and Applied Analysis 3 Theorem 1.2 Rassias 18 . Let X be a real normed linear space and Y a real complete normed linear space. Assume that f : X → Y is an approximately additive mapping for which there exist constants θ ≥ 0 and p, q ∈ R such that r p q / 1 and f satisfies the inequality ∥ ∥f ( x y ) − f x − f(y)∥∥ ≤ θ‖x‖p∥∥y∥∥q 1.5 for all x, y ∈ X. Then there exists a unique additive mapping L...

We prove that the smallest degree of an apolar 0-dimensional scheme of a general cubic form in n+1 variables is at most 2n+2, when n ≥ 8, and therefore smaller than the rank of the form. For the general reducible cubic form the smallest degree of an apolar subscheme is n+ 2, while the rank is at least 2n.

We give an error analysis of Strang-type splitting integrators for nonlinear Schrödinger equations. For Schrödinger-Poisson equations with an H4-regular solution, a first-order error bound in the H1 norm is shown and used to derive a second-order error bound in the L2 norm. For the cubic Schrödinger equation with an H4-regular solution, first-order convergence in the H2 norm is used to obtain s...

By using a nonassociative algebra argument, we prove that u ≡ 0 is the only cubic homogeneous polynomial solution to the p-Laplace equation div|Du|p−2Du(x) = 0 in Rn for any n ≥ 2 and p 6∈ {1, 2}.

In this paper, we propose a modeling approach that captures the dependence of the power dissipation of a (combinational or sequential) logic circuit on its input/output signal switching statistics. The resulting power macromodel, consists of a quadratic or cubic equation in four variables, that can be used to estimate the power consumed in the circuit for any given input/output signal statistic...