The algebraic functional equation of Riemann’s theta function

Functional Equation for Theta Series

In this short paper, we find the transformation formula for the theta series under the action of the Jacobi modular group on the Siegel-Jacobi space. This formula generalizes the formula (5.1) obtained by Mumford in [3, p. 189].

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...

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...

Solving the Algebraic Riccati Equation with the Matrix Sign Function

This paper presents solne inrprovements to the matrix-sigll-fllnction algorithn~ for the alge\,raic Riccati equation. A simple reorganization changes nonsynnnetric watrix inversion5 into syinmetric niatrix inversions. Scaling accelerates convergence of the basic iteration ant1 yields a new qnadratic formula for certain 2-by-2 algebraic Riccati eqnation5. Numerical experience suggests the algori...

On the Stability of the Orthogonally Quartic Functional Equation