For a decreasing real valued function ψ, pair (A,b) of m×n matrix A and b∈Rm is said to be ψ-Dirichlet improvable if the system‖Aq+b−p‖m<ψ(T)and‖q‖n<T has solution p∈Zm, q∈Zn for all sufficiently large T, where ‖⋅‖ denotes supremum norm. Kleinbock Wadleigh (2019) established an integrability criterion Lebesgue measure non-improvable set. In this paper, we prove similar Hausdorff Also, extend re...

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. a graph $g$ is said to be $a$-magic graph if there exists a labeling$l:e(g)rightarrow a^{*}$ such that the induced vertex labeling$l^{+}:v(g)rightarrow a$, define by $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,where $n(v)$ denotes the s...

A revised analysis of the effect of long-range nonspherical terms in the intermolecular potential on the second virial coefficient is presented with a preferred Hartree-Fock-Dispersion functional (HFD-C) spherical core treatment of the integrations for small intermolecular distances. A set of modified numerical tables for the accurate calculation of the nonspherical contribution to the sec...

The objective of this study was to estimate variance components and genetic parameters for growth curve parameters in Shall sheep. Studied traits were parameters of Brody growth model which included A (asymptotic mature weight), B (initial animal weight) and K (maturation rate). The data set and pedigree information used in this study were obtained from the Animal Breeding Center of Iran and co...

(2)1 For every set X and for all functions f , g such that X ⊆ dom f and f ⊆ g holds f X = g X . (3) For every non empty set A and for every set b such that A 6= {b} there exists an element a of A such that a 6= b. (4) For all sets X , Y holds every non empty subset of X→̇Y is a non empty functional set. (5) Let B be a non empty functional set and f be a function. Suppose f = ⋃ B. Then dom f = ⋃...

We deal with a non–empty set of functions and a non– empty set of functions from a set A to a non–empty set B. In the case when B is a non–empty set, B is redefined. It yields a non–empty set of functions from A to B. An element of such a set is redefined as a function from A to B. Some theorems concerning these concepts are proved, as well as a number of schemes dealing with infinity and the A...

A three types competition model governed by directed last passage percolation on N 2 is considered. We prove that coexistence of the three types, i.e. the sets of vertices of the three types are simultaneously unbounded, occurs with positive probability. Moreover, the asymptotic angles formed by the two competition interfaces with the horizontal axis are determined and their probability of bein...

The Rodin tool for Event-B supports formal modelling and proof using a mathematical language that is based on predicate logic and set theory. Although Rodin has in-built support for a rich set of operators and proof rules, for some application areas there may be a need to extend the set of operators and proof rules supported by the tool. This paper outlines a new feature of the Rodin tool, the ...

an interaction potential at different orientation for the ch4 and co2 complex was derived at theb3lyp level of theory and 6-31+g* basis sets. the potential energy surface was computed on somemolecular geometries. the complete basis set limit of the interaction energies were fitted to wellknownanalytical functions. to determine the second virial coefficients b, u(r) is used to obtain themodel’s ...