I am currently facing an issue as regards stability analysis and I will be glad if anyone can offer me some suggestions.  My aim is to have a Theorem in my research stating that the Disease free equilibrium is locally asymptotically stable if R0 (Basic reproduction number) < 1 and unstable if R0 > 1. The same applies to the endemic equilibrium.  I am trying to carry out a stability analysis using Linearization. However, due to the nature of my model, not all my eigenvalues are negative. Below is my Jacobian Matrix:

ROW 1                           ROW 2                       ROW 3                         ROW 4

Column 1:=                                                                                                      

Column 2:=                 -psi                                     0                                   M

Column 3:=                                                                                                           

Column 4:=                 0                                0                                0                        +  M +  -

By using the Routhz Hurwitz criterion, I reduced the matrix block from 4 by 4 to 3 by 3 by using column 4 as co-factor, however, after this matrix reduction, I was still unable to get all terms relating to my basic reproduction number for me to compare and see if the conditions in Routh Criterion is satisfied using the condition R0 < 1 holds.

My Basic Reproduction Number is as follows:

Are there any other methods to  carry out local stability analysis? and Can local stability analysis be done using maple?

Thank you in advance

Hi everybody!

I want to make the substitution  Int(x^n u(x),x=-Infinity..Infinity) by m_n (m index n), the subs command doesn't seems to work...

Thank you!

I can calculate real number eigenvector with QR algorithm from rotation matrix

but this real number is just magnitude of complex number

what is the rotation matrix for calculating complex number?

what algorithm do maple use to calculate fraction eigenvector?

are complex decimal and complex fraction eigenvectors are two different algorithm?

Hello everyone!

how to solve system of 5 equations like as in attachment, but much more faster?

I tried to do this on my computer (CPU 8 Core 3,4 GHz, RAM DDR3 2x8 GB, SSD) but after 12 hour my computer doesn't respond.

What I can do if I don't have a supercomputer?

Forum.mw

with(LinearAlgebra):
A := Matrix([[1,2,3],[4,5,6],[7,8,9]]);
v, e := Eigenvectors(A):
evalf(e);
A := Matrix([[1,2,3+0*0.1],[4,5,6+0*0.1],[7,8,9+0*0.1]]);
v, e := Eigenvectors(A):
evalf(e);

Hi!

Hoped everything is fine. I want to integrate the following expression under the different conditions of discriments Delta. 

int(1/(a[3]*(u(eta)^3+d[2]*u(eta)^2+d[1]*u(eta)+d[0])), eta);

when Delta = 0;Delta > 0 and Delta < 0.

where discriments Delta = -27*(2*(d[2])^3/27+d[0]-d[1]*d[2]/3)^2-4*(d[1]-(d[2])^2/3)^3;

I am waiting your positive respone.

@acer @Carl Love @Kitonum @Preben Alsholm

Hello, I have a problem which might be very basic but I can't get over it.

I need to compute Christoffel symbols with the "Christoffel" command of the "Tensor" package. However, I noticed that whenever I give maple a metric with a vanishing diagonal element, I get the following error:

Error, (in DifferentialGeometry:-Tensor:-InverseMetric) expected 1st argument to be a metric tensor. Received: _DG([["tensor", M, [["cov_bas", "cov_bas"], []]], [`...`]])

For example, I tried with a very simple 2D case, giving coordinates (t,x) and a metric ds²=f(x)dtdx+h(x)dx²
for which I can compute by hand Christoffel symbols without any problem. The problem really seems to be about the missing diagonal element since if I add it, everything works fine.

By the way, I also noticed that if I apply the "InverseMetric" command I get exactly the same error, even though the matrix is invertible (except possibly at zeros of the functions f and h).

I will be grateful for any suggestion.

Consider the following expression (omega being the socalled minimal spin connection in the vierbein formalism of general relativity):

with(Physics):
with(Tetrads):
omegaDef := omega[mu,c,d] = 1/2*(
   +e_[~rho,c]*(d_[mu](e_[rho,d]) - d_[rho](e_[mu,d]))
   -e_[~rho,d]*(d_[mu](e_[rho,c]) - d_[rho](e_[mu,c]))
)
-1/2*e_[~a,mu]*e_[~rho,c]*e_[~sigma,d]*(d_[rho](e_[sigma,a]) - d_[sigma](e_[rho,a]));
Define(omegaDef):

The Define command raises "Error, (in Physics:-Define) numeric exception: division by zero" in Schwarschild spacetime (loaded with g_[sc]), but not, say, in Tolman spacetime (loaded with g_[tolman]). Furthermore, if either the first two terms, or the last term, are/is removed in omega, then no error is raised in Schwarzschild spacetime. What is going on?

I need to evaluate a variable inside the function definition in the moment it is defined and not every time it is called. Is there a way around?

a:=3;
f := x-> a*x;
f(t);

a:=4;
f(t);

I want the function "f" to be 3*x even if "a" is modified after the declaration. In Mathematica I am used to the so called immediate assignmet(=) and delayed assignment(:=) for which I cannot find an equivalent command in Maple. 

Any help is appreciated!

Hi

For the data presented below, assuming a linear model yields to observe the great amounts of standard errors.

Is there a way (an appropriate command) to find the best statistical model?

Y := `<,>`(.2, .2, .2, .2, .2, .3, .3, .3, .3, .3, .3, .35, .35, .35, .35, .35, .35);

X := `<,>`(2, 2.2, 2.4, 2.6, 2.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 2, 2.2, 2.4, 2.6, 2.8, 3);

Z := `<,>`(15, 33.7, 62.8, 188, 394, 5.47, 5.82, 6.21, 8.3, 11.5, 24.1, .372, .485, .675, 1.11, 1.27, 1.35);

Statistics:-Fit(add(add(a[k, n-k]*x^k*y^(n-k), k = 0 .. n), n = 0 .. 2), `<|>`(X, Y), Z, [x, y], summarize = embed)

I want the output from a line to be used for the definition of a function, but it doesn't work. What am I missing?

x^2;
f := X -> eval(%, x=X);
f(t);

Thank you, Ale

I want to fetch the trigger time.
I use rhs function.
 

Download RHS_TEST.mw

I want to find all complex numbers such that 
abs(z)*(z-4-I)+2*I = (5-I)*z.
I tried solve(abs(z)*(z-4-I)+2*I = (5-I)*z, z)
and got the answer is z = -1.
This is a question in a test with multiple choice. The key of question is three numbers.

Is my commant wrong? Where is wrong?

If I have an expression which contains an unknown function f(t) e.g.

ex:=1+exp(f(t))*f(t+1)+f(t/2)

how do I replace it with some defined function F(t)?

Do I need to work with ::anything, i.e. something like

subs(f(t::anything)=F(t::anything),ex)

?

However this doesn't work.

Download Rindler_simulation_v2.mw