For self-dual codes with all weights divisible by an integer greater than one, the minimum distance is bounded by the Mallows-Sloane upper bounds and by their improvements due to Krasikov-Litsyn and Rains. We obtain the improved upper bounds from short relations with constant coefficients on suitable binomial moments of the codes. In this approach, the Mallows-Sloane bounds are analogues of the...

In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

Abstract The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of equations that arise are solved with Newton’s method. There a trade-off between solving Newton systems directly, which give high quality solutions, and many approximate computationally less expensive but lower solutions. We propose partial full solutions to systems. speci...

this study was carried out to examine aflatoxin b1 (afb1) removal ability of four strains of lactic acidbacteria (lab). three indigenous (lactobacillus rhamnosus tmu094, lactobacillus fermentum tmu121and pedioccus pentosaceus tmu457) and a non-indigenous (labacillus rhamnosus ptcc1637) isolateswere studied. the strains were incubated with (afb1) at different time. the toxin residual in the supe...