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Mathematics : Recent Questions and Answers (Page 49)

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

Matrix Norm With Respect to Another Matrix?

I'm reading through a book on numerical analysis right now and in its treatment of linear iterative method the author takes the norm of a matrix with respect to...

Asked on 12/06/2021

1 answer

Number of partitions of a number

I've been trying to find out how many partitions of a number I can make if I restrict the partition size, The specific problem I am trying to tackle is,...

Asked on 12/06/2021 by 666User666

2 answer

Poisson equation with stochastic source

In a physical set-up, one can consider an electrostatic problem where the charge density at each point in space is a random variable, and try to find the electric potential...

Asked on 12/06/2021

1 answer

Laplace Transformations of $left(frac{cos sqrt t}{sqrt t}right)$ and $left(sin sqrt tright)$

Find the Laplace transforms of the following: 1.$left(dfrac{cos sqrt t}{sqrt t}right)$, 2.$left(sin sqrt tright)$.Well, in the first, I used the cosine series expansion and solved the problem.But...

Asked on 12/06/2021 by Ajit Kumar

1 answer

What is the probablity that the sum of two dice is 4 or 6?

What is the probablity that the sum of two dice is 4 or 6?The explanation I found is as follows:Total number of outcomes $6 times6 = 36$Number...

Asked on 12/06/2021 by tnxy

4 answer

Transient, Positive Recurrent, or Null Recurrent

Given the following sets of transition probabilities, how do I determine whether the irreducible DTMC is transient, positive recurrent or...

Asked on 12/06/2021 by user287133

1 answer

How do I find all functions $F$ with $F(x_1) − F(x_2) le (x_1 − x_2)^2$ for all $x_1, x_2$?

In calculus class we were given this so-called "coffin problem" originally from Moscow State University. Find all real functions $F(x)$, having the property that for any $x_1$ and...

Asked on 12/06/2021 by Yan Qin

2 answer

Modeling the contraction of HIV between a couple assuming one partner is infected

The question Assume the rate of transmission of HIV is between $frac{1}{100}$ and $frac{1}{1000}$. Taking the chance of transmission to be 1%, find the risk of becoming infected...

Asked on 12/06/2021 by sirrahe73

1 answer

Evaluating S depending upon following condition: Calculate the sum $S=Sigma Sigma Sigma x_{i} x_{j} x_{k},$

Suppose that $x_{1}, x_{2}, ldots, x_{n}(n>2)$ are real numbers such that $x_{i}=x_{n-i+1}$ for $1 leq i leq n .$ Consider the sum $S=Sigma Sigma Sigma x_{i}...

Asked on 12/06/2021

0 answer

Found bounds for a sum of binom coefficients(generalization of Vandermonde's identity)

I am trying to find some upper and lower bounds for the following expression:$$sum_{v=0}^t {{x-v}choose{y}} cdot {xchoose{v}}cdot {z-x choose {t-v}}$$Given that $x-t>y>0,z>x+t,tgeq 1$. Finding...

Asked on 12/06/2021

3 answer

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