An injective map f : E(G) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f*: V (G) → Z − {0} defined by f*(v) = (Sigma e∈Ev) f (e) is one-one, where Ev denotes the set of edges in G that are incident with a vetex v and f*(V (G)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} U {k(p+1)/2} accordin...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

The distribution of the sum negative binomial random variables has a special role in insurance mathematics, actuarial sciences, and ecology. Two methods to estimate this have been published: finite-sum exact expression series by convolution. We compare both methods, as well new normalized saddlepoint approximation, normal single approximations. show that used lots memory when number was high (&...

Ethnicity and religion are known to be important factors associated with substance use and misuse (SUM). Ethnic Bosniaks, Muslims by religion, are the third largest ethnic group in the territory of the former Yugoslavia, but no study has examined SUM patterns among them. The aim of this study was to explore the prevalence of SUM and to examine scholastic-, familial- and sport-factors associated...

The negative-parity baryons are studied by a novel approach in the QCD sum rule. It is found that the parity of the ground-state nucleon is determined by the sign of the quark condensate. We predict the mass of negative-parity nucleon.

Diversity maximization is an important concept in information retrieval, computational geometry and operations research. Usually, it is a variant of the following problem: Given a ground set, constraints, and a function f(·) that measures diversity of a subset, the task is to select a feasible subset S such that f(S) is maximized. The sum-dispersion function f(S) = ∑ x,y∈S d(x, y), which is the...