In this paper, for an odd prime p such that p ≡ 3 mod 4, odd n, and d = (pn +1)/(pk +1)+ (pn −1)/2 with k|n, the value distribution of the exponential sum S (a, b) is calculated as a and b run through Fpn . The sequence family G in which each sequence has the period of N = pn − 1 is also constructed. The family size of G is pn and the correlation magnitude is roughly upper bounded by (pk + 1) √...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex 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} according a...

We prove that the error in prime number theorem can be quantitatively improved beyond Riemann Hypothesis bound by using versions of Montgomery’s conjecture for pair correlation zeros zeta-function which are uniform long ranges and with suitable terms.

Dust particles immersed within a plasma environment, such as those in protostellar clouds, planetary rings or cometary environments, will acquire an electric charge. If the ratio of the inter-particle potential energy to the average kinetic energy is high enough the particles will form either a “liquid” structure with short-range ordering or a crystalline structure with long range ordering. Man...

Recent studies have shown that a system composed from several randomly interdependent networks is extremely vulnerable to random failure. However, real interdependent networks are usually not randomly interdependent, rather a pair of dependent nodes are coupled according to some regularity which we coin inter-similarity. For example, we study a system composed from an interdependent world wide ...