‎In this paper we consider the special classes of Sonnenschein matrices‎, ‎namely the Karamata matrices $K[alpha,beta]=left(a_{n,k}right)$ with the entries‎ ‎[{a_{n,k}} = sumlimits_{v = 0}^k {left( begin{array}{l}‎ ‎n\‎ ‎v‎ ‎end{array} right){{left( {1‎ - ‎alpha‎ - ‎beta } right)}^v}{alpha ^{n‎ - ‎v}}left( begin{array}{l}‎ ‎n‎ + ‎k‎ - ‎v‎ - ‎1\‎ ‎,,,,,,,,,,k...

 In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.

for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.

the effects of different levels of nitrogen (100, 200, 300 and 400 mg/l) and potassium (125, 250 and 375 mg/l) on yield and leaf n and k concentrations of tomato were investigated in perlit culture using a factorial randomized design with three replications. the highest fruit yield was obtained with 200 mg/l n. higher levels of nitrogen decreased tomato yield. with increasing nitrogen concentra...

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...

The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.

Let L/[0, k&1]. A family F is called an (n, k, L)-system (or (k, L)system, L-system for short) if F/( [n] k ) and |F & F$| # L holds for all distinct F, F$ # F. Define m(n, k, L) :=max[ |F | : F is (n, k, L)-system]. If there exist constants c, c$, : depending only on k and L, and satisfying cn<m(n, k, L)<c$n, then we define :(k, L) :=: which is called the exponent of (k, L)-system. Conjecture ...