We consider a multiple-rule, generalized modus ponens inference scheme, with an interpretation based on compositional rule of inference (CRI) and a residuated implication. We show that such a system is equivalent, as far as CRI is concerned, to a system that satis5es the “basic requirement for fuzzy reasoning”, proposed by Turksen and Tian (Fuzzy Sets and Systems 58 (1993) 3–40). We establish a...

The description of the error dynamics (30) in our paper [1] contains an omission that leads to some bounds used in the conditions of Theorem 8 and Corollary 2 in the paper to be incorrectly defined. In what follows, the correct error dynamics and the corresponding conditions are given. Instead of (30) in [1], the error dynamics are actually given by ė = m ∑ i=1 wi(z)[(Ai − LiC +MiAδi)e +Mi(Āδix̂...

the degree of aromaticity of mono-substituted derivatives of benzene has beeninvestigated using a new index based on electric field gradient index, by using two mechanicalquantum methods with gaussian 03. two different basis sets have applied to study and theresults compared. this strategy has demonstrated that, due to violation of symmetry in have pisystems,how the degree of aromaticity can ha...

Recently, Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilistic mean, variance and covariance of fuzzy numbers and Fuller and Majlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have in...

This paper is a brief summary of “M.Takahashi, T.Murofushi, S.Asahina, A new necessary and sufficient condition for the Egoroff theorem in non-additive measure theory, Fuzzy Sets and Systems, to appear.” This paper states that a newly defined condition, called condition (M), is a necessary and sufficient condition for the Egoroff theorem in non-additive measure theory. The existing necessary an...

Auxiliary basis sets for density fitting second-order Moller-Plesset perturbation theory (DF-MP2) have been optimized for use with the triple-zeta nonrelativistic all-electron correlation consistent orbital basis sets, cc-pVTZ-NR and aug-cc-pVTZ-NR, for the 3d elements Sc-Zn. The relative error in using these auxiliary basis sets is found to be around four orders of magnitude smaller than that ...

The aim of this paper is to prove that if a planar set A has a difference set ∆(A) satisfying ∆(A) ⊂ Z + s for suitable s than A has at most 3 elements. This result is motivated by the conjecture that the disk has not more than 3 orthogonal exponentials. Further, we prove that if A is a set of exponentials mutually orthogonal with respect to any symmetric convex set K in the plane with a smooth...

We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basi...

With recent advances in electronic structure methods, first-principles calculations of electronic response properties, such as linear and nonlinear polarizabilities, have become possible for molecules with more than 100 atoms. Basis set incompleteness is typically the main source of error in such calculations since traditional diffuse augmented basis sets are too costly to use or suffer from ne...

Basis set pairings for dual-basis calculations are presented for the aug-cc-pVXZ (X = D, T, Q) series of basis sets. Fidelity with single-basis results is assessed at the second-order Møller-Plesset perturbation theory (MP2) level within the resolution-of-the-identity (RI) approximation, using the S22 set of noncovalent interactions and a series of electron affinities from the G3 set. Root-mean...