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0 answers

117 views

Integral with respect to spectral measure

asked Aug 22, 2019 at 21:27

4 votes

2 answers

79 views

Show $\sup_{x\in[0,1]} | x -f(x)|\geq \frac{1}{2}$ for any $f$ with $f(0)=0$ and $\int^1_0 f(t)dt=0$. [closed]

asked Dec 3, 2018 at 18:12

4 votes

0 answers

108 views

Evans Chapter 4 Problem 16, initial value problem to Schrödinger equation, convergence

asked Sep 19 at 19:55

3 votes

0 answers

112 views

Euler Class Definition (Spivak)

asked Mar 31, 2020 at 17:59

2 votes

0 answers

199 views

Definition of Dirichlet energy

asked Feb 18, 2019 at 19:52

2 votes

2 answers

105 views

Searching for a connected neighborhood of fixed radius for every point of a submanifold

asked Feb 23, 2019 at 14:33

2 votes

1 answer

769 views

If $T$ is self-adjoint then $T^2$ is also self-adjoint,

asked Jul 31, 2019 at 22:23

2 votes

2 answers

121 views

How do I prove that the area of a sphere is the least possible area for a given volume?

asked May 4, 2015 at 12:58

2 votes

2 answers

2k views

Determinant of symmetric matrix $A^TA$

asked Jan 10, 2018 at 11:05

2 votes

0 answers

97 views

Existence of coordinate charts which coordinate vectors are principal directions

asked Jul 14, 2018 at 19:08

1 vote

1 answer

332 views

Proof doubt: $\ell^\infty$ is not separable

asked Aug 31, 2018 at 23:16

1 vote

1 answer

66 views

Rank of a matrix in $Z_p^{r\times n}$.

asked Jun 17, 2018 at 21:21

1 vote

1 answer

293 views

Why is $K[\alpha]$ a polynomial ring and the smallest subring containing $K$ and $\alpha$ of $L$?

asked Apr 4, 2018 at 11:59

1 vote

2 answers

182 views

Number of edges of a graph with singles and pairs is 62. How many vertices are there?

asked Apr 13, 2018 at 5:57

1 vote

0 answers

44 views

Show that each two normal lines near a point with non zero curvature of a curve with arc length parametrization do intersect.

asked May 1, 2018 at 20:45

1 vote

4 answers

728 views

Power series expansion of a holomorphic function

asked Feb 7, 2017 at 20:25

1 vote

1 answer

433 views

Partition of unity and Riemannian metric

asked Mar 30, 2017 at 6:19

1 vote

0 answers

567 views

Trivial fundamental group iff $f:S^1\to X$ can be extended to $D^2$

asked Jun 20, 2017 at 11:43

1 vote

1 answer

245 views

Parallel transport and affine connection proof explanation

asked Jun 22, 2017 at 19:21

1 vote

0 answers

55 views

local expression of bundle valued differential forms

asked Sep 23, 2022 at 18:50

1 vote

0 answers

46 views

Domain of unbounded selfadjoint operator

asked Aug 23, 2019 at 15:18

1 vote

1 answer

74 views

Derivative of a generic polynomial function

asked Nov 19, 2019 at 21:34

1 vote

1 answer

181 views

Poincare Duality and Integration Isomorphism

asked Mar 31, 2020 at 13:25

1 vote

0 answers

44 views

All points umbillical $\iff$ Surface is either contained in a sphere or in a plane.

asked Jul 13, 2018 at 17:57

1 vote

0 answers

24 views

$R$ UFD and integral domain $\Rightarrow$ every $a\neq 0 \in R\setminus R^\times$ is a product of prime elements

asked Feb 12, 2019 at 23:03

1 vote

3 answers

85 views

Suppose $f:V\times V \rightarrow \mathbb R$ is a symmetric indefinite bilinearform. Show $\exists v\neq0:f(v,v)=0$

asked Sep 13, 2018 at 19:52

1 vote

2 answers

180 views

Show that set of functions with Lipschitz constant $\leq n$ has no interior in $(C[0,1],\Vert \cdot \Vert_\infty)$

asked Nov 2, 2018 at 18:34

1 vote

1 answer

38 views

$\mathbb C P^1\cong (D^2\times\{1\}+ D^2\times \{-1\})\big /_\sim $

asked Nov 12, 2018 at 20:37

0 votes

3 answers

25 views

Showing ${(np+1)^{1/p}}{(nq+1)^{-1/q}}$ is unbounded.

asked Nov 15, 2018 at 15:13

0 votes

1 answer

49 views

For all matrices A exists unique matrix B with $B^2=A$ in a sufficient neighborhood.

asked Jan 18, 2019 at 18:22

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40 Questions

Integral with respect to spectral measure

Show $\sup_{x\in[0,1]} | x -f(x)|\geq \frac{1}{2}$ for any $f$ with $f(0)=0$ and $\int^1_0 f(t)dt=0$. [closed]

Evans Chapter 4 Problem 16, initial value problem to Schrödinger equation, convergence

Euler Class Definition (Spivak)

Definition of Dirichlet energy

Searching for a connected neighborhood of fixed radius for every point of a submanifold

If $T$ is self-adjoint then $T^2$ is also self-adjoint,

How do I prove that the area of a sphere is the least possible area for a given volume?

Determinant of symmetric matrix $A^TA$

Existence of coordinate charts which coordinate vectors are principal directions

Proof doubt: $\ell^\infty$ is not separable

Rank of a matrix in $Z_p^{r\times n}$.

Why is $K[\alpha]$ a polynomial ring and the smallest subring containing $K$ and $\alpha$ of $L$?

Number of edges of a graph with singles and pairs is 62. How many vertices are there?

Show that each two normal lines near a point with non zero curvature of a curve with arc length parametrization do intersect.

Power series expansion of a holomorphic function

Partition of unity and Riemannian metric

Trivial fundamental group iff $f:S^1\to X$ can be extended to $D^2$

Parallel transport and affine connection proof explanation

local expression of bundle valued differential forms

Domain of unbounded selfadjoint operator

Derivative of a generic polynomial function

Poincare Duality and Integration Isomorphism

All points umbillical $\iff$ Surface is either contained in a sphere or in a plane.

$R$ UFD and integral domain $\Rightarrow$ every $a\neq 0 \in R\setminus R^\times$ is a product of prime elements

Suppose $f:V\times V \rightarrow \mathbb R$ is a symmetric indefinite bilinearform. Show $\exists v\neq0:f(v,v)=0$

Show that set of functions with Lipschitz constant $\leq n$ has no interior in $(C[0,1],\Vert \cdot \Vert_\infty)$

$\mathbb C P^1\cong (D^2\times\{1\}+ D^2\times \{-1\})\big /_\sim $

Showing ${(np+1)^{1/p}}{(nq+1)^{-1/q}}$ is unbounded.

For all matrices A exists unique matrix B with $B^2=A$ in a sufficient neighborhood.