The tag has no usage guidance.

learn more… | top users | synonyms

0
votes
4answers
19 views

How to find the root value of a fibonacci sequence from two consecutive values?

I'm stuck on a question that was given to me on a list of problems. It's to do with the fibonacci sequence such that if I have the a=f(n) and b=f(n+1) of a sequence that is a fibonacci sequence, find ...
0
votes
0answers
17 views

Graph theory decision tree

I have a graph G in $\R^4. |V(G)| = 15, vertices are 15 points in R^4. I am trying to build the largest graph possible without significantly changing it's independence number. I have a set of ...
0
votes
0answers
39 views

graph theory regions

new here and I tried searching (here and generally) but my knowledge of graph theory is scant, so not sure what to search. I have a simple, planar, non-directional graph that represents a plan of a ...
0
votes
0answers
18 views

Complex conjugation of Fourier transform in frequency domain

If I have some function (which is an array in Python or Matlab) $F(\nu)$ and want to derive $F^*(-\nu)$, I can do an inverse Fourier transform on $F(\nu)$ to get $f(t)$, then complex conjugation on $...
0
votes
0answers
9 views

What should be expected values of weights in statistics (specifically a set of biweight weightings)

I am working on a project that involves taking the biweight sample variance of a velocity dataset. This is defined as $\sigma_{BI}^2 = N\dfrac{\sum_{|u_i|<1}(1-u_i^2)^4(v_i-\bar{v})}{D(D-1)}$ ...
1
vote
2answers
46 views

Legendre Polynomial coefficients

Can you please write out explicitly the formula for the coefficients? From Wikipedia, \begin{aligned} P_{n}(x)&={\frac {1}{2^{n}}}\sum _{k=0}^{n}{n \choose k}^{2}(x-1)^{n-k}(x+1)^{k}\\&=\sum ...
0
votes
5answers
67 views

How to solve quadratic equation in 4 variables?

I am trying to solve the equation $a^2 + b^2 + c^2 + d^2 = \alpha$ where alpha is a constant and $a, b, c$, and $d$ are the $4$ variables. I need to find some integer values of $a, b, c$ and $d$ which ...
0
votes
0answers
27 views

Orthogonality of spherical Bessel functions

Please consider the following toy function $$ k_{i}\int^{\infty}_{0}j_{l}(k_{i}*x)*j_{l}(k*x)dx $$ where $j_{l}$ are spherical Bessel functions (sbf) and $k_{i}$ and $k$ are positive constants. It ...
1
vote
2answers
47 views

How to check if two sets of vectors span the same space in matlab/python?

In MATLAB/Python, is there a way to compare the subspaces span by two different sets of vectors and check if they are the same?
0
votes
1answer
50 views

Generalized Hermite Function as eigenfunction of a differential operator

I'm going through this paper. The article defines function function $\phi_n^\mu(x)$ that is orthonormal on $L^2$ with measure $dm = dx$: \begin{equation} \phi^\mu_n =\left(\frac{\gamma_\mu(n)}{\...
2
votes
0answers
28 views

Tensor Eigenstates

I have the following equation: $$f_i^´(t+1)=\sum_{jk}R_{i|jk}\tilde{f_j}(t)\tilde{f_k}(t)$$ It is about evolution of a population. I use this equation in my python program in the following way: <...
0
votes
1answer
56 views

What is the name of this formula??

Let formula_a = lambda array: sum(array) / len(array). We may rename this formula to be average or ...
0
votes
0answers
15 views

How to change position of the axes values of a Sage plot.

I am plotting 2D functions on Sage, and I would like to move the values displayed along the $y$ axis (the ticks) from the left of the axis to the rigth, because they bother me there. I had a look and ...
1
vote
0answers
57 views

Finite field and its element with symbols [Sage / Python / …]

I have a finite field $T=GF(2^3)$, normal basis $(a, a^2, a^4)$ and polynomial $f$ from field $T$, which contains unknown variables / symbols. Is it possible to get vector with coordinates of f in ...
0
votes
0answers
22 views

Computationally check for roots/positiveness of a big polynomial in a given interval

For a proof, I need to check that given a little interval $(0, 0.28)$ some concrete polynomials $\in \mathbb{Q}[w]$ (polynomials in one variable ranging over the real numbers, with degrees around 50) ...
0
votes
0answers
28 views

Discretization of nonlinear system for using extend Kalman filter in python

I have a continuous nonlinear system which includes three differential equations: $\dot{x}=f(x, u)+\omega_k$ Now I wanna use numerical method to make discretization of it. Then I can use it in a ...
1
vote
0answers
24 views

Finding equilibrium points of a system of nonlinear differential equations

I am currently working on a spatially explicit ODE model with dispersion to study the population dynamics of mosquitoes. I wish to compute the equilibrium values of the populations as functions of the ...
1
vote
1answer
30 views

How to draw cubic plane curve?

In Python, using MatPlotLib, given [vector] parameters $a$ and $b$ and [scalar] parameter $c$, I want to draw a general cubic plane curve in 2-dimensional space (regular plane with $x$ and $y$ axes): $...
0
votes
1answer
65 views

python code for parallel vectors

Wrote some Python code to verify if my Vectors are parallel and/or orthogonal. Parallel seems to be alright, orthogonal however misses out in one case. I thought that if the dotproduct of two vectors =...