# אליהו צלע

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An expert is a man who has made all the mistakes, which can be made, in a very narrow field. (Niels Bohr)

 Mar11 comment Inexact Newton method. @LutzL I know the Newton-Kantorovich theorem and its several versions. The point is that this question calls for a robust version of the Kantorovich theorem. And not only robust robust locally but globally robust. Feb13 comment If $f,g$ are uniform continuous with $f$ bounded, then $fg$ is uniform continuous. @user128216 It was a small error that does not affect the answer. Thanks for pointing out. I've corrected Feb4 comment Growth Rate. A precise definition. OK. Recently I realized that his point of view refers to something we can call "discrete derivative". Could you explain your point of view? An example? I thank you. Jan28 comment Suppose G has order 4, but contains no element of order 4. A) prove that no element of G has order 3.? This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post. Jan25 comment how to find $\lim\limits_{x \to \infty} \left(\sqrt{x^2 +1} +\sqrt{4x^2 + 1} - \sqrt{9x^2 + 1}\right)$ Very nice this trick! Jan14 comment Proof that $x^k < k^x$ @Setzer22 yes, $\log_{\,k} k=1$. Jan7 comment Growth Rate. A precise definition. Thanks and +1. After a while I discovered that the answer given by the source of this problem is 20.050 copies Dec29 comment Dirichlet Problem on the unit disk Welcome to Math StackExchange. Please be more clear in your question. Define C-harmonic function. Dec28 comment properties of positive definite matrix @user115927, I use in my answer the fact that $Av=\lambda\cdot v\Leftrightarrow v^T(Av)=v^T(\lambda\cdot v)=\lambda\|v\|^2$. Then, $\lambda\geq 0\Leftrightarrow v^T(Av)\geq 0$. Dec24 comment The problem of the most visited point. @GitGud This is the classic solution to the problem of the most visited point. In this case I would have to calculate the number of two distinct paths connecting two points. It seems to be a promising approach. But I have not had progress with this approach. Nov16 comment For what values will f(x) be necessarily one-one? possible duplicate of How to prove that f is one-to-one Nov16 comment Equicontinuity and Uniform Boundedness @Tom I think that the result might be right if $f$ is constant on the boundary of $U$. Nov16 comment Equicontinuity and Uniform Boundedness @John Would not need the compactness of the $U$? Nov13 comment Find the limit of $\lim_{x\to\infty}\frac{\sin[xf(x)]}{x\cdot\sin[f(x)]}$ I think you should add the hypothesis that $\lim_{x\to \infty}x\cdot f(x)=0$. Use the Limit Theorem for Composite Functions: $\lim_{u\to \infty}h(u)=M$ and $\lim_{x\to a}u(x)=L$ implies $\lim_{x\to a}h(u(x))=M$ Nov12 comment Equivalence of intrinsic and extrinsic metrics of embedded manifolds. As you can clearly see that small $d_{\mathcal{M}}$ implies $d_{}$ small? Nov12 comment Frobenius Norm with Unitary Operators @user108149 Now I think my answer clearer for you enteder. I have helped. Oct30 comment Percolation and number of phases in the 2D Ising model. See question too on physics.stackexchange.com/questions/81903/… Oct29 comment Implicit derivitave of a general ellipse It makes no sense to say 'derived from ellipse'. Derivatives are defined only for functions. I imagine you want to get the implicit differentiation from (this is also something well defined) the ellipse equation. Oct25 comment Partial derivatives of a function which is constant on the diagonal You understand that the second derivatives operators $\frac{\partial}{\partial x_i}\frac{\partial}{\partial x_i}$ and $\frac{\partial}{\partial y_i}\frac{\partial}{\partial y_i}$ to be different? Oct22 comment Excercise of Convex Analysis Which definition of $K^*$ ?