On certain equidimensional polymatroidal ideals

The class of equidimensional polymatroidal ideals are studied. In particular, we show that an unmixed polymatroidal ideal is connected in codimension one if and only if it is Cohen-Macaulay. Especially a matroidal ideal is connected in codimension one precisely when it is a squarefree Veronese ideal. As a consequence we indicate that for polymatroidal ideals, the Serre's condition $(S_n)$ for some $n\geq 2$ is equivalent to Cohen-Macaulay property. We also give a classification of generalized Cohen-Macaulay polymatroidal ideals.Comment: To appear in Manuscripta Mathematic

Recent advances in intelligent-based structural health monitoring of civil structures

This survey paper deals with the structural health monitoring systems on the basis of methodologies involving intelligent techniques. The intelligent techniques are the most popular tools for damage identification in terms of high accuracy, reliable nature and the involvement of low cost. In this critical survey, a thorough analysis of various intelligent techniques is carried out considering the cases involved in civil structures. The importance and utilization of various intelligent tools to be mention as the concept of fuzzy logic, the technique of genetic algorithm, the methodology of neural network techniques, as well as the approaches of hybrid methods for the monitoring of the structural health of civil structures are illustrated in a sequential manner

Modules with Finite Cousin Cohomologies Have Uniform Local Cohomological Annihilators

Let A be a Noetherian ring. It is shown that any finite A--module M of finite Krull dimension with finite Cousin complex cohomologies has a uniform local cohomological annihilator. The converse is also true for a finite module M satisfying (S_2) which is over a local ring with Cohen--Macaulay formal fibres.Comment: 9 pages, to appear in Journal of Algebr

Shedding vertices and Ass-decomposable monomial ideals

The shedding vertices of simplicial complexes are studied from an algebraic point of view. Based on this perspective, we introduce the class of ass-decomposable monomial ideals which is a generalization of the class of Stanley-Reisner ideals of vertex decomposable simplicial complexes. The recursive structure of ass-decomposable monomial ideals allows us to find a simple formula for the depth, and in squarefree case, an upper bound for the regularity of such ideals.Comment: 13 page