Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module

Let ${(R, \mathfrak{m})}$ be a commutative Noetherian local ring of Krull dimension d, and let C be a semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing module if and only if the top local cohomology module of ${R, H _{\mathfrak{m}} ^{d} (R)}$ , has finite G _C -injective dimension. This generalizes a recent result due to Yoshizawa, where the ring is assumed to be complete Cohen-Macaulay.     

k-torsionless modules with finite Gorenstein dimension

Let R be a commutative Noetherian ring. It is shown that the finitely generated R-module M with finite Gorenstein dimension is reflexive if and only if M _p is reflexive for p ∈ Spec(R) with depth(R _p) ? 1, and $G - {\dim _{{R_p}}}$ (M _p) ? depth(R _p) ? 2 for p ∈ Spec(R) with depth(R _p) ? 2. This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for n ? 2 we give a characterization of n-Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown that every R-module has a k-torsionless cover provided R is a k-Gorenstein ring.     

Shellable quasi-forests and their h-triangles

In this paper we show that a quasi-forest is shellable if and only if its h-triangle satisfies ${h_{i,j}(\Delta)=0 \quad \forall i, \forall j >1 }$ . In addition, it will be shown that a quasi-forest is sequentially Cohen-Macaulay if and only if it is shellable.     

Aqua one-pot,three-component synthesis of dihydropyrano[3,2-c]chromenes and amino-benzochromenes catalyzed by sodium malonate

Research on Chemical Intermediates - The widespread biological properties of dihydropyrano[3,2-c]chromenes, 2-amino-4-aryl-4H-benzo[h]chromenes, and 3-amino-1-aryl-1H-benzo[f]chromenes have led to...     

A meshfree method with a non-overlapping domain decomposition method based on TPS for solving the forward-backward heat equation in two-dimension

Numerical Algorithms - We present a truly meshless method based on the thin plate splines for the numerical solution of the two dimensional forward-backward heat equation and give a robust...     

Experimental Evaluation of the Influence of the Seawater Characteristics on Spatial and Temporal Variations of the Sound Speed in the Southern Abyssal,Intermediate and Shelf Zones of the Caspian Sea

Acoustical Physics - The results of the evaluation on the spatial and temporal changes of the underwater sound speed in the southern abyssal zone of the Caspian Sea are investigated. Experimental...     

Erratum to: Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module

This note makes a correction to the paper “Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module”.     

A Theoretical Study on Chapman Rearrangement

Some Chapman rearrangements are investigated using HF and B3LYP methods combined with two different basis sets (6‐31G** and 6‐31++G**) and both finite difference model and Janak's approximation. It is shown that although minimum polarizability (MPP) and maximum hardness (MHP) principles are always valid in these reactions, minimum electrophilicity principle (MEP) is followed just when DFT method (B3LYP) is used. The Morrel's rules are also successfully applied in predicting the validity of MEP in these rearrangements. Therefore, it seems that in the study of this kind of reaction, the results of DFT are more reliable than those of HF.     

On the latest starting times and criticality of activities in a network with imprecise durations

This paper deals with problems of computing possible values of latest starting times and determining types of criticality for all activities in a network with interval or fuzzy activity durations. Although the problem of computing the latest starting times has been solved, a novel polynomial algorithm which is easy to understand and improves complexity is proposed.