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1 vote
1 answer
52 views

What is the area of this triangle?

0 votes
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3 views

Need help to solve Sturm-Liouville ODE of form $\frac{dy}{dx}\Big(p(x)\frac{dy}{dx}\Big) + (\lambda)w(x)y = 0$

13 votes
1 answer
108 views

What is minimum of the integral function $I(x)= \int_0^\infty \frac{1}{(1+t^x)^x} \,dt$

0 votes
0 answers
4 views

Generalization of $\max$ and $\min$ of $Ax^2+Bxy+Cy^2$ with given $x^2+y^2=k$.

2 votes
1 answer
34 views

How to prove that the feasible set of a two-asset portfolio is a hyperbola?

0 votes
0 answers
21 views

An inequality about the image of holomorphic functions on unit disk

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0 answers
2 views

Can separation of variable be used for mixed boundary conditions where boundary conditions are dependent on one another?

0 votes
0 answers
8 views

Relationship between the boundaries of two convex sets

1 vote
2 answers
34 views

Show that $\lim_{n\to \infty} \int_{A_n}X(\omega)dP(\omega)=0$

0 votes
1 answer
15 views

Sufficient condition for an attaching space to be Hausdorff

1 vote
0 answers
26 views

How to solve the SDE $\mathrm{d}X(t)=-X^{3}(t)\mathrm{d}t+\mathrm{d}B(t)$

2 votes
0 answers
11 views

Confusion on exercise on $(\mathbb Z, +)$ in Buechler's Stability theory book

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0 answers
32 views

Find the least number that obtained when divided by $A$ and $B$ leaves the remainder $a$ and $b$ respectively. Also $A-a=B-b=d$.

0 votes
1 answer
22 views

Prove the interior of a finite intersection of sets is equal to the finite intersection of interiors

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1 answer
24 views

Proving the irreducibility of a polynomial in a field extension.

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0 answers
20 views

Resultant of two univariate polynomials in a Ring $R = \mathbb{Z}/(p^{k}\mathbb{Z})$

3 votes
1 answer
1k views

Does every convex-linear map have an affine extension?

0 votes
1 answer
26 views

What happens to an interval when both endpoints are equal?

6 votes
2 answers
231 views

$x^5=y^2+10$ has no solutions

3 votes
1 answer
27 views

Interior and closure of sets on metric spaces combined $ A, A^{\circ}, \overline{A^{\circ}}, \ldots $

1 vote
0 answers
40 views

Convergence of $f_n(x) = \chi_{B(0,1) \setminus B(0,\frac{1}{n} )}(x) \cdot n \ln(\frac{1 + n ||x||^{\alpha}}{n ||x||^{\alpha}})$

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1 answer
15 views

Asymptotics of $\int_{0}^{1} \frac{\tan^{-1}(x^n)}{\sqrt{1 - x^n}} \, dx $

0 votes
0 answers
13 views

examples of trigonometric functions $f(x)$ such that $\int_0^M e^{if(x)} dx$ becomes a desired value

1 vote
2 answers
29 views

What is the correct argument definition for the complete elliptic integral?

0 votes
0 answers
9 views

Pointwise limit of sequence of holomorphic functions given constraint on their derivatives at the origin

1 vote
0 answers
14 views

Power series of matrices that is similar to hyperbolic sine

-2 votes
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7 views

Expected number of real roots of a polynomial with independent, uniformly distributed coeffients

0 votes
0 answers
26 views

Show that there exists a connected component $C'$ of $U' \cap G$ such that $C' \cap C \neq \varnothing.$

1 vote
1 answer
195 views

Prob. 5, Exercises 8.14, in Apostol's CALCULUS Vol II: Find constants such that the directional derivative

0 votes
1 answer
18 views

Why is the uniqueness theorem for 1st order differential equations involve taking a partial dervative?

5 votes
2 answers
185 views

Is there a closed form for $\int_0^\infty \frac{1-\cos(tx)}{e^t-1}dt$?

0 votes
1 answer
51 views

Approximation needed

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0 answers
6 views

Correspondence of forms of the same solution of a system of linear equations

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-1 votes
1 answer
966 views

Combinations and permutations soccer team

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34 views

Proof of Cartan's Lemma in Lee's Smooth Manifolds

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9 views

How to generalise the argument in Chap. 1 in Baby Rudin to show that these sets $A$ and $B$ have no largest and smallest elements, respectively?

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1 answer
23 views

Tensor product Ore division ring of fractions

1 vote
1 answer
47 views

How to build a $6\times 6\times 6$ cube using 4-unit T-shaped pieces?

30 votes
0 answers
474 views
+50

If $f(n)$ is the number of groups of order $n$, then is $f(a)\cdot f(b)\leq f(a\cdot b)$?

0 votes
0 answers
11 views

For the complex exponential function, how can we transform the constraints on the exponential term to apply to the whole function?

0 votes
0 answers
22 views

How to tell if a parameterization covers all integer solutions (particularly for $x^2 + y^n = z^2$)

0 votes
1 answer
14 views

Natural way of constructing $\sigma(A)$ from $A$ Shiryaev

0 votes
0 answers
7 views

Does the nondegenerate eigenvector for the sum of projectors constructed from a set of unit vectors imply a symmetry of the set of unit vectors?

1 vote
0 answers
15 views

implicit function theorem to determine minimum of a function

0 votes
0 answers
10 views

Improper Integral of a complex-valued function with a singularity on the real line

0 votes
1 answer
12 views

For a measurable subset D of E, f is measurable on E if and only if the restrictions of f to D and E/D are measurable

0 votes
0 answers
3 views

Bounds on the volume of the image of a cube, through bounds on area of cross sections

0 votes
0 answers
12 views

Behavior on a conjugacy class of SL in a split extension

0 votes
0 answers
29 views

Reference request: existence of the finite fields without using the algebraic closure

2 votes
3 answers
37 views

Is every continuum-sized dense subset of the irrationals order isomorphic to the irrationals?

3 votes
2 answers
29 views

Kernel of restriction and cokernel of corestriction of group cohomology

0 votes
0 answers
9 views

Relations between Schur polynomials and Specht modules

3 votes
1 answer
45 views

How do we prove that $X\perp Y$ when $f_{X,Y}(x,y) = \frac{1}{2\pi}e^{\frac{-1}{2}(x^2+y^2)}$?

3 votes
1 answer
55 views

Finding solution of a nonlinear equation containing both the vector and its norm

1 vote
0 answers
24 views

How to evaluate $\int_1^{\infty}\frac{t^2\ln^2 t\ln(t^2-1)}{1+t^6}{\rm d}t $

2 votes
0 answers
17 views

Bounded linear functional with specific values at linearly independent vectors

1 vote
0 answers
15 views

Gradient of a complex-valued function with complex-valued variables

2 votes
1 answer
28 views

Exercise 9.1 in Introduction to stochastic processes by Lawler

3 votes
1 answer
122 views
+100

Topology of sets defined by real-valued functions (again)

2 votes
0 answers
14 views

Show that $\text{Lip}_1(X,x_0)$ is compact

0 votes
0 answers
29 views

How can i find the way to escape robot?

0 votes
1 answer
30 views

Bound an integral by a function with an appropriate decay

0 votes
0 answers
22 views

Existence and continuity of inverse operator

0 votes
0 answers
24 views
+150

Question about the index of two elliptic operators over a 4-dimensional Riemannian manifold

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0 answers
28 views

Induction proof for product of $a^x$ is less than or equal to the sum of $x\times a$

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0 answers
10 views

Embedding degree of an elliptic curve

0 votes
0 answers
12 views

VC dimension of indicator of convex sets in $\mathbb{R}^2$

4 votes
4 answers
586 views

Combinatorial proof of a binomial identity: $\sum_k \binom {2r} {2k-1}\binom{k-1}{s-1} = 2^{2r-2s+1}\binom{2r-s}{s-1}$

0 votes
0 answers
8 views

Limit definition of multiple derivatives handling more cases than iteratively differentiating -- is there a reason to prefer iterated derivatives?

0 votes
0 answers
10 views

Influence of elements order in Vandermonde matrix on the result of polynomial regression

0 votes
0 answers
18 views

Is there a closed form inverse cdf function for a quartic kernel?

1 vote
0 answers
9 views

Longest Increasing Subsequence Upper Bound

1 vote
0 answers
10 views

Categories internal to the category of convex sets

0 votes
0 answers
22 views

Can one directly find the square root of a perfect square of n Base-10 digits when given only n/2 or (n+1)/2 end digits of that perfect square?

0 votes
1 answer
49 views

Hello, I am having trouble understanding why the graph of the function shifts to the right and not the left.

-1 votes
0 answers
24 views

Representing Virginia Duck Limits Combinatorically

4 votes
1 answer
89 views
+50

Preliminary lemma to Hahn's decomposition theorem

0 votes
0 answers
12 views

Spectrum of the Laplacian in a Rigged Hilbert Space Defined by Bilateral Laplace Transform

0 votes
0 answers
16 views

Finding Surface area of an N-sided concave polygon in 3 dimensions

0 votes
0 answers
23 views

Definition of Random Set

2 votes
1 answer
27 views

Spinorial representation of Weyl group of SO(8)

1 vote
0 answers
23 views

What's the distinction between an elliptic curve and its rational points?

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0 answers
18 views

Properties of onto transformation matrix

0 votes
1 answer
43 views

Example of an integrable function $f$ such that $|\int(1+x^2)f(x)\,dx|<|\int f(x)\,dx|$

0 votes
0 answers
10 views

sample from isotropic Gaussian distribution on SO(3) group

6 votes
1 answer
2k views

Approximate point spectrum of a normal operator

0 votes
0 answers
14 views

Some questions on Gamma function expression as infinite product

2 votes
0 answers
16 views

Number of combinations of distinct and identical objects?

205 votes
32 answers
42k views

Counterintuitive examples in probability

1 vote
0 answers
9 views

Is $ W^{k,p}(\mathbb{R}^n) $ equal to $ W^{k,p}_{loc}(\mathbb{R}^n) $?

4 votes
1 answer
30 views

If $X$ is a continuous supermartingale, why is, for every $N$, $(X_s)_{s\leq N}$ uniformly integrable?

2 votes
0 answers
6 views

Proving lower bound for the length of a cycle in a 2-connected graph.

0 votes
2 answers
81 views

Is my proof that $X \setminus (Y\cup Z)=(X\setminus Y)\cap (X \setminus Z)$ valid?

0 votes
0 answers
17 views

How can we prove the derivatives of displacement?

3 votes
0 answers
8 views

Spiric sections by imaginary planes

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