We solve analytically the energy eigenvalue problem of narrow semiconductor quantum rings with a general spin-orbit term that includes as special case Rashba and Dresselhaus interactions acting simultaneously. The eigenstates eigenenergies system are found for arbitrary values coupling constants without making use approximations. expressed products scalar Mathieu function spinor factor which is...

A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of T0-periodic PC-mild solution for homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of fixed point for a suitable operator. Further the alternative res...

Let R be a ring with center Z, Jacobson radical J , and set N of all nilpotent elements. Call R generalized periodic-like if for all x ∈ R \ (N ∪ J ∪ Z) there exist positive integers m, n of opposite parity for which xm − xn ∈ N ∩ Z. We identify some basic properties of such rings and prove some results on commutativity. Let R be a ring; and let N = N(R), Z = Z(R) and J = J(R) denote respective...

In this paper we investigate the periodic structure of rich words (i.e., words having the highest possible number of palindromic factors), giving new results relating them with periodic-like words. In particular, some new characterizations of rich words and rich palindromes are given. We also prove that a periodic-like word is rich if and only if the square of its fractional root is also rich.

In this paper, we analyse the existence and uniqueness of a time-periodic solution to chemotaxis-shallow water system in periodic domain. Under assumption some smallness symmetric external force, is established using method parabolic regularization limit process. The proved by energy estimates.

In this paper we establish a multiplicity result for a second-order non-autonomous system. Using a variational principle of Ricceri we prove that if the set of global minima of a certain function has at least k connected components, then our problem has at least k periodic solutions. Moreover, the existence of one more solution is investigated through a mountain-pass-like argument.