‎Let $tilde{F}=(Q,S,tilde{R},Z,omega,tilde{delta},‎ F_1,F_2)$‎ ‎be a general fuzzy automaton and the set of its states be a group.‎ ‎The aim of this paper is the study of applications of a group in a‎ ‎general fuzzy automaton‎. ‎For this purpose‎, ‎we define the concepts‎ ‎of fuzzy normal kernel of a general fuzzy automaton‎, ‎fuzzy kernel‎ ‎of a general fuzzy automaton‎, ‎adjustable‎, ‎multip...

A subset S ⊆ V (G) is an independent set of G if no two vertices of S are adjacent in G. A subset Q ⊆ V (G) is a 2-dominating set of G if each vertex from V (G)\Q has at least two neighbours in Q. We define new kind of kernels in graphs. Using existing concepts of an independent set and a 2-dominating set, we define in the natural way the concept of 2-dominating kernels in graphs. A subset J ⊂ ...

We introduce and study invariant (weighted) transport-kernels balancing stationary random measures on a locally compact Abelian group. The first main result is an associated fundamental invariance property of Palm measures, derived from a generalization of Neveu's exchange formula. The second main result is a simple sufficient and necessary criterion for the existence of balancing invariant tra...

This paper analyses the construction of the kernel graph of a non-synchronizing transformation semigroup and introduces the inverse synchronization problem. Given a transformation semigroup S ≤ Tn, we construct the kernel graph Gr(S) by saying v and w are adjacent, if there is no f ∈ S with vf = wf . The kernel graph is trivial or complete if the semigroup is a synchronizing semigroup or a perm...

Let f(t) be a real continuous function on an interval, and consider the operator function f(X) defined for Hermitian operators X. We will show that if f(X) is increasing w.r.t. the operator order, then for F (t) = ∫ f(t)dt the operator function F (X) is convex. Let h(t) and g(t) be C1 functions defined on an interval I. Suppose h(t) is non-decreasing and g(t) is increasing. Then we will define ...

the initial step in any breeding program including the breeding of walnut is an evaluation of the genetic diversity of its population and on identification of its superior and promising genotypes. this research was carried out during 2009-2010 growing seasons to evaluate the walnut genotypes, population grown in the vicinities of eghlid city, as one of the richest walnut population regions in t...

The crude oil, crude protein, crude ash, crude fiber, total phenol and antioxidant activity values, peroxide values, specific gravity, the refraxtive index and  acid value of Citrullus lanatus and their oils were determined. Fatty acid composition of seeds belong to both watermelon were determined by Gas Chromotography (GC). These oils are important sources of essential fatty acid,...

We investigate a two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged compact region K whose charge density is determined by its equilibrium potential at an inverse temperature corresponding toβ= 2. When the charge on the region, s , is greater than N , the particles accumulate in a neighborhood of the boundary o...