The functional equation and beyond endoscopy

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...

Problems Beyond Endoscopy

We give a short introduction to Beyond Endoscopy, a proposal by Langlands for attacking the general principle of functoriality. We shall try to motivate the proposal by emphasizing its structural similarities with the actual theory of endoscopy. We shall then discuss a few of the many problems that will need to be solved, some of which are suggested by the recent work of A. Altuğ . Mathematics ...

Perforation following colorectal endoscopy: what happens beyond the endoscopy suite?

BACKGROUND The risk factors for perforation from colorectal endoscopy have been well studied, but little is known about clinical outcomes beyond the immediate event. OBJECTIVE To evaluate short- and long-term outcomes of iatrogenic colorectal perforation following colorectal endoscopy. DESIGN Retrospective review over 16 years at a single tertiary care institution. MAIN OUTCOME MEASURES T...

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...

On the Stability of the Orthogonally Quartic Functional Equation