Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if Ext_Λⁱ(M,N)=0 for all i?0, then Ext_Λⁱ(M,N)=0 for all i?n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.     

Determination of ultra-trace gold in natural water by graphite furnace atomic absorption spectrophotometry after in situ enrichment with thiol cotton fiber

A simple method of determining ultra-trace Au in natural water was presented by using graphite furnace atomic absorption spectrophotometry (GFAAS) after in situ enrichment with thiol cotton fiber (TCF). The sample solution was adjusted to pH 1.5-2.0 with HCl, then the water sample was passed through a column packed with 0.10-0.20 g TCF and the flow rate was controlled at 20-40 ml min⁻¹. The effects of interferences, such as complexing and oxidizing agents and other elements adsorbed on TCF were overcome by chemical treatments prior to the desorption of Au. The adsorbed Au was adsorbed with 2.0 ml hot acid, then it was extracted with 1.00 ml methyl isobutylketone (MIBK). For a 5 l water sample, the detection limit of Au is 0.02 ng l⁻¹. The relative standard deviation (R.S.D.) for the determination of 1.44 ng l⁻¹ Au was 9.4%.The method was applied to determine ultra-trace Au both in suspended phase and soluble phase in natural water, the concentrations of total Au in natural water samples range from 0.51 to 67.82 ng l⁻¹. The recovery of added 0.50-6.00 ng l⁻¹ Au was 80-95%. The method is useful in prospecting for Au deposits by means of hydrogeochemical methods. The enrichment is carried out in the field, and then the determination of Au is completed later in the laboratory.     

Eigenvalue and stability of singular differential delay systems

The eigenvalue and the stability of singular differential systems with delay are considered. Firstly we investigate some properties of the eigenvalue, then give the exact exponential estimation for the fundamental solution, and finally discuss the necessary and sufficient condition of uniform asymptotic stability.     

Controlled/living polymerization of 2‐(diethylamino)ethyl methacrylate and its block copolymer with tert‐butyl methacrylate by atom transfer radical polymerization

Polymerization of 2‐(diethylamino)ethyl methacrylate (DEAEMA) via homogeneous atom transfer radical polymerization under various reaction conditions is described. The effects of the initiators and solvents were examined. With 1,1,4,7,10,10‐hexamethyl triethylenetetramine/copper(I) chloride/p‐toluenesulfonyl chloride as the ligand/catalyst/initiator system in methanol, poly(DEAEMA) with a polydispersity index as low as 1.07 was synthesized. Kinetic studies demonstrated the polymerization was very well controlled and exhibited the living characteristic of the process. Well‐defined block copolymers of DEAEMA and tert‐butyl methacrylate (tBMA) were successfully synthesized. The copolymers could be synthesized with equally good results by starting with either p(DEAEMA) or p(tBMA) as the macroinitiators. However, only the macroinitiators terminated with chlorine should be used. The corresponding macroinitiators with bromine as a transferable group did not yield well‐defined copolymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2688–2695, 2003     

D-N交替法与Schwartz交替法的收敛关系分析

This paper has demonstrated that the Schwartz alternating process must converge if D-N alternating process has converged. Its technique is that the overlapping regions in Schwartz alternating process are considered as independent domains, then Schwartz alternating process could be transformed into D-N alter-nating process. Finally the convergence estimation of Schwartz alternating process could be obtained. The results show that its convergence rate is same as that of D-N alternating process.     

Random Walks And The Colored Jones Function

It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagram, and another in terms of counting paths of intersecting chords. Electronic supplementary material to this article is available at and is accessible to authorized users. * S. G. was partially supported by an NSF and by an Israel-US BSF grant. † M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education.     

Shape Optimization for Semi-Linear Elliptic Equations Based on an Embedding Domain Method

We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in ℝ². A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in the case where the principal part of the differential operator is the Laplacian. Online publication 23 January 2004.     

Spectral enhancement of Polish vowels to improve their identification by hearing impaired listeners

Abnormalities in the cochlear function usually cause broadening of the auditory filters which reduces the speech intelligibility. An attempt to apply a spectral enhancement algorithm has been undertaken to improve the identification of Polish vowels by subjects with cochlear-based hearing-impairment. The identification scores of natural (unprocessed) vowels and spectrally enhanced (processed) vowels has been measured for hearing-impaired subjects. It has been found that spectral enhancement improves vowel scores by about 10% for those subjects, however, a wide variation in individual performance among subjects has been observed. The overall vowels identification scores obtained were 85% for natural vowels and 96% for spectrally enhanced vowels.     

肿瘤微波热疗的温度场预示及热损伤研究

本文将热损伤的产生和影响引入到肿瘤的微波热疗中。运用微波能量比吸收率SAR的分布分析了微波在组织中的传输和吸收过程,并对微波热疗过程中的温度场、热损伤分布以及血液灌注率的变化进行了数值模拟。