Artinian cofinite modules over complete Noetherian local rings

Let (R, m) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R-module. In this paper it is shown that if p is a prime ideal of R such that dim R/p = 1 and (0:M p) is not finitely generated and for each i ? 2 the R-module Ext _R ⁱ (M,R/p) is of finite length, then the R-module Ext _R ¹ (M, R/p) is not of finite length. Using this result, it is shown that for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext _R ⁱ (N,M) are of finite length, if and only if, for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext _R ⁱ (M,N) are of finite length.     

A New Complexity Analysis for Full-Newton Step Infeasible Interior-Point Algorithm for Horizontal Linear Complementarity Problems

In this paper, we first present a full-Newton step feasible interior-point algorithm for solving horizontal linear complementarity problems. We prove that the full-Newton step to the central path is quadratically convergent. Then, we generalize an infeasible interior-point method for linear optimization to horizontal linear complementarity problems based on new search directions. This algorithm starts from strictly feasible iterates on the central path of a perturbed problem that is produced by a suitable perturbation in the horizontal linear complementarity problem. We use the so-called feasibility steps that find strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, we obtain a strictly feasible iterate close enough to the central path of the new perturbed problem. The complexity of the algorithm coincides with the best known iteration bound for infeasible interior-point methods.     

A mild and efficient palladium–triethylsilane system for reduction of olefins and carbon–carbon double bond isomerization

The versatility of palladium(II) acetate and palladium on activated charcoal catalysts with triethylsilane has been investigated in the hydrogenation and the isomerization of carbon–carbon double bond of 1‐alkenes. The reduction of 1‐alkenes was carried out in the presence of triethylsilane, ethanol and a catalytic amount of palladium(II) acetate or palladium on activated charcoal, at room temperature. This facile and efficient method affords high yields for hydrogenation of unsaturated alkenes to the corresponding alkanes. Then the carbon–carbon double bond isomerization of 1‐alkenes was tested using the same catalysts in the absence of solvent. The system palladium(II) acetate‐triethylsilane was found to be more effective compared with palladium on an activated charcoal–triethylsilane system at room temperature, while comparable results were obtained at 50 °C for both catalysts. Copyright © 2006 John Wiley & Sons, Ltd.     

Synthesis,spectroscopy, and X-ray crystal structures of copper(II) complexes of the tridentate ONS ligand formed by condensation of 4,4,4-trifluoro-1-(2-thienyl)-2,4-butanedione with S-benzyldithiocarbazate

A new tridentate ONS ligand, H₂L, has been synthesized by condensing thenoyltrifluoroacetone(4,4,4-trifluoro-1-(2-thienyl)-2,4butaneanedione) with S-benzyldithiocarbazate and its structure determined by X-ray diffraction. In the solid state, the Schiff base exists as the ketoamine-thioketo tautomer but in solution and in the presence of copper(II), it converts to the enol-thiol form and deprotonates to give copper(II) complexes of formula, [CuL] and [CuLL¹] (L = doubly deprotonated form of the ligand; L¹ = py, bipy or phen] which have been characterized by magnetic, spectroscopic, and X-ray diffraction studies. An X-ray crystallographic analysis shows that [CuL(py)] has a square-planar geometry with the ligand coordinated to the copper(II) center via the enolate oxygen, the azomethinic nitrogen and the thiolate sulfur, the fourth coordination position being occupied by pyridine. The [CuL(bipy)] complex is five-coordinate with a structure close to square-pyramidal in which the Schiff base acts as a doubly deprotonated tridentate ONS ligand and bipy is bidentate.     

Recent advances in oxidation catalysis using ionic liquids as solvents

Ionic liquids are an interesting alternative to classical solvents presenting several advantages. A variety of catalysts show good or even enhanced activities when applied in ionic liquids. Oxidation catalysis represents a large segment of industrial chemistry, providing both bulk chemicals and intermediates for high value added special products and pharmaceuticals. Particularly for the latter products organometallic and inorganic catalysts are being developed that can be applied in systems consisting of or containing ionic liquids. This work provides an overview on recent developments in this field.     

Bilinearization and Soliton Solutions of a Supersymmetric Multicomponent Coupled Dispersionless Integrable System

Theoretical and Mathematical Physics - We present a supersymmetric generalization of a multicomponent coupled dispersionless (SUSY-MCD) integrable system. Expanding the superfields of the SUSY-MCD...     

Epoxidation of Olefins Catalyzed by Sulfate-based Supramolecular Ion Pairs

The development of inexpensive and effective catalysts for the epoxidation of olefins to epoxides, which are key commodities for the chemical industry, is a continuing challenge. In this context, we present a supramolecular solution with the development of new host-guest assemblies of sulfate ions and amidoammonium receptor cations that, for the first time, are shown to act as catalysts for olefin epoxidation by hydrogen peroxide under biphasic conditions. Analysis of the reaction mechanism shows that the reactive and oxidizing peroxymonosulfate is formed in the organic phase. Furthermore, a variety of readily available precursors may be used to form the supramolecular ion pairs (SIPs), which is enabling a large-scale synthesis of the catalysts while maintaining catalytic control and effectiveness.     

Syringic Acid Ameliorates Cardiac,Hepatic, Renal and Neuronal Damage Induced by Chronic Hyperglycaemia in Wistar Rats: A Behavioural,Biochemical and Histological Analysis

This study investigated the effects of syringic acid (SA) on renal, cardiac, hepatic, and neuronal diabetic complications in streptozotocin-induced neonatal (nSTZ) diabetic rats. STZ (110 mg/kg i.p) was injected into Wistar rat neonates as a split dose (second and third postnatal day). Diabetes mellitus was diagnosed in adults by measuring fasting blood glucose levels, urine volume, and food and water intake. The treatment of SA (25 mg/kg, 50 mg/kg p.o) was given from the 8th to 18th postnatal week. To assess the development of diabetic complications and the effect of therapy, biochemical indicators in serum and behavioural parameters were recorded at specific intervals during the study period. SA (25 mg/kg, 50 mg/kg p.o) treatment reduced hyperglycaemia, polydipsia, polyphagia, polyuria, relative organ weight, cardiac hypertrophic indices, inflammatory markers, cell injury markers, glycated haemoglobin, histopathological score, and oxidative stress, and increased Na/K ATPase activity. These findings suggest that SA might significantly alleviate diabetic complications and/or renal, neuronal, cardiac, and hepatic damage in nSTZ diabetic rats.     

Tauberian Constants for Double Series

The object of this paper is to extend a result of Agnew in [1]for single series to double series, and so enable Tauberianconstants between matrix transformations of double sequencesto be calculated using the technique that many authors haveused previously for single sequences (see, for instance, [2,3, 8]). This method (see below) gives the best possible Tauberianconstants in the form of certain upper limits, and we attemptto calculate these for Cesàro summability with variousknown Tauberian conditions. In Section 2, we introduce our notationand review earlier work. In Section 3, we prove our main result,and we discuss applications to Cesàro summability inSection 4.