lcz

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These are questions asked by lcz

Empty result set on `pdsolve` in Maple2...

Asked: lcz 994 Product: Maple 2019

April 06 2020

1 1

Hello! I'm trying to solve the following:

pde1 := (y+z)*(diff(u(x, y, z), x))+(z+x)*(diff(u(x, y, z), y))+(x+y)*(diff(u(x, y, z), z)) = 0;
{pdsolve(pde1,u(x,y,z))}

Unfortunately, after calling pdsolve , I get an empty result set . Can you help me figure out what's going on? Does it really have no solution?

Whose minimum value is more reliable？...

Asked: lcz 994 Product: Maple 2019

March 24 2020

1 6

I have a problem about extremal function.

The function is shown below with restricted condition of x and a: x>=2 and -1 < a <0.

(x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)

I guess that it's minimum value is greater than 0. In other words, I want prove that (x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)>0

when I use Minimize function,

Optimization:-Minimize((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a),{x>=2, -1<a, a<0})

I 'm not seeing but Error, (in Optimization:-NLPSolve) strict inequalities are not valid constraints. I cannot but add the condition of equality of a : -1<=a, a<=0.

Optimization:-Minimize((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a),{x>=2, -1<=a, a<=0})

A result is returned with a warning:
Warning, no iterations performed as initial point satisfies first-order conditions
[0.000000, [a = -2.225074*10^(-308), x = 2.000000]]

Local or Global ?

When I read recent question post

https://www.mapleprimes.com/questions/229132-Maximize-Function-Does-Not-Work?ref=Feed:MaplePrimes:New%20Questions

I'm worrying that Maple only returns local extremun. So I use the freely maple package DirectSearch. We can get it from https://www.maplesoft.com/applications/view.aspx?SID=101333.

DirectSearch:-GlobalOptima(-((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)),{x>=2, -1<a, a<0},maximize);

Note: I add a minus sign to find maximize value .

It returns: [0.002264, [a = -0.000203, x = 1.019590*10^13], 605]

But I substitute the value of a and x into the function，it returns strange result: 4078.360000 not -0.002264.

I’m confused..

I try to use Mathematica,

NMinimize[{(x - 3/2)^a - (x - 1)^
a + (1 - 2^(a - 1))*((x - 3/2)^a - (x - 1/2)^a) -
x*((x - 3/2)^a + x^a - (x - 1/2)^a - (x - 1)^a),
x >= 2 && a > -1 && a <= 0}, {x, a}]

It retruns {0., {x -> 13.256, a -> 0.}} May be well.

mimimize.mw

How to determine if a graph is Outerpla...

Asked: lcz 994 Product: Maple 2019

March 23 2020

2 3

Any idea is good for me !

According to Wikipedia https://www.wikidata.org/wiki/Q3115604 ,

Outerplanar graph is a graph that can be drawn without crossings in the plane (means it is planar graph) with all vertices on the outer face.

For example

Recently in my project, I need to judge whether a planar graph is a outerplanar graph.

I tried to find some algorithms but failed.

Maple only considers how to test wheather a graph is planar.

like following:

with(GraphTheory):
with(SpecialGraphs)
K4 := CompleteGraph(4)
IsPlanar(K4, 'F')

Why are different solutions of sa...

Asked: lcz 994 Product: Maple 2019

March 13 2020

3 7

Hello everyone!

I want to find all solutions of following equations :

I used Maple 2019:

solutions:=solve([abs(1+1/3*lambda+1/18*lambda^2-1/324*lambda^3+1/1944*lambda^4)-1=0],[lambda]);
evalf(solutions)

The output is:

So we have two solutions. But when I use Matlab 2018,
four solutions are returned.

syms lambda
eqn =abs(1+1/3*lambda+1/18*lambda^2-1/324*lambda^3+1/1944*lambda^4)-1==0;
solx1=solve(eqn, lambda)

%%
solx1 =
root (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 1)
root (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 2)
roots (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 3)
roots (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 4)

solx3=solve(eqn, lambda, 'MaxDegree', 4)
double(solx3)

%%The solution is:
-4.2681 + 0.0000i
0.0000 + 0.0000i
5.1340 -11.2012i
5.1340 + 11.2012i

It is easy to check that first two in Maple and Matlab are same.

Who is right? Does Maple miss complex solutions?

Can we draw curved edges in the graph t...

Asked: lcz 994 Product: Maple 2019

March 02 2020

1 1

Recently I often drew some graphs in Graph Theory by Maple. I tried to use DrawGraph, but I found that evey edge only meets straight line style in this package.

For example:

restart:
with(GraphTheory):
with(SpecialGraphs):
a:=CycleGraph(8):
DrawGraph(a)