In this article, we characterize the involutiveness of the linear combination of the forma1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,and A2 is arbitrary, under certain properties imposed on A1 and A2.

Background: In this study, the effects of three structural analogues of adenosine upon proliferation of human tumor cells were investigated. Previous research showed a cytotoxic effect of adenosine via A3 receptor and A1 receptor and sometimes this effect was receptor independent. The researches showed a differential cytotoxic effect of adenosine and its A3 agonists on cancerous cells, while ot...

We study a recently introduced two-person combinatorial game, the (a,b)-monochromatic clique transversal game which is played by Alice and Bob on graph G. As we observe, this equivalent to (b,a)-biased Maker–Breaker clique-hypergraph of Our main results concern threshold bias a1(G) that smallest integer such can win in (a,1)-monochromatic G if she first play. Among other results, determine poss...

For given positive integers a1,a2,⋯,ak with gcd(a1,a2,⋯,ak)=1, the denumerant d(n)=d(n;a1,a2,⋯,ak) is number of nonnegative solutions (x1,x2,⋯,xk) linear equation a1x1+a2x2+⋯+akxk=n for a integer n. p, let Sp=Sp(a1,a2,⋯,ak) be set all n’s such that d(n)>p. In this paper, by introducing p-numerical semigroup, where N0\Sp finite, we give explicit formulas p-Frobenius number, which maximum N0\S...

background: women with polycystic ovary syndrome have lower pregnancy rates, possibly due to the decreased uterine  receptivity.successful implantation depends on protein networks that are essential for cross-talk between the embryo and endometrium.apolipoprotein a1 has been proposed as a putative anti-implantation factor. in this study, we evaluated apolipoprotein a1 expression in human endome...