Articles of reference request

Properties of generalized limits aka nets

I want to find some article or a book which contains all general properties of nets. Of course some of them similar to properties of sequences with almost the same proofs, but I don’t fill the edge, where nets and sequences starts to behave differently. Also it would be nice to find complete survey on […]

Reference Request: Finding an Op-Ed by J. Hammersley

I’m interested in finding an online copy of J. Hammersley’s article entitled On the enfeeblement of mathematical skills by Modern Mathematics and by similiar soft intellectual trash in schools and universities, which was published in the Bulletin of the Institute of Mathematics and its Applications, Band 4, 1968, S. 66–85. I’ve searched both the name […]

Proof of an elliptic equation.

I’d like to see a proof of the theorem Theorem:Let $u \in H^1(B_1)$ a weak solution of \begin{equation} – \operatorname{div}(a_{ij}(x)\nabla u(x)) = 0 \quad \text{in} \quad B_1 \end{equation} where. Then, given $0< \alpha <1$ there exists $\varepsilon = \varepsilon(n,\lambda,\Lambda,\alpha)$ such that if $\| a_{ij} -A\|_{L^\infty(B_1)}< \varepsilon $ and $A$ is constant matrix satisfying $\lambda \le […]

Good introductory probability book for graduate level?

Would you please suggest a good, readable introductory probability book for graduate level ? I have Shiryaev ‘s Probability with me, however i want to find another one. Preferably with solution manual for self study.

$\mathcal{C}^1$ implies locally Lipschitz in $\mathbb{R}^n$

This question already has an answer here: A continuously differentiable map is locally Lipschitz 3 answers

What textbook should I get to self-learn Calculus?

This question already has an answer here: What are the recommended textbooks for introductory calculus? 8 answers Which calculus text should I use for self-study? 6 answers

Understanding differentials

What is a good reference to learn about differentials and related topics. Some of my questions are: Why is it possible to split $dy/dx$ into individual terms $dx$ and $dy$? In a separated differential equation such as $F(x)dx + G(y)dy = 0$, what is the physical intuition behind “$F(x)dx$”? When integrating the latter equation, what […]

Reference request for the independence of $ \text{Con}(\mathsf{ZFC}) $.

Gödel’s Second Incompleteness Theorem says that if $ \mathsf{ZFC} $ is consistent, then $ \mathsf{ZFC} \nvdash \text{Con}(\mathsf{ZFC}) $, i.e., $ \text{Con}(\mathsf{ZFC}) $ is not provable in $ \mathsf{ZFC} $. Does anyone know of an authoritative reference that contains the claim that $ \neg \text{Con}(\mathsf{ZFC}) $ is also not provable in $ \mathsf{ZFC} $ if $ […]

An easy reference for genetic algorithm

My field is Coding Theory and my background is Algebraic, there are many applications of Genetic Algorithm in Coding Theory, I would to know the easiest and the most elementary and introductory note about “Genetic Algorithm in Coding Theory”, also is this algorithm using in Crypto too?

Equivalence between norms in $H_0^1(\Omega)\cap H^2(\Omega)$.

Based in many questions and answers like [1, 2, 3 ] and a comment a good comment here [4]. I would like to know that the space $H=H_0^1(\Omega)\cap H^2(\Omega)$ can be equiped with this norm $$\tag{1}\|\cdot\|_H=||\Delta\cdot||_{L^2}+||\nabla\cdot||_{L^2}+||\cdot||_{L^2},$$ this is the $H^2$-norm. Or, is it equipped with this one $$\tag{2}\|\cdot\|_H=||\Delta\cdot||_{L^2}+||\cdot||_{L^2}.$$ Can I say that if $H$ is […]