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Jan
29
comment Single reference to classical results in analysis.
@David, now believe that there are no problems in the theorem. Thanks for the comment.
Jan
29
comment Single reference to classical results in analysis.
@David, I repaired the question.
Jan
27
comment Single reference to classical results in analysis.
@JohnSteinbeck $D\subset \mathbb{Y}$.
Jan
27
comment Single reference to classical results in analysis.
@sinbadh, books or articles.
Jan
22
comment Limit problem arctg (1 ^ infinty)
Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level.
Jan
7
comment Prove that $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}} \leq \frac{3}{2}$
What is the meaning of the symbol $\sum_{cyc}$?
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer I will improve my argument and edit my attempt proof. Thank you for your comments.
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer I hope this argument is correct. Otherwise I'll edit my attempt proof.
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer The equality involving the limit above $\lim_{k\to \infty}f_2\bigl(u_1^{\ast}(u_2^k,x_3,\dotsc,x_n), u_2^k,x_3,\dotsc,x_n\bigr)=f_2\bigl(u_1^{\ast}(\tilde{u}_2^,x_3,\dotsc,x_n), \tilde{u}_2,x_3,\dotsc,x_n\bigr)=0$ implies continuity of $u_2 \mapsto f_2\bigl(u_1^{\ast}(u_2,x_3,\dotsc,x_n), u_2,x_3,\dotsc,x_n\bigr)$.
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer I refer the function $(x_2,\ldots, x_n)\mapsto u_1(x_2,\ldots, x_n)$. But about the function $u_2 \mapsto f_2\bigl(u_1^{\ast}(u_2,x_3,\dotsc,x_n), u_2,x_3,\dotsc,x_n\bigr)$ for all sequence $\{u^k_2| f_2\bigl(u_1^{\ast}(u_2,x_3,\dotsc,x_n), u_2,x_3,\dotsc,x_n\bigr)=0\}$ such that $u_2^k\to \tilde{u}_2$ we have $\lim_{k\to \infty}f_2\bigl(u_1^{\ast}(u_2^k,x_3,\dotsc,x_n), u_2^k,x_3,\dotsc,x_n\bigr)=f_2\bigl(u_1^{\ast}(\tilde{u}_2^,x_3,\dotsc,x_n), \tilde{u}_2,x_3,\dotsc,x_n\bigr)=0$.
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer If we observe the argument, the continuity of $u_1^\ast( x_2,\ldots, x_n)$ is irrelevant. Note that we have $f_1(u_1(x_2,\ldots,x_n),x_2,\ldots,x_n) =0\;\forall x_2\in[a_2,b_2],\;\forall x_3\in[a_3,b_3],\ldots,\;\forall x_n\in[a_n,b_n]$.
Dec
15
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer, Fixed $u_1^*$ the function $u_2\mapsto f_2(u_1^*,u_2,x_3,\ldots,x_n)$ continuously depends only on $(u_2,x_3,\ldots,x_n)$ once the $f$_2 function is continuous in its 'n' coordinates, which will also be continuously follows the 'n-1' remaining coordinates.
Dec
15
comment Tentative proof of Poincaré-Miranda theorem?
@Alex, "But it may be that ff has a 0 that cannot be solved algebraically, so its existence won't so easily follow from the IVT". But the conclusion of existence of IVT not depend on any algebraic construction.
Nov
2
comment Extended version of Mean-Value Theorem, lower bound result and reference request.
@DanielFischer This is a counter example ? If $f (x, y) = e^x (\cos y, \sin y)$ then there not exists $m> 0$ and $M> 0$ such that $m<\|Df(x)\|_{\mathscr{L}(\mathbb{R}^2,\mathbb{R}^2)}<M$ because $\inf_{(x,y)}\|Df(x)\|_{\mathscr{L}(\mathbb{R},\mathbb{R}^m)}=0$ and $0<\|Df(x,y)\|_{\mathscr{L}(\mathbb{R}^2,\mathbb{R}^2)}<e^x$.
Oct
15
comment quadratic programing with both norm constraint and linear constraint
Get sufficient KKT [en.wikipedia.org/wiki/… optimality conditions of the problem. Then apply Kantorovich theorem [en.wikipedia.org/wiki/Kantorovich_theorem] on Newton method to obtain a solution of the problem.
Oct
3
comment $f'(x) > 0$, does that imply the limit as $x\rightarrow \infty$ is $\infty$?
This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post.
Oct
3
comment Improving Newton Iteration
This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level.
Oct
3
comment Prove that $\lim \limits_{n \to \infty}{\sqrt[n]{a^n+b^n}}=\max(a,b)$ if $(a_n,b_n)\to(a,b)$
Possible duplicate of How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$?
Sep
5
comment How strong is the operator norm topology?
Your comment this makes your question more precise and interesting. I suggest incorporating this enlightening comment to your question.
Sep
5
comment How strong is the operator norm topology?
What do you mean exactly by "how strong is the topology T"?