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0 votes
0 answers
4 views

How to obtain explicit formula of coefficients for generating functions

1 vote
2 answers
37 views

Limiting value of $\frac{4x^2+2y^2-6xy}{6x^2+√2y-8xy}$ as point $(x,y)$ on curve $x^2+y^2=1$ approaches the position $(\frac1{√2},\frac1{√2})$

1 vote
0 answers
6 views

Hadamard's inequality via Lagrange multiplier

6 votes
3 answers
199 views

Problem when proving the series $1+\frac 13-\frac 12+\frac 15+\frac17-\frac 14 +\frac 19+\frac 1{11}-\frac 16+...$ converges to $\frac 32\log 2.$

0 votes
0 answers
27 views

Brezis' exercise 6.2.3: $T(B)$ is not closed

2 votes
1 answer
45 views

Understanding how to formally use the definition of stopping time to prove something is a stopping time

0 votes
0 answers
13 views

How do I find the optimal panel length for a fence?

2 votes
2 answers
48 views

Solving: $\ddot{y}+\dot{y}+\frac{1}{x}y=\frac{1}{x^2}$

1 vote
4 answers
299 views

How to find the constant $C$ such that $f(x)\geq Cx$

1 vote
1 answer
43 views

Find $f(\frac{2\pi k}{2^n \pm1})$ given $f(x)=\prod_{i=1}^{n-1}[2\cos(2^{i-1}x)-1],n\geq1$.

5 votes
3 answers
1k views

Number of positive integers that cannot be expressed as $ax+by$

2 votes
0 answers
57 views
+100

a functional inequality (positive functions on circle).

0 votes
1 answer
15 views

Determine $T^*$ such that $T(A):M_2(K) \rightarrow AM-MA$ and inner product $tr(B^tA) = \langle A,B\rangle$

1 vote
2 answers
38 views

About density matrices as both the vertices of a convex hull and the basis of a matrix space

3 votes
1 answer
96 views

How to think and deduce optimal strategy move for both Alice and Bob

0 votes
0 answers
29 views

Unprovable over $\mathbb{R}$, provable over $\mathbb{C}$?

1 vote
0 answers
17 views

Does $\int_{x-r}^{x+r} f > 0$ for any $x \in \mathbb{R}$ imply $f>0$ a.e. on $\mathbb{R}$?

2 votes
1 answer
95 views

Are there any Mathematical Theorems that Can Prove the Results of this Experiment?

0 votes
0 answers
24 views

How can I evaluate $\int \sin^{7/2} x dx$

0 votes
0 answers
13 views

Why the assumption 'L is contained in an algebraic closure of K' is required in the definition of normal extension?

3 votes
1 answer
11 views

Implicit and explicit definability over $\mathbb{R}$ of the exponential function

2 votes
1 answer
31 views

Every eigenvector of $T$ is an eigenvector of $T^*$. Prove that $T$ is a normal operator.

1 vote
0 answers
11 views

Using Stirling's formula to show that random walk density is asymptotically normal

0 votes
0 answers
16 views

When is the absolute value of logarithm equal to the input?

2 votes
3 answers
48 views

Principal value of 1/|x|

0 votes
1 answer
51 views

Proving 111...111 is divisible by $3^n$

-1 votes
0 answers
15 views

UKMT Maclaurin Olympiad 2023 Q6: Could someone explain a solution to it, and how to get to said solution?

1 vote
0 answers
35 views
+50

Inequality regarding kostka numbers in representation theory

1 vote
0 answers
19 views

If $H$ has a normal complement then it has the character restriction property

0 votes
1 answer
17 views

Prove that there is a rank one matrix $B$ so that $Bx = y$ where $B$ has matrix norm $1$

0 votes
0 answers
11 views

Commensurator of $SL_{2}(\mathbb{Z})$ on $GL_{2}^+(\mathbb{R})$.

1 vote
1 answer
3k views

can a quartic graph have 2 turning points?

0 votes
0 answers
27 views

Riemannian metrics on the n-dimensional torus

1 vote
1 answer
28 views

An inequality for probability measures on finite measure spaces

3 votes
2 answers
33 views

Proving inequality containing multiple square roots

0 votes
0 answers
16 views

Rational values of sin(pi + x) in degrees

4 votes
2 answers
185 views
+50

Intersections of two cones with parallel axes

0 votes
0 answers
24 views

Meaning of precedence of logical connectives

0 votes
0 answers
5 views

Finding a polynomial of order h from the first h+1 terms

16 votes
2 answers
418 views
+50

Show that: $\sum_{k=1} (-1)^k\left[ k\ln\left(\frac{k^4+2k^3+k^2}{k^4+2k^3+3k^2+2k+2}\right)+\ln\frac{k^2+2k+1}{k^2+1} \right]=4\coth^{-1}(e^\pi)$

0 votes
0 answers
8 views

Given descriptive stats for two sets $(x_1,y_1)$ and $(x_2, y_2)$, can $\rho^2$ be found for their union $(\{x_1 \cup x_2\}, \{y_1 \cup y_2\})$?

2 votes
1 answer
35 views

Find the sum upto $n$ terms: $\frac{1/2}{a^2}+\frac{1/4}{4a^2}+\frac{1/8}{9a^2}+\frac{1/16}{16a^2}+\frac{1/32}{25a^2}+...$

1 vote
0 answers
24 views

Global uniqueness of the solution for ODE $y'(t)=F(y(t))$ if $F : \mathbb{R}^n \to \mathbb{R}^n$ is smooth?

1 vote
0 answers
31 views

Gradient tends to zero in gradient descent/flow?

0 votes
0 answers
9 views

Are these functions proper defined Mollifiers kernels? Why? Why not?

0 votes
0 answers
34 views

Is the cap product $H_p(X,Z)\times H^p(X,Z)\to H_0(X,Z)=Z$ a perfect duality?

1 vote
0 answers
7 views

Is my little proof of lub axiom using (lub axiom in any way)?

3 votes
1 answer
56 views

Switch map on double suspension is homotopic to the inverse of the cogroup

0 votes
0 answers
7 views

Notation for “either a value or the identity”

-1 votes
0 answers
29 views

Observation on harmonic series

1 vote
0 answers
29 views

How many objects can I perceive to all be travelling at speed arbitrarily close to $\sqrt 2\cdot c$ relative to each other?

1 vote
0 answers
6 views

Check if directed graph G1 is edge-induced subgraph isomorphic to directed graph G2

0 votes
0 answers
14 views

Is the leading term of a polynomial the product of the leading terms of the factors

1 vote
1 answer
16 views

If the ultrafilter space is Hausdorff, must the base space be discrete?

0 votes
0 answers
13 views

A symmetric distribution of probabilites among N objectives

2 votes
1 answer
20 views

Generate a randomly-oriented vector $\vec{w}$ at a specific angle $\theta$ from another vector $\vec{v}$ in $\mathbb{R}^n$

0 votes
0 answers
21 views

Interplay of additive and multiplicative characters of a field.

0 votes
0 answers
25 views

Given a point on the surface of a sphere, how to find points at a given angle?

2 votes
1 answer
20 views

Domination Number of Random Graphs

-1 votes
0 answers
21 views

Counter example for the compact embedding

0 votes
0 answers
3 views

Canonical linear extension of a partial order for addition-subtraction chains

0 votes
0 answers
8 views

G/G/1 vs M/G/1 queues

0 votes
0 answers
10 views

Given a modulus p, two primitive roots and the two products of the modular exponentiation attained swapping the exponents. Find the exponents.

0 votes
0 answers
6 views

Fitting a Bezier curve between two parallel lines

0 votes
0 answers
6 views

Decision/Logic tree behavior for solving integral convergence

2 votes
0 answers
21 views

$f:[0,\infty)\to \mathbb{R}$ right continuous with left limits. Then is $\{y:\lambda(t:f(t)=y)=0\}$ dense in $\mathbb{R}$?

0 votes
0 answers
21 views

Rational Parameterization of $c^2 = a^2 + b^2 = d^2 + 4 b^2$

1 vote
1 answer
20 views

An easy way to calculate the residue of $\tan^2z$

1 vote
1 answer
35 views

If $w^2+x^2+y^2=z^2$ , then $z$ is even if and only if $w$ , $x$ , and $y$ are even

0 votes
0 answers
11 views

Holomorphic differential on a compact Riemann surface

1 vote
1 answer
23 views

Generalization of Kakutani-Ky Fan Theorem without convexity assumptions

2 votes
1 answer
30 views

How can I simulate on R the total variation distance between the Law of the number of fixed points and Pois(1)?

1 vote
0 answers
29 views

Equivalent for an integral

0 votes
1 answer
9 views

Related rates problem with cube and its space diagonal - what did I do wrong?

1 vote
0 answers
30 views

Show that the predicate $y = x + 1$ is not definable in the interpretation $(\mathbb{Z}, =, f)$, where $f$ is a unary function $x \to (x + 2)$.

1 vote
0 answers
47 views

Ideal Currency In Terms Of Coin Values

1 vote
0 answers
21 views

Probability of a pair in "strip" card shuffle.

0 votes
0 answers
26 views

How to determine if a differential equation is periodic and calculate its period?

2 votes
1 answer
39 views

How to derive the solution for the SDE $dX_t = \theta(t)X_t dB_t$ from Itô's formula?

3 votes
1 answer
20 views

Radon-Nikodym Density $\mathrm{d}\mathbb{P}/\mathrm{d}\mathbb{Q}$ if distribution of r.v. $X$ is known under $\mathbb{P}$ and $\mathbb{Q}$

1 vote
1 answer
19 views

Determine all values $\lambda$ for which $\mu \succ 0 \succ \upsilon$

1 vote
0 answers
17 views

Does this way to prove that the integral of a strictly positive function is positive work?

2 votes
0 answers
29 views

Finding unknown function $f(y)$ from $\int_0^{y_{max}} \frac{dy}{\sqrt{\left(\frac{f(0)}{f(y)\cos(\alpha)}\right)^2 -1}} = \frac{d}{2}$

1 vote
0 answers
33 views

Does the term (1 - x) have a meaningful name in mathematics

0 votes
1 answer
35 views

Verifying that a space is a Manifold via compatible charts

1 vote
0 answers
11 views

Correlation between hinge loss function, Langrage function and $a_i$

3 votes
1 answer
17 views

Derivation of expectation of random variable with delayed differential equation

1 vote
0 answers
22 views

Is there a way to minimize the $p$-distance between a point and a line?

0 votes
0 answers
8 views

Closed Form Solution to Linear Optimization Problem

1 vote
0 answers
14 views

How to compute the gradient and hessian of a vector valued function

0 votes
0 answers
12 views

Locus points with a distance $d$ from a plane $\alpha$

1 vote
3 answers
109 views

Understanding approximate identity of non-unital Banach algebras through left regular representation

2 votes
0 answers
13 views

Limit involving average distance from origin to points with prime number coordinates

2 votes
1 answer
19 views

Is there any literature on union of random mappings?

2 votes
0 answers
55 views
+50

How to use second-order Gateaux derivative for convex optimization?

0 votes
0 answers
38 views

Definition of a parallelogram

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