In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

in this paper we obtain a necessary and a sufficient condition for the set of ω_0-nearest points ( ω_0-farthest points) to be non-empty or a singleton set in normed linear spaces. we shall find a necessary and a sufficient condition for an uniquely remotal set to be a singleton set.

New correlation consistent-like basis sets have been developed for the post-d group 13–15 elements ~Ga–As, In–Sb, Tl–Bi! employing accurate, small-core relativistic pseudopotentials. The resulting basis sets, which are denoted cc-pVnZ-PP, are appropriate for valence electron correlation and range in size from (8s7p7d)/@4s3p2d# for the cc-pVDZ-PP to (16s13p12d3 f 2g1h)/ @7s7p5d3 f 2g1h# for the ...

Sequences of basis sets that systematically converge towards the complete basis set (CBS) limit have been developed for the first-row transition metal elements Sc-Zn. Two families of basis sets, nonrelativistic and Douglas-Kroll-Hess (-DK) relativistic, are presented that range in quality from triple-zeta to quintuple-zeta. Separate sets are developed for the description of valence (3d4s) elect...

The formulation of strong and weak laws of large numbers for fuzzy random variables based on variance is given. The concept of the variance of fuzzy random variables, introduced by K1 orner (Fuzzy Sets and Systems 92 (1997) 83) and by Feng (Fuzzy Sets and Systems 120 (2001) 487) demonstrates its e2ciency. c © 2002 Elsevier Science B.V. All rights reserved.

In this note, we show by counterexamples that some results of Qiu and colleagues [On the restudy of fuzzy complex analysis: Part I. The sequence and series of fuzzy complex numbers and their convergences, Fuzzy Sets and Systems 115 (2000) 445–450; On the restudy of fuzzy complex analysis: Part II. The continuity and differentiation of fuzzy complex functions, Fuzzy Sets and Systems 120 (2001) 5...

The aim of this paper is to point out and correct some errors of two theorems for IFSs in Atanassov (Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 2000) and bring forward a new theorem for IFSs. In the end, some elementary, but non-standard equalities between IFSs were formulated.

Using mid-infrared and radio criteria, we select a sample of candidate z ∼ 2 obscured quasars. Optical spectroscopy confirms about half of these as type-2 quasars, and modelling the population suggests 50-80% of the quasars are obscured. We find some flat radio spectrum type-2 quasars, and tentative evidence for obscuration unrelated to the torus. Using a similar sample, we also find evidence f...

in this work, theoretical investigations on carbon nanotube with oxygen atom have been carried out by firstprinciplescalculations and density functional theory and hartree fock theory in 3-216 and 6-316 basis sets. theinteraction energy of the oxygen atom to a cnt is calculated. the effects of this substitutions have beeninvestigated on the during transplantation (10,0) single-walled carbon nan...

Auxiliary basis sets specifically matched to the correlation consistent cc-pVnZ-PP, ccpwCVnZ-PP, aug-cc-pVnZ-PP and aug-cc-pwCVnZ-PP orbital basis sets (used in conjunction with pseudopotentials) for the 5d transition metal elements Hf-Pt have been optimized for use in density fitting second-order Møller-Plesset perturbation theory and other correlated ab initio methods. Calculations of the sec...