The papers [5], [12], [3], [1], [6], [2], [10], [9], [4], [11], and [7] provide the notation and terminology for this paper. We introduce BCI stuctures with complements which are extensions of BCI structure with 0 and zero structure and are systems 〈 a carrier, an external complement, an internal complement, a zero 〉, where the carrier is a set, the external complement and the internal compleme...

Permutations over F22k with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well known example is that the Advanced Encryption Standard (AES) chooses a differentially 4-uniform permutation, the multiplicative inverse function, as its S-box. In this...

EA-equivalence classes and the more general CCZ-equivalence classes of functions over GF (2) each preserve APN and AB properties desirable for S-box functions. We show that they can be related to subsets c[T ] and g[T ] of equivalence classes [T ] of transversals, respectively, thus clarifying their relationship and providing a new approach to their study. We derive a formula which characterise...

in order to determine the best index for evaluating maize genotypes, 15 maize inbred lines were evaluated in two planting dates, 6 july to coincide heat stress with pollination time and 27 july as normal planting to avoid high temperature during pollination and grain filling period, using a randomized complete block design with three replications, in shushtar city, in 2007. result showed that i...

We present a short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem based on Ore’s Defect Formula and Anderson’s proof of Tutte’s 1-Factor Theorem from Hall’s Theorem. The fundamental theorems on matchings in graphs have been proved in many ways, and generally they all imply each other. The most well-known is Hall’s Theorem [7] characterizing when a bipartite graph has ...

In the present paper, we consider biflatness of certain classes of semigroupalgebras. Indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. Also, for a certain class of inversesemigroups S, we show that the biflatness of ell^{1}(S)^{primeprime} is equivalent to the biprojectivity of ell^{1}(S).