Every quasigroup (S, ·) belongs to a set of 6 quasigroups, called parastrophes denoted by (S, πi), i ∈ {1, 2, 3, 4, 5, 6}. It is shown that isotopy-isomorphy is a necessary and sufficient condition for any two distinct quasigroups (S, πi) and (S, πj), i, j ∈ {1, 2, 3, 4, 5, 6} to be parastrophic invariant relative to the associative law. In addition, a necessary and sufficient condition for any...

At the 100th anniversary of the birth of George Kingsley Zipf, one striking fact about the statistical regularity that bears his name, Zipf's law, is that it seems to appear everywhere. We may ask these questions related to the ubiquity of Zipf's law: Is there a rigorous test in fitting real data to Zipf's law? In how many forms does Zipf's law appear? In which fields are the data sets claiming...

Although the word “love” appears less frequently in the Qur‟an than in the Bible, Love is a cornerstone of both Islam and Christianity. As the Bible and the Qur‟an agree on many things, why then do Muslims and Christians perceive each other so differently and so often misunderstand each other? Such a question, of course, deserves an in-depth, multi-faceted answer; however, we...

abstract: a time domain semi-analytical solution to study thermoelastic creep behavior of  functionally graded rotating axisymmetric disks with variable thickness is presented. the rate type governing differential equations for the considered structure are derived and analytically solved. to solve these  equations, the disk is divided into some virtual sub-domains. general solution of  equilibr...

The problem of monitoring an electric power system is placing as few measurement devices as possible. In graph theoretical representation, it can be considered as a variant of domination problem, namely, power domination problem. This problem is to find a minimum power domination set S of a graph G = (V,E) with S ⊆ V and S can dominate all vertices and edges through the observation rules accord...

Let$ P_{n}(x)= sum_{i=0}^{n} A_{i}x^{i}$ be a random algebraicpolynomial, where $A_{0},A_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. Thus $A_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}H_{j}(t)}$, where $H_j(t)$'s are complex slowlyvarying functions.Under the assumption that there exist ...

literary and artistic joint works are prepared by two or more authors. it's importance, have increasingly grown today, particularly in academic areas. one of the issues related to these works is the problem of identifying the concept and realization of the joint works in the different legal systems which has similarities and differences. this research is a comparative study in mentioned is...