# All Questions

1,402,559 questions
Filter by
Sorted by
Tagged with
12 views

### number of ways, n can be written as a product of k integers

For $k\ge2$, let $d_k(n)$ denote the number of ways of writing $n$ as a product of $k$ positive integers (so that $d_2(n) = d(n)$ where $d(n)$ counts the number of positive integral divisors of $n$). ...
53 views

### Crisp subgroup extracted from a $\mathbb Z_n$ considered as a fuzzy set

*Suppose we have a finite crisp set, but elements is fuzzy numbers which of a fuzzy set. So I make definition of the set. A = {$\tilde{0}$,$\tilde{1}$,$\tilde{2}$,...,$\tilde{n}$-$\tilde{1}$} For ...
6 views

11 views

### I want to model a function. Input can be natural numbers, The function should give output as zero when all of the input variables are different.

I need a non linear preferably continuous function which can detect whether all the input variables are different. The input variables are constrained to positive integers. eg input [4,3,2,1] f(x) ...
204 views

### How is this a function? - Analysis.

Let $X = \{1, 2, 3\}, Y = \{4, 5, 6\}$. Define $F \subseteq X \times Y$ as $F = \{(1, 4),(2, 5),(3, 5)\}$. Then $F$ is a function. I simply do not see how this could be a function, as there is ...
800 views

### The probability that a linear Brownian motion will hit a curve

Summary I am trying to estimate the probability that a standard linear Brownian motion will hit some curve. To make things a bit simple, I can assume that the curve is a graph of a function, that is ...
23 views

### Where is my mistake in calculating the Fresnel integral?

I want to prove the equation: $$\int_0^\infty \sin x^2dx=\frac{1}{2}\sqrt\frac{\pi}2{}$$ This was my calculating process: $$||e^{iz^2}||=||e^{iR^2e^{i\theta}}||=e^{-R^2\sin \theta}$$ Using the ...
37 views

### Normalizing a joint PDF $f(x,y)$ and finding the marginal PDF's $f_X(x)$ and $f_Y(y)$

I have the following joint PDF: $$f_{UV}(u,v):= C \cdot \unicode[STIXGeneral]{x1D7D9}_{\{ (u,v): 0\le u \le 1, u \le v \le u+1 \}}(u,v)$$ (In case the subscript of the indicator function is a bit hard ...
27 views

### Evaluating number of collisions between particles in a closed container

This question is regarding whether the following method of calculating number of collisions in a closed container is correct or not. So, it goes as follows:- First of all we make a table about the ...
27 views

### How to show sequence converges

What I want to show is that the following sequence converges to 1. $a_n = \frac{\sum_{i=0}^n i!}{n!}$ My initial strategy was to use the monotone sequence theorem. It's obvious that each term is ...
14 views

23 views

26 views

### Morphism of tangent space induce from a morphism of varieties.

I am trying to show that a morphism of varieties $f: X \to Y$ induces a linear map between the tangent spaces $\tilde{f}: T_aX \to T_{b} Y$, for $a \in X$ and $b = f(a) \in Y$. My idea was to use the ...
7 views

### partial derivative of a definite integral of products of two functions

why is it that the derivative of the the following definite (from 0 to v) integral ∫C(i)*P(i)di is P(i) and not ∫P(i)di. Thanks
25 views

I see this identity pop up a, but I have not seen a proof for it, nor can I prove it myself. The only progress I have made is that $\frac{k}{n}{n \choose k} = {n - 1 \choose k - 1}$, so that $\sum_{k=... 0answers 10 views ### Tate twist in Poincaré duality for étale cohomology of varieties with$\mathbb F_q$-structure Let$q$be the power of some prime number, let$\mathbb F_q$be the field with$q$elements and let$\overline{\mathbb F}$be an algebraic closure of$\mathbb F_q$. Let$X$be a smooth quasi-... 4answers 9k views ###$c\mid a,b\iff c\mid\gcd(a,b)$[GCD Universal Property] If$c$is a common divisor of$a$and$b$then$c$divides the greatest common divisor of$a$and$b\$. What can we use to prove this?
The given ODE is $$x^2y''-xy'+(x^2-4)y=0$$. How do we convert this into standard bessel equation?