Beurling regular variation, Bloom dichotomy, and the Gołąb–Schinzel functional equation

the effect of functional/notional approach on the proficiency level of efl learners and its evaluation through functional test

in fact, this study focused on the following questions: 1. is there any difference between the effect of functional/notional approach and the structural approaches to language teaching on the proficiency test of efl learners? 2. can a rather innovative language test referred to as "functional test" ge devised so so to measure the proficiency test of efl learners, and thus be as much reliable an...

A Dichotomy Theorem for Regular Types

stability of the quadratic functional equation

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

University of Cambridge on a Functional Riccati Equation Regular Solutions of the Shabat Equation

The Shabat equation f 0 (t) + q 2 f 0 (qt) + f 2 (t) ? q 2 f 2 (qt) = ; t 2 R; where and q are parameters, is the simplest self-similar reduction of the so called dressing chain for constructing and analysing exactly solvable Schrr odinger equations. It is also relevant to the study of the q-oscillator algebra in quantum mechanics. The main objective of this paper is to investigate whether the ...

On the Stability of the Orthogonally Quartic Functional Equation