We study scattering properties of a PT -symmetric square well potential with real depth larger than the threshold of particle-antiparticle pair production as the time component of a vector potential in the Dirac equation. Spontaneous pair production inside the well becomes tiny beyond the strength at which discrete bound states with real energies disappear, consistently with a spontaneous break...

This paper introduces a general method for obtaining lower bounds for the total energy and the minimal inter-particle distance in optimal atom cluster problems with pair potential functions under weak general conditions on the pair potential. The bounds obtained are sharper than those previously known for both the Lennard-Jones potential and various Morse potentials. Statistics on the putative ...

Let $G$ be a graph with $p$ vertices and $q$ edges. The graph $G$ is said to be a super pair sum labeling if there exists a bijection $f$ from $V(G)cup E(G)$ to ${0, pm 1, pm2, dots, pm (frac{p+q-1}{2})}$ when $p+q$ is odd and from $V(G)cup E(G)$ to ${pm 1, pm 2, dots, pm (frac{p+q}{2})}$ when $p+q$ is even such that $f(uv)=f(u)+f(v).$ A graph that admits a super pair sum labeling is called a {...

‎the frobenius complement of a given frobenius group acts on its kernel‎. ‎the scheme which is arisen from the orbitals of this action is called ferrero pair scheme‎. ‎in this paper‎, ‎we show that the fibers of a ferrero pair scheme consist of exactly one singleton fiber and every two fibers with more than one point have the same cardinality‎. ‎moreover‎, ‎it is shown that the restriction of a...

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...

BACKGROUND AND AIM: Sesame has a high content of calcium. Regarding to the lack of adequate data about its remineralizing potential, we conducted this study to evaluate the surface hardness of enamel exposed to sesame extraction gel in comparison to artificial saliva and fluoride.METHODS: After mounting and polishing twenty-four caries-free human premolars, the baseline microhardness was record...

Sex-allocation theory predicts that females should preferentially produce offspring of the sex with greater fitness potential. In socially monogamous animal species, extra-pair mating often increases the variance in fitness of sons relative to daughters. Thus, in situations where offspring sired by a female's extra-pair mate(s) will typically have greater fitness potential than offspring sired ...

Let (X, T ) and (Y, S) be two subshifts so that Y is a factor of X. For any asymptotically sub-additive potential Φ on X and a = (a, b) ∈ R with a > 0, b ≥ 0, we introduce the notions of a-weighted topological pressure and a-weighted equilibrium state of Φ. We setup the weighted variational principle. In the case that X, Y are full shifts with one-block factor map, we prove the uniqueness and G...