Self-reciprocal functions

On Properties of Self Reciprocal Functions

Local Self-concordance of Barrier Functions Based on Kernel-functions

 Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functio...

Self-reciprocal Polynomials Over Finite Fields

The reciprocal f ∗(x) of a polynomial f(x) of degree n is defined by f ∗(x) = xf(1/x). A polynomial is called self-reciprocal if it coincides with its reciprocal. The aim of this paper is threefold: first we want to call attention to the fact that the product of all self-reciprocal irreducible monic (srim) polynomials of a fixed degree has structural properties which are very similar to those o...

Reciprocal vector theory for diffractive self-imaging.

A reciprocal vector theory for analysis of the Talbot effect of periodic objects is proposed. Using this method we deduce a general condition for determining the Talbot distance. Talbot distances of some typical arrays (a rectangular array, a centered-square array, and a hexagonal array) are derived from this condition. Further, the fractional Talbot effect of a one-dimensional grating, a squar...

The Self System in Reciprocal Determinism

Explanations of human behavior have generally favored unidirectional causal models emphasizing either environmental or internal determinants of behavior. In social learning theory, causal processes are conceptualized in terms of reciprocal determinism. Viewed from this perspective, psychological functioning involves a continuous reciprocal interaction between behavioral, cognitive, and environm...