The hierarchical reference theory (HRT) and the self-consistent Ornstein-Zernike approximation (SCOZA) are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as the phase coexistence and equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. Earlier i...

A new reconstruction method is given for the spherical mean transform with centers on a plane in R which is also called Sonar transform. Standard inversion formulas require data over all spheres, but typically, the data are limited in the sense that the centers and radii are in a compact set. Our reconstruction operator is local because, to reconstruct at x, one needs only spheres that pass nea...

‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...

The linear Weingarten condition with ellipticity for the mean curvature and extrinsic Gaussian on a surface in three-sphere can define Riemannian metric which is called elliptic metric. We established some local characterizations of round spheres tori immersed 3-dimensional unit sphere, along Laplace operator, spherical Gauss map associated

in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...

This paper presents a practical method of adding problem-specific notation to an established computer language. Our idea is to use unrestricted operator overloading as a tool to map the problem domain notation directly into an existing programming language. Our method introduces new operator symbols and function names into a host language by overloading existing usage. We extend the host progra...

We consider maps of the family of convex bodies in Euclidean ddimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d ≥ 3, a representation theorem for such maps is given, showing that they are mixtures of certain prototypes. These prototypes are obtained by app...