User user475680

24 votes

2 answers

32k views

Prove local minimum of a convex function is a global minumum (using only convexity)

asked May 13, 2015 at 12:42

5 votes

1 answer

613 views

Prove $f(\sum^k_{i=1} \alpha_i x_i) \leq \sum^k_{i=1} \alpha_i f(x_i) $ for a convex function f

asked May 12, 2015 at 14:02

4 votes

2 answers

3k views

For a PAC learnable hypothesis Show that its sample complexity $m_{\mathcal{H}}$ is monotonically non-increasing in each of its parameters

asked Apr 15, 2015 at 10:34

4 votes

3 answers

331 views

Finding the limit of $ \frac{1}{n}\sum_{k=1}^{n}\sqrt[k]{k} $

asked Dec 4, 2013 at 15:56

3 votes

1 answer

176 views

Prove that the sequence $1+\sum_{k=1}^{n}\frac{k+1}{3^{k}+1}$ converges using Cauchy

asked Dec 11, 2013 at 14:57

3 votes

2 answers

92 views

Prove $A^{2}=0$ iff $C\left(A\right)=R^{0}\left(A\right) $

asked Mar 4, 2014 at 15:49

3 votes

1 answer

355 views

Prove the following: $\int_{a}^{b}|f\left(t\right)|dt\leq\left(b-a\right)\int_{a}^{b}|f'\left(t\right)|dt$

asked Apr 29, 2014 at 16:18

3 votes

3 answers

532 views

Does $\int _1^{\infty }\left(\sin \left(x^2\right)\right)dx$ converge or diverge? [duplicate]

asked May 14, 2014 at 11:57

2 votes

2 answers

192 views

Calculate $\lim_{n\rightarrow\infty}\frac{1}{n}\left(\prod_{k=1}^{n}\left(n+3k-1\right)\right)^{\frac{1}{n}}$

asked Apr 30, 2014 at 8:59

2 votes

2 answers

1k views

Show that two bounded sequences have convergent subsequences with the same index sequence

asked Dec 6, 2013 at 17:31

2 votes

1 answer

332 views

Prove that for every subspace we can find a finite number of linear functionals such that $W=\ker l_{1}\cap\cdots\cap \ker l_{k}$

asked Mar 13, 2014 at 17:27

2 votes

1 answer

420 views

Prove $\forall z\left(\left(\exists xA\rightarrow A_{x}[z]\right)\rightarrow B\right)\vDash B$

asked Jan 27, 2015 at 17:33

2 votes

2 answers

687 views

Prove that a multivariable function has a global minimum

asked Mar 2, 2015 at 17:08

1 vote

2 answers

237 views

Modifying the result matrices of SVD so that $\Sigma$ is canonical form

asked Dec 15, 2015 at 19:07

1 vote

3 answers

232 views

Question on how to prove sup(A) = sup(B) = sup(C)

asked Nov 6, 2013 at 20:08

1 vote

1 answer

112 views

Prove that $ (\sqrt{a_{n}})_{n=1}^{\infty}\rightarrow \sqrt{a} $ when $ (a_{n})_{n=1}^{\infty}\rightarrow a $

asked Nov 19, 2013 at 17:41

1 vote

2 answers

88 views

Prove that $ \left(a_{n}\right)_{n=1}^{\infty} $ converges when $|a_{n+1}-a_{n}|<q|a_{n}-a_{n-1}|$ for $ 0<q<1 $

asked Dec 11, 2013 at 15:18

1 vote

1 answer

138 views

Find values of $\alpha$ for $ f:\left[0,1\right]\rightarrow\left[0,1\right] $ such that $ f\left(c\right)=\alpha\cdot c$

asked Dec 31, 2013 at 16:48

1 vote

2 answers

1k views

Prove that the Rational function $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$ is uniformly continuous

asked Feb 18, 2014 at 16:32

1 vote

1 answer

240 views

If $\int _1^{\infty }f\left(x\right)dx$ converges absolutely then $\int _1^{\infty }\sin \left(x\right)f\left(x\right)dx$ exists

asked May 18, 2014 at 11:57

1 vote

2 answers

152 views

First Order Logic - coming up with an example

asked Dec 30, 2014 at 21:29

1 vote

2 answers

537 views

First Order Logic and groups: Prove that no $T$ exists such that $M \vDash T \cup T_{grp}$ IFF

asked Jan 13, 2015 at 17:37

0 votes

1 answer

496 views

First Order Logic prove there exists a Model that has an infinite member

asked Jan 14, 2015 at 13:09

0 votes

1 answer

51 views

Help with Dual Spaces - Prove that either $w\in Im(f)$ or there exists ${l\in W^{}}$ such that $f^{}\left(l\right)=0$ and $l(w)=1$"

asked Mar 13, 2014 at 17:00

0 votes

1 answer

275 views

Prove or disprove that there exists a linear map given a set of vectors and their mapping

asked Dec 15, 2013 at 9:47

0 votes

2 answers

101 views

Prove that $\limsup\left(b_{n}a_{n}\right)=\limsup\left(a_{n}\right) $ when $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$

asked Dec 7, 2013 at 9:24

0 votes

1 answer

201 views

Prove $K_4-Cover$ is NP-Complete

asked Aug 4, 2015 at 12:44

Stack Exchange Network

27 Questions

Prove local minimum of a convex function is a global minumum (using only convexity)

Prove $f(\sum^k_{i=1} \alpha_i x_i) \leq \sum^k_{i=1} \alpha_i f(x_i) $ for a convex function f

For a PAC learnable hypothesis Show that its sample complexity $m_{\mathcal{H}}$ is monotonically non-increasing in each of its parameters

Finding the limit of $ \frac{1}{n}\sum_{k=1}^{n}\sqrt[k]{k} $

Prove that the sequence $1+\sum_{k=1}^{n}\frac{k+1}{3^{k}+1}$ converges using Cauchy

Prove $A^{2}=0$ iff $C\left(A\right)=R^{0}\left(A\right) $

Prove the following: $\int_{a}^{b}|f\left(t\right)|dt\leq\left(b-a\right)\int_{a}^{b}|f'\left(t\right)|dt$

Does $\int _1^{\infty }\left(\sin \left(x^2\right)\right)dx$ converge or diverge? [duplicate]

Calculate $\lim_{n\rightarrow\infty}\frac{1}{n}\left(\prod_{k=1}^{n}\left(n+3k-1\right)\right)^{\frac{1}{n}}$

Show that two bounded sequences have convergent subsequences with the same index sequence

Prove that for every subspace we can find a finite number of linear functionals such that $W=\ker l_{1}\cap\cdots\cap \ker l_{k}$

Prove $\forall z\left(\left(\exists xA\rightarrow A_{x}[z]\right)\rightarrow B\right)\vDash B$

Prove that a multivariable function has a global minimum

Modifying the result matrices of SVD so that $\Sigma$ is canonical form

Question on how to prove sup(A) = sup(B) = sup(C)

Prove that $ (\sqrt{a_{n}})_{n=1}^{\infty}\rightarrow \sqrt{a} $ when $ (a_{n})_{n=1}^{\infty}\rightarrow a $

Prove that $ \left(a_{n}\right)_{n=1}^{\infty} $ converges when $|a_{n+1}-a_{n}|<q|a_{n}-a_{n-1}|$ for $ 0<q<1 $

Find values of $\alpha$ for $ f:\left[0,1\right]\rightarrow\left[0,1\right] $ such that $ f\left(c\right)=\alpha\cdot c$

Prove that the Rational function $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$ is uniformly continuous

If $\int _1^{\infty }f\left(x\right)dx$ converges absolutely then $\int _1^{\infty }\sin \left(x\right)f\left(x\right)dx$ exists

First Order Logic - coming up with an example

First Order Logic and groups: Prove that no $T$ exists such that $M \vDash T \cup T_{grp}$ IFF

First Order Logic prove there exists a Model that has an infinite member

Help with Dual Spaces - Prove that either $w\in Im(f)$ or there exists ${l\in W^{}}$ such that $f^{}\left(l\right)=0$ and $l(w)=1$"

Prove or disprove that there exists a linear map given a set of vectors and their mapping

Prove that $\limsup\left(b_{n}a_{n}\right)=\limsup\left(a_{n}\right) $ when $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$

Prove $K_4-Cover$ is NP-Complete