In the present article we study the asymptotic behavior of the sums n≤x cn+1 pn+1 − cn pn and n≤x pn+1 cn+1 − pn cn , and of the series ∞ n=1 cn+1 pn+1 − cn pn α , where p n denotes the n-th prime number while c n stands for the n-th composed number.

OBJECTIVE The (CTG)(n) polymorphism in the serum carnosinase (CN-1) gene affects CN-1 secretion. Since CN-1 is heavily glycosylated and glycosylation might influence protein secretion as well, we tested the role of N-glycosylation for CN-1 secretion and enzyme activity. We also tested whether CN-1 secretion is changed under hyperglycemic conditions. RESULTS N-glycosylation of CN-1 was either ...

We consider the upper bounds of the finite block length capacity Cn,FB(P ) of the discrete time Gaussian channel with feedback. We also let Cn(p) the nonfeedback capacity. We prove the relations Cn(P ) ≤ Cn,FB(P ) ≤ Cn(αP ) + 1 2 ln(1 + 1 α ) and Cn(P ) ≤ Cn,FB(P ) ≤ (1 + 1 α )Cn(αP ) for any P > 0 and any α > 0, which induce the half-bit and factor-of two bounds given by Cover and Pombra in th...

a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...

The objective of our study was to evaluate whether cognitively normal (CN) elderly participants showing elevated cortical beta-amyloid (Aβ) deposition have a consistent neuroanatomical signature of brain atrophy that may characterize preclinical Alzheimer's disease (AD). 115 CN participants who were Aβ-positive (CN +) by amyloid PET imaging; 115 CN participants who were Aβ-negative (CN -); and ...