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Question about Pasch's Postulate, line going through all three sides of a triangle
geometry triangles axiomatic-geometry- 10.5k
A tough number theory problem: Prove that $2^n$ can be expressed as $7x^2+y^2$ for $n \geq3$
real-analysis algebra-precalculus number-theory elementary-number-theory diophantine-equations- 667
Taylor coefficients of complex function - please check my attempt?
complex-analysis taylor-expansion- 42.3k
Can one separate variables as a sum in PDE?
calculus ordinary-differential-equations partial-differential-equations- 42.3k
Maximum of product of raised sinusoid functions with different phase and frequency
trigonometry optimization nonlinear-optimization trigonometric-series- 42.3k
How to perform multiple rotations by direction vectors?
matrices complex-numbers vectors rotations quaternions- 726
Integral of angle between tangent and line
calculus geometry- 1,147
Z transform of $\sin \alpha k$
trigonometry complex-numbers trigonometric-series z-transform- 517
Finding a bound on a certain number of sums
combinatorics discrete-mathematics- 69k
Proving an upper bound on a grid function
discrete-mathematics coloring extremal-combinatorics- 121
Characterization of linear differential operators in $\mathbb{R}^n$
real-analysis linear-algebra partial-differential-equations- 1,839
Product of symmetric matrices equals Zero matrix
matrices- 549
Constraint formulation for an MILP optimization problem
optimization constraints mixed-integer-programming- 842
$f \in H^{s}(\mathbb{R}^{n})$, $s > n/2$, then $f$ is uniformly Holder continuous of $\alpha \in (0,1)$ order??
partial-differential-equations fourier-analysis sobolev-spaces fourier-transform holder-spaces- 6,096
Partitioning vertices and deriving an upper bound for the number of edges of a vertex subset
combinatorics discrete-mathematics graph-theory extremal-graph-theory- 4,670
Triangulation of Mobius Strip to find the fundamental group
homology-cohomology homotopy-theory- 23
Max and min of a function with absolute values
derivatives absolute-value maxima-minima- 1
Is there a way to use the Weierstrass Substitution for $n\theta$?
trigonometry- 36.5k
Area of Complete Hyperbolic surface
differential-geometry algebraic-geometry hyperbolic-geometry- 1
Proving Equality for Subsets
elementary-set-theory- 726
Number of solutions for $x ^ y = y ^ x = k$
algebra-precalculus exponentiation- 5,134
convex function with global minimum but no local minimum
convex-analysis- 325
Estimate the limit or bounds of the smallest eigenvalue of a symmetric matrix
linear-algebra matrices eigenvalues-eigenvectors symmetric-matrices- 19k
This is a question from the book Introduction to Game Theory by Martin Osborne. The question number is exercise 44.1.
discrete-mathematics game-theory- 1
Why, in a set category, are all possibly functions included?
category-theory- 36
Is there any method other than Feynman’s Integration Technique to find $ \int_{0}^{\frac{\pi}{2}} \ln \left(a \cos ^{2} x+b \sin ^{2} x+c\right) d x?$
calculus integration definite-integrals- 6,107
Two differential forms are the same if they are the same locally.
differential-geometry differential-topology differential-forms- 26.5k
Given that $f(x) = x^k$ where $k < 0$, what is the range of $f(x)$ on the interval $[1, \infty)$?
functions- 67
Isogenous Elliptic Curves and Reduction Type
number-theory algebraic-geometry elliptic-curves- 21.6k
A clopen one-dimensional set in $\mathbb R^2$?
real-analysis general-topology terminology- 513
The geometry of $\operatorname{PSO}(4)$ and the quaternions
quaternions projective-geometry- 15.3k
What are the most known and optimized libraries for SDE in Python?
ordinary-differential-equations computational-mathematics stochastic-differential-equations python computational-science- 311
Chaotic discrete dynamical system on circle and torus
dynamical-systems ergodic-theory- 5
Why a retraction from a building to an apartment is not isometric?
group-theory metric-geometry coxeter-groups buildings affine-geometry- 101
The number of orbits of $\langle\pi\rangle$ on $\Omega$ is $\frac{1}{m}\sum_{d\mid m}f(\pi^d)\varphi(m/d)$
group-theory discrete-mathematics- 1,152
Can we determine the transition semigroup of a Markov process by its resolvent?
probability-theory measure-theory stochastic-processes markov-process semigroup-of-operators- 12.9k
How can I perform Union operation into two events?
probability solution-verification upper-lower-bounds- 853
Why the degree of $\pi$ does not increase
geometry analysis recreational-mathematics volume- 5,472
Asymptotic formula for logarithmic derivate of zeta function
number-theory asymptotics analytic-number-theory riemann-zeta- 1
What is the best interval size to consider in calculating the probabilities of a normally distributed sample?
probability normal-distribution- 208
Equivalence of different versions of Markov property
stochastic-processes stochastic-calculus stochastic-integrals stochastic-analysis- 319
Stereographic Projection Continuity Via Open Balls
general-topology continuity open-map stereographic-projections- 121
Does almost surely convergence implies convergence in $L^p$?
probability probability-theory convergence-divergence- 888
latin sqare on $\mathbb{F_q}$
discrete-mathematics latin-square- 343
a digit Divisible Number
number-theory- 8,310
What is the probability the statement is true given A and B contradict each other??(Slight twist in a very unique question)
probability recreational-mathematics- 9,341
Need help plugging in bounds in a u-substitution
calculus integration definite-integrals- 598
Show That Wigner’s Theorem Defines a Homomorphism $\operatorname{U}(2) \rightarrow \operatorname{SO}(3)$
abstract-algebra group-theory group-homomorphism quantum-mechanics- 15k
Can I derive the first moment when I am know the second and forth?
statistics maximum-likelihood- 669
Numerical approximation of Lamé curve perimeter for $n >2$
calculus approximation plane-curves arc-length- 31.3k
Problems about moving plane method
functional-analysis partial-differential-equations elliptic-equations- 21
Estimate the norm of the solution of an elliptic partial differential equations of second order
partial-differential-equations sobolev-spaces elliptic-equations- 21
Can these quadratic constraints be linearized?
optimization constraints linearization- 33.4k
Evan's statement about integral of the divergence of a vector field.
calculus integration partial-differential-equations divergence-theorem- 2,301
Positive semi-definite (psd) matrices associated with a family of partially recovering subsets of a given finite set
matrices elementary-set-theory eigenvalues-eigenvectors correlation positive-semidefinite- 46.1k
Probability of markov chain in a finite set
probability combinatorics markov-chains- 440
Measurable functions could be injective but not bijective?
real-analysis measure-theory- 35.9k
Is union of family of inner models also an inner model?
set-theory model-theory- 1,092
Need help finding a formula for question that was solved by trial and error
geometry area- 1
How do I express vectors as linear combinations?
linear-algebra- 726
Proving that $\angle MAC = 30^{\circ}$
geometry euclidean-geometry triangles angle- 437
Application of time reversal property of DFT
fourier-analysis- 1
Find the marginal density of $Y$ and $\mathbb{P}(Y>X)=\frac{5}{8}$.
probability probability-theory probability-distributions solution-verification- 837
What are the conditions for two vectors to be equal?
linear-algebra vectors physics- 7,291
Asymptotics of an integral with singular derivation
integration definite-integrals asymptotics approximation- 7,778
Non-trivial $P^1$ bundle over complex tori
differential-geometry algebraic-geometry complex-geometry fiber-bundles- 57
For every affine plane (P,L) of order n: every quivalence class of parallel lines has n lines.
discrete-mathematics affine-geometry- 343
Exponential generating function of the relation $B(n,k)=B(n-1,k-1)+(n-1)B(n-2,k-1)$ —just over $n$—
combinatorics generating-functions combinatorial-proofs- 119
Counting permutations $\pi \in S_n$ such that $\pi(i) \neq i$ and $\pi(i) - k \not\equiv i \bmod n$.
combinatorics permutations oeis derangements- 25.1k
What is the form of the normalizing constant of the continuous categorical distribution when two or more parameters are equal?
solution-verification- 26
Interesting probability problem on infinite processes
probability- 577
Polynomial factorization with three variables.
algebra-precalculus- 51
Using non-integer inputs for the Fourier Series
fourier-series fourier-transform- 37.9k
Deduce that $\{a_0,a_1,\cdots,a_{m-1}\}$ is not a complete set of residues $\mod m$.
number-theory elementary-number-theory modular-arithmetic- 2,625
Are circle-tangent polynomials always either odd or even?
algebraic-geometry polynomials- 186
Complex plane deprived from or deprived of closed disk?
article-writing- 139
Parameters in survival function not changing output.
probability random-variables parametrization- 256
If set $C$ has 60 elements, and set $B_i$ has 9 elements randomly sampled from $C$, what is the mean value of $i$ to seeing all elements of $C$?
probability statistics elementary-set-theory set-theory- 323
Kindly assist with with fourier series square waves
fourier-series- 1
Prove that $f^*(a)$ is a regular surface.
differential-geometry surfaces- 701
Log supermodularity property of Bivariate Normal CDF
probability-distributions normal-distribution bivariate-distributions- 1
Asymptotics of a two dimensional integral
integration definite-integrals asymptotics approximate-integration- 73
IDFT sum to find the center of the circle
fourier-transform- 105
Torsion Free Spin Connection
differential-geometry differential-topology differential-forms connections gauge-theory- 826
Strong mixing of a function of strong mixing and convergence sequence
probability convergence-divergence mixing- 440
Prove: at most two circles are needed to be tangent to all the circle sequence
sequences-and-series euclidean-geometry mobius-inversion- 684
Non-obvious Trigometric Integral
integration trigonometric-integrals- 2,388
Quotient of graded ring is graded - confusion about the formalisms
abstract-algebra ring-theory graded-rings- 13
Show that $M :=\{J\in M_{2n}(\mathbb{R}); J^2 = -I\}$ is a submanifold of $M_{2n}(\mathbb{R})$
linear-algebra geometry differential-geometry manifolds geometric-topology- 17.2k
Failure of the Lebesgue differentiation theorem
measure-theory metric-spaces lebesgue-integral measurable-functions- 1,482
Cauchy net equivalent condition
general-topology analysis cauchy-sequences topological-vector-spaces nets- 57.6k
Error types and statistical tests
probability statistical-inference hypothesis-testing- 1
Is ${G}/\ker(\phi)$ uniquely isomorphic to $\phi(G)$?
abstract-algebra group-theory group-isomorphism group-homomorphism- 1
Tricky convergence
real-analysis sequences-and-series convergence-divergence- 3,928
General form of integral possibly related to arctan function?
real-analysis calculus integration derivatives trigonometric-integrals- 35.3k
Preimage of zero under a continuous function on compact real interval has at most countable connected components
continuity cardinals connectedness infinity- 1,199
