Quasi-cyclic (QC) codes form an important generalization of cyclic codes. It is well know that QC codes of length sl with index s over the finite field F are F[y]-submodules of the ring F[x, y]/< x − 1, y − 1 >. The aim of the present paper, is to study QC codes of length sl with index s over the finite field F and find generator polynomials and generator matrix for these codes. To achieve this...

Let ∆ be the ball |x| < 1 in the complex vector space C, let f : ∆ → C be a holomorphic mapping and let M be a positive integer. Assume that the origin 0 = (0, . . . , 0) is an isolated fixed point of both f and the M -th iteration f of f . Then for each factor m of M, the origin is again an isolated fixed point of f and the fixed point index μfm(0) of f m at the origin is well defined, and so ...

function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...

In this work we shall provide a model-independent general calculation of the running spectral index for vacuum $F(R)$ gravities. We exploit functional form and tensor-to-scalar ratio in order to present $n_s-r$ relation gravity theories. As show, viable theories can be classified two classes models regarding their prediction index. The $R^2$-attractor predict range $-10^{-3}<a_s<-10^{-4}$, whic...

Recently several algorithms have been deveh|ped which achieve high e|tMent:y index in enclosing a na~t of the equati|m f (x ) = 0 in an interval [a, b] ,ver whk:h f ( x ) is continu|ms and f (a) f (b) < 0. The highest efficiency index, 1.6686 . . . . was achieved in [4] using the inveme cuhic interl~|latitat. This paper studies the po.~sibility of impr|wing eftlciency index by using high order ...

In this talk we present some results concerning the interpolation of discontinuous functions. First we consider an index of convergence associated to converging subsequences of a general sequence of real numbers (x n) n≥1. Namely, if L ∈ R, the index of convergence of (x n) n≥1 to L is defined by The definition can be extended to the cases L = ±∞ and also to the case where A ⊂ R. In the case wh...