In 1940, Ulam 1 gave a wide ranging talk before the mathematics club of the University of Wisconsin in which he discussed a number of important unsolved problems. Among those was the question concerning the stability of group homomorphisms: “Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a function h : G1 → G2 satisfies...

Our purpose is to find an upper bound for the length of s-extremal codes over F2 (resp. F4) when d ≡ 2 (mod 4) (resp. d odd). This question is left open in [6], [2]. More precisely, we show that there is no s-extremal binary code of length n ≥ 21d− 82 if d > 6 and d ≡ 2 (mod 4). Similarly we show that there is no s-extremal additive F4 code of length n ≥ 13d− 26 if d > 1 and d is odd. We also d...

We calculate the decay constant ratios fηc/fJ/ψ and fηb/fΥ. In the calculation we take into account the mock meson structures of the mesons, as well as the difference of the wave functions at origin of the vector and pseudoscalar mesons studied by Ahmady and Mendel. We find that the different spin structures of the mesons much affect the ratios. We incorporate our results in the prediction of t...

In this paper we will generalize  some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .

$!!!!$ In this paper, the notion of fuzzy $!$ Krasner $!(m, n)$-hyperrings($!F^{(m, n)}!$-hyperrings) by using the notion of$F^m$-hyperoperations and $F^n$-operations is introduced and somerelated properties are investigated. In this regards,relationships between Krasner $F^{(m, n)}$-hyperrings and Krasner$(m, n)$-hyperrings are considered. We shall prove that everyKrasner $F^{(m, n)}$-hyperrin...