‎‎for any group $g$‎, ‎we define an equivalence relation $thicksim$ as below‎: ‎[forall g‎, ‎h in g gthicksim h longleftrightarrow |g|=|h|]‎ ‎the set of sizes of equivalence classes with respect to this relation is called the same-order type of $g$ and denote by $alpha{(g)}$‎. ‎in this paper‎, ‎we give a partial answer to a conjecture raised by shen‎. ‎in fact‎, ‎we show that if $g$ is a nilpot...

the present article investigates the application of high order tsk (takagi sugeno kang) fuzzy systems in modeling photo voltaic (pv) cell characteristics. a method has been introduced for training second order tsk fuzzy systems using anfis (artificial neural fuzzy inference system) training method. it is clear that higher order tsk fuzzy systems are more precise approximators while they cover n...

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

The same-order type τe(G) of a finite group G is set formed the sizes equivalence classes containing same order elements G. In this paper, we study an arithmetical property set. More exactly, outline some results on classification and existence groups whose types are arithmetic progressions 3 or 4 elements, latter being maximum size such sequence.

We prove that the mapping class group of a compact surface with a nite number of punctures and non-empty boundary is order automatic. More precisely, the group is right-orderable, has an automatic structure as described by Mosher, and there exists a nite state automaton that decides, given the Mosher normal forms of two elements of the group, which of them represents the larger element of the g...