Related papers: Directional Lower Porosity

We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies…

Local porosity distributions for a three-dimensional porous medium and local porosity distributions for a two-dimensional plane-section through the medium are generally different. However, for homogeneous and isotropic media having finite…

In this paper, we consider the directional differentiability of metric projection and its properties in uniformly convex and uniformly smooth Bochner space Lp(S; X), in which (S, A, mu) is a positive measure space and X is a uniformly…

We study the obstructions to coarse universality in separable dual Banach spaces. We prove coarse non-universality of several classes of dual spaces, including those with conditional spreading bases, as well as generalized James and James…

We prove a separable reduction theorem for sigma-porosity of Suslin sets. In particular, if A is a Suslin subset in a Banach space X, then each separable subspace of X can be enlarged to a separable subspace V such that A is sigma-porous in…

We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…

A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the…

This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…

Let $X$ be a separable Banach space, $Y$ a Banach space and $f: X \to Y$ a mapping. We prove that there exists a $\sigma$-directionally porous set $A\subset X$ such that if $x\in X \setminus A$, $f$ is Lipschitz at $x$, and $f$ is G\^ateaux…

We prove that if a unital Banach algebra $A$ is the dual of a Banach space $\pd{A}$, then the set of weak* continuous states is weak* dense in the set of all states on $A$. Further, weak* continuous states linearly span $\pd{A}$.

The aim of this work is to describe subsets of Banach limits in terms of a certain functional characteristic. We compute radii and cardinalities for some of these subsets.

We consider the one-dimensional porous medium equation $u_t=\left (u^nu_x \right )_x+\frac{\mu}{x}u^nu_x$. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some…

The interrelations between (upper and lower) Minkowski contents and (upper and lower) surface area based contents (S-contents) as well as between their associated dimensions have recently been investigated for general sets in R^d (cf. [3]).…

The category $Ban$ of Banach spaces and linear maps of norm $\leq 1$ is locally $\aleph_1$-presentable but not locally finitely presentable. We prove, however, that $Ban$ is locally finitely presentable in the enriched sense over complete…

We study a relation between three different formulations of theorems on separable determination - one using the concept of rich families, second via the concept of suitable models and third, a new one, suggested in this paper, using the…

We study the unknown differences between the size of slices and relatively weakly open subsets of the unit ball in Banach spaces. We show that every Banach space containing isomorphic copies of $c_0$ can be equivalently renormed so that…

We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.

We study existence and uniqueness of bounded solutions to a fractional nonlinear porous medium equation with a variable density, in one space dimension.

We investigate weak$^*$ derived sets, that is the sets of weak$^*$ limits of bounded nets, of convex subsets of duals of non-reflexive Banach spaces and their possible iterations. We prove that a dual space of any non-reflexive Banach space…

The condensation rank associates any topological space with a unique ordinal number. In this paper we prove that the condensation rank of any infinite dimensional injective Banach space is equal to or greater than the first uncountable…