Taking into account the effects of multi-proportional delays and D operator, this paper investigates stability issue a general class neutral-type SICNNs (shunting inhibitory cellular neural networks). With help fixed point theorem some novel differential inequality techniques, we derive new sufficient conditions to ensure existence, uniqueness exponential weighted pseudo almost periodic solutio...

Relativistic massive bosons with spin one are considered in several quantization schemes. In all of them the system is shown described by a non-Hermitian Hamiltonian H 6= H and helicity operator Λ. Constructively we show that in all of the contemplated schemes both these operators H and Λ prove simultaneously PT −symmetric, i.e., pseudo-Hermitian with respect to a certain not too complicated in...

The present paper is concerned with semilinear partial differential equations involving a particular pseudo-differential operator. It investigates both fractal conservation laws and non-local HamiltonJacobi equations. The idea is to combine an integral representation of the operator and Duhamel’s formula to prove, on the one side, the key a priori estimates for the scalar conservation law and t...

The index of a pseudo B-Fredholm operator will be defined and generalize the usual operator. This concept used to extend some known results in Fredholm’s theory. Among other results, nullity, deficiency, ascent descent extended for pseudo-Fredholm

We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components the Hamiltonian operator. These are represented an anti-commutativity graph which contains necessary sufficient information for computing full partition function. derive second-order differential equation extended function $z[\beta, \beta', J]$ describes transformation from...