Gorenstein modules of finite length

In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Symmetrically Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers. We show that their graded minimal free resolution is selfdual in a strong sense. Applications include a proof of the dependence of the monoid of Betti tables of Cohen‐Macaulay modules on the characteristic of the base field. Moreover, we give a new proof of the failure of the generalization of Green's Conjecture to characteristic 2 in the case of general curves of genus 2ⁿ ?1. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

效应代数的直觉模糊滤子

引入效应代数的直觉模糊滤子和它的水平滤子的概念,讨论了直觉模糊滤子与水平滤子间的关系,给出了直觉模糊滤子的等价描述,研究了直觉模糊滤子的几个运算性质。在两个经典效应代数的效应态射与效应同构意义下,讨论了这种直觉模糊滤子的像和前像问题。     

TORSION THEORIES FOR FINITE VON NEUMANN ALGEBRAS

ABSTRACT

The study of modules over a finite von Neumann algebra 𝒜 can be advanced by the use of torsion theories. In this work, some torsion theories for 𝒜 are presented, compared, and studied. In particular, we prove that the torsion theory (T, P) (in which a module is torsion if it is zero-dimensional) is equal to both Lambek and Goldie torsion theories for 𝒜.

Using torsion theories, we describe the injective envelope of a finitely generated projective 𝒜-module and the inverse of the isomorphism K ₀(𝒜) → K ₀ (𝒰), where 𝒰 is the algebra of affiliated operators of 𝒜. Then the formula for computing the capacity of a finitely generated module is obtained. Lastly, we study the behavior of the torsion and torsion-free classes when passing from a subalgebra ? of a finite von Neumann algebra 𝒜 to 𝒜. With these results, we prove that the capacity is invariant under the induction of a ?-module.     

Right-Left Symmetry of Right Nonsingular Right Max-Min CS Prime Rings

In this article we show, among others, that if R is a prime ring which is not a domain, then R is right nonsingular, right max-min CS with uniform right ideal if and only if R is left nonsingular, left max-min CS with uniform left ideal. The above result gives, in particular, Huynh et al. (2000 Huynh , D. V. , Jain , S. K. , López-Permouth , S. R. ( 2000 ). On the symmetry of the goldie and CS conditions for prime rings . Proc. Amer. Math. Soc. 128 : 3153 – 3157 . [Google Scholar]) Theorem for prime rings of finite uniform dimension.     

The numerical inversion of the Laplace transform in reproducing kernel Hilbert spaces for ill-posed problems

In this paper we have converted the Laplace transform into an integral equation of the first kind of convolution type, which is an ill-posed problem, and used a statistical regularization method to solve it. The method is applied to three examples. It gives a good approximation to the true solution and compares well with the method given by Rodriguez.     

(∈,∈∨ q(λ,μ))-模糊布尔代数

给出(∈,∈∨q(λ,μ))-模糊布尔代数及广义模糊布尔代数的概念,得到了(∈,∈∨ q(λ,μ))-模糊布尔代数的一些等价刻画及基本性质,另外,还研究了它的的同态像与同态原像的基本性质.     

Greedy Differencing Edge-Contraction heuristic for the Max-Cut problem

The Max-Cut problem is a classical NP-hard problem where the objective is to partition the nodes of an edge-weighted graph in a way that maximizes the sum of edges between the parts. We present a greedy heuristic for solving Max-Cut that combines an Edge-Contraction heuristic with the Differencing Method. We compare the heuristic’s performance to other greedy heuristics using a large and diverse set of problem instances.