For a nite group G the commutativity degree denote by d(G) and dend:$$d(G) =frac{|{(x; y)|x, yin G,xy = yx}|}{|G|^2}.$$ In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.

Using new sets of stellar evolution models at very low metallicities (Z = 10, 10) and previously published grids we examine spectral properties of the ionising continua, the Lyman-break, and the Lyα and He ii λ1640 recombination lines in starbursts. The metallicity dependence of these properties, especially the transition from primordial galaxies (Population III) to currently observed metallici...

BACKGROUND Maternal and infant mortality are highly devastating, yet, in many cases, preventable events for a community. The human development of a country is a strong predictor of maternal and infant mortality, reflecting the importance of socioeconomic factors in determinants of health. Previous research has shown that the Human Development Index (HDI) predicts infant mortality rate (IMR) and...

This paper reviews the dust content of the high redshift (z > 2) universe. Studies of the various " species " in the high-z " zoo " show that almost all have strong evidence for containing dust. The one exception, where the evidence is not yet convincing, is in quasar absorption line systems, particularly those with low column density. These may not even be associated with galaxies. The high-z ...

The charge reduction effect, produced by the nonlinear Debye screening of high-Z charges occuring in strongly-coupled plasmas, is investigated. An analytic asymptotic expression is obtained for the charge reduction factor (fc) which determines the Debye-Hückel potential generated by a charged test particle. Its relevant parametric dependencies are analyzed and shown to predict a strong charge r...

Automata theory has played an important role in theoretical computer science since last couple of decades. The algebraic automaton has emerged with several modern applications, for example, optimization of programs, design of model checkers, development of theorem provers because of having certain interesting properties and structures from algebraic theory of mathematics. Design of a complex sy...

This paper analyzes the spatial clustering of galaxies in the Canada-France Redshift Survey (CFRS). We have used the projected two-point correlation function, w(rp), to investigate the spatial distribution of the 591 galaxies with secure redshifts between 0 ≤ z ≤ 1.3 in the five CFRS fields. The slope of the two-point correlation function for the sample as a whole is γ = 1.64 ± 0.05, very simil...

Here the simulation design is the same as that in scenario 1 described in the main text with two partially missing variables X1 and X2. Missing data were created by following the two non-ignorable mechanisms, 1) logit{pr(Rk = 1|X1, X2, Y, Z)} = 0.25Y + 0.25Z + X2 + X1 and 2) logit{pr(Rk = 1|X1, X2, Y, Z)} = 0.75 + Y + 0.25Z −X1 + X2, for k = 1, 2. Although in both mechanisms Rk strongly depends...

In argumentation theory, Dung’s abstract framework provides a unifying view of several alternative semantics based on the notion of extension. Recently, a new semantics has been introduced to solve the problems related to counterintuitive results produced by literature proposals. In this semantics, extensions can be decomposed and constructed along the strongly connected components of the defea...

We construct twelve infinite families of pseudocyclic and non-amorphic association schemes, in which each nontrivial relation is a strongly regular graph. Three of the twelve families generalize the counterexamples to A. V. Ivanov’s conjecture by Ikuta and Munemasa [13].