A free action of a finite group on an odd-dimensional sphere is said to be almost linear if the action restricted to each cyclic or 2– hyperelementary subgroup is conjugate to a free linear action. We begin this survey paper by reviewing the status of almost linear actions on the 3–sphere. We then discuss almost linear actions on higher-dimensional spheres, paying special attention to the group...

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...

In the present paper, we show that $S^*$ iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that this iteration method is equivalent to CR iteration method  and it produces a slow convergence rate compared to the CR iteration method for the class of almost contraction mappings. We also present table and graphic to support this result. F...

Abstract We prove that if M is a closed n -dimensional Riemannian manifold, $$n \ge 3$$ n≥3 , with $$\mathrm{Ric}\ge n-1$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Ric≥n-<mm...

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...