On cohomological dimension and depth under linkage

Some relations between cohomological dimensions and depths of linked ideals are investigated and discussed by various examples.Comment: 7 page

Tameness and Artinianness of Graded Generalized Local Cohomology Modules

Let $R=\bigoplus_{n\geq 0}R_n$, \fa\supseteq \bigoplus_{n> 0}R_n and $M$ and $N$ be a standard graded ring, an ideal of $R$ and two finitely generated graded $R$-modules, respectively. This paper studies the homogeneous components of graded generalized local cohomology modules. First of all, we show that for all $i\geq 0$, H^i_{\fa}(M, N)_n, the $n$-th graded component of the $i$-th generalized local cohomology module of $M$ and $N$ with respect to \fa, vanishes for all $n\gg 0$. Furthermore, some sufficient conditions are proposed to satisfy the equality \sup\{\en(H^i_{\fa}(M, N))| i\geq 0\}= \sup\{\en(H^i_{R_+}(M, N))| i\geq 0\}. Some sufficient conditions are also proposed for tameness of H^i_{\fa}(M, N) such that i= f_{\fa}^{R_+}(M, N) or i= \cd_{\fa}(M, N), where f_{\fa}^{R_+}(M, N) and \cd_{\fa}(M, N) denote the $R_+$-finiteness dimension and the cohomological dimension of $M$ and $N$ with respect to \fa, respectively. We finally consider the Artinian property of some submodules and quotient modules of H^j_{\fa}(M, N), where $j$ is the first or last non-minimax level of H^i_{\fa}(M, N).Comment: 18pages, with some revisions and correction

A note on quasi-Gorenstein rings

In this paper, after giving a criterion for a Noetherian local ring to be quasi-Gorenstein, we obtain some sufficient conditions for a quasi- Gorenstein ring to be Gorenstein. In the course, we provide a slight generalization of a theorem of Evans and Griffith.Comment: To appear in Arch. Mat

Study of distribution and diversity of Polychaeta due to impact bottom trawling in Bahrakan fishing area (Persian Gulf)

The study took place to survey the changes in diversity and distribution of Polychaetes in fishing area of Bahrakan, due to the trawling. Sampling was taken before (15 May) of trawling and two weeks (5 Sep) and three months (14 Nov) after trawling in 2010, in three period in Bahrakan coast. Therefore, eighteen stations placed with the depth of 6 meters and 10 meters.The amount abundance Polychaetes had decreased significantlyin both depths two weeks after trawling (P0.05). Only in 10m depth, abundance Polychaetes after three months comparing to two weeks after trawling had increased significantly (p<0.05). Changing biomass Polychaetes was similar to Changing abundance. After the trawling, small size individuals became dominant.Abundance Species ofCossura longicirrattahad increased in both depths in two weeks after the trawling. Also in both depths, Shannon Diversity and Margalef Species Richness indices showedprocess decreasing and Simpson dominant Index showedprocess increasing. In both depths, Pielou Evenness Index two after trawling had increased. While, after three months comparing to two weeks after trawling had decreased and most effects of trawling were on 6m depth

Trace refinement in labelled Markov decision processes

Given two labelled Markov decision processes (MDPs), the trace-refinement problem asks whether for all strategies of the first MDP there exists a strategy of the second MDP such that the induced labelled Markov chains are trace-equivalent. We show that this problem is decidable in polynomial time if the second MDP is a Markov chain. The algorithm is based on new results on a particular notion of bisimulation between distributions over the states. However, we show that the general trace-refinement problem is undecidable, even if the first MDP is a Markov chain. Decidability of those problems was stated as open in 2008. We further study the decidability and complexity of the trace-refinement problem provided that the strategies are restricted to be memoryless