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Top Questions

0 votes
2 answers
12 views

Some identities involving roots of a quadratic polynomial

2 votes
3 answers
56 views

Is every Fermat number that is not equal to $3$ a Connell Number?

0 votes
0 answers
6 views

Prove this binomiale sum: $\sum_{k=0}^{n}{2^{n-k}\binom{n+k}{k}} = 4^{n} $

0 votes
1 answer
21 views

Ball into bins with a twist in the domain

0 votes
0 answers
3 views

If $A$ and $C$ are dependent random variables, is $\mathsf E(AC|A=a)=a\mathsf E(C|A=a)$?

0 votes
0 answers
6 views

Can we generate a quadratic expression for compound interest?

1 vote
1 answer
25 views

How to derive this Lie group multiplication formula?

-2 votes
1 answer
40 views

Complex Analysis - proof of open set via continuity of preimages.

2 votes
2 answers
33 views

Why does $\int_{0}^{1}a\sin\left(a\sin^{-1}x\right)dx=\frac{a^{2}-a\sin\left(\frac{\pi}{2}a\right)}{a^{2}-1}$?

0 votes
0 answers
8 views

Probability of alien civilizations reaching Earth by combining the Drake Equation with Random Walks.

0 votes
0 answers
61 views

What is the fractional square-root-derivative of $\frac{dy}{dx}$?

0 votes
1 answer
165 views

A $3n-2$ Conjecture for the Redheffer Matrix.

1 vote
1 answer
10 views

Norm on the space of rapidly decreasing and continuous functions

1 vote
1 answer
44 views

Find Cov$(Z_n^i,Z_n^j)$ where $Z_n^i=\min\{N_i,p\}$

2 votes
1 answer
65 views

$𝑉$ is finite-dimensional. $𝑈, 𝑊$ are subspaces of $𝑉$. $𝑉 = 𝑈 + 𝑊$. Prove that there exists basis of $𝑉$ consisting of vectors in $𝑈\cup𝑊$

1 vote
0 answers
5 views

Finding a power series and domain of convergence of $ln(\frac{1-x}{1+x^2})$

0 votes
1 answer
32 views

How to modify these two functions to meet certain criteria? Problem with instantaneous rate of change

0 votes
0 answers
10 views

In which circumstances is the integral of a quasiconvex function again quasiconvex?

0 votes
0 answers
24 views

spivak chapter 22 (3ed.) - exercise 6

0 votes
0 answers
7 views

stability of rank one perturbation of stochastic matrix

0 votes
0 answers
7 views

Subgraphs of a Cayley graph of $S_n$

2 votes
1 answer
63 views

$\sum_{n=0}^{+\infty} \frac{x^n}{1+nx} \stackrel{x \to 1^-}{\sim} -\ln(1-x)$

2 votes
1 answer
40 views

When are similar matrices identical?

1 vote
1 answer
1k views

Are two vector bundles Möbius band and $S^1\times \mathbb{R}$ isomorphic as vector bundles over $S^1?$

0 votes
0 answers
26 views

How to arrange objects in groups where arrangement of groups and objects themselves matter?

0 votes
0 answers
35 views

Counting pairs $(x,y)$ of positive integers such that $x\leq y$, $GCD(x,y)=5!$, and $LCM(x,y) =50!$. What's wrong with my reasoning?

0 votes
0 answers
7 views

Characteristic function and Student's t-distribution; a problem

8 votes
1 answer
939 views

Connectedness of the orthogonal subgroup $O^+_+(k,l)$

1 vote
1 answer
52 views

A locally connected topological space has open connected components

0 votes
0 answers
4 views

On uniform convergence of integrals with respect to a sequence of Gaussian measures

1 vote
1 answer
22 views

The expected value of the sum of squared positives of $n$ i.i.d. normal random variables

1 vote
0 answers
58 views

Bertrands Postulate - Version $2n-2$

-2 votes
0 answers
22 views

Prime Numbers on the Circle

2 votes
1 answer
29 views

Silverman's book, the arithmetic of elliptic curves, p.399, $E(K)/\hat{\phi}(E'(K))\cong \Bbb{Z}/2\Bbb{Z}$

0 votes
0 answers
16 views

Pullback metric and pullback distance

2 votes
0 answers
29 views

Graphing the rational function $f(x)=\frac{3x}{x^2+x-2}$

4 votes
0 answers
107 views

Closed form of $\sum_{n=0}^{\infty}\frac{1}{(n!)^3}$

0 votes
0 answers
16 views

An inequality involving $|(1/\zeta)^{(n)}(x)|$

0 votes
0 answers
29 views

subrings of $\mathbb{Z}/(n)$, the ring of integers modulo $n$

0 votes
0 answers
17 views

What is an absolutely irreducible smooth curve and how to determine if a curve is as such over a finite field F_q?

1 vote
0 answers
23 views

Interesting vanishing identities of Gaussian integrals

-1 votes
0 answers
20 views

The infinite category of simplicial commutative ring is stable

0 votes
0 answers
61 views

Introduction to quaternion's geometrical intuitions starting from a set of three complex numbers

1 vote
0 answers
11 views

Analog of chord-and-tangent for elliptic curves in 3 or higher dimensions

0 votes
1 answer
28 views

Frobenius norm and spectral decomposition

1 vote
1 answer
39 views

Legendre polynomials: prove that $P'_{n+1}(x) - P'_{n-1}(x) = (2n+1)P_{n}(x)$ without generating function

0 votes
0 answers
14 views

Absolute continuity of time-dependent inner product

5 votes
1 answer
87 views

I need help to prove that :$\sum_{k=1}^{n}\frac{2^k}{k}\frac{(2n-k)!n!}{(2n)!(n-k)!}=\sum_{k=1}^n\frac{1}{2k-1}$

0 votes
0 answers
22 views

How do we describe the 'isomorphism subspace' of the mapping space $Map_{C}(x,y)$ for an infinite category C?

1 vote
2 answers
34 views

How to find the period of a trigonometric function out of its graphical representation

-1 votes
0 answers
35 views

formal proof to truth table proof

0 votes
0 answers
25 views

Continuity of $x \in X \mapsto \int_\Omega f(x,\cdot) \mathrm{d}\mu_x \in \mathbb{R}$

3 votes
1 answer
51 views

A trace inequality of the product of two matrices

0 votes
0 answers
5 views

How to find the generator matrix for the quotient group $C/C^{⟂}$ using a list of coset representatives of $C^{⟂}$ in $C$?

0 votes
1 answer
29 views

Distance of consecutive terms of a sequence goes to zero implies convergence in functional spaces.

1 vote
0 answers
21 views

Calculate the normal cone of a set of increasing functions

0 votes
0 answers
9 views

reference for Lemma 1.5 of Fermat's dream book

1 vote
0 answers
15 views

If $p_t(x,y)>0 $ for some $t$, then $p_t(x,y) >0 $ for all $t\geq 0 $.

1 vote
0 answers
12 views

Question in proof of Proposition 10.24 in "Lectures on von Neumann algebras"

0 votes
0 answers
7 views

Reference request - Density of smooth functions in Sobolev space with zero trace on part of boundary

2 votes
0 answers
15 views

Changing the field of an irreducible representation leaves it irreducible.

0 votes
0 answers
10 views

Eisenbud Section 17.5, Koszul complex is a graded complex

0 votes
0 answers
16 views

reconstructing a position using angles

2 votes
1 answer
20 views

Eigenvalues of the product of a stochastic matrix and a doubly stochastic matrix

0 votes
1 answer
16 views

Equivalent ways to obtain the reduced closed subscheme associated to the whole space

0 votes
0 answers
8 views

Hasse invariant determine the isomorphism classes of its isometric groups

0 votes
1 answer
36 views

Does rectifiability imply continuity?

-1 votes
0 answers
13 views

Is the tensor product of a free module with any other module free?

0 votes
3 answers
262 views

Prove the series $\sum_{n=1}^\infty (n(f(\frac{1}{n}) - f(-\frac{1}{n})) - 2f'(0)) $ converges

8 votes
1 answer
193 views

Prove that $BE^{\alpha}$ is a Banach Space

1 vote
0 answers
25 views

Continuation of the “Lorenzified” Riemann zeta $\zeta_{L}(x)$?

2 votes
0 answers
16 views

Strict stochastic ordering and expectations of strictly increasing functions

0 votes
0 answers
13 views

Confusion regarding domain of covariant derivative acting on section of a vector bundle

6 votes
0 answers
164 views
+300

Curvature operator of a Kähler manifold with constant holomorphic sectional curvature

0 votes
0 answers
6 views

Heuristics for centrality measures?

3 votes
0 answers
47 views

Are linear maps Borel?

2 votes
0 answers
20 views

Does a particle undergoing perfectly elastic collisions within a rectangle repeat its paths?

1 vote
0 answers
18 views

For the left action $G\times S \to S$, $\psi: G \to A(S)$ is a homomorphism, where $A(S)$ is group of permutations of $S$. Is $\psi$ onto necessarily?

-1 votes
0 answers
19 views

The solvability of a certain quadratic diophantine equation

0 votes
0 answers
24 views

How to estimate the expression about triangle and orthocenter.

0 votes
0 answers
13 views

Maximum principle for $\partial_t u = e^{-u}\Delta u$ on 2-manifolds

0 votes
0 answers
22 views
+50

Experimental Design: Selecting value of $n$ given desired width of credible interval

0 votes
0 answers
10 views

How is a Sturm sequence applied to the eigenvalue problem of a matrix.

3 votes
0 answers
38 views
+50

Characterization of self-conjugate spin$^c$ structures

0 votes
0 answers
5 views

Is Cesàro limit of a stochastic matrix always Block diagonalized with Block being either diagonalized or rank 1 (up to some permutation)?

1 vote
0 answers
15 views

The existence of $f$ $k$-lipschitz in the subset $Y\subset \mathbb{R}$ implies the existence of a real $k$-lipschitz function $g$ such that $g|_Y=f$.

0 votes
0 answers
10 views

Holder continuous function whose inverse is also holder continuous?

5 votes
1 answer
5k views

Finding the mode of the negative binomial distribution

1 vote
0 answers
9 views

Proving that two points are isogonal and then proving Pascal's Theorem

10 votes
2 answers
219 views

How many different rectangles can be formed by connecting four dots in a 4x4 square array of dots, such that the sides are parallel to the grid?

0 votes
1 answer
51 views

Does $\forall x, \exists x$ also needs to be quantified over some sets in zfc subset axiom?

2 votes
0 answers
19 views

Transversality condition and line bundles

6 votes
0 answers
59 views

Does the functional square root of the sine adhere to a "Sum = Integral" identity?

2 votes
1 answer
1k views

Generalize the idea of $A^2 = I_2$ to find a $5 \times 5$ matrix such that $M^2 = 0$ and $C$ is a nonzero $2 \times 3$ matrix

0 votes
2 answers
61 views

What is the name of this permutation?

34 votes
4 answers
4k views

Exercise 1.6.3 from Alon & Spencer's *The Probabilistic Method*: prove that $Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1]$ for i.i.d. real RVs $X$ and $Y$


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