## Maximum value of a function...

Hi Users!

Hope everyone is fine here. I want to find the values of M and L for any functions f(x,y) and y(x) such that

abs(diff(f, y))       for all a ≤ x ≤ b, -∞ < y < ∞ and

abs(diff(y, x, x, x))   for all a ≤ x ≤ b, -∞ < y < ∞

For example for

f:=y-x^(2)+1; 0 ≤ x ≤ 2, -∞ < y < ∞ and

y:=(x+1)^2-.5*exp(x); 0 ≤ x ≤ 2, -∞ < y < ∞

the values of L = 1 and M = 0.5exp(2)

## I have a set of boundary conditions that i want t...

`# I solved the differential equation using a fourier series decomposting method. I found with the help of "Dsolve" the different expressions of the fourier constants and now I will apply the boundary conditions to find the expressions of its constants.`

#this my boundary conditions

#this my system of equations

## Cannot find integration...

Cannot find integration proplem_in_maple.mw

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## Is there a way to solve numerically a system of in...

Hello everybody,

While i was trying to work on a physical math problem, a system of 4 integral equations is obtained. The right hand sides of these equations are known functions of r. The left hand sides contain double integrals with respect to lambda and t. i believe that an analytical determination of the 4 unknown functions f_1(t), f_2(t), f_3(t), and f_4(t) is far from being trivial, thus recourse to a numerical technique is necessary and indispensable.

i tried to express the unknown functions as series expansions in t and solve the resulting linear system of equations for the expansion coefficients, but unfortunately the coefficients are very large and the solution is strongly dependent on the number of coefficients. i was wondering whether someone here has some experience with such integral problems and is willing to assist and help. Any hint is highly appreciated.

i attach a Maple script including the equations.

Thank you,

>>>>>> Question.mw

## how do i make ( isentropic-process) ?...

what is the wrong in this operations for isentropic process ( isentropic-process)

Restart: with(RealDomain) : interface(dispalyprecision=4) : ; Isentropical := proc(N,v) local K,PTR,KM1,KP1,GO, M,MS,C,PPT,TTT,RRT,AAS,eq,o ; K : = G() : KM1 : = k - 1 : KP1 : = K + 1 : GO := 1 : If N=1 then M := v Elif N=2 then PPT := v : M := sqrt ( 2 * (PPT^(-KM/K) -1 ) : Elif N=3 then MS := v : M := sqrt ( 1 / (KP1/ (2*MS^2) –KM1/2 ) : Elif N=4 then C := v : M := sqrt ( 2 / (KM1* (1 /(C^2) -1 )) ) : Elif N=5 then TTT := v : M := sqrt ( 2 * (1/TTT-1 ) / KM1 : Elif N=6 then RRT := v : M := sqrt ( 2 * (1/RRT^KM1 -1 ) / KM1 : Elif N=7 then AAS := v : eq :=AAS- (2*(1+KM1*M^2/2)/ KP1) ^ (KP1/ (2*KM1)) /M : M := fsolve(eq,M,0..1) : GO :=2 : Elif N=8 then AAS := v : eq :=AAS- (2*(1+KM1*M^2/2)/ KP1) ^ (KP1/ (2*KM1)) /M : M := fsolve(eq,M,1..infinity) : GO :=2 : Fi:fi GO<>2 then ASS := (2 *(1+ KM1*M^2/2/KP1) ^ (KP1/ (2*KM1)) /M fi: PTR := (1+ KM1*M^2/2/KP1) : PPT := PTR^(-K/KM1) : TTT:=PTR^ (-1) : RRT:+PTR^(-1/KM1) : If N <> 3 then MS := sqrt ( KP1 / ( 2 / ( M^2)+KM1) ) If N <> 3 then C := sqrt( 1 / (2 / (KM1*M^2) + 1 ) ) O := evalf([m,1./PPT,MS,C,1./TTT,1./RRT,AAS]) end : irp := proc (N, v) local f; f:=Isentropic1(N,v) : printf(cat(`% 9.4f `\$7, ` \ n`) , f[ii\$ii=1..7]) end : G := ( ) -> 1.4 : For mi form .1 to .5 do irp(1.mi) od : > > > Eq := table( [ (M2) = M2 , (MS2) = (K+1) /2 (2 / ( M2)+ (K-1) ) (C2) = 1 / (2 / (K-1)*M2+1 ) (PP0) = (1+(K-1)*M2/2)^(-K/(K-1) ) (RR0) = (1+(K-1)*M2/2)^(-1/(K-1) ) (TT0) = (1+(K-1)*M2/2)^(-1) (AAS) = (2 *(1 +(K-1)*M2/2 ) / (K+1) )^( (k-1) /(2*(k-1)))/ squt(M2) ]) : if vL=M then M2v := solve ( M2 -Eq[M2 ] , M2 ) : M2v := eval(M2v ,M2 = VR^2 ) : elif vL=MS then M2v := solve( M2 -Eq[MS2 ] , M2 ) : M2v := eval(M2v ,MS2 = VR^2 ) : elif vL=C then M2v := solve( M2 -Eq[C2 ] , M2 ) : M2v := eval(M2v ,C2 = VR^2 ) : elif vL=PP0 then M2v := solve( M2 -Eq[PP0] , M2 ) : M2v := eval(M2v ,PP0 = VR ) : elif vL=RR0 then M2v := solve( M2 -Eq[RR0] , M2 ) : M2v := eval(M2v ,RR0 = VR ) : elif vL=TT0 then M2v := solve( M2 -Eq[TT0] , M2 ) : M2v := eval(M2v ,TT0 = VR ) : elif vL=AASsub then M2v := fsolve( M2 -Eq[AAS] , M2 ) : M2 :=0..1 : elif vL=AASup then M2v := fsolve( M2 -Eq[AAS] , M2 ) : M2 :=1..infinity : fi: Eqsva1 := eva1(Eq, M2 = M2v) : Eqava1 [M] := sqrt(EqsVa1[M2] ) : Eqsva1[MS] := sqrt(EqsVa1[MS2] ) : Eqava1 [C] := sqrt(EqsVa1[C2] ) : 1var := [M, MS, C, PP0, RR0, TT0, AAS] : [seq(1var[i]=EqsVA1[1var[i] ] , I=1…nope(1var))] end: Egs :=[M=0.5, MS=0.53452, C=0.2182, P0P=0.84302, RR0=0.88517, TT0=0.95238, AASsub=1.33985, AASsup=0.95238] : For i from 1 to nops(Egs) do print(I,Isentropic2(Egs[i])) od : (process)

## How to define the smitform of a matrix over finit...

Suppose that A is an nxn matrix over the finite field Z:=GF(2,q) for some q. I wan to get the smitform of A over Z. First I used the package

with(LinearAlgebra[Generic])

and after that I applied the command

S := SmithForm[Z](A)

but the mentioned command made some errors. In fact, I do not how to define commands igcdex, iquo, irem, sign and abs for SmithForm over finite fields.

Thanks for any suggestions

## Cannot evaluate the solution past the initial poin...

Hi. Can anyone help me with this error, it says

Error, (in unknown) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

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 shoot: Step #  1 shoot: Parameter values :  alpha = 3.0125 beta = -2.31 Psi = -0. Error, (in unknown) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up
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## Problem in comparing the coefficient from an exres...

Dear Users!

Hope you would be fine. I want to construct system of equations by comparing the likes powers of x^i*y^j*t^k1*exp(k2*eta) for an expression H1 present in attached file. Please see the fix my problem. I shall be very thankful for your kind help.

Help.mw

## what package I need to add in order to use command...

what package I need to add in order to use commands named "Drawmatrix, Translatemat and Transform" ? I add package named Lamp but it is not working. I have maple 15. Please try to respond as soon as possible because its urgent.

Thank you

## Want to draw of the graph of system of PDEs...

Dear all

Hope everything is fine with everything. I want to draw the graph of the u(x,0.5) and T(x,0.5) for different values of alpha like alpha =0.4,0.6,0.8 while keeping Gr, R and Pr are fixed. Please solve the following problem I shall be vary thankful to you. Thanks in advance

with the following BCs

## Need numerical solution of PDE...

Dears

Hope you would be fine. I want to solve the following PDEs by numerically for v[nf]=alpha[nf]=Ec=mu[nf]=C=1 and Pr=6.2

Eq1 := diff(u(x, t), t) = v[nf]*(diff(u(x, t), x, x));

Eq2 := diff(u(x, t), t) = alpha[nf]*(diff(theta(x, t), x, x))/Pr+Ec*mu[nf]*C*(diff(u(x, t), x))^2;

ICs := u(x, 0) = 0, theta(x, 0);

BCs := u(0, t) = 1, theta(0, t) = 1, u(10, t) = 0, theta(10, t) = 0;

and find the values of (diff(u(0, t), x))/(1-phi)^2.5 for different values of phi. Thanks in advace

With my best regards and sincerely.

School of Mathematical Sciences
Peking University, Beijing, China

## Problem to solve system of linear PDEs with BSc an...

Hello

Hope everything going fine with you. I am facing problem to fine the exact (numerical) solution of the attached system of linear PDEs associated with BSc and ICs. I tried to solve it without BCs and ICs, with BCs and with ICs also all the times I failed. Please solve it either general, with ICs or BCs. You can try to solve it numrically. In attached file H(t) represent the unit step function. I am waiting your positive response.

With my best regards and sincerely.

School of Mathematical Sciences
Peking University, Beijing, China

## Maple 15 and MapleSym 5 installation in Windows 10...

What shall I do to install Maple 15 and MapleSym 5 in a Windos 10 environment.

I find the procedure in Maplesoft site up to Windows 8.

May I follow it for Windows 10.

Thank you for any help. Kind regards

## How to solve 12 nonlinear equations with 12 variab...

Im trying to solve 12 equations with 12 variables but I can't solve. Please help and advise me to solve this problem. Iproject3.mw
project3.mw