In this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$  is orthogonality in the sense of Ratz.

recently the previous caspian ecosystem is in a catastrophic condition which caused changes in the absolute and relative abundance of the commercially important caspian kutum (rutilus frisii kutum) in iranian waters. the paper presents estimates of yield-per-recruit and spawning biomass-per-recruit under various harvest strategies of fmax, f0.1, f30%. it proposes a method for estimating accepta...

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.

Consider y" (t) + A (t)y (t) + 0, y is a real n-dimensinal vector and A(t) is a real nxn matrix, continuous on some interval. Some positivity properties of solutions and conjugate points of y"(t) + A(t)y (t) = 0 appeared in literature. We prove similar results for focal points

in this paper, we introduce the notion of derivation on krasner hyperrings as follows: the function d : r  r isa derivation on a krasner hyperring r if for all , , ry x  ) ( ) ( = ) ( y d x d y x d   andd (x  y) d (x)  y  x  d ( y). then, we investigate some fundamental properties of derivation on krasnerhyperings and prime krasner hyperrings. also, we introduce differential krasner hy...

PART I CLONING TECHNIQUES 1 Cloning Neuropeptide Tyrosine cDNA Carolyn A. Worby ......................................................................... 3 2 Human Y1/Y5 Receptor Gene Cluster: Isolation and Characterization Herbert Herzog............................................................................ 13 3 HumanType 2 Neuropeptide Y Receptor Gene: Isolation and Characterization Davi...