in this paper, we use the structure theory to prove an analog to a well-known theorem of herstein as follows: let r be a ring with center c such that for all x,y ? r either [x,y]= 0 or x-x [x,y]? c for some non negative integer n= n(x,y) dependingon x and y. then r is commutative.

A function F from Fpn to itself is planar if for any a ∈F ∗ pn the function F (x+ a)−F (x) is a permutation. CCZ-equivalence is the most general known equivalence relation of functions preserving planar property. This paper considers two possible extensions of CCZ-equivalence for functions over fields of odd characteristics, one proposed by Coulter and Henderson and the other by Budaghyan and C...

When first encountering data structures such as arrays, records and pointers programmers are often presented with pictorial representations. The use of pictures to describe data structures and their manipulation can help establish basic programming intuitions. The same is true of program proving where pictures are frequently used within the literature to describe program properties such as loop...

In this paper a new mixing condition for sequences of random variables is considered. This mixing condition is termed γ-mixing. Whereas mixing conditions such as α-mixing are typically defined in terms of entire σ-fields of sets generated by random variables in the distant past and future, γ-mixing is defined in terms of a smaller class of sets: the finite dimensional cylinder sets. This leads ...

History.?In October 1910, the patient, Sepoy T. K., 27th Punjabis, showed me some pigmented spots on iiis face, hands and left leg. They first appeared in March, 1U0S, when the patient was living in Jhandola. He believed that quinine, which he was taking prophylactically at that time, caused their appearance. No fresh spots have appeared since then, but some of the original areas have increased...

background & importance: iniencephaly is a rare cranio-cervical deformity. it belongs to neural tube defects. this disorder is characterized by a retroflexion of head, a very short neck, varying degrees of incomplete posterior closure of vertebrae and cervical and thoracic spinal synostosis. this malformation is associated with central nervous system and systemic malformations. most of patients...

let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

Papadatos, C., Alexiou, D., Nicolopoulos, D., Mikropoulos, H., and Hadzigeorgiou, E. (1974). Archives of Disease in Childhood, 49, 927. Congenital hypoplasia of depressor anguli oris muscle: a genetically determined condition? The frequency of hypoplasia of the depressor anguli oris muscle was 37 cases among 4 530 consecutive births (8 -2 %). Diagnosis was based on clinical and electromyographi...

We give a simple characterization for a nonassociative algebra A, having characteristic 6= 2, to be commutative. Namely, A is commutative if and only if it is exible with a commuting set of generators. A counterexample shows that characteristic 6= 2 is necessary. Both the characterization and the counterexample were discovered using the computer algebra system in [2].