Math Questions & Answers

Meaning of the inverse of a differential operator
Meaning of the inverse of a differential operator Consider the Poisson's equation...

probability of the output of a truly random function
probability of the output of a truly random function Suppose $ f:\{0,1\}^n \rightarrow \{0,1\}^l $ is a function sampled...

Write regular expresiond and find finite automata
Write regular expresiond and find finite automata I am learning about finite automata and regular expressions, but I...

Recurrence relation for the integral, $I_n=\int (a^2x^2)^n dx$ [closed]
Recurrence relation for the integral, $I_n=\int (a^2x^2)^n dx$ [closed] Express (by parts) recurrent relation of the...

Preference relation
Preference relation Let $X= \{(a,b)a,b\in \mathbb R\}$. Suppose that we have a weak preference relation $R$ (its strict...

Prove that $\displaystyle \prod_{j=1}^{2n}\left(j^j(2n+j)^{j1}\right)$ is a perfect square
Prove that $\displaystyle \prod_{j=1}^{2n}\left(j^j(2n+j)^{j1}\right)$ is a perfect square For any positive integer...

Affinities and Riemann Zeta function
Affinities and Riemann Zeta function RH states that all the non trivial zeroes of the Riemann Zeta function lie on a...

Looking for Computational Topology procedures
Looking for Computational Topology procedures I looking for the best computer procedures to compute things related to...

Similar to PIE but works quite exact in this case, why?
Similar to PIE but works quite exact in this case, why? Take a number. $n=100,000$ suppose. To get the count of numbers...

$k$ litres of Milk delivery with minimum cost
$k$ litres of Milk delivery with minimum cost Assume that you are the CEO of a milk delivery company and want to deliver...

Angle between two straight lines
Angle between two straight lines Two straight lines are given: $$ \left( \begin{array}{c} 1\\ 1\\ 4 \end{array} \right)...

Calculate arc length. How to know the limits of integration?
Calculate arc length. How to know the limits of integration? The task: $$x(t) = \frac{\cos(3t)}{t^3}; \...

Find minimum sum in matrix
Find minimum sum in matrix I have given matrix with size $n$ by $m$,such that $n<100, m<15$, for example here is...

What could be an example of a sequence of real numbers such that every x∈[0,1] is an accumulation point of this sequence?
What could be an example of a sequence of real numbers such that every x∈[0,1] is an accumulation point of this sequence?...

Optimal value for the zeroth weight of a least square minimization problem
Optimal value for the zeroth weight of a least square minimization problem We have some data $D = \{x_n, t_n\}$ and a...

Expected cycle time of arrived job at two busy workstation
Expected cycle time of arrived job at two busy workstation A job can be processed by workstation $A$ or workstation $B$....

For $p$ prime and greater than 3, prove that $42p$ divides $3^p  2^p  1$
For $p$ prime and greater than 3, prove that $42p$ divides $3^p  2^p  1$ Prove the following: $$42p \;\; 3^p  2^p ...

Question regarding two statements in Titchmarsh p. 266
Question regarding two statements in Titchmarsh p. 266 I am currently reading Titchmarsh's book about the Riemann Zeta...

Source and sink Fluid dynamics
Source and sink Fluid dynamics In a region bounded by fixed quadrantal arc and its radii, deduce the motion due to a...

$\Bbb R^2$ is not equal to $span(a,b)$ for any $(a,b)\in \Bbb R^2$ [closed]
$\Bbb R^2$ is not equal to $span(a,b)$ for any $(a,b)\in \Bbb R^2$ [closed] As $(1 ,0)$ belong to span of $(1, 1)$ but...

Complex numbers calculus problem
Complex numbers calculus problem Let $a_1,a_2,a_3$ be three nonzero complex numbers such that their imaginary and real...

how can i prove Bernoulli's inequality? [closed]
how can i prove Bernoulli's inequality? [closed] Could you help me prove Bernoulli's inequality: For all $x\geq...

Compute : $\int\frac{x+2}{\sqrt{x^2+5x}+6}~dx$
Compute : $\int\frac{x+2}{\sqrt{x^2+5x}+6}~dx$ Question: Compute this integral $$\int\frac{x+2}{\sqrt{x^2+5x}+6}~dx$$...

Is it possible to find a surjection from any set to the interval $[0,1]$?
Is it possible to find a surjection from any set to the interval $[0,1]$? Is it possible to find a surjection from any...

Prove that the given function is bijective
Prove that the given function is bijective Let $X$ be a nonempty set. Let $\mathscr{F}$ be the set of all functions...