mm-278  

Subject: Question on SDE by support1.mathforum.org
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by legacy.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.10 $, legacy) id i1ONTGU31649I need help with the
solution to the following SDE:dX = (a + b*X)dt + (c +
d*X)dWwhere a,b,c and d are constant and dW is the wiener
process.I can solve the special cases where a=c=0 or b=d=0.
But i can't solvethe general case where all the parameters are
different from zero.
===
Subject: Re: Question on SDE >I need help
with the solution to the following SDE: >dX = (a + b*X)dt +
(c + d*X)dW >where a,b,c and d are constant and dW is the
wiener process. >I can solve the special cases where a=c=0 or
b=d=0. But i can't solve >the general case where all the
parameters are different from zero. > you want a closed
solution or numerical solution. it is not mu filed, butmaybe
the following resources are of help:from my
annotations:begin{citation}Stochastic Calculus is a very
technical field. You need a good knowledgeof Probability
Measure theory in order to fully understand and appreciateit.
If you do not have a measure theory strong backgound than
myrecommendation is to start with Klebaner Introduction to
StochasticCalculus with Applications. It's the least technical
among all stochasticcalculus books I have seen. A really good
place to start. Another greatintroduction to the topic is
Stochastic Calculus and FinancialApplications by Steele. In my
opinion it's a more demanding book, butit's very nice to read,
because it's written in very informal maner. Ilearn SC from
it, and I am really satisfied. You can also find many
usefulthings in Shreve's lecture notes on Stochastic Calculus
and Finance. Youcan download it for free from
http://www.cs.cmu.edu/~chal/shreve.htmlFinally, the major
textbook in this area is Karatzas, I. and Shreve, S.E.(1991),
Brownian Motion and Stochastic Calculus, Second
Edition,Springer-Verlag, New York. It's much more demanding
than the first two. The URL: http://www.taygeta.com/sdes.html
contains an introdutory tutorial, references plus references
and software for NUMERICAL integration of SDEs as
well.end{citation}hthpeter 
===
Subject: Re: Question on SDE by
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
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legacy.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.10 $, legacy) id i1PLnVw19526Actually, i am looking for a
closed form solution. Is it possible tosolve it analytically
or do i have to use numerical methods? It kinda looks like an
extended Geometric Brownian motion, so ireferences
though.Mariano
===
Subject: Re: Polynomial Roots by
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
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1.10 $, legacy) id i1P2Ifa19441This examines a 7th degree case,
but you can seethe pattern to extrapolate to higher orders.The
exact solution is as yet unfinished, sinceI don't know the
significance of the intersectionof L[1] and L[2], but hope
this much helps.A NONLINEAR SOLUTIONeqn of plane
pi[1]:a[1]x[1]+a[2]x[2]+a[3]x[3]+a[4]x[4]+a[5]x[5]+a[6]x[6]+a[
7]x[7]+a[0]=0N[1]=(a[1],a[2],a[3],a[4],a[5],a[6],a[7])
normalT=(t,t^2,t^3,t^4,t^5,t^6,t^7) space curveN[1]*T + a[0]=0
7th degree polynomial
ora[1]t+a[2]t^2+a[3]t^3+a[4]t^4+a[5]t^5+a[6]t^6+a[7]t^7+a[0]=
0Due to symmetry between components of the space curve, the
result iseqn of plane p[2]: ( a[3]t^2)x[1]+(
-a[3]t+a[4]t^2)x[2]+(a[3]-a[4]t+a[5]t^2)x[3]+(a[4]-a[5]t+a[6]t
^2)x[4]+(a[5]-a[6]t+a[7]t^2)x[5]+(a[6]-a[7]t )x[6]+(a[7]
)x[7]+ a[0]+a[1]t+a[2]t^2 = 0The normal to pi[2] is,N[2]= (
a[3]t^2, -a[3]t+a[4]t^2, a[3]-a[4]t+a[5]t^2,
a[4]-a[5]t+a[6]t^2, a[5]-a[6]t+a[7]t^2, a[6]-a[7]t , a[7]
)Solve N[2]*N=-a[0] for t using the quadradic formula:
(a[1]a[3]+a[2]a[4]+a[3]a[5]+a[4]a[6]+a[5]a[7])t^2-(a[2]a[3]+a[
3]a[4]+a[4]a[5]+a[5]a[6]+a[6]a[7])t+
a[3]^2+a[4]^2+a[5]^2+a[6]^2+a[7]^2+a[0] = 0Sub this t in N[2]
for the intersection of N[2] with the plane pi[1]. Call this
point P. Let Q=(-a[0]/|N|^2)N. pi[1] intersects pi[2] along
the line L[1]. The line through P and Q is line L[2]. T must
lie on L[1], ofwhich one possibility is the intersection of
L[1]&L[2]Jon GiffenBelmont Technical College
===
Subject: Rational
Equations by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i1P3nme22064; by
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legacy.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.10 $, legacy) id i1P3iWJ31948I cant solve these can you
help???x+1/3 -1=x-1/23/x=4=5/xa-4/a-1=a+2/a-24/x-3+2x/x
squared-9=1/x+3????? help
===
Subject: Re: Rational Equations1.
subtract x both sides and get -2/3=-1/2 Yuck (Yuck=Italianfor
No solution dude)2. multiply by x all sides and get 3=4x=5
Yuck3 subtract a-4a both sides and get -1=-2/a-2 or a = 3/2 a
solution!4. The last one is a cubic which you can get to
6x^3-5x^2+54x-27=0 thensolve that one> I cant solve these can
you help???> x+1/3 -1=x-1/2> 3/x=4=5/x> a-4/a-1=a+2/a-2>
4/x-3+2x/x squared-9=1/x+3> ????? help
===
Subject: Re: i need
helpThat is a fundamental identityArcsin(x)+Arccos(x)=Pi/2if
q=Arcsin(x) then Sin(q)=x( Cos(q)=(1-x^2)^(1/2) =
sin(Arccos(x)) )Then you can use the trig functions in terms
of one another to arrive at
theidentity...................................................
..............................................................
...............> how can i prove that> sin inverse + cos
inverse = by/2
===
Subject: Excel Solver Doesn't Find any Answer,
Even Though a Correct Answer is Available?I'm using the Excel
solver on a diet nutrition matter. I've found a case in which
a correct answer exists, and if I manually enter this answer,
the Solver recognizes it as valid -- that is, it says it has
found the answer, even though I initialized all the variables
to the values required for the correct answer. However, if I
initialize all the variables to 0, Solver cannot find the same
correct answer, and says it was unable to find any correct
answer. info.-Vik
===
Subject: Re: Excel Solver Doesn't Find any
Answer, Even Though a Correct Answer is Available?> I'm using
the Excel solver on a diet nutrition matter. I've found a
case> in which a correct answer exists, and if I manually
enter this answer,> the Solver recognizes it as valid -- that
is, it says it has found the> answer, even though I
initialized all the variables to the values> required for the
correct answer. However, if I initialize all the> variables to
0, Solver cannot find the same correct answer, and says it> was
unable to find any correct answer.> info.In the Excel go to
Tools-Options-Calculations. The calculation TAB hasiterations
setting. Choose appropriate number of iterations and also
thevalue for maximum change. May need some
trials.HTH************************Mohan PawarMIO Instruments
LLC> -Vik
===
Subject: Re: Excel Solver Doesn't Find any Answer,
Even Though a Correct Answer is Available?> I'm using the
Excel solver on a diet nutrition matter. I've found a case >
in which a correct answer exists, and if I manually enter this
answer, > the Solver recognizes it as valid -- that is, it says
it has found the > answer, even though I initialized all the
variables to the values > required for the correct answer.
However, if I initialize all the > variables to 0, Solver
cannot find the same correct answer, and says it > was unable
to find any correct answer. > info.Nonlinear solvers often
depend on a reasonable starting point forreaching a solution.
Try starting with a meaningful first guess(preferably close to
the solution) instead of just all zeros.Arnold Neumaier
===
Subject:
Re: Excel Solver Doesn't Find any Answer, Even Though a Correct
Answer is Available?> Nonlinear solvers often depend on a
reasonable starting point for> reaching a solution. Try
starting with a meaningful first guess> (preferably close to
the solution) instead of just all zeros.each food item already
in the spreadsheet, I just copied them to the initial starting
points for each food item. It worked very well.-Vik
===
Subject:
Finding the combinations by support1.mathforum.org
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i1PCZrV31635; by support1.mathforum.org (8.11.6/8.11.6/The
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by legacy.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.10 $, legacy) id i1PCCR312623Hi all,Suppose If I
have to share 5 seats among 7 people in a 7-day workingweek,
making sure each individual gets a 2 days break (need not be
onconsecutive days), how do I find an optimal combination
among theindividuals??Also, the following factors have to be
taken in to account 1) Resources associated with each seat. (A
Computer, Drawer & aphone) 2) Individuals are to be seated
close to their original place, asmuch as possible. 3)
Individuals who belong to the same group (say, same project)
areto be seated closer to each other (optional) 4) And, some
more factors which can be introduced in to the system ata
later stage :)Kannan Ramanathan
===
Subject: Re: Finding the
combinationsOptimization problemprobably by hand, as the four
factors are not specific enough to constrainthe problem for a
solution, and it seems overconstrained, may have to dropsome
of the factors or enlarge the number of seats/people to get a
solution. 1) introduces 3 variables, or 8 possibilities per
seat (some are nullcases, probably) 2) introduces two
dimensional problem, and ownership of a seat by anindividual
3) introduces subgroupings based on another variable projects
4) more factors..........A weighted or ranked sorting can
work, where the 5 days on, 2 days off isfirst (daily
assignment list)then who can work at what stationsthen who is
on what projectthen.......> Hi all,> Suppose If I have to
share 5 seats among 7 people in a 7-day working> week, making
sure each individual gets a 2 days break (need not be on>
consecutive days), how do I find an optimal combination among
the> individuals??> Also, the following factors have to be
taken in to account> 1) Resources associated with each seat.
(A Computer, Drawer & a> phone)> 2) Individuals are to be
seated close to their original place, as> much as possible.>
3) Individuals who belong to the same group (say, same
project) are> to be seated closer to each other (optional)> 4)
And, some more factors which can be introduced in to the system
at> a later stage :)> Kannan Ramanathan
===
Subject: calculation
nodal stress by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i1PCZn431547; by
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legacy.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.10 $, legacy) id i1P8wGi30181dear,pls, can you tell how the
nodal stresses can be calculated afterfinding element stresses
in FE
===
Subject: Kalman filtering by support1.mathforum.org
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i1PDCjk02365; by support1.mathforum.org (8.11.6/8.11.6/The
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by legacy.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.10 $, legacy) id i1PD7V817459questions relating
to some basis of modeling and KF itself, using asimple 2 wheel
robot. I am pretty weak in areas of modeling mathequations and
stuff, so pls forgive me for my weak basis.I am currently
computing my location (x, y) and orientation (teta) bydoing
some geometrical calculations according to the number
ofrevolutions my wheel turn. I now wish to use the kalman
filter toimprove my localisation.1) Should i apply KF on the
wheel encoder values or the computed data(x, y, teta)? What
difference does it make?2) I have read that KF is only useful
for linear systems while the EKFis used for non linear
systems, what difference are the 2? 3) Can someone guide me to
resources where as a beginner i can learnmore about this
modelling of math equation for my scenario? 
===
Subject: Re:
Jacobi polynomial derivative>>
((n(alpha+beta-(2n+alpha+beta)x)Pn(x)+2(n+alpha)(n+beta)Pn-1(x
))>>
Pn'(x)=-------------------------------------------------------
-------->> (2n+alpha+beta)(1-x^2)> Look in Abramowitz &
Stegun. Derivative formulas for all standard> orthogonal
polynomials are given.Ok, I found it - thank you very
much!.s.s.
===
Subject: Re: Jacobi polynomial derivativeYes, page
783. But the question is, I guess, how to verifyor how to
prove?The relation for the derivative can be obtained
fromRodrigues' formula (which may be used as a definitionfor
the Jacobi polynomials; see p. 785 of A&S).You can also use
the sum representation, in powers of (1-x),in terms of the
hypergeometric function (see p. 779 of A&S).Hope this helps.
Nico.=========================================================
===Nico M. Temme, http://homepages.cwi.nl/~nicot/C W I:
Centrum voor Wiskunde en InformaticaKruislaan 413, NL-1098 SJ
Amsterdam Tel +31 20 592 4240P.O. Box 94079, NL-1090 GB
Amsterdam Fax +31 20 592
4199==========================================================
==> 
===
Subject: Re: Jacobi polynomial derivative>>
((n(alpha+beta-(2n+alpha+beta)x)Pn(x)+2(n+alpha)(n+beta)Pn-1(x
))>>
Pn'(x)=-------------------------------------------------------
-------->> (2n+alpha+beta)(1-x^2)> Look in Abramowitz &
Stegun. Derivative formulas for all standard> orthogonal
polynomials are given.> Ok, I found it - thank you very much!>
.s.s.
===
Subject: I need help by support1.mathforum.org
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i1PLqju20753; by support1.mathforum.org (8.11.6/8.11.6/The
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by legacy.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.10 $, legacy) id i1PLl3W19220with the following
stochastic differential equation:dX = (a + b*X)dt +
(c+d*X)dWwhere a,b,c and d are constant parameters and dW is a
Wiener ProcessI can solve it for the cases a=c=0 (a geometric
brownian motion) orb=d=0 (the linear case) but i have trouble
when i want to solve thegeneral case where all the parameters
are different from 0.