Associated primes and cofiniteness of local cohomology modules

Let be an ideal of Noetherian ring R and let s be a non-negative integer. Let M be an R-module such that is finite R-module. If s is the first integer such that the local cohomology module is non -cofinite, then we show that is finite. In particular, the set of associated primes of is finite. Let be a local Noetherian ring and let M be a finite R-module. We study the last integer n such that the local cohomology module is not -cofinite and show that n just depends on the support of M.The research of the first author was supported in part by a grant from IPM (No. 83130114).The second author was supported by a grant from University of Tehran (No. 6103023/1/01).     

Control uncertain Genesio–Tesi chaotic system: Adaptive sliding mode approach

An adaptive sliding mode control (ASMC) technique is introduced in this paper for a chaotic dynamical system (Genesio–Tesi system). Using the sliding mode control technique, a sliding surface is determined and the control law is established. An adaptive sliding mode control law is derived to make the states of the Genesio–Tesi system asymptotically track and regulate the desired state. The designed control scheme can control the uncertain chaotic behaviors to a desired state without oscillating very fast and guarantee the property of asymptotical stability. An illustrative simulation result is given to demonstrate the effectiveness of the proposed adaptive sliding mode control design.     

Tensor and Torsion Products of Relative Injective Modules with Respect to a Semidualizing Module

Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In this paper, we show that C is generically dualizing if and only if the tensor products of injective and C-injective R-modules are injective. This leads to a characterization of dualizing modules as well as generalizes a result of Enochs and Jenda.     

Independent fuzzy events

An algorithm for the reconstruction of a symmetric matrix from the spectral data is given. All cases in which the number of solutions is finite are determined. These results are applied to a certain inverse eigenvalue problem which arises in molecular spectroscopy.     

On (Strongly) Gorenstein Von Neumann Regular Rings

In this article, we introduce and study the rings over which every module is (strongly) Gorenstein flat, which we call them (strongly) Gorenstein Von Neumann regular rings.     

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”.     

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.     

Synthesis of new TCH/Ni‐based nanocomposite supported on SBA‐15 and its catalytic application for preparation of benzimidazole and perimidine derivatives

A stable nickel‐decorated SBA‐15 nanocomposite (Ni/TCH@SBA‐15) was synthesized through surface modification of silica nanoparticles with 3‐chloropropyltriethoxysilane (CPTES) and thiocarbohydrazide (TCH) followed by metal–ligand coordination with Ni (II). The structure of this organometallic nanocomposite was characterized by Fourier transform‐infrared, field emission‐scanning electron microscopy, EDAX, transmission electron microscopy, atomic absorption spectroscopy and N₂ adsorption–desorption (Brunauer–Emmett–Teller) techniques. The catalytic performance of Ni/TCH@SBA‐15 (NNTS‐15) was determined for the synthesis of 2‐aryl‐substituted benzimidazoles and 2,3‐dihydroperimidines. The excellent yields within shorter reaction times, simplicity of catalytic methods, non‐toxicity and clean reactions, mild reaction conditions and easy work‐up procedure are the important merits of these synthetic protocols. Moreover, the Ni (II) bonded to the SBA‐15 surface was stable under the catalytic reaction conditions resulting in its efficient recycling and reuse.     

Optimized mercapto-modified resorcinol formaldehyde xerogel for adsorption of lead and copper ions from aqueous solutions

Journal of Sol-Gel Science and Technology - Resorcinol formaldehyde (RF) xerogel was modified by mercapto functional groups for removal of Pb(II) and Cu(II) ions from aqueous solutions. The...     

The solution of Pennes' bio-heat equation with a convection term and nonlinear specific heat capacity using Adomian decomposition

Journal of Thermal Analysis and Calorimetry - Pennes' bio-heat equation is the most widely used equation to analyze the heat transfer phenomenon associated with hyperthermia and cryoablation...