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15

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Prove that $2^{2m}\sin^{2m} x = \sum\limits_{k=0}^{m-1} (-1)^{m+k} C^{2m}_k \cos (2m-2k)x + C^{2m}_m$

complex-analysis complex-numbers summation

answered 1 min ago zinoviev 642

0

votes

0

answers

3

views

Limit of CDFs and inverse CDFs for transformed random variables

probability probability-theory

asked 1 min ago NPHA 337

0

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0

answers

20

views

Show $\lim \limits_{t \to \infty} x(t) = 0$ exponentially for any $x(0)\in \mathbb{R}^n$ if $\lim \limits_{t \to \infty} u(t) = 0$ exponentially.

linear-algebra control-theory linear-control

modified 5 mins ago Shawn 1

0

votes

0

answers

4

views

Relative magnitude of the mean and the root mean squared?

convex-analysis exponential-function variance average mean-square-error

asked 7 mins ago andrewH 195

8

votes

2

answers

85

views

How can I find the exact value of $ \int_{0}^{\frac{\pi}{2}} \frac{x}{\sin ^{8} x+\cos ^{8} x} d x $ using substitutions?

integration trigonometry

modified 8 mins ago Claude Leibovici 200k

0

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0

answers

12

views

Proving definition of $m-n$ in $\mathbb{N}$

elementary-number-theory

asked 9 mins ago Lambert 21

0

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0

answers

6

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Faulty proof in the claim "If a polynomial is irreducible in $Z_p [x]$ then it is irreducible in $Z_{p^k} [x]$?

number-theory modular-arithmetic irreducible-polynomials polynomial-rings

asked 10 mins ago Jaculex9000 23

0

votes

1

answer

21

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How do we calculate the derivative of the inverse of a matrix?

derivatives approximation

modified 10 mins ago nejimban 1,557

0

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0

answers

10

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Weakening of $\diamondsuit$ implies CH

set-theory

asked 11 mins ago Good Morning Captain 1,766

0

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1

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28

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Law of large numbers with convergence in mean

probability-theory measure-theory random-variables lp-spaces

answered 13 mins ago StratosFair 912

0

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0

answers

9

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how do i solve this complex variables equation?

complex-numbers logarithms

modified 13 mins ago user10354138 29.8k

0

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0

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21

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Proving that $\frac{2n+1}{n+1}$ is not an integer for any $n>0$

proof-writing

modified 14 mins ago werner_b 13

-1

votes

0

answers

24

views

Prove $\left( {\frac{{a + b}}{2}} \right)^x$ > $\frac{{{a^x} + {b^x}}}{2}$ or $\left( {\frac{{a + b}}{2}} \right)^x$ < $\frac{{{a^x} + {b^x}}}{2}$?

inequality solution-verification

modified 15 mins ago e2e000 1

0

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1

answer

30

views

Elliptic curve over $\mathbb{Q}$ with two distinct non-torsion points $P$ and $Q$ such that $nP \neq mQ$ for all $n,m \in \mathbb{Z}-\{0\}$.

number-theory elliptic-curves torsion-groups

modified 15 mins ago Atratrana Suna 43

0

votes

0

answers

3

views

Best subset selection

optimization convex-optimization gradient-descent

asked 16 mins ago user13 1,580

0

votes

1

answer

23

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Limit question: Does $(k-n)/\sqrt{n} \to x$ imply $k-n \to x\sqrt{n}?$

calculus probability-limit-theorems

answered 18 mins ago Gary 15.4k

0

votes

0

answers

3

views

Find the value of k for which the line integral depends only on the coordinates of the end points of C.

calculus linear-algebra algebra-precalculus line-integrals greens-theorem

modified 20 mins ago Yuwen Aw 1

2

votes

0

answers

24

views

Conditional expectation for random vectors

probability-theory conditional-expectation

modified 22 mins ago StubbornAtom 13.9k

1

vote

1

answer

24

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Learning representation of Lie algebras for someone who knows representations of the symmetric group

representation-theory lie-algebras symmetric-groups

answered 24 mins ago Dac0 8,472

1

vote

0

answers

9

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Does holomorphic functional calculus for unital $C^{\ast}$-algebra preserve involution?

operator-theory c-star-algebras banach-algebras functional-calculus

modified 25 mins ago Just a user 1,464

0

votes

0

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26

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Conditional expectation and indicator function

probability-theory measure-theory conditional-probability conditional-expectation measurable-functions

modified 27 mins ago StubbornAtom 13.9k

0

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0

answers

8

views

Compute the Fourier coefficients of $f( \theta) = \theta(\pi − \theta)$

fourier-analysis fourier-transform

asked 31 mins ago singleton 21

2

votes

1

answer

32

views

Sub-base theorem Is this proof correct?

general-topology

modified 36 mins ago Henno Brandsma 213k

1

vote

0

answers

14

views

Is the axiom of countable choice equivalent to the statement that every infinite set has a countably infinite subset?

set-theory

modified 37 mins ago Noah Schweber 209k

0

votes

1

answer

36

views

Question about Heine-Borel Theorem

real-analysis measure-theory

modified 40 mins ago StubbornAtom 13.9k

-1

votes

0

answers

13

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Image of orthonormal basis under bounded operator

hilbert-spaces orthonormal

modified 40 mins ago Aniruddha Deshmukh 3,358

0

votes

0

answers

11

views

Vestrup Measure and Integration Exercise 5.1.6

real-analysis measure-theory lebesgue-measure measurable-functions

modified 40 mins ago thewatcher 717

-1

votes

0

answers

9

views

Can A Shear Transformation be Represented in Cartesian Form

linear-algebra linear-transformations

asked 44 mins ago Arkhaven369 19

0

votes

0

answers

4

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Concrete bounds on the expected width of a conditioned Galton-Watson tree?

probability-distributions trees upper-lower-bounds

asked 45 mins ago Daniel-耶稣活着 111

0

votes

1

answer

30

views

Little "oh" and prime number theorem

combinatorics number-theory prime-numbers analytic-number-theory

answered 48 mins ago Jacob 1,646

0

votes

0

answers

4

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Corresponding graphs to matrices

linear-algebra algebraic-graph-theory

modified 49 mins ago Choomno Moos 3

1

vote

0

answers

9

views

Harmonic function extension and Conformal maps

complex-analysis analysis harmonic-functions conformal-geometry potential-theory

asked 50 mins ago porridgemathematics 1,354

3

votes

1

answer

926

views

Is my proof for if ab = 0 then either a=0 or b=0, when we are using integers, correct?

real-analysis solution-verification integers

modified 53 mins ago CommunityBot 1

0

votes

1

answer

13

views

Minimum # of subsets in partition $\{2, 3, 4..., 2^n\}$ so that every subset contain only numbers that are not multiples of each other.

number-theory set-partition

answered 54 mins ago Misha Lavrov 99.3k

1

vote

0

answers

12

views

Useful form of $SL(2, \mathbb{R})$ matrices

linear-algebra matrices functional-analysis

asked 55 mins ago Adam 443

1

vote

0

answers

66

views

Setup complex line integral $\int_{\gamma}x^2+y^2 dz$, where $\gamma$ is the line segment from $i+2$ to $-i-1$

integration complex-analysis solution-verification complex-integration line-integrals

modified 55 mins ago BCLC 10.8k

0

votes

0

answers

21

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Evaluating $\int_{\gamma} (z^2 \sin^3z-(z-i)^3+2z+1)dz$

integration complex-analysis solution-verification complex-integration line-integrals

modified 58 mins ago BCLC 10.8k

-1

votes

0

answers

51

views

rank $n-1$ implies nonzero minor of size $(n-1) \times (n-1)$

linear-algebra matrices solution-verification determinant matrix-rank

modified 1 hour ago BCLC 10.8k

0

votes

1

answer

47

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Determinant of sort of companion matrix

linear-algebra matrices solution-verification determinant companion-matrices

modified 1 hour ago BCLC 10.8k

1

vote

2

answers

26

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Making Sense of Method of Characteristics Solution Geometry

geometry partial-differential-equations 3d characteristics transport-equation

answered 1 hour ago Calvin Khor 29.1k

0

votes

0

answers

4

views

Contour Integration of Fresnel Integrals, Help with Trig Steps

complex-analysis contour-integration

asked 1 hour ago lightnesscaster 316

0

votes

0

answers

3

views

Solving a LPP question using BIG-M method

linear-programming simplex-method

modified 1 hour ago heera thakur 65

1

vote

1

answer

60

views

How to prove that $\left(1+\frac{1}{x^n}\right)\left(1+\frac{1}{y^n}\right)>(1+2^n)^2.$

inequality

answered 1 hour ago See Hai 1,866

0

votes

0

answers

28

views

A file is locked with an integer password that is 1 digit long

probability

asked 1 hour ago Changhe Qiao 11

4

votes

0

answers

25

views

"rotating" a matrix instead of transposing it

linear-algebra matrices

modified 1 hour ago Phenomenom 71

0

votes

0

answers

4

views

A simple and more generalised way to define this coefficient

combinatorics binomial-coefficients generating-functions

asked 1 hour ago Aji Wibowo 13

0

votes

0

answers

6

views

What's the likelihood function? Lactose intolerant exercise

bayes-theorem

asked 1 hour ago Raibek 86

-1

votes

0

answers

27

views

Polynomial remainder theorem where only one remainder is given and it is in quadratic form

polynomials

modified 1 hour ago user984036 1

0

votes

0

answers

15

views

Let $ f \in R([0,2 \pi]) $. Then, $ \forall \epsilon>0 $ there exists a continuous function $ g $ on $ [0, 2 \pi ] $ s.t. $ || f - g || < \epsilon $.

real-analysis fourier-series riemann-integration

modified 1 hour ago hazelnut_116 1,001

0

votes

0

answers

16

views

Show that $\mathbb{Z}[i]=\{m+in\colon\; m,n\in\mathbb{Z}\}$ is a P.I.D

abstract-algebra number-theory principal-ideal-domains gaussian-integers

modified 1 hour ago Choripán con pebre 761

0

votes

0

answers

5

views

How to find transformed representation of coordinates using transformation matrix?

linear-transformations

modified 1 hour ago Saurav Yadav 1

0

votes

0

answers

8

views

Recursive Formula to Explicit

sequences-and-series polynomials recursion geometric-series

asked 1 hour ago abc123321 1

0

votes

0

answers

7

views

Consider the function f(x)=[x] +|1-x| . (-1≤ x≤ 3) where [ ] is gif. Find the number of points where f(x) is discontinuous.

calculus limits functions continuity

asked 1 hour ago Bornil Buragohain 1

0

votes

1

answer

24

views

Find the expectation and variance of the random variable $X$ in the following cases:

probability probability-theory statistics

answered 1 hour ago Kavi Rama Murthy 280k

4

votes

2

answers

1k

views

Combinatorics - Counting the number of binary strings with specified length and sum, with substring constraints

combinatorics binary

modified 1 hour ago CommunityBot 1

-2

votes

0

answers

20

views

How woul you solve this?

real-analysis sequences-and-series

asked 1 hour ago Ian Bollschweiler Vargas 1

0

votes

0

answers

17

views

How to prove the 3rd HBL derivability condition in PA?

first-order-logic incompleteness

modified 1 hour ago 정재우 73

1

vote

1

answer

17

views

Dimension of ring by $\dim_k (m^i/m^{i +1})$ for all $i(2≦i＜∞)$ is the same as the embedding dimension?

abstract-algebra ring-theory vector-spaces dimension-theory-algebra

modified 1 hour ago Martin Sleziak 51.6k

1

vote

1

answer

30

views

What's the expectation $E[A^2(A+B)]$ given A and B are jointly normal variables?

normal-distribution expected-value

answered 1 hour ago Brian Moehring 12.6k

0

votes

1

answer

29

views

Line integral work done = 0

integration vector-fields

answered 2 hours ago Doug M 5,101

2

votes

0

answers

78

views

Given: $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{3}{2}.$ prove: $\frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b}+3\ge\sum_{cyc}{\sqrt{a^2+b^2+1}}$

inequality

modified 2 hours ago Mars 53

0

votes

0

answers

12

views

Set notation to describe the set of sub-intervals of an interval $L$ over which $f(t)\leq f^$ and over which a minimum of at least $f^-1$ occurs

notation set-theory

modified 2 hours ago tardigrade 5

1

vote

0

answers

29

views

Books reccomendation after '(advanced topics of )the arithmetic of elliptic curves'

reference-request book-recommendation arithmetic-geometry

modified 2 hours ago dandelion 3,514

0

votes

1

answer

28

views

Projectile distance estimation

calculus algebra-precalculus polynomials taylor-expansion physics

answered 2 hours ago Claude Leibovici 200k

0

votes

0

answers

26

views

Decipher the following encrypted message using $e = 37$, $m = 10807$ : $1$ $1819$ $8975$ $1933$ $2794$ $7318$ $4570$ $3563$ $10014$ $2843$ $207$ RSA

number-theory modular-arithmetic cryptography

asked 2 hours ago ddswsd 1,175

1

vote

0

answers

18

views

Monte Carlo for estimating small

probability statistics numerical-methods monte-carlo simulation

asked 2 hours ago Almost nice 136

0

votes

1

answer

12

views

Expected time taken for the first event among 2 events belonging to exponential distribution.

probability-theory probability-distributions exponential-distribution

modified 2 hours ago angryavian 75.2k

1

vote

0

answers

26

views

Nondimensionalization Trick

ordinary-differential-equations partial-differential-equations nonlinear-system non-linear-dynamics dimensional-analysis

asked 2 hours ago user10478 1,627

0

votes

1

answer

11

views

Criterion for continuity of function defined on a colim of topological spaces

general-topology continuity category-theory

answered 3 hours ago Kevin Arlin 46.6k

4

votes

1

answer

1k

views

Is p(x)dx equal to dp(x)?

probability probability-theory

answered 3 hours ago Archibald Chain 11

2

votes

0

answers

17

views

Proving existence of point in an interval where integral's value is 0

real-analysis riemann-integration

asked 3 hours ago jclu12 51

1

vote

0

answers

15

views

Is maximum entropy loss (maxent) convex?

optimization convex-analysis convex-optimization

modified 3 hours ago Sepide 935

0

votes

1

answer

20

views

Is it possible to construct arbitrary direct sums in the category of R modules?

category-theory modules homological-algebra direct-sum abelian-categories

answered 3 hours ago Erik D 554

0

votes

0

answers

19

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Zero tensors in the tensor product of two vector spaces?

linear-algebra tensor-products

modified 3 hours ago Eric Wofsey 283k

0

votes

0

answers

8

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Compete direct sum

modules

asked 3 hours ago Hussein Eid 359

1

vote

0

answers

14

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How can we taking derivatives on $UV$ w.r.t a vector $\mathbf{x}$ by using the chain rule and $d(UV)=dU\cdot V + U\cdot dV$?

derivatives chain-rule hessian-matrix

modified 3 hours ago Gary 15.4k

0

votes

0

answers

27

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Are quaternions algebraic numbers?

algebraic-number-theory quaternions

asked 3 hours ago Vlad 1

0

votes

0

answers

14

views

Question about convergent sequences in a metric space

real-analysis

asked 3 hours ago fairlife4life 25

0

votes

0

answers

15

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Prove that $ P(T>n)=P\left(X_{n}>Y_{n}\right)-P\left(X_{n}<Y_{n}\right) $

probability markov-process random-walk stopping-times

asked 3 hours ago codelearner 249

0

votes

1

answer

27

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Logarithmic differentiation with Riccati's differential equation

ordinary-differential-equations logarithms systems-of-equations

modified 3 hours ago electrical apprentice 637

0

votes

0

answers

4

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Inequality with truncated vectors

analysis inequality hilbert-spaces

asked 3 hours ago kers_bun 15

0

votes

0

answers

6

views

How to prove this upper bound of generalized Mangoldt function?

number-theory analytic-number-theory upper-lower-bounds arithmetic-functions

asked 3 hours ago QWQ 1

1

vote

0

answers

35

views

Ratios of integers in Bezout's Identity

elementary-number-theory approximation rational-numbers diophantine-approximation

modified 4 hours ago Integrand 8,403

2

votes

0

answers

17

views

Determine whether if T where $T:P_2\to P_2$ defined by $T(a+bx+cx^2)=a+b(x+1)+b(x+1)^2$ is linear and then prove.

linear-algebra proof-writing linear-transformations

modified 4 hours ago Thomas Andrews 160k

1

vote

1

answer

21

views

continuity of a function with singular integrand

real-analysis calculus

modified 4 hours ago zugzug 5,010

2

votes

3

answers

53

views

Approximate solution to a transcendental equation

approximation problem-solving transcendental-equations

modified 4 hours ago Claude Leibovici 200k

0

votes

0

answers

10

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Homogeneous components of a module

modules

asked 4 hours ago Hussein Eid 359

0

votes

0

answers

6

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Queueing average time with 3 servers

stochastic-processes exponential-distribution queueing-theory

asked 4 hours ago jimmyAtUCLA 133

0

votes

0

answers

11

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Hessenburg matrix properties when sub-diagonal entries are non-zero

linear-algebra eigenvalues-eigenvectors numerical-linear-algebra

modified 4 hours ago 311411 2,174

0

votes

0

answers

6

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Time Evolving Diffusion Equation

partial-differential-equations heat-equation

asked 4 hours ago FluidMan 77

0

votes

0

answers

13

views

Statement about Jordan curves

complex-analysis homotopy-theory curves

asked 4 hours ago matty_k_walrus 504

0

votes

1

answer

11

views

Set builder notation for time at which a stationary equilibrium is reached?

set-theory

answered 4 hours ago Eric Towers 62.4k

1

vote

2

answers

49

views

Prove $\forall (m,n)\in \mathbb{N}^{2}: m<n\implies m-n\notin \mathbb{N}$

elementary-number-theory

modified 5 hours ago Lambert 21

1

vote

3

answers

49

views

Show that $\{T \in \mathcal{L}(\mathbb{R}^5, \mathbb{R}^4) : \text{dim}(\text{null}(T)) > 2\}$ is not a subspace

linear-algebra

modified 5 hours ago Shoebagel 13

2

votes

1

answer

29

views

Can it be shown that $r^2=\frac{1}{1-\varepsilon\cos(2\theta)}$ gives a conic section?

analytic-geometry conic-sections polar-coordinates

modified 6 hours ago Blue 67.1k

0

votes

0

answers

18

views

Analytic solution for $A\cos(x+\theta)+B\cos{2x}+Cx+D=0$?

algebra-precalculus trigonometry

asked 6 hours ago Hamid 29

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