mate selection is either the effect of the love or romantic relationship or a cause of formation of pre-marital romantic relationships among today’s generations. few number of sociological researches performed in this area necessitates its examination. so, the current research aims to present a deep understanding of romantic relationship and its destructive aspects among women. this study attem...

We prove that for every graph $G$ on $n$ vertices and with minimum degree five, the domination number $\gamma(G)$ cannot exceed $n/3$. The proof combines an algorithmic approach discharging method. Using same technique, we provide a shorter known upper bound $4n/11$ of graphs four.

We give an upper bound for the L condition number of the triangular Bernstein basis for polynomials of total degree at most n in s variables. The upper bound grows like (s + 1) when n tends to infinity. Moreover the upper bound is independent of s for s ≥ n− 1.

We revisit the problem of estimates of moments E Tr(An) 2s of random n × n matrices of Wigner ensemble by using the approach elaborated by Ya. Sinai and A. Soshnikov and further developed by A. Ruzmaikina. Our main subject is given by the structure of closed even walks w2s and their graphs g(w2s) that arise in these studies. We show that the total degree of a vertex α of g(w2s) depends not only...