and a method A of summability by means of which a given sequence Su S2, • • • is summable to <r as w—»oo. If a sequence sn is summable A, we say that A {sn} exists and that sn belongs to the summability field of A. If sn is summable A to <r, we say that A {sn} = <r. The method A is regular if A {sn} = lim sn whene...

The grant number of the National Natural Science Foundation of China should be ‘‘10774061,’’ not ‘‘50602020’’ as appeared in the published paper. Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

We consider the asymmetric simple exclusion process (ASEP) on the integers in which the initial density at a site (the probability that it is occupied) is given by a periodic function on the positive integers. (When the function is constant, this is the step Bernoulli initial condition.) Starting with a result in earlier work, we find a formula for the probability distribution for a given parti...

Hall’s condition for the existence of a proper vertex list-multicoloring of a simple graph G has recently been used to de-ne the fractional Hall and Hall-condition numbers of G, hf(G) and sf(G). Little is known about hf(G), but it is known that sf(G) = max[|V (H)|= (H);H 6G], where ‘6’ means ‘is a subgraph of’ and (H) denotes the vertex independence number of H . Let f(G) and cf(G) denote the f...

A denotational semantics and a Hoare programming logic for a subset of the standard hardware description language vhdl are set out here. Both define the behaviour of synchronously clocked vhdl simulators in declarative and compositional style. The logic is proved complete with respect to the denotational semantics and a natural implementation of the logic in prolog as a validation condition gen...

a simple, mild and practical procedure has been developed for the synthesis of symmetrical and unsymmetrical ethers by using dmso, tbai in the presence of k2co3. we extended the utility of  potassium carbonate as an efficient base for the preparation of ethers. a wide range of alkyl aryl and dialkyl ethers are synthesized from treatment of aliphatic alcohols and phenols with various alkyl halid...

sulfonated polystyrene/montmorillonite nanocomposite (ommt/ps-so3h) was prepared and used as a novel, efficient and inexpensive heterogeneous acid catalyst in the one-pot reaction three-component mannich reaction of ketones, aromatic aldehydes and amines under solvent-free conditions. the catalyst was characterized by xrd, sem, tg, bet and ft-ir techniques. this method has advantages of high yi...

This study investigated the functional significance of the N2 response to novel stimuli. In one condition, background, target, and deviant stimuli were simple geometric figures. In a second condition, all stimulus types were unfamiliar/unusual figures. In a third condition, background and target stimuli were unusual figures and deviant stimuli were simple shapes. Unusual figures, whether they w...