Mixed multiplicities,Hilbert polynomials and homaloidal surfaces

We investigate the relationship among several numerical invariants associated to a (free) projective hypersurface V : the sequence of mixed multiplicities of its Jacobian ideal, the Hilbert polynomial of its Milnor algebra, and the sequence of exponents when V is free. As a byproduct, we obtain explicit equations for some of the homaloidal surfaces in the projective 3‐dimensional space constructed by C. Ciliberto, F. Russo and A. Simis.     

On noncommutative piecewise Noetherian rings

We extend the definition of a piecewise Noetherian ring to the noncommutative case, and investigate various properties of such rings. In particular, we show that a ring with Krull dimension is piecewise Noetherian. Certain fully bounded piecewise Noetherian rings have Gabriel dimension and exhibit the Gabriel correspondence between prime ideals and indecomposable injective modules.     

Comprehensive evaluation of solvent in dispersive liquid-liquid microextraction for determination of itraconazole and hydroxy itraconazole by high performance liquid chromatography with fluorescence detection

This paper aims to propose a multicriteria decision analysis (MCDA) method to evaluate and select solvent in a dispersive liquid-liquid microextraction (DLLME) approach. The DLLME is applied to the determination of itraconazole and hydroxy itraconazole in plasma by high performance liquid chromatography with fluorescence detection (HPLC-FLD). To achieve this goal, extraction efficiency, chromatographic resolution, and greenness of solvent were identified as the three indicators in MCDA. Then, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) was employed to evaluate and select the solvent. Weight assignment was set up by integrating the subjective scoring from experienced analysts and the objective approach using Shannon’s entropy weight method. Under chosen parameters (extraction solvent: 1-decanol 40 μL, dispersing solvent: methanol 400 μL), the method was validated satisfactorily and applied successfully to the analysis of itraconazole and hydroxy itraconazole in real human plasma samples. The results show that the comprehensive weighted TOPSIS analysis is a promising tool to choose experimental conditions toward an integrative goal. It can provide analysts with a decision making reference to maintain a balance between the analytical performance and eco-friendliness.     

Integral closure,basically full closure,and duals of nonresidual closure operations

We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [5], extending our previous results to the expanded context. We apply this duality in particular to integral and basically full closures and their respective cores to obtain integral and basically empty interiors and their respective hulls. We also dualize some of the known formulas for the core of an ideal to obtain formulas for the hull of a submodule of the injective hull of the residue field. The article concludes with illustrative examples in a numerical semigroup ring.     

The Lattice of Deductive Systems on Hilbert Algebras

The concept of deductive system on a Hilbert algebra was introduced by A. Diego. We show that the set Ded A of all deductive systems on a Hilbert algebra A forms an algebraic lattice which is distributive.AMS Classification (2000): 06F35, 03G25, 08A30     

关于实Hilbert环

通过引进“强实Hilbert环”这一概念,本文证明了,一个环A是强实Hilbert环,当且仅当多项式环A[X]是实Hilbert环,当且仅当A[X]的每个实极大理想在A上的局限是实极大的,从而文献[1]中两个主要结果被否定.此外,本文还研究了所谓的“严格的实Hilbert环”,这类环对于半代数零点定理等方面的探讨更具应用意义.     

Idealization of a decomposition theorem

In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A _I-sets and A _I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A _I-continuous. This revised version was published online in June 2006 with corrections to the Cover Date.     

Combinatorial coverings from geometries over principal ideal rings

A t-(v, k, λ) covering is an incidence structure with v points, each block incident on exactly k points, such that every set of t distinct points is incident on at least λ blocks. By considering certain geometries over finite principal ideal rings, we construct infinite families of t-(v, k, λ) coverings having many interesting combinatorial properties. © 1999 John & Sons, Inc. J Combin Designs 7: 247–268, 1999     

Evaluations of initial ideals and Castelnuovo-Mumford regularity

This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.

     

关于强正则环的刻画

通过单边理想是广义弱理想来刻画强正则环,证明了下列条件是等价的:①R是强正则环;②R是半素的左GP-V′-环,且每一个极大的左理想是广义弱理想;③R是半素的左GP-V′-环,且每一个极大的右理想是广义弱理想.