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3 votes
1 answer
25 views

$0 \leqslant a \leqslant b \Rightarrow \|a\| \leqslant \|b\|$ in a $C^*$-algebra

3 votes
1 answer
59 views

Are there more real numbers in the interval $[1,\infty)$ than in the interval $(0,1]$? Or not?

1 vote
3 answers
37 views

For what values of $p>0$ is $\lim_{n\rightarrow\infty}\int_0^n\frac{(1-\frac{x}{n})^ne^x}{n^p}=0$?

0 votes
0 answers
2 views

Abstract integral interpretation

2 votes
1 answer
3k views

Find the potential function of a conservative vector field

1 vote
0 answers
4 views

Dependency of the value of this Integral on the path taken.

2 votes
1 answer
38 views

Is there a function $f$ from reals to reals such that every non-vertical line intersects $f$ infinitely many times?

1 vote
0 answers
6 views

Show that $f(x)=x^2+\frac{a}{x}$ cannot have a local maximum for any value of $a$.

2 votes
0 answers
21 views

Given matrix associated to linear transformation find the basis it corresponds to

1 vote
0 answers
19 views

Exercise on continuous functions, analysis 1

4 votes
3 answers
52 views

If $ax^2 + 2hxy + by^2 = 0$ (here $a, b, h$ are real constants), then find $\frac{dy}{dx}$.

3 votes
2 answers
18 views

In definition of a topology, is including the empty set and the set itself redundant?

1 vote
1 answer
19 views

Number of functions under some conditions

2 votes
0 answers
25 views

Sum of Zero Nim-sum k-tuple Revisited

2 votes
1 answer
13 views

Direct sum of small modules is small, also direct summands of small modules are small.

2 votes
2 answers
16 views

Maximality of matching after contracting an odd cycle in a graph

1 vote
0 answers
5 views

Expand [a+b*log(1-x)]^{-1} as power seires in x

1 vote
1 answer
8 views

Evaluate/asymptotic of the sum $\sum_{a = 1}^{L \left({N}\right)} \left({- 1}\right)^{\left\lfloor{N/\left({2\, a + 1}\right)}\right\rfloor}$

2 votes
0 answers
18k views

3-digit chopping vs 3-digit rounding and relative error

1 vote
0 answers
7 views

Geometric Interpretation of Jacobson rings -- Every locally closed subsets of $\mathrm{Spec} A$ consists of a single point is closed

3 votes
1 answer
61 views

Find the derivative of $\frac{d}{dx}\left(\tan \left(\sqrt{x}\right)\right)$ - no chain rule

3 votes
1 answer
53 views

A positive semidefinite bilinear form must be degenerate?

1 vote
0 answers
7 views

Limiting probability measure on an increasing sequence of finite products

2 votes
0 answers
50 views

Proof from Lang’s Basic Mathematics

0 votes
0 answers
19 views

consider the following relation on the set of positive integers.

2 votes
1 answer
41 views

Meaning of $\big|_{t=0}$ beside a derivative in a theorem about the properties of the characteristic function of a random variable.

6 votes
1 answer
31 views

The coupon collector's most collected coupon

0 votes
0 answers
15 views

What are the conditions for cosets of a certain group to form a group themselves?

0 votes
0 answers
5 views

This is Stein fourier analysis. In section 3.3,I really don't understand how he gets to the final result(equation (4)),can someone explain in detail?

3 votes
1 answer
82 views

Find a polynomial of the form $F(x,y,z)$ of degree $3$ such that $F(a,b,c) = 0 \pmod{5}$ iff $a,b,c= 0 \pmod{5}$

0 votes
0 answers
19 views

Second inner product.

1 vote
1 answer
13 views

Properties of conformal maps

-1 votes
0 answers
8 views

Are there any theorems about the restriction of a partial order?

1 vote
0 answers
10 views

definition of closed immersions of schemes

1 vote
2 answers
9 views

Must a certain continuous map have 0 in its image, given that its restriction to the unit sphere is homotopic to the identity?

0 votes
0 answers
8 views

Find a process $\left(A_{n}\right)_{n}$ such that $\left(\sum^{n} X_{i}\right)^{2}-A_{n}$ is a martingale.

0 votes
1 answer
22 views

$u$ be the sol of $\Delta u+ a_i(x)\frac{\partial u}{\partial x_i}= f(x)$ if $f\geq 0$ then u is constant and $f=0$

2 votes
2 answers
1k views

Semi-Infinite String equation

0 votes
3 answers
33 views

Let $A\in\mathbb{R}^{2\times 2}$ be such that $\det(A)=d\ne0$ and $\det(A+d\cdot\text{Adj}(A))=0$. Evaluate $\det(A-d\cdot\text{Adj}(A))$.

0 votes
1 answer
15 views

Origin of a term in an inequality.

1 vote
0 answers
8 views

Elliptic regularity with right-hand side in $H^{-1/2}$

0 votes
0 answers
10 views

When we calculate the irr, how to decide the initial range of irr?

0 votes
1 answer
10 views

Almost Sure Convergence of a Random Variable

0 votes
0 answers
18 views

Why is "More Data Better than Less Data"?

1 vote
0 answers
13 views

Elementarily equivalent models of arithmetic that are not isomorphic.

0 votes
1 answer
22 views

Function class consisting of gradients of real-valued convex functions

0 votes
0 answers
22 views

What is the difference between the principal square root of $x$ and $x^{1/2}$?

0 votes
0 answers
6 views

Conditional distribution of one of the two exponential random variables, given one is smaller than the other

0 votes
1 answer
22 views

Pullback is not exact

1 vote
0 answers
6 views

Are we able to Compare the Fisher Information of Two Variables?

0 votes
0 answers
9 views

can we always get the variables of a system of linear equations given the system is valid?

3 votes
0 answers
29 views

Calculation on Riemannian manifolds

1 vote
0 answers
55 views

Prove that if $y \neq 0$ and $n$ is odd, then $x^n+y^n=(x+y)^n$ only if $x=0$ or $x=-y$ (Spivak's Calculus, Ch. 11)

0 votes
0 answers
11 views

Homology of the complement of a simple closed curve in a surface

0 votes
0 answers
15 views

Cardinal of a set (proof verification)

4 votes
1 answer
99 views

Why this partial function is not computable?

0 votes
0 answers
23 views

I cannot prove that $T$ is diagonalizable $\Rightarrow$ $T|_{V_1},T|_{V_2},\dots,T|_{V_r}$ are diagonalizable.

2 votes
0 answers
29 views

An interesting recurrent equality, possibly easier to solve in its differential form?

6 votes
1 answer
3k views

Bayesian Interpretation for Ridge Regression and the Lasso

0 votes
1 answer
22 views

How to linearize a state space equation with higher order $>2$?

0 votes
0 answers
16 views

For a compactly supported, continuously differentiable function $f$, do we have $\frac{f(x+h)-f(x)}{h}\to f'(x)$ uniformly?

2 votes
0 answers
21 views

"Spanning" of solutions of ordinary differential equations

2 votes
0 answers
37 views

Help showing that two sets are equal.

1 vote
0 answers
21 views

Why does the following remark on probability space not work on infinite, yet countable, sets?

2 votes
1 answer
21 views

Proof of Wronskian relation using induction

1 vote
1 answer
41 views

The derivative of a semialgebraic map is semialgebraic

6 votes
0 answers
53 views

Why does Galois theory most naturally take place in the context of fields?

3 votes
1 answer
38 views

On the number of roots of $p(z,\bar z)$

5 votes
4 answers
150 views

Inequality involving sums with binomial coefficient

2 votes
2 answers
72 views

What does it mean to lift a curve $\gamma$ in $\mathbb{C}\mathbb{P}^n$?

3 votes
1 answer
25 views

What do the elements of the chains of a simplicial complex represent?

1 vote
0 answers
21 views

Global Langlands for tori?

1 vote
1 answer
13 views

Conditioning in Event Language VS Proposition Language

2 votes
0 answers
32 views

Why is $\int_{0}^{2\pi} \int_0^{2\pi} \frac{\ln(21-4(\cos x+\cos y+\cos(x+y)))}{2\ln(9/2)}\frac{dx}{2\pi} \frac{dy}{2\pi}$ almost $1$?

1 vote
1 answer
29 views

An inequality: from the complex to the real case.

3 votes
0 answers
33 views

What' s the asymptotic behaviour of this integral?

1 vote
0 answers
25 views

Determine if $f(x,y)=e^{-xy}\cos(2x)\cos(y)$ is integrable via Fubini

2 votes
0 answers
21 views

Calculating the angle between 2 one-sided surfaces.

2 votes
2 answers
78 views

Are $\frac{p^2+1}{2}$ and $\frac{p^{5n}(p^5-1)}{2}$ are coprime to each other, $n \in \mathbb{N}$?

1 vote
0 answers
14 views

Exemple where tower property of conditional expectation is NOT verify

1 vote
0 answers
15 views

Approximating an open set in measure with another open set whose boundary has zero measure

1 vote
0 answers
21 views

Quadratic Reciprocity as an Analytic Statement

9 votes
0 answers
103 views

Collatz conjecture but with $n^2-1$ instead of $3n+1.$ Does the sequence starting with $13$ go to infinity?

1 vote
0 answers
27 views

Proof: $C^\infty[0,1]$ is dense in $L^2[0,1]$

0 votes
0 answers
9 views

What set of matrices $X,Y$ satisfy $X \circ Y = X P Y$ for at least one permutation matrix $P$?

3 votes
1 answer
25 views

Are invertibly cobordant manifolds diffeomorphic

0 votes
0 answers
10 views

Find $\mathbb{E}[\hat{\alpha}]$. Suggest a new estimate $\check{\alpha}$ of $\alpha$ which is unbiased, such that $\mathbb{E}[\check{\alpha}]=a$

1 vote
0 answers
15 views

General form of rank $2$ tensor invaiant under certain rotations

0 votes
0 answers
17 views

Goldbach Conjecture and Triangular Number

0 votes
2 answers
56 views

Solution of $\theta$ when $\tan(\theta)-\sin(\theta)=\frac{\sqrt3}{2}$

2 votes
0 answers
13 views

Can we calculate the opponent's hidden values in this statistical battle?

0 votes
2 answers
1k views

Probability of being selected in a raffle

3 votes
1 answer
97 views

Prob. 10, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: A countable product of separable spaces is also separable

1 vote
0 answers
9 views

Decomposing a big and nef divisor into ample + effective

3 votes
0 answers
9 views

Divisibility of unitriangular matrices over a field of characteristic 0

0 votes
0 answers
42 views

How to know what to study based on past examinations?

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