0
votes
0answers
37 views

Solution of definite integral of product of bessel function and exponential

I have an integral $I=\int_{\theta} \int_r J_m(k_1r)e^{-j[P_x r \cos(\theta)+P_y r \sin(\theta)]} r dr d\theta$ $0\leq\theta\leq2\pi; r<\infty$ is there any method to solve this?
0
votes
0answers
106 views

Arithmetic progression and average of two prime numbers

Let $A=(a_n : n \in \mathbb{N})$ be the sequence given by: $$ \ a_n = a_1 + (n - 1)d,\quad a_1,\ d,\ n \in \mathbb N,\quad d\gt a_1,\quad \gcd(a_1,\ d)=1. $$ For all terms of $A$ greater than $\ ...
0
votes
0answers
34 views

Prove an inequality involving $Si(x)$ and $Si(2x)$

How Is it possible to prove the following inequality? $$xSi(2x)-2Si(x)*\sin(x)\lt x^2$$ for $x\in\mathbb{R}$ Thanks
0
votes
0answers
20 views

A simple plot of a list in R

This is a very easy question, I guess. But unfortunately I struggle to solve it in an easy way: I have a list in R. I would like to plot the entries of each column vertically and label the x-axis to ...
0
votes
0answers
42 views

UMVUE using complete and sufficient statistic

Let $X_1,X_2,...,X_n$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. I showed that $(\bar X,S^2)$ is jointly sufficient for estimating ($\mu$,$\sigma^2$) where ...
0
votes
0answers
61 views

Differentiable curves that are not smooth

We call a curve admitting a parameterization $t\to z(t)$, $t\in[0,1]$ differentiable if the vector function $z$ is differentiable. We call the curve smooth if it is differentiable and its derivative ...
0
votes
0answers
20 views

How many kinds of simple coordinates are there in a 2D space?

The question comes form an idea to solve a motion-with-potential problem in 1D space by finding a mathematically equivalent uniform-motion problem in 2D space. ...
0
votes
0answers
23 views

Permutation certification. A cryptographic hash function for permutations?

Alice has a secret permutation $\alpha$ (a random permutation of an $n$-set; $n=18$ would be a decent choice for the application I have in mind). She wants to convince Bob that she has $\alpha$, but ...
0
votes
0answers
11 views

Difference between containing point and pass through point?

I do not understand this, What is the difference between the equation of the plane containing the points and the equation of the plane through the point? Is it the same thing or are they different?
0
votes
0answers
25 views

Maximum Likelihood estimators in linear models

Consider two simple linear models. $y_{1j}=\alpha _1+\beta_{1}x_{1j}+\epsilon_{1j}$ and $y_{2j}=\alpha _2+\beta_{2}x_{2j}+\epsilon_{2j}$ , $ j=1,2,...,n>2$ where $ ...
0
votes
0answers
26 views

Splitting a list into two lists, depending on a condition.

So I have this list of n real numbers called A, which is sorted least to greatest. Let B be a list of n real numbers with NormalDistribution[]. IF A+B = Sort[A+B], then we keep it, and if A+B != ...
0
votes
0answers
37 views

Reference Request: Fubini's theorem for non-negative functions

I have never seen this (1st page) formulation of Fubini's theorem in the literature. Does anyone know where I can find it? In every calculus book (e.g. Apostol, Courant, etc.) I looked, the authors ...
0
votes
0answers
41 views

Card Shuffling and Convergence in Probability

There are $4n$ cards, and we denote the set of cards with number $4k,k \in \{1,2,\ldots,n\}$ as $S$. The we shuffle the whole cards randomly, which means that each permutation will happen with the ...
0
votes
0answers
33 views

Can I solve this problem with matrices?

So I have some two dimensional data sets thats I want to analyse. They can be viewed in 2D form as below: $M1$: $$\begin{matrix}00 & 00 & 00 & 00 & 00 & 00 & 00 & 00 ...
0
votes
0answers
30 views

Properties of real matrix in Schur Form

This question is from an old exam qualifier. 1.) Show that any $n \times n$ real matrix $A$, may be written as $A = QRQ^{*}$, where $Q$ is unitary and $R$ is upper triangular. Neither $Q$ nor $R$ ...
0
votes
0answers
21 views

How could you find the probability that the estimator is within 0.03 of the mean?

p = fraction of large population that smokes n = sample size y = # in sample that smoke The maximum likelihood estimate of p is p-hat = y/n Consider the random variable Y and estimator F = Y/n ...
0
votes
0answers
37 views

Finding the largest eigenvalue of a sparse matrix

I would like to find the largest eigenvalue of a sparse matrix by hand- this is part of analyzing a mathematical model for infectious diseases. The nonzero entries are very complicated - hence Maple ...
0
votes
0answers
37 views

On an interesting boundary condition

So I am tackling an interesting boundary condition, where $B(Du)=0$, for $x\in\Omega$, where $B$ is the signed distance function to $\Omega^*$ (where $\Omega,\Omega^*$ are convex domains in $\Bbb ...
0
votes
0answers
61 views

Mathematica Integrate gives back the integrand

i'm trying to Integrate the following function: (q (1 + q) - E^-q Sinh[q])/(-q + Cosh[q] Sinh[q]) - ( 2 q Tanh[q])/(-q + Cosh[q] Sinh[q]) I already solved ...
0
votes
0answers
19 views

Finding the smallest possible set of euler angles, without changing the end-rotation

Euler angles aren't unique, so one rotation can be represented through different combinations of pitch, yaw and roll. In my case I have a set of euler angles and I need to find out if there's a ...
0
votes
0answers
17 views

Question about the formal justification of nondimensionalization

Assume I have the following (very simple) problem: $\frac{\partial f}{\partial \theta} =0 $ and I want to make a change of variables to make it nondimensional. So, I can write: $ F = \frac{f}{f^*}$ ...
0
votes
0answers
10 views

Extension of premeasure to outer measure

I'm stucked in this problem. Show that all outer measure $\mu_*$ can be expresed of the form $$\mu_*(A)=\inf_{A\subset\cup C_i}\sum \tau(C_i)$$ where $\tau$ is a premeasure of a colection of sets ...
0
votes
0answers
74 views

Devise formula for Finding the number of permutations with repetition whose sum APPROACH a target number

Suppose a given set $s = \{2,3,4\}$ and lower limit $= 7$. I need to devise a formula for calculating the number of all possible permutations with repetition satisfying the following conditions: The ...
0
votes
0answers
34 views

AM-GM-HM on expression with parameters?

This question, which I believe is easier to answer, is related to my previous question: Finding a value that makes an expression negative I am persistent - and need some ideas to help me prove ...
0
votes
0answers
24 views

Select machines to minimise latencies between them

I am working in an optimisation problem. I am still trying to model it and solve it. The problem is: There is a number of different types of virtual machines. Each type has different hourly cost ...
0
votes
0answers
14 views

Infimum simple function and stepfunction

If $A_n$ is a simple function and $B_n$ is a Stepfunction, then the infimum ($A_n\wedge B_n$) is a stepfunction. Why is this true?
0
votes
0answers
41 views

A mixtilinear tangency

Let ABC be a triangle with incircle $\gamma$ and circumcircle $\Gamma$. Let $\Omega$ be the circle tangent to rays $AB, AC,$ and to $\Gamma$ externally, and let $A^{\prime}$ be the tangency point of ...
0
votes
0answers
18 views

Methods of showing that a non-trivial solution exists for a functional equation?

I am just looking at a one variable functional equation, I won't put it down here because it is university related, and I keep thinking that 0 is the only possible solution so it got me wondering how ...
0
votes
0answers
26 views

Operator Equation?

A space of polynomials $\{f_n\}$ is given, where $f_n$ is of degree $n$. The operator $T$ in this space, satisfy the relation $$T^2(f_n)+a_nT(f_n)-f_n=0$$ where $a_n$ is a scalar depending on $f_n$. ...
0
votes
0answers
20 views

Total change of a signal overtime

I have some signals whose analytic type I do not know. I can only sample them every 0.1 secs. I want to pick that signal that changes as little as possible. For example, between sin2t and sint I ...
0
votes
0answers
28 views

calculating the position of a given digit in a constant (e.g. $\pi$)

I'm aware that there are a lot BBP type formulas out there which extract the n-th digit of the observed constant. I'm asking for the reverse action, namely, is it possible to find the first ...
0
votes
0answers
13 views

Holonomy group of codimension 1 foliation

This is the Ex2.29(2) in the book Introduction to Foliations and Lie Groupoids by : I. Moerdijk / J. Mrcun Let F be a foliation of codimension 1 with only compact leaves, then the holonomy ...
0
votes
0answers
49 views

What Will be permutation of this question?

Sereja call two arrays A and B with length n almost equal if for every $\,i (1 \le i \le n), CA(A[i]) = CB(B[i])$. $CX[x]$ equal to number of index $j (1 \le j \le n)$ such that $X[j] < x$. For ...
0
votes
0answers
36 views

How to calculate a bezier curve given derivative of endpoints, location of endpoints, and points on the curve?

I know how to calculate a hermite spline, which has known derivatives and locations for each point, and I know how to calculate bezier curves which go through certain points, but I need to be able to ...
0
votes
0answers
74 views

Analytical Models for Hysteresis of Complicated Systems

I’ve been working with a system that exhibits hysteresis and I’ve found that the more common models do not work for me. I am wondering if anyone is aware of other models that might be out there for ...
0
votes
0answers
67 views

Functional Analysis Question

Let $(X,\|\cdot\|_1)$ and $(X,\|\cdot\|_1)$ be Banach spaces. Does it imply that $\|\cdot\|_1-\|\cdot\|_2$ (equivalent)? It is know that if $\|\cdot\|_1-\|\cdot\|_2$ and $(X,\|\cdot\|_1)$, then ...
0
votes
0answers
25 views

zeros of Incomplet Gamma function

for which values of complex variable $z$ let us getting the zeros of incomplet gamma function ($\Gamma(0.5,z)$) ? I would be interest for any replies or any comments
0
votes
0answers
15 views

Must the weight function be nonnegative for the greedy algorithm to be optimal for both a matroid and a greedoid?

Must the weight function be nonnegative for the greedy algorithm to be optimal for both a matroid and a greedoid? For a matroid, the codomain of the weight function is $[0,\infty)$, from Wikipedia ...
0
votes
0answers
35 views

Reference for understanding Frechet and Gateaux derivatives

In multivariable calculus, when we were discussing directional derivatives, we were told that the fact that the directional derivative equals the gradient times the direction vector $( \partial^{\vec ...
0
votes
0answers
18 views

Deriving lower bound for eigenvalues of laplace operator

Let $u$ be a function such that $$ \Delta u + \lambda u = 0 \quad \mbox{ on } \quad D, \quad u = 0 \quad \mbox{ on } \partial D $$ and let $w$ be a function such that $\Delta w + \beta w < 0$ ...
0
votes
0answers
184 views

Distributing cards among players

Moderator Note: This is a current contest question on codechef.com. N players sit around a round table. There are $n \cdot m$ cards with unique numbers of range $1\ldots n\cdot m$. Each player ...
0
votes
0answers
24 views

In an infinite cyclic field of non zero units, characteristic $\neq 2$, can an element $-u \neq u$ be expressed as $u^t$ for some finite integer $t$?

For the sake of a proof using contradiction ( to be used somewhere), Lets assume that an infinite cyclic field $F$ of non zero units exists with characteristic $\neq 2$ . In this infinite cyclic field ...
0
votes
0answers
48 views

set notation for the maximum value in a mathematical equation

I am trying to represent the maximum value in a mathematical equation. Currently, I am representing the maximum value as below. max{leva,b(|a|,|b|)} ...
0
votes
0answers
55 views

Compact-Open topology on C(X).

Let $C(X)$ denote the set of all real-valued continuous functions on a Tychonoff space X. And for a subset $A$ of $X$ and subset $V$ of $\mathbb{R}$, let $[A, V] = \{f \in C(X): f(A) \subseteq V\}$. ...
0
votes
0answers
29 views

Lienard Theorem

I have a problem with asking me to prove that equation $x''-(x')^2-(1-x^2)=0$ has periodic solution by Lienard theorem but, I can think of no change variables to take the form of an equation Lienard. ...
0
votes
0answers
20 views

Time-change of a Hamiltonian diffeomorphism

Let $(X, \omega)$ denote a symplectic manifold and let $\phi : X \to X$ denote a Hamiltonian diffeomorphism, so $\phi = \phi_H^1$ is the time-1 map of the flow $\phi_H^t$ of the vector field $\xi_H$ ...
0
votes
0answers
26 views

Simplification of a power weighted alternating binomial sum

Given positive integers $T$, $n$ and $m$ and real number $p$ with $0< p < 1$, how can I simplify the following binomial sum: $$ \sum_{k=m}^{\lfloor ...
0
votes
0answers
19 views

Why $\dim(K\cap N(I)) +1 \geq \dim(K)$ if the index of the index form equals 1?

Let $c:[0,1]\rightarrow O$ a geodesic, $O$ Riemann manifold and let $\mathcal{W}$ the space of piecewise smoothl normal vector fields $W(t)$ along $c$ mit $W(0)=W(1)=0$. $N(I)$ is the nullspace of ...
0
votes
0answers
41 views

Is there a class of second order homogeneous differential equation with a finite set of discrete eigenvalues?

I not sure how to separate differential equations from having a continuum of eigenvalues versus having discrete eigenvalues, but of the set of differential equations with discrete eigenvalues, is ...
0
votes
0answers
26 views

Seams/net of curved surfaces

Like with the seams of a piece of clothing or inflatable, what would the methodology be to creating a flat net of a curved 3d object? I would like to create a model of a mobius torus, and would like ...

15 30 50 per page