Question

Convergence of slowly decreasing sequences

score 170 · Answer 1 · 2026-04-13 01:34:06

170

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Convergence of slowly decreasing sequences

Published on 13 Apr 2026 - 1:34

score 201 · Answer 2 · 2026-04-12 15:34:15

201

Views

Motivation of Haar Measure

Published on 12 Apr 2026 - 15:34

score 538 · Answer 3 · 2026-04-10 08:00:20

538

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Verification of Integral identity

Published on 10 Apr 2026 - 8:00

score 111 · Answer 4 · 2026-04-14 15:19:34

111

Views

Instability of a system subject to periodic perturbation

Published on 14 Apr 2026 - 15:19

score 178 · Answer 5 · 2026-04-14 13:44:49

178

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Variational formulation of a parabolic equation

Published on 14 Apr 2026 - 13:44

score 1.2k · Answer 6 · 2026-04-14 19:27:47

1.2k

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Proof that a strictly decreasing sequence of nested intervals boils down to a single point.

Published on 14 Apr 2026 - 19:27

score 58 · Answer 7 · 2026-04-16 07:27:48

58

Views

Prove: $\dim E= +\infty \Longleftrightarrow \forall \;n\geq 1,\;\exists \;\;B=\{u_1,u_2,\cdots,u_n\}$ such that $B$ is Linearly independent

Published on 16 Apr 2026 - 7:27

score 1k · Answer 8 · 2026-04-16 18:47:22

Define a sequence $(a_n)$ as follows $a_1 = 1$ and for $n\geq 1,\;a_{n+1} = (-1)^n\frac{1}{2} \left(|a_n| + \frac {2}{|a_n|}\right)$

score 66 · Answer 9 · 2026-04-13 04:10:41

66

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Prove $\lim_{(h,k)\to 0} \dfrac{|f(h,k)|}{|(h,k)|}=0$ for bilinear $f$

Published on 13 Apr 2026 - 4:10

score 92 · Answer 10 · 2026-04-14 10:06:52

92

Views

What exactly is the meaning of/why exactly do we write $dy = y'(x) dx$?

Published on 14 Apr 2026 - 10:06

score 44 · Answer 11 · 2026-04-15 19:47:59

If $K⊆ℝ^d$ is compact and $f:[0,T]×K×K→ℝ$ is continuous with $f(t,\;⋅\;,\;⋅\;)∈C^{0+β}$, is $t↦\left\|f(t,\;⋅\;,\;⋅\;)\right\|_{C^{0+β}}$ continuous?

score 2.1k · Answer 12 · 2026-04-16 12:38:38

2.1k

Views

Show continuity at $(0,0)$ of $f(x,y)=\frac{xy}{\sqrt{x^2+y^2}}$ for $(x,y)\neq (0,0)$ and $f(0,0)=0$

Published on 16 Apr 2026 - 12:38

score 29 · Answer 13 · 2026-04-12 11:02:24

29

Views

Solvability of integral equation $f(x)=g(A(||g||)x)$

Published on 12 Apr 2026 - 11:02

score 272 · Answer 14 · 2026-04-13 04:19:21

272

Views

What do you call this property involving a function between two complete metric spaces?

Published on 13 Apr 2026 - 4:19

score 291 · Answer 15 · 2026-04-16 13:35:49

291

Views

Diff$(S^1)$ is deformation retracts to $O(2)$

Published on 16 Apr 2026 - 13:35

List Question

Convergence of slowly decreasing sequences

Motivation of Haar Measure

Verification of Integral identity

Instability of a system subject to periodic perturbation

Variational formulation of a parabolic equation

Proof that a strictly decreasing sequence of nested intervals boils down to a single point.

Prove: $\dim E= +\infty \Longleftrightarrow \forall \;n\geq 1,\;\exists \;\;B=\{u_1,u_2,\cdots,u_n\}$ such that $B$ is Linearly independent

Define a sequence $(a_n)$ as follows $a_1 = 1$ and for $n\geq 1,\;a_{n+1} = (-1)^n\frac{1}{2} \left(|a_n| + \frac {2}{|a_n|}\right)$

Prove $\lim_{(h,k)\to 0} \dfrac{|f(h,k)|}{|(h,k)|}=0$ for bilinear $f$

What exactly is the meaning of/why exactly do we write $dy = y'(x) dx$?

If $K⊆ℝ^d$ is compact and $f:[0,T]×K×K→ℝ$ is continuous with $f(t,\;⋅\;,\;⋅\;)∈C^{0+β}$, is $t↦\left\|f(t,\;⋅\;,\;⋅\;)\right\|_{C^{0+β}}$ continuous?

Show continuity at $(0,0)$ of $f(x,y)=\frac{xy}{\sqrt{x^2+y^2}}$ for $(x,y)\neq (0,0)$ and $f(0,0)=0$

Solvability of integral equation $f(x)=g(A(||g||)x)$

What do you call this property involving a function between two complete metric spaces?

Diff$(S^1)$ is deformation retracts to $O(2)$

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