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Interesting 16 Bountied Hot Week Month
7 votes
5 answers
708 views

Canonicity of the push-pull map for sheaves of sets

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AprilGrimoire
  • 567
1 vote
2 answers
116 views

How to decompose $Sym^n V \otimes V$, where V is some irreducible representation?

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Vladimir Lysikov
  • 5,520
10 votes
3 answers
399 views
+100

Six circles in a rectangle: show that two lengths are equal

dfnu's user avatar
dfnu
  • 8,522
2 votes
2 answers
50 views

Is this infinite series for $\pi$ already known?

Bowei Tang's user avatar
Bowei Tang
  • 4,633
3 votes
0 answers
34 views

Cycles and terminating sequences in the recurrence $N_{k+1}=N_k-\operatorname{rev}(N_k)$.

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projectilemotion
  • 16k
0 votes
2 answers
20 views

Discarding absolute value symbol while solving a linear differential equation.

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Artem
  • 15.1k
13 votes
3 answers
517 views

Compare $\log_5(\log_4 3)$ and $\log_6(\log_6 3)$

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Игорь
  • 171
0 votes
1 answer
755 views

Upper and Lower Bounds Proof for Positive Functions

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CommunityBot
  • 1
1 vote
3 answers
70 views

Topologist's Comb: why can't you produce a deformation retraction to a point on one of the teeth?

freakish's user avatar
freakish
  • 47.8k
2 votes
1 answer
59 views

derivative of integral of a function with respect to the same function

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Abezhiko
  • 15.1k
3 votes
2 answers
51 views

Why does $\left(1+\frac1{x-0.5}\right)^x$ converge to $e$ quicker than $\left(1+\frac1x\right)^x\approx e$?

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Maxime Jaccon
  • 5,596
1 vote
0 answers
31 views

$2^n-1$ can't be a powerful number?

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Lhachimi
  • 624
8 votes
1 answer
170 views

Polyhedron with least number of vertices whose diagonals enclose an interior solid region

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Haoran Chen
  • 941
0 votes
0 answers
14 views

Generalizing the Bellissard non-commutative approach for disordered systems to Hamiltonians of self-similar fractal graphs

ml0.0 lm's user avatar
ml0.0 lm
  • 1
-2 votes
1 answer
43 views

Why elements of a (Lie) algebra act on the algebra, in the adjoint representation?

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Shaun♦
  • 48.5k
2 votes
1 answer
61 views

Robinson's word vs Rotman's word: can the second be derived from the first?

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Shaun♦
  • 48.5k
2 votes
1 answer
59 views

Do real plane algebraic curves have a factorization corresponding to connected components?

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hbghlyj
  • 6,293
0 votes
0 answers
18 views

Localization at a prime of a subring preserves noetherianity

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Alosch
  • 131
1 vote
0 answers
32 views

Is this connection between an infinite series and OEIS A152619 known?

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Tomas Zubizarreta
  • 11
0 votes
1 answer
776 views

Outer Measure is not Finite Additive

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CommunityBot
  • 1
0 votes
2 answers
124 views

Prove $\sum \frac{x(4x-y-z)}{4x^2+(y+z)^2}\ge \frac{3}{4}$ for real variables

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River Li
  • 51.3k
0 votes
0 answers
5 views

Let $r_n$ be the least $N$ s.t. every $p^n$-th power mod $\mathfrak{m}_K^N$ lifts. Do we almost have $r_n=r_{n-1}+e$ for $e$ the ramification index?

Jianing Song's user avatar
Jianing Song
  • 2,813
1 vote
0 answers
86 views

Can the Impossible Cube be isometrically embedded as geodesics in Nil geometry, just as the Penrose triangle is a geodesic triangle?

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hbghlyj
  • 6,293
2 votes
3 answers
3k views

What is foundations of mathematics ? And why isn't it taught more often?

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fabmeyer
  • 1
4 votes
1 answer
112 views
+50

Expected number of lattice points in a randomly inscribed triangle

Maxime Jaccon's user avatar
Maxime Jaccon
  • 5,596
3 votes
1 answer
117 views

Checking if the determinant of a quasi-tridiagonal matrix is nonzero

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Rodrigo de Azevedo
  • 23.6k
118 votes
16 answers
13k views

Ways to evaluate $\int \sec \theta \, \mathrm d \theta$

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Elite
  • 192
1 vote
0 answers
17 views

Are there existing results on the number of solutions to $x^2 - y^2 = n$ in the quadratic ring $\mathbb{Z}_{m}[\sqrt D]$?

ACBD's user avatar
ACBD
  • 11
0 votes
1 answer
759 views

How to express subset notation in first order set theory?

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  • 1
0 votes
0 answers
7 views

Additive discrete group actions of self-Pontrjagin dual topological rings with pro-Lie stabilizer

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BertrandUtilsworth
  • 11
2 votes
2 answers
82 views

Calculation of lower branch of Lambert W-function based on root of principal branch

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njuffa
  • 2,283
0 votes
0 answers
24 views

When a cubic irrational can be written in terms of two nonnegative powers?

mezzoctane's user avatar
mezzoctane
  • 1,750
-2 votes
1 answer
118 views

Why does $x^\circ \approx 14 + 29\tan x^\circ$ work so well for $30\leq x\leq55$?

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naturallyInconsistent
  • 422
0 votes
0 answers
45 views

A question on Remark A.1.2.8 in Higher Topos Theory

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Ben Steffan
  • 10.8k
27 votes
4 answers
7k views
+100

Prove the inequality $\frac{b+c}{a(y+z)}+\frac{c+a}{b(z+x)}+\frac{a+b}{c(x+y)}\geq \frac{3(a+b+c)}{ax+by+cz}$

River Li's user avatar
River Li
  • 51.3k
2 votes
1 answer
86 views

Simplify expression for lemniscate tangent function

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user1658693
  • 63
142 votes
30 answers
60k views

Proofs of AM-GM inequality

ecbc's user avatar
ecbc
  • 11
-1 votes
1 answer
114 views

Two conics with $e \ge 1$ are tangent at 2 points. The conic with the greater eccentricity lies on the "outside"

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hbghlyj
  • 6,293
0 votes
0 answers
168 views
+50

$\Omega^1_{k[[X]]/k}$ is not finitely generated over $k[[X]]$

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Stanis LaRochelle
  • 283
1 vote
1 answer
2k views

Probability of Guessing a Code

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CommunityBot
  • 1
1 vote
0 answers
11 views

Question on Stokes phenomenon in Picard-Lefschetz theory

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schris38
  • 351
4 votes
1 answer
89 views

Why are these two quotient spaces homeomorphic?

Dennis's user avatar
Dennis
  • 2,764
3 votes
2 answers
164 views

For which functions $f$ is $\displaystyle \int_{t_0}^t f(s)\exp(s) ds$ solvable in elementary functions?

Marco's user avatar
Marco
  • 4,005
13 votes
1 answer
431 views

Help with $\int_{0}^{\pi /4} x^3 (\sqrt{\tan (x)} + \sqrt{\cot (x)}) dx$

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Mariusz Iwaniuk
  • 6,823
5 votes
2 answers
161 views

Getting different answers evaluating $ \int_{-1}^{1} \frac{\sin(\cot^{-1}x) + \cos(\tan^{-1}x)}{x^2 + 1}\,\mathrm{d}x$ with different identities

Angelo's user avatar
Angelo
  • 14.5k
1 vote
1 answer
1k views

Calculating the expected difference in observations

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CommunityBot
  • 1
3 votes
1 answer
145 views

Converting an elliptic curve to Edwards form

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Jan-Magnus Økland
  • 6,089
8 votes
10 answers
653 views

Evaluate $\int_0^{\frac\pi2}\frac{\mathrm dx}{a\sin ^2x+b\cos ^2x}$ without using its antiderivative

Lai's user avatar
Lai
  • 33.2k
0 votes
1 answer
43 views

Why is $\pi_{0} \left(G \right)$ a discrete and countable Lie group

Pauli's user avatar
Pauli
  • 1,192
0 votes
3 answers
310 views

How to show that $p_{K}(x)<1$ iff $x$ is an interior point of convex set $K.$

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Roberto Rastapopoulos
  • 421
7 votes
5 answers
603 views

$E[X_T]$ for $T=\min\{n: \sum_{i=1}^nX_i\geq1\}$ where $X_i\sim U[0,1]$.

Letac Gérard's user avatar
Letac Gérard
  • 4,033
1 vote
1 answer
771 views

Is the negation of on injective and surjective statements

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CommunityBot
  • 1
0 votes
1 answer
74 views
+50

Is Riemann integrability of Banach-valued functions preserved under uniform limits?

peek-a-boo's user avatar
peek-a-boo
  • 68.4k
3 votes
2 answers
140 views

Easy approach for the expected number of dice throws to achieve a run of identical numbers

true blue anil's user avatar
true blue anil
  • 49.7k
2 votes
2 answers
134 views

Double integration with $\log$

Bhaskar Vashishth's user avatar
Bhaskar Vashishth
  • 11.8k
6 votes
5 answers
28k views

As many even numbers as natural numbers.

Bill Dubuque's user avatar
Bill Dubuque
  • 285k
2 votes
0 answers
11 views

Conditional convergence of uniformly integrable submartingale?

Bart's user avatar
Bart
  • 1,495
1 vote
2 answers
117 views

Statistics: Using Stirling's Approximation with $3 N$

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Lee Davis-Thalbourne
  • 562
1 vote
1 answer
757 views

Stochastic differential equations vs stochastic initial conditions

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CommunityBot
  • 1
1 vote
0 answers
34 views

$(X, \Sigma, \mu)$ finite measure space and $(f_n)_{n\in\mathbb{N}}$ is sequence in $L^p(X)$. If $f_n \to f$ uniformly on $X$, then $f \in L^p(X)$.

John Pi's user avatar
John Pi
  • 163
42 votes
3 answers
5k views

How is Gosper's approximation to factorial derived?

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DroneBetter
  • 717
0 votes
0 answers
21 views

On the branch cut selection for evaluating a Gaussian integral with complex exponent

Aria's user avatar
Aria
  • 440
0 votes
0 answers
14 views

Decreasing rearrangement is nonexpansive

user124910's user avatar
user124910
  • 3,357
4 votes
0 answers
56 views

Is a compact subspace of a quotient of a topological vector space contained in the image of a compact subspace of the original space?

Elia Immanuel Auer's user avatar
Elia Immanuel Auer
  • 5,018
7 votes
1 answer
192 views

How fast can I guarantee convergence on a compact interval?

Nate Eldredge's user avatar
Nate Eldredge
  • 102k
4 votes
4 answers
1k views

$\gcd(a,b)=1, x^a = y^b\Rightarrow x = n^b$, $ y = n^a$ for an integer $n$.

Bill Dubuque's user avatar
Bill Dubuque
  • 285k
2 votes
1 answer
89 views

Where do logarithmic functions fit in the order of operations? Eg, is "$\ln2x$" equivalent to $\ln(2x)$ or to $(\ln2)(x)$?

ryang's user avatar
ryang
  • 45.4k
3 votes
1 answer
150 views

Use Beta function to find integral $\int_{0}^{1}\frac{\ln(x)\ln(1-x)}{x(1-x)}dx$

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Claude Leibovici
  • 298k
2 votes
1 answer
764 views

Proof about twice differentiable function.

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CommunityBot
  • 1
0 votes
0 answers
193 views

Deriving the formula $M= \frac {Ar(1+r)^n}{(1+r)^n-1}$ for the monthly payment $M$ of a mortgage $A$ with interest rate $r$, using $n$ payments

Blue's user avatar
Blue
  • 85.6k
4 votes
1 answer
427 views

Acyclic Model Theorem

John Palmieri's user avatar
John Palmieri
  • 9,586
3 votes
3 answers
241 views

Simplify into reduced form

user21820's user avatar
user21820
  • 61.4k
0 votes
1 answer
764 views

How to linearly extrapolate a quantity correctly?

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CommunityBot
  • 1
2 votes
1 answer
49 views

Perturbative expansion of eigenvalues

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Chris Grossack
  • 43.4k
1 vote
0 answers
61 views

Down-to-earth definition of "genus".

142857's user avatar
142857
  • 91
2 votes
1 answer
781 views

Inversion of power series computational formula

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CommunityBot
  • 1
2 votes
1 answer
63 views

Do non-GNS representations of C*-algebras exist?

David Gao's user avatar
David Gao
  • 25.8k
3 votes
0 answers
139 views
+50

Creative Alternatives to Vieta's formulas/Newton's identities

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Maxime Jaccon
  • 5,596
1 vote
1 answer
67 views

Test the convergence of a series arising from birth-death processes

The Other Terry's user avatar
The Other Terry
  • 1,999
0 votes
0 answers
127 views

Diophantine equation $x^3 + y^3 + z^3 = 2$

Somos's user avatar
Somos
  • 37.7k
0 votes
2 answers
2k views

Number of possible outcomes in which at least one die shows $5$

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CommunityBot
  • 1
4 votes
0 answers
76 views

Prove that the number of sign changes $\sim x^{3/4}$ (square-free integers)

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Maxime Jaccon
  • 5,596
5 votes
0 answers
765 views

Punctured complex projective space

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CommunityBot
  • 1
2 votes
1 answer
210 views

integral inequality involving $\sup|f'|$

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Chicori
  • 3,434
0 votes
0 answers
14 views

Functor from the category of finitely generated modules of a bound quiver algebra to the category of finite-dimensional bound quiver representations

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Meier_Kreis
  • 11
1 vote
2 answers
125 views

Find the number of quadruples of non negative integers $(a,b,c,d)$ such that $105a + 70b + 42c + 30d = 2025$

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RobPratt
  • 52.5k
2 votes
0 answers
52 views

similar to a classical geometry result

moshpit's user avatar
moshpit
  • 21
0 votes
0 answers
23 views

How to find a fibre metric associated with an Ehresmann Connection?

Horned Sphere's user avatar
Horned Sphere
  • 815
1 vote
0 answers
27 views

field extensions of incomplete fields with regard to an absolute value (valuation)

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J. W. Tanner
  • 64.6k
0 votes
0 answers
15 views

Question about my conclusions from Poisson Point Processes axioms

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Mhafez
  • 1
0 votes
1 answer
771 views

Weibull Distribution

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CommunityBot
  • 1
2 votes
2 answers
301 views

Why are left and right cosets different in the non-normal case?

Shaun's user avatar
Shaun♦
  • 48.5k
1 vote
0 answers
157 views

uniqueness of fixed point using a non-linear function

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flikhamud45
  • 11
11 votes
4 answers
456 views

Integral $\int_0^{1/\phi^2}\frac{\ln(1-x)}{x} dx $

Quanto's user avatar
Quanto
  • 125k
1 vote
1 answer
125 views

Show that $p$ is singular in $X \cap T_pX$

Xander Henderson's user avatar
Xander Henderson♦
  • 33k
5 votes
0 answers
57 views

Is the PB–Basic–007 “solution” in DeepSeek-Math-V2 correct? Possible flaw in its convex-hull argument

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