 20) of rigid members (rods), linked to > each
other endwise to form a chain. > I may want to solve for the
true dynamics, and it seems to me that this > could be quite a
hard problem, since in some sense it is very stiff. Is > this a
well-known problem?You'd consult books about robotics, e.g., J.
Angeles, Fundamentals of Robotic Mechanical Systems, Springer,
New York 1997.This is all about your systems..sArnold
===
NeumaierSubject: Beam FEA help...I was wondering if anyone can
help.I am doing a research project and need to do FEA of a
beam.It was suggested to me that FEMLAB would be my best
route, but ata minimum price tag of $1295.00, its a little out
of my league.I need the following criteria met:1) Nonlinear
analyses for large deflections, the software will have
toiteratively compute the deflections, changing the node
locations andstiffness matrix for each time step.2) Ability to
do transient dynamic simulations, where forces change
asfunction of time3) Ability to program forces as a function
of time.4) Use beam or frame elements for 2D analyses. Each
node should have 3degree of freedom (two translations and one
rotation) at each nodeThe most important criteria right now is
4.I was looking at the freeware on this
site:http://www.engr.usask.ca/~macphed/finite/fe_resources/
node12.htmlbut there is a lot to look through.I was hoping,
either someone can point me to a freeware program or let
meknowof some software that is a lot lower priced.If you reply
===
to me directly, remove the 'z' from jfrancoz@diet...Subject:
Re: Beam FEA help...> I was wondering if anyone can help.> I
am doing a research project and need to do FEA of a beam.> It
was suggested to me that FEMLAB would be my best route, but
at> a minimum price tag of $1295.00, its a little out of my
league.> I need the following criteria met:> 1) Nonlinear
analyses for large deflections, the software will have to>
iteratively compute the deflections, changing the node
locations and> stiffness matrix for each time step.> 2)
Ability to do transient dynamic simulations, where forces
change as> function of time> 3) Ability to program forces as a
function of time.> 4) Use beam or frame elements for 2D
analyses. Each node should have 3> degree of freedom (two
translations and one rotation) at each node> The most
important criteria right now is 4.> I was looking at the
freeware on this site:>
http://www.engr.usask.ca/~macphed/finite/fe_resources/node12.
html> but there is a lot to look through.> I was hoping,
either someone can point me to a freeware program or let me>
know> of some software that is a lot lower priced.> If you
reply to me directly, remove the 'z' from
jfrancoz@diet...There is another FEM resources web
site:http://www.engr.usask.ca/%7Emacphed/finite/fe_resources/
fe_resources.htmlthough I suspect many of the links are the
same.In FEM, as in most things in life, there is a time-money
tradeoff. If you dont want to spend money, it will cost you
time.So it depends: how valuable is your time? If you are an
aerospaceengineer at ,say, Lockheed-Martin, your labor cost is
$140 to$200/hr. Ergo if a $1500 black-box package saves you one
week of timeyou are way ahead. If you are an RA or postdoc at a
school, your costis $20-40 /hr so doing your own code could be
cost effective if youare fast with your fingers, and you start
from a grey box tool likeMatlab.In between there is the option
of downloading free low-level publicdomain software. This
often has to be modified and then you have todebug it. The
plus side is that you may gain a better understanding ofthe
===
method by suffering through a debug process.Subject:
.8bs.b9.b2.82274H.81[CapitalThorn].8f[RegisteredTrademark][@w[
CapitalCCedilla].86n.b9BA[CapitalThorn][DownQuestion]s[
CapitalYAcute][CapitalYAcute],
z|[Micro]o.b2{.b3ouO[CapitalIGrave][Hyphen].be|.b3http://
===
www.msi-team.com/wchenSubject: New source of the math!!!I have
come across a source providing good support to
thoseexperiencing difficulties with doing homework in maths
includingarithmetic(http://www.bymath.com/studyguide/ari/form1
.htm),
geometry(http://www.bymath.com/studyguide/geo/pro/pro1/pro1.
htm),
algebra(http://www.bymath.com/studyguide/alg/pro/pro1/pro1.htm
), functionsand graphics
(http://www.bymath.com/studyguide/fun/pro/pro.htm),principles
of
analysis(http://www.bymath.com/studyguide/ana/pro/pro1/pro1.
htm),all this is also supported by a good deal of examples
===
andillustrations.Subject: differencing two audio
samplesHi:I've gave considerable thought into this but my math
sucks.. I havetwo sound samples, each 10-20 seconds of sound at
something like 44Khz- I need to subtract one from another, so I
end up with a prototypeand a difference, where the difference
should be very small, andoverall uses less storage. Supposed
both samples are extremelysimilar to our human ears, and the
beat of the samples are at quitegood matches. This problem is
very similar to the joint-stereocompression used by
mp3/ogg/etc, if any different at all, but I'mstuck at
differencing, here are the things I've tried:1. I could do
subtraction in time domain, but the result is more likea union
of the two samples rather then difference - the problem is
thephase is all different even though they sounded the same to
our ear. The difference computed this way is useless to me
because they are toobig.2. I tried it in DCT domain - the
problem is when I subtract thecoefficients of the two time
series in this domain, the resultdifference is still too large
- afterall, I'm not dealing with'stereo' difference, but rather
similarity between samples that couldbe off sync at multiple
places with different - say - backgroundaccompanyment.Are
there existing good algorithms for dealing with this?
===
E.g.combine time-warping with DCT?BillSubject: Re:
differencing two audio samplesTry comp.dsp .> Hi:> I've gave
considerable thought into this but my math sucks.. I have> two
sound samples, each 10-20 seconds of sound at something like
44Khz> - I need to subtract one from another, so I end up with
a prototype> and a difference, where the difference should be
very small, and> overall uses less storage. Supposed both
samples are extremely> similar to our human ears, and the beat
of the samples are at quite> good matches. This problem is very
similar to the joint-stereo> compression used by mp3/ogg/etc,
if any different at all, but I'm> stuck at differencing, here
are the things I've tried:> 1. I could do subtraction in time
domain, but the result is more like> a union of the two
samples rather then difference - the problem is the> phase is
all different even though they sounded the same to our ear. >
The difference computed this way is useless to me because they
are too> big.> 2. I tried it in DCT domain - the problem is
when I subtract the> coefficients of the two time series in
this domain, the result> difference is still too large -
afterall, I'm not dealing with> 'stereo' difference, but
rather similarity between samples that could> be off sync at
multiple places with different - say - background>
accompanyment.> Are there existing good algorithms for dealing
===
with this? E.g.> combine time-warping with DCT?> BillSubject:
Re: Is there any book on system of ordinary differential
equations? > Can somebody introduce me some good books on how
to solve system of >ordinary differential equations by finite
difference? I only have >Numerical Analysis by Richard L.
Burden and J. Douglas Faires. But >this book doesn't tell much
about system of ODEs. >Peng1) the book: Hairer-Norsett-Wanner
Solving ordinary differential equations I Hairer-Wanner
Solving ordinary differential equations II (stiff systems) has
a lot of inforamtion, well written, even with software but may
be a bit advanced2) Eriksson-Estep-Hansbo-Johnson:
computational differential equations studentlitteratur Lund,
ISBN 91-44-49311-8 intended for beginners, used succesfully in
student courses, contains the essentials3) Asher & Petzold:
computer methods for ordinary differential equations and
===
similar to 2)hthpeterSubject: Re: eigenvalues of large,
symmetric, matrces with many zeroes. >I need to compute the
eigenvalues of a symmetric, >real, nXn matrix A where: >1.
each row of A is a vector of zeroes with >at most 4 ones >2. n
is very large, of order 10^5 or 10^6. >Any suggestions are
greatly appreciated. >Federico Echenique I assume you want
only some ... (the largest , the smallest, some in
someinterval .... , otherwise you must proceed completely
different
...)http://www.ime.unicamp.br/~chico/arpack++http://
===
www.caam.rice.edu/software/ARPACKhthpeterSubject: Re:
Hexagonal and pentagonal finite element> You are right:
misprint, it should say face 235.> I beleieve you are using
wrong natural coordinates and wrong> shape functions for the
pyramid.OK. I can see the paper error: Wrong natural
coordinates.The element I call Pyra5 has been used for over 25
years in 3D FEMsolid codes, initially in the nuclear reactor
codes of the mid 1970s. It is in Ansys and (I believe) Abaqus.
I use it occasionally (as atransition element) and works
OK.Generally too stiff for stress analysis (Pyra13 and Pyra14
are betterbutmore expensive) but fine in acoustics, thermal
and hydro. Passes thepatch test when mixed with Hexa8 and
Tetr4, which is important sincethat's the whole purpose of
transition elements. One has to be a bitcareful with gradient
recovery at the apex , because of the 0/0ratios. Extrapolating
from Gauss points does the trick.So when I saw a post claiming
this element does not exist, I lookedat the calendar, but it
===
is not April 1 yet.Subject: Re: Hexagonal and pentagonal
finite element> Is this the paper you are talking about ?>
http://www.cs.brown.edu/publications/techreports/reports/CS-00
-03.html> As you seems to be very aware of those kind of
problems, did you ever > heard of a method for
hexagonal/pentagonal shape functions ? I only find > x^2y^2
shape function (and it is only in
2D)p://www.cs.brown.edu/publications/techreports/reports/CS-00
-03.html> As you seems to be very aware of those kind of
problems, did you ever > heard of a method for
hexagonal/pentagonal shape functions ? I only find > x^2y^2
shape function (and it is only in 2D)Let me try to answer this
one. Conforming shape functions forpolyhedra elements of
arbitrary shape can be constructed in severalways. One method
I am aware of, although I have not used it myself,is the
extended FEM of Belytschko and Moran. This was callednatural
FEM in earlier publications. Extended means that theelement
can be enriched with discontinuities on arbitrary planes
forproblems like cracks. Some references: IJNME, v48,
pp1475ff, 2000and IJNME, v 43, pp839ff, 1998.My friend and
colleague Sergio Idelhsohn has used a variation of thatidea
for Lagrangian hydrodynamic simulations, in which a new 3D
meshis constructed on the fly at each timestep using Voronoi
methods. Such mesh typically consists of a high proportion of
tetrahedra, say90%, but the rest can be polyhedra of arbitrary
number of faces:5, 6, .. etc . This happens because his
generator tries to avoidslivers when there are fragmentation,
spills or recombinations. There was a recent publication of
===
this method in EC, but I dont havethe reference handy.Subject:
Re: R_E_A_D T_H_I_SIn sci.math.num-analysis,
susan.thornburn@stees.nhs.uk<susan.thornburn@stees.nhs.uk<
12030414.3534@stees.nhs.uk>:> Could someone please send me
some info about the thread above this one.> Any pictures would
be helpful too.> Susan.thornburn@stees.nhs.ukThe thread above
this one is highly meaningless, since Usenet isan inherently
dynamic medium. Also, it depends on how yournewsreader
presents information; most modern newsreaders sortthe subjects
alphabetically (which means the previous thread, asof today on
my newsreader, has to do with Runge-Kutta). However,many also
take threading into account; subject changes may
notnecessarily factor if they're not a root. (This post [a
reply],for instance, is branching off your post, with your
post as root.)As for pictures -- it is possible to send
pictures but it'sdiscouraged in most newsgroups (there are
however Usenetnewsgroups dedicated to pictures -- the most
well-knownexample arguably being
alt.binaries.pictures.erotica, butalt.binaries.pictures has
other stuff too). In thisnewsgroup the pictures I would hope
to see are graphplots,which might be better done by simply
sending lists of numbersinto a program such as gnuplot, or a
spreadsheet such asExcel, Gnumeric, or OpenOffice Calc.For
example, the list of x,y coordinates-10 100-8 64-6 36-4 16-2
40 02 44 166 368 6410 100is an approximation of the parabola y
= x^2, and should be easilyplottable.It should also be easier
to feed to various statistical analysis packages.-- #191,
===
ewill3@earthlink.netIt's still legal to go .sigless.Subject:
Re: constrained brownian motion> You are missing a lot,
including your specification.> When x reaches a boundary, just
changing the sign of> s will not keep it from exceeding the
boundary, so I> do not know exactly what is your model. Also,
simulation> must be done much more carefully than usual; I had
a> somewhat different problem 30 years ago.>ok, i was not clear
enough to describe what i am doing. I first only changed>the
sign and clamped the X value to the boundary. Then i computed
the>missing random walk, i.e, knowing that the collision
occurs between t_i>rather at x=0.6-eps, eps being here the
difference between the value>computed with s=1 and the
boundary.This is very unclear. Also, when it comes to
crossings,simulation of a brownian motion at anything other
thanan ultrafine set of points is not adequate; this is
thesimulation problem I handled for maxima and minima.One
could either use a process which is constrained tokeep away
from the boundary; this would be locally aBessel process of
order 3. Or one could continuallyreflect the process (not the
trend) until it leaves theboundary. This reflection procedure
will still have anuncountable number of collisions. Either
method mightwell be treatable, the second probably easier. The
behavior of a brownian motion with constant drift between two
points, given the values at the points, does not depend on the
drift.It is still not clear what your problem 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)494-0558Subject: Fourier transform of exp(-at+bt^2)
functionThe Fourier transform of a function exp(-at) is
a/(a^2+(2*PI*f)^2)and the Fourier transform of a function
exp(-bt^2) is p*exp(-qf^2) where pand q are known fucntions of
b.Now, what is the Fourier transform of a function
exp(-at-bt^2)?Can it be represented by an analytical
expression?Can it be approxamated by c1/(a^2+(2*PI*f)^2)
===
+c2*exp(-q1*f^2)?Haifang LiSubject: Re: Fourier transform of
exp(-at+bt^2) function> The Fourier transform of a function
exp(-at) is a/(a^2+(2*PI*f)^2)> and the Fourier transform of a
function exp(-bt^2) is p*exp(-qf^2) wherep> and q are known
fucntions of b.> Now, what is the Fourier transform of a
function exp(-at-bt^2)?Do your own homework.> Can it be
represented by an analytical expression?Yes> Can it be
approxamated by c1/(a^2+(2*PI*f)^2) +c2*exp(-q1*f^2)?No.Hint:
===
complete the square.You're welcome,Gerry T.Subject: Re: all
the roots of a nonlinear equationDistribution: inet >(sorry
for posting to sci.math!) > I realize this is probably a dumb
question but I've looked at numerical >analysis books and
racked my brain but I must be missing something obvious. >I
have equations which are sums of sines and cosines an example
being: >2 Cos[x] - Cos[2 x] - Sin[x] + 3 Sin[2 x] - Sin[3 x] =
0 >I need to find all the roots of this equation in the range
-pi to pi. >The algorithms I've looked at only give me one
root and if based on a >bisection technique dont always give
an answer in the range I mentioned >above. >I tried using
NSolve in mathematica for this above equation and it does'nt
>return any roots (there are 4 when looking at the plot). >I
am interested in an algorithm that I could implement in C /
Fortran for >later use that would give me all the roots of the
above types of functions >automatically. >Is this possible? Or
have I missed something very obvious? as you later detected,
mathematica can do that (for this simple system).there are
harder cases, but as long asthe dimension of the system
doesn't becomelarge (in this context maybe 10 to 20...)
thenhttp://www.netlib.org/toms/681 (INTBIS) does the
===
job.hthpeterSubject: Re: Linear (Nonlinear) Curve Fitting with
Constraints >Hello to all, >I have a set of data points that I
wish to fit to a model of the >following form under two
situations. >y(x)=Summation_Over_i ( Ai / (1 + 10^(x-Bi) ) >In
situation 1 the Bi parameters are known. Thus, I will be only
>fitting for the Ai. >In situation 2 both Ai and Bi must be
fitted for. >In both cases there is the additional constraint:
>Summation_Over_i (Ai) = 1 >I know that in the first case I
need a general linear least square >curve fitting program with
constraints and a non linear one also with >constraints in the
second case. >Is there any specific FORTRAN code available on
the net that will >Zacenlsip does that job and also nlscon
(since you provide only an equation as constraint). are there
no constraints on Bi ???also dqed is a choice (which uses the
partially separable structure of theproblem) but this might
get trouble with bad fits (since it employs nolinesearch/trust
region test) because of the simplicity of that constraint you
could also eliminate formally, then express the remaining Ai
as functions of the Bi via linear least squares and so reduce
the problem to an unconstrained one with respect to the Bi and
feed this into elsunc.you find these
here:http://plato.la.asu.edu/topics/problems/
===
nlolsq.htmlhthpeterSubject: How to do feedback analysis on
signals by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i2D0Fj820225;How to do
feedback analysis on signals