Contra-correspondence and Reciprocation

Contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions as a new generalization of contra continuity.

Polynomials Associated with Reciprocation

Polynomials are defined recursively in various ways associated with reciprocation; e.g., Sn+1(x)/Tn+1(x) = Sn(x)/Tn(x) ± Tn(x)/Sn(x). Under certain conditions, the zeros of Sn interlace those of Tn. Identities for Sn, Tn, and related polynomials are derived, as well as recurrence relations and infinite sums involving roots of polynomials.

Contra-ω-Continuous and Almost Contra-ω-Continuous

The Convergence of Reciprocation

People often interact repeatedly: with relatives, through file sharing, in politics, etc. Many such interactions are reciprocal: reacting to the actions of the other. In order to facilitate decisions regarding reciprocal interactions, we analyze the development of reciprocation over time. To this end, we propose a model for such interactions that is simple enough to enable formal analysis, but ...

Entanglement reciprocation between qubits and continuous variables.

We investigate how entanglement can be transferred between qubits and continuous-variable (CV) systems. We find that one ebit borne in maximally entangled qubits can be fully transferred to two CV systems which are initially prepared in a pure separable Gaussian field with high excitation. We show that it is possible to retrieve the entanglement back to qubits from the entangled CV systems. The...