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.     

Diffraction of the Electromagnetic Wave on a Small Obstacle of Elliptic Form in a Layer

The problem on the diffraction of the electromagnetic plane wave on a small obstacle included in a layer is investigated. The obstacle is assumed to be an elliptic cylinder whose diameter and focal distance are small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a point source, and its amplitude is proportional to the area of the cross-section and the jumps of the dielectric and magnetic constants on the interfaces. Bibliography: 5 titles.     

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.     

Theory of two-frequency excitation in<Superscript>14</Superscript>N NQR

A simple and effective technique for calculating the transient signals in three-level spin systems irradiated at one and two frequencies is described. All possible signals are presented and discussed. The application of the two-frequency excitation technique for the investigation of the inhomogeneity of the crystalline lattice is suggested.     

Synthesis and Photochemistry of Novel 3,5-Diacetyl-1,4-dihydropyridines. II [1]

In continuation of previous work some novel 3,5-diacetyl-1,4-dihydropyridine derivatives were synthesized and their photochemical behavior was studied under oxygen and argon atmosphere. Oxidation of the dihydropyridine ring and formation of pyridine derivatives was the result of the reaction. The presence of oxygen affects not only on the rate of oxidation, but also the formation of some unidentified by-products was observed on irradiation under this atmosphere.     

Plasmon resonance in a nanosphere

The phenomenon of plasmon resonance in a nanosphere and a nanospheroid is considered. As is known, this phenomenon does not depend explicitly on the size of these nanoparticles. However, it is shown that, actually, the resonance conditions are determined by the diameter of the nanosphere and by the length of the major axis of the nanospheroid.