Given a set of positive integers A = {a1, . . . , ad} with gcd(a1, . . . , ad) = 1, we call an integer n representable if there exist nonnegative integers m1, . . . ,md such that n = m1a1 + · · ·+ mdad . The linear diophantine problem of Frobenius asks for the largest integer which is not representable. We call this largest integer the Frobenius number g(a1, . . . , ad). One fact which makes th...

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...

Given relatively prime positive integers a1, . . . , an, the Frobenius number is the largest integer that cannot be written as a nonnegative integer combination of the ai. We examine the parametric version of this problem: given ai = ai(t) as functions of t, compute the Frobenius number as a function of t. A function f : Z+ → Z is a quasi-polynomial if there exists a period m and polynomials f0...