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 th...

‎Let $G$ be a finite $p$-group of order $p^n$ and‎ ‎$|{mathcal M}(G)|=p^{frac{1}{2}n(n-1)-t(G)}$‎, ‎where ${mathcal M}(G)$‎ ‎is the Schur multiplier of $G$ and $t(G)$ is a nonnegative integer‎. ‎The classification of such groups $G$ is already known for $t(G)leq‎ ‎6$‎. ‎This paper extends the classification to $t(G)=7$.

today multinational studies using genome-wide association scan (gwas) for >1000,000 polymorphisms on >100,000 cases with major psychiatric diseases versus controls, combined with next-generation sequencing have found ~100 genetic polymorphisms associated with schizophrenia (scz), bipolar disorder (bd), autism, attention deficit and hyperactivity disorder (adhd), etc. however, the effect size of...

In this paper we will generalize a singular value inequality that was proved before. In particular we obtain an inequality for numerical radius as follows: begin{equation*} 2 sqrt{t (1-t)} omega(t A^{nu}B^{1-nu}+(1-t)A^{1-nu}B^{nu}) leq omega(t A + (1- t) B), end{equation*} where, $ A $ and $ B $ are positive semidefinite matrices, $ 0 leq t leq 1 $ and $ 0 leq nu leq frac{3}{2}.$

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...