Question

Smooth convex function with unique minimizer is not strictly convex?

score 63 · Answer 1 · 2023-12-14 05:11:49

63

Views

Smooth convex function with unique minimizer is not strictly convex?

Published on 14 Dec 2023 - 5:11

score 73 · Answer 2 · 2023-12-17 00:54:21

73

Views

Can a function be differentiable but not strongly differentiable (Knuth)?

Published on 17 Dec 2023 - 0:54

score 88 · Answer 3 · 2023-12-23 06:57:54

It is very easy to find a $C^\infty$ partition of unity for $A$. Is this really true? I feel strange. "Calculus on Manifolds" by Michael Spivak.

score 30 · Answer 4 · 2023-12-25 11:28:24

30

Views

What does "by (2) for each $x$ this sum is finite in some open set containing $x$" mean? ("Calculus on Manifolds" by Michael Spivak.)

Published on 25 Dec 2023 - 11:28

score 76 · Answer 5 · 2023-12-28 02:23:51

76

Views

I want you to check if I understand the case 1 in the proof of Theorem 3-11. (Partitions of unity in "Calculus on Manifolds" by Michael Spivak)

Published on 28 Dec 2023 - 2:23

score 91 · Answer 6 · 2024-01-05 18:24:19

91

Views

Simple proof for complete, metric vector space

Published on 05 Jan 2024 - 18:24

score 101 · Answer 7 · 2026-03-25 12:49:52

101

Views

Showing that the isomorphism of the general linear group of a vector space with the group of invertible matrices is smooth

Published on 25 Mar 2026 - 12:49

score 53 · Answer 8 · 2026-02-24 21:02:22

53

Views

Convergence of a series of the product of two functions when one of them is shifted by one

Published on 24 Feb 2026 - 21:02

score 54 · Answer 9 · 2024-01-09 20:55:22

54

Views

How to calculate the derivative of composition map on smooth manifold?

Published on 09 Jan 2024 - 20:55

score 53 · Answer 10 · 2024-01-10 11:35:02

53

Views

Question about external derivative

Published on 10 Jan 2024 - 11:35

score 50 · Answer 11 · 2024-01-13 00:58:18

50

Views

Can smooth approximations always preserve injectivity?

Published on 13 Jan 2024 - 0:58

score 72 · Answer 12 · 2024-01-15 11:53:00

72

Views

Smoothness of Fourier transform

Published on 15 Jan 2024 - 11:53

score 27 · Answer 13 · 2024-01-16 01:19:35

27

Views

Restricted Strong Smoothness vs Strong Smoothness

Published on 16 Jan 2024 - 1:19

score 72 · Answer 14 · 2026-03-25 18:31:21

72

Views

Let $F: \mathbb R^n \to \mathbb R^m$ be smooth and such that for all $a \in \mathbb R$, $x \in \mathbb R^n$, $F(ax) = aF(x)$. Prove $F$ is linear

Published on 25 Mar 2026 - 18:31

score 47 · Answer 15 · 2024-01-16 07:32:16

47

Views

Let $F: \mathbb R^m \to \mathbb R^n$ be smooth, $F(0) = 0$. Let $H(t,x) = \frac{F(tx)}{t}$ if $t \neq 0$ and $DF|_0(x)$ otherwise. Show $H$ is smooth

Published on 16 Jan 2024 - 7:32

List Question

Smooth convex function with unique minimizer is not strictly convex?

Can a function be differentiable but not strongly differentiable (Knuth)?

It is very easy to find a $C^\infty$ partition of unity for $A$. Is this really true? I feel strange. "Calculus on Manifolds" by Michael Spivak.

What does "by (2) for each $x$ this sum is finite in some open set containing $x$" mean? ("Calculus on Manifolds" by Michael Spivak.)

I want you to check if I understand the case 1 in the proof of Theorem 3-11. (Partitions of unity in "Calculus on Manifolds" by Michael Spivak)

Simple proof for complete, metric vector space

Showing that the isomorphism of the general linear group of a vector space with the group of invertible matrices is smooth

Convergence of a series of the product of two functions when one of them is shifted by one

How to calculate the derivative of composition map on smooth manifold?

Question about external derivative

Can smooth approximations always preserve injectivity?

Smoothness of Fourier transform

Restricted Strong Smoothness vs Strong Smoothness

Let $F: \mathbb R^n \to \mathbb R^m$ be smooth and such that for all $a \in \mathbb R$, $x \in \mathbb R^n$, $F(ax) = aF(x)$. Prove $F$ is linear

Let $F: \mathbb R^m \to \mathbb R^n$ be smooth, $F(0) = 0$. Let $H(t,x) = \frac{F(tx)}{t}$ if $t \neq 0$ and $DF|_0(x)$ otherwise. Show $H$ is smooth

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