For $$p \in (1,N)$$ and $$\Omega \subseteq {\mathbb {R}}^N$$ open, the Beppo-Levi space $${\mathcal {D}}^{1,p}_0(\Omega )$$ is completion of $$C_c^{\infty }(\Omega with respect to norm $$\left[ \int _{\Omega }|\nabla u|^p dx \right] ^ \frac{1}{p}.$$ Using p-capacity, we define a then identify Banach function {H}}(\Omega set all g in $$L^1_{loc}(\Omega that admits following Hardy–Sobolev ty...

The concept of compactness is a necessary condition of any system that is going to call itself a finitary method of proof. However, it can also apply to predicates of sets of formulas in general and in that manner it can be used in relation to level functions, a flavor of measure functions. In what follows we will tie these concepts of measure and compactness together and expand some concepts w...

Let s ⊃ ΞG . Every student is aware that there exists a smoothly Volterra compactly connected set. We show that there exists a reducible and Pascal locally separable, measurable ring. In future work, we plan to address questions of compactness as well as stability. In [7], it is shown that Milnor’s conjecture is false in the context of solvable paths.

Well known results related to the compactness of Hankel operators of one complex variable are extended to little Hankel operators of two complex variables. Critical to these considerations is the result of Ferguson and Lacey [5] characterizing the boundedness of the little Hankel operators in terms of the product BMO of S.-Y. Chang and R. Fefferman [2,3].

Shock wave theory was studied in literature by many authors. This article presents a survey with references about various topics related to shock waves: Hyperbolic conservation laws, Well-posedness theory, Compactness theory, Shock and reaction-di¤usion wave, The CJ and ZND theory, Existence of detonation in Majda’s model, Premixed laminar ‡ame, Multidimensional gas ‡ows, Multidimensional Riema...

If a finite group G acts freely and simplicially on a complex homotopy equivalent to a sphere S, then G has periodic Tate cohomology: H (G;Z) ∼= H (G;Z) for all i > 0. Swan proved in [26] that this condition was also sufficient. For free topological actions on S itself, the first additional restriction is: Theorem. [19] A finite dihedral group does not act freely and topologically on S. Milnor’...

We obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. Also weconsider relations Kadec-Klee property and shur property with this objects.These theorems are extend of papers mohebi and Narayana.

we show that in {bf zf} set theory without choice, the ultrafilter mbox{principle} ({bf up}) is equivalent to several compactness theorems for alexandroff discrete spaces and to rudin's lemma, a basic tool in topology and the theory of quasi-continuous domains. important consequences of rudin's lemma are various lift lemmas, saying that certain properties of posets are inherited by th...

This paper is concerned with emptyness of the essential spectrum, or equivalently compactness of the semigroup, for perturbations of selfadjoint operators that are bounded below (on an L2-space). For perturbations by a (nonnegative) potential we obtain a simple criterion for compactness of the semigroup in terms of relative compactness of the operators of multiplication with characteristic func...

We call a topological space X locally compact with defects if all points in possess neighborhoods except for some points. investigate this weaker version of local compactness. show that x ∈ X• the partition singletons X\(X• ∪ (U\U)) is finite, where U ̸= an open neighborhood x, then Tychonoff space. Let be T1c such each has union pairwise disjoint subsets S s∈S Fs. Then, we family {Fs}s∈S finite...