We prove that for any separable Banach space X, there exists a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space contains a complemented subspace isomorphic to X. As a consequence we give an example of a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space fails the approximation property and we prove that ther...

In this paper, a family of high-order compact finite difference methods in combination preconditioned methods are used for solution of the Diffusion-Convection equation. We developed numerical methods by replacing the time and space derivatives by compact finitedifference approximations. The system of resulting nonlinear finite difference equations are solved by preconditioned Krylov subspace m...

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to...

Valid-time indeterminacy is “don’t know when” indeterminacy, coping with cases in which one does not exactly know when a fact holds in the modeled reality. In this paper, we first propose a reference representation (data model and algebra) in which all possible temporal scenarios induced by valid-time indeterminacy can be extensionally modeled. We then specify a family of sixteen more compact r...

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

The multiscale multigrid method is presented in this article to solve the linear systems arising from a fourth order discretisation. We used a symbolic algebra packageMathematica to derive a family of finite difference approximations on a 27 point compact stencil. The unknown solution and its second derivatives are carried as unknowns at selected grid points. A set of test problems are presente...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

Throughout the early and mid 1990s, there was widespread faith in the compact city model's ability to provide urban sustainability. However, where compact city policies had been implemented, follow-up studies began to show the predicted benefits did not happen as they should be. The article tries to peruse two opposite approaches of "Urban Sprawl" and "Compact City", with an analytical - cri...

A family of compact submanifolds with boundary has a nonempty stable interior intersection in R provided a certain geometric estimate holds. As a global application we establish a sharp intersection criterion for a family of properly embedded mj -dimensional submanifolds Mj ⊂ R that is based solely on their Gauss maps Gj : Mj → G(n−mj , n) , Gj(p) = [TpMj ]⊥ .