User Hans

16 votes

3 answers

611 views

Convexity of $x\left(1+\frac1x\right)^x,\ x\ge 0$

asked Jan 25, 2017 at 9:23

12 votes

5 answers

3k views

Minimize $\min_{f\in E}\left(\int_0^1f(x) dx\right)$

calculus real-analysis inequality optimization contest-math

asked Nov 10, 2017 at 22:48

11 votes

3 answers

729 views

Local maximum uniqueness of the logarithm of the Student-t distribution

real-analysis inequality special-functions maxima-minima gamma-function

asked May 15, 2021 at 1:20

10 votes

1 answer

300 views

permutation search game

combinatorics algorithms combinatorial-game-theory

asked Mar 5, 2013 at 14:10

9 votes

1 answer

6k views

Expectation of Exponential of Stochastic Integral

stochastic-calculus brownian-motion stochastic-integrals

asked Nov 9, 2014 at 19:02

9 votes

3 answers

498 views

Compute $\int_{0}^{\infty} \frac{\sqrt{x}\sin(x)}{1+x^2} dx$

integration definite-integrals improper-integrals contour-integration

asked Aug 12, 2017 at 0:05

8 votes

1 answer

185 views

range of a fractional function

inequality

asked Mar 3, 2013 at 18:31

8 votes

3 answers

8k views

Example of continuous but not absolutely continuous strictly increasing function

real-analysis functions examples-counterexamples absolute-continuity

asked Dec 17, 2013 at 18:05

7 votes

1 answer

2k views

Convergence to the Dirac Delta Function

real-analysis probability-theory distribution-theory dirac-delta

asked May 9, 2015 at 22:21

7 votes

3 answers

256 views

functional equation $f(x^2)=xf(x)$

functional-equations

asked Dec 18, 2019 at 23:01

6 votes

5 answers

172 views

Prove $\sqrt{a^2+4}+\sqrt{b^2+4}\leq\frac{\sqrt{2}}{4}(a+b)^2$ with $\frac1a+\frac1b=1$.

inequality cauchy-schwarz-inequality a.m.-g.m.-inequality

asked Jan 24, 2020 at 17:15

6 votes

2 answers

293 views

Prove $\sum_{\text{cyc}}^{}\sqrt[3] {1+2ac} \le 3\sqrt [3] {3}$.

inequality

asked Dec 14, 2019 at 18:43

6 votes

1 answer

203 views

Seeking a More Elegant Proof to an Expectation Inequality

real-analysis probability-theory inequality alternative-proof integral-inequality

asked May 22, 2015 at 17:48

6 votes

3 answers

201 views

No Adjacency Combinatorics Problem via Generating Function

probability combinatorics generating-functions

asked Jun 27, 2015 at 19:30

6 votes

3 answers

331 views

Nonuniqueness of Stochastic Differential Equation

ordinary-differential-equations stochastic-processes stochastic-analysis

asked Jun 26, 2016 at 19:55

6 votes

1 answer

798 views

Hermite polynomials approximate of a function and its derivatives

real-analysis approximation-theory orthogonal-polynomials hermite-polynomials

asked Oct 4, 2017 at 20:53

6 votes

2 answers

673 views

The asymptotic expansion of an integral of an exponential function

real-analysis asymptotics

asked Aug 22, 2018 at 4:21

5 votes

1 answer

151 views

Guessing the number of other $1$'s in a binary sequence

discrete-mathematics recreational-mathematics puzzle information-theory coding-theory

asked Sep 22, 2019 at 7:13

5 votes

2 answers

306 views

Quadratic surd continued fraction convergent ratio limit

number-theory continued-fractions

asked Jun 4, 2018 at 22:24

5 votes

2 answers

172 views

An integral inequality for variance

real-analysis inequality integral-inequality

asked Dec 21, 2017 at 22:26

5 votes

0 answers

66 views

Arranging Points Uniformly on the Unit Sphere

linear-algebra geometry optimization quadratic-programming

asked Feb 2, 2017 at 0:33

5 votes

2 answers

958 views

Why Is Inverse of a Polynomial Still a Polynomial?

polynomials ring-theory field-theory extension-field

asked Jan 1, 2017 at 9:01

5 votes

0 answers

1k views

sum of digits in different bases

number-theory elementary-number-theory

asked Mar 22, 2013 at 18:23

4 votes

2 answers

276 views

Is Fibonacci sequence the minimum of unique pairwise sum sequence?

sequences-and-series elementary-number-theory fibonacci-numbers

asked Jul 30, 2013 at 4:28

4 votes

3 answers

452 views

A convolution like integral equation

real-analysis fourier-analysis laplace-transform integral-transforms integral-equations

asked Jan 6, 2014 at 4:17

4 votes

1 answer

186 views

optimal sorting

algorithms extremal-combinatorics

asked Mar 3, 2013 at 18:10

4 votes

1 answer

277 views

Derivation of the Fourier Sine Transform of a Rational Function

integration fourier-analysis improper-integrals fourier-transform contour-integration

asked Aug 31, 2017 at 23:19

4 votes

1 answer

286 views

A functional equation of a matrix

linear-algebra matrices polynomials determinant functional-equations

asked Sep 23, 2018 at 20:51

4 votes

0 answers

129 views

Partial differential equation with a nowhere differentiable boundary

reference-request partial-differential-equations boundary-value-problem fractals elliptic-equations

asked Jan 4, 2019 at 2:19

3 votes

0 answers

303 views

Interchanging Integration Order involving Fourier Transform

integration fourier-transform distribution-theory harmonic-analysis

asked Feb 16, 2019 at 21:59

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193 Questions

Convexity of $x\left(1+\frac1x\right)^x,\ x\ge 0$

Minimize $\min_{f\in E}\left(\int_0^1f(x) dx\right)$

Local maximum uniqueness of the logarithm of the Student-t distribution

permutation search game

Expectation of Exponential of Stochastic Integral

Compute $\int_{0}^{\infty} \frac{\sqrt{x}\sin(x)}{1+x^2} dx$

range of a fractional function

Example of continuous but not absolutely continuous strictly increasing function

Convergence to the Dirac Delta Function

functional equation $f(x^2)=xf(x)$

Prove $\sqrt{a^2+4}+\sqrt{b^2+4}\leq\frac{\sqrt{2}}{4}(a+b)^2$ with $\frac1a+\frac1b=1$.

Prove $\sum_{\text{cyc}}^{}\sqrt[3] {1+2ac} \le 3\sqrt [3] {3}$.

Seeking a More Elegant Proof to an Expectation Inequality

No Adjacency Combinatorics Problem via Generating Function

Nonuniqueness of Stochastic Differential Equation

Hermite polynomials approximate of a function and its derivatives

The asymptotic expansion of an integral of an exponential function

Guessing the number of other $1$'s in a binary sequence

Quadratic surd continued fraction convergent ratio limit

An integral inequality for variance

Arranging Points Uniformly on the Unit Sphere

Why Is Inverse of a Polynomial Still a Polynomial?

sum of digits in different bases

Is Fibonacci sequence the minimum of unique pairwise sum sequence?

A convolution like integral equation

optimal sorting

Derivation of the Fourier Sine Transform of a Rational Function

A functional equation of a matrix

Partial differential equation with a nowhere differentiable boundary

Interchanging Integration Order involving Fourier Transform