The classical lattice A ,*, whose Voronoi cells tile Euclidean n-space by permutohedra, can be given the generalized balance ternary ring structure GBT, in a natural way as a quotient ring of Z [xl. The ring GBT, can also be considered as the set of all finite sequences sO sl.. . sk, with si E GBT,/srGBT, for all i, where M is an appropriately chosen element in GBT,. The extended generalized ba...

We find new families of nonbinary sequences of period 1 with symbols from a finite field for any prime 3. The sequences have two-level ideal autocorrelation and are generalizations of recently found ternary sequences with ideal autocorrelation. Difference sets with parameters

In this paper, we construct a new weakly universal cellular automaton on the ternary heptagrid. The previous result, obtained by the same author and Y. Song required six states only. This time, the number of states is four. This is the best result up to date for cellular automata in the hyperbolic plane.

In a binary decision diagram (BDD), a non-terminal node representing a function f = xf0_xf1 has two edges for f0 and f1. In the arithmetic ternary decision diagram (Arith TDD), each non-terminal node has three edges, where the third edge denotes f2 = f0 + f1, and + is an integer addition. The Arith TDD represents the extended weight function, an integer function showing the numbers of true mint...

In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an...