User cs89

11 votes

Prove $ \frac{x_1-x_2}{x_n+x_1} + \frac{x_2-x_3}{x_1+x_2}+\cdots+ \frac{x_n-x_1}{x_{n-1} +x_n}\le 0$ s.t. $x_1+\cdots+x_n=1$

answered Apr 30, 2023 at 22:20

10 votes

Accepted

Shape that a bending rod makes

answered May 15, 2023 at 15:18

9 votes

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Is a piecewise linear function always a sum of concave and convex functions?

answered May 15, 2023 at 18:50

5 votes

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A Question on the Proof of A Form of the Minkowski Inequality

answered Apr 13, 2023 at 16:01

4 votes

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Can solution of any differential equation be expressed as power series?

answered Apr 14, 2023 at 7:03

4 votes

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Generalisation of Baker–Campbell–Hausdorff (Matrix exponential simplification)

answered Mar 10, 2023 at 8:44

4 votes

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Closedness of operator Hardy type

answered Mar 31, 2023 at 19:57

4 votes

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Pontryagin's Principle is a "necessary" condition?

answered Apr 30, 2023 at 16:30

4 votes

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Does the convergence of $\int_{0}^\infty |f(x)|\,dx$ imply the convergence of $\int_{0}^\infty f(x)\,dx$?

answered Apr 21, 2023 at 8:00

4 votes

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Can a cubic polynomial in two real variables have exactly three isolated critical points?

answered May 15, 2023 at 21:29

4 votes

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Is $x^a $sin$(x^{-a})$ Hölder continuous?

answered May 15, 2023 at 10:13

3 votes

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Binomial Expansion error approximation

answered May 17, 2023 at 20:36

3 votes

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Change of variable in an $L^\infty$ norm

answered May 13, 2023 at 20:27

3 votes

$F(u) = \int_{0}^{1} \big(e^{u' (x)} + u(x)^2 \big) \; dx$ does not have a minimizer on $X \cap C^2 [0,1] .$

answered Apr 20, 2023 at 22:28

3 votes

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Sign of a function near the boundary

answered Apr 24, 2023 at 13:53

3 votes

Accepted

Proof check: limit of product is equal to product of limits

answered Apr 25, 2023 at 7:41

3 votes

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Boundedness of a simple differential equation's solution

answered Apr 20, 2023 at 8:54

3 votes

Accepted

Supremum norm of derivative of Lipschitz continuous function

answered Apr 20, 2023 at 16:01

3 votes

Accepted

Proof that bilinear form $(u,v)_{L^2(\Omega)} \mapsto (\nabla u, \nabla v)_{L^2(\Omega)}$ is not coercive in $H^1(\Omega)$

answered Apr 25, 2023 at 12:33

3 votes

Leibniz integral rule for differentiation under the integral sign - is this condition needed?

answered Apr 6, 2023 at 10:20

3 votes

Breaking a rose up into distinct pieces

answered Apr 18, 2023 at 9:36

3 votes

Accepted

Solving $\sqrt{3} \sin x = \cos x$ for $0<x<2\pi$. There should be only two solutions, but I get four.

answered Apr 13, 2023 at 6:55

2 votes

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Are $L^p$ functions continuous almost everywhere?

answered Apr 12, 2023 at 14:15

2 votes

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Sequence function on $C[-2,2]$ is Cauchy Sequence

answered Apr 18, 2023 at 12:17

2 votes

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Reference on correlation and linear regression connection

answered Apr 19, 2023 at 15:27

2 votes

Ratios of higher order derivatives with exponentially growing bound.

answered Apr 18, 2023 at 17:10

2 votes

Accepted

Compact Sobolev embedding on unbounded domain

answered Apr 3, 2023 at 12:37

2 votes

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$I(u)= \int_{-1}^1x^2(u'(x))^2dx$ How do I prove that the condition $\exists$ $c_1 >0, c_2 \ge 0 $ ,$f(x,y,z)\ge c_1|z|^2-c_2 $ does not hold?

answered Apr 4, 2023 at 7:47

2 votes

Lie Groups and Lie Algebra for Nonlinear System Dynamics

answered Mar 10, 2023 at 9:00

2 votes

Accepted

Does continuity imply the following property?

answered Apr 27, 2023 at 20:04

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104 Answers

Prove $ \frac{x_1-x_2}{x_n+x_1} + \frac{x_2-x_3}{x_1+x_2}+\cdots+ \frac{x_n-x_1}{x_{n-1} +x_n}\le 0$ s.t. $x_1+\cdots+x_n=1$

Shape that a bending rod makes

Is a piecewise linear function always a sum of concave and convex functions?

A Question on the Proof of A Form of the Minkowski Inequality

Can solution of any differential equation be expressed as power series?

Generalisation of Baker–Campbell–Hausdorff (Matrix exponential simplification)

Closedness of operator Hardy type

Pontryagin's Principle is a "necessary" condition?

Does the convergence of $\int_{0}^\infty |f(x)|\,dx$ imply the convergence of $\int_{0}^\infty f(x)\,dx$?

Can a cubic polynomial in two real variables have exactly three isolated critical points?

Is $x^a $sin$(x^{-a})$ Hölder continuous?

Binomial Expansion error approximation

Change of variable in an $L^\infty$ norm

$F(u) = \int_{0}^{1} \big(e^{u' (x)} + u(x)^2 \big) \; dx$ does not have a minimizer on $X \cap C^2 [0,1] .$

Sign of a function near the boundary

Proof check: limit of product is equal to product of limits

Boundedness of a simple differential equation's solution

Supremum norm of derivative of Lipschitz continuous function

Proof that bilinear form $(u,v)_{L^2(\Omega)} \mapsto (\nabla u, \nabla v)_{L^2(\Omega)}$ is not coercive in $H^1(\Omega)$

Leibniz integral rule for differentiation under the integral sign - is this condition needed?

Breaking a rose up into distinct pieces

Solving $\sqrt{3} \sin x = \cos x$ for $0<x<2\pi$. There should be only two solutions, but I get four.

Are $L^p$ functions continuous almost everywhere?

Sequence function on $C[-2,2]$ is Cauchy Sequence

Reference on correlation and linear regression connection

Ratios of higher order derivatives with exponentially growing bound.

Compact Sobolev embedding on unbounded domain

$I(u)= \int_{-1}^1x^2(u'(x))^2dx$ How do I prove that the condition $\exists$ $c_1 >0, c_2 \ge 0 $ ,$f(x,y,z)\ge c_1|z|^2-c_2 $ does not hold?

Lie Groups and Lie Algebra for Nonlinear System Dynamics

Does continuity imply the following property?