Axiomatizability and completeness of some classes of partially ordered polygons

We study partially ordered monoids over which a class of free (over sets and over posets), projective, and (strongly, weakly) flat partially ordered polygons is axiomatizable, complete, or model complete. Similar issues for polygons were dealt with in papers by V. Gould and A. Stepanova. Supported by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-2810.2008.1). Translated from Algebra i Logika, Vol. 48, No. 1, pp. 90–121, January–February, 2009.     

Solvent effect of ionic liquids on the distribution constant of 2-thenoyltrifluoroacetone and its nickel(II) and copper(II) chelates and the evaluation of the solvent properties based on the regular solution theory

Distribution constants of 2-thenoyltrifluoroacetone (Htta) and its Ni(II)and Cu(II) chelates between 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (C_nmimTf₂N; n = 4, 6, and 8) as ionic liquid (IL) and an aqueous phase were determined. The enol fraction of Htta in ILs was spectrophotometrically measured to calculate the distribution constant of the enol form (K_D,HE) of Htta. The K_D,HE values in ILs were evaluated by comparing those in various molecular solvents such as alkanes, aromatic hydrocarbons, chlorohydrocarbons, ethers, ketones, and esters previously reported on the basis of the regular solution theory (RST). It was elucidated that the IL solutions of Htta (enol) can be taken as apparently regular solutions as expected in the organic solvents. On the other hand, the effect of ILs on the distribution constant of metal(II) chelates (K_D,M) was fairly complicated. The Cu(tta)₂-IL solutions behaved like the alkane and aromatic hydrocarbon solutions but the Ni(tta)₂-IL (C₄mimTf₂N) like ether and ketone solutions. In the Ni(II) case, some specific interactions between the Ni(II) chelate and IL was suggested. Finally, the solubility parameters of ILs were calculated using K_D,HE by RST and were in good agreement with the literature values obtained by the enthalpy of vaporization.     

Regular open sets in fuzzifying topology redefined

In 2000 [1], Zahran introduced the concept of regular open sets in fuzzifying topology. In 2004 [2], Sayed and Zahran, gave an example to illustrate that the statements:

• (1)$\models A\in R_{\tau }\to A\in \tau$ (Lemma 2.2 [1]); and
• (2)$\models (A\in R_{\tau }\wedge B\in R_{\tau })\to A\cap B\in R_{\tau }$ (Theorem 2.4 [1]),

are incorrect. In the present paper we redefine this concept to make these statements correct. Furthermore, by making use of our definition of regular open sets, the concepts of almost continuity and δ-continuity are introduced and studied in fuzzifying topology.     

Codimension Two PL Embeddings of Spheres with Nonstandard Regular Neighborhoods

For a given polyhedron K(?)M,the notation RM(K)denotes a regular neigh- borhood of K in M.The authors study the following problem:find all pairs(m,k) such that if K is a compact k-polyhedron and M a PL m-manifold,then R_M(f(K))≌R_M(g(K))for each two homotopic PL embeddings f,g:K→M.It is proved that R_S~(k 2)(S~k)(?)S~k×D~2 for each k(?)2 and some PL sphere S~k(?)S~(k 2)(even for any PL sphere S~k(?)S~(K 2)having an isolated non-locally flat point with the singularity S~(k-1)(?) S~(k 1)such thatπ_1(S~(k 1)-S~(k-1))(?)Z).     

Some Regularity Criteria for Affine Semilocal Rings

The purpose of this article is to study an existence of p-bases and mainly to give some regularity criteria for semilocal rings essentially of finite type over fields.     

基本的弱正则*-半群的结构

本文给出了基本的弱正则＊－半群的一个结构定理．作为这一结构定理的特 殊情形，基本的正则＊－半群的一个新的结构被给出．     

Gauss-Green cubature and moment computation over arbitrary geometries

We have implemented in Matlab a Gauss-like cubature formula over arbitrary bivariate domains with a piecewise regular boundary, which is tracked by splines of maximum degree p (spline curvilinear polygons). The formula is exact for polynomials of degree at most 2n−1 using N∼cmn² nodes, 1≤c≤p, m being the total number of points given on the boundary. It does not need any decomposition of the domain, but relies directly on univariate Gauss-Legendre quadrature via Green’s integral formula. Several numerical tests are presented, including computation of standard as well as orthogonal moments over a nonstandard planar region.