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.     

Characterisation of the photocatalyst Pilkington Activ™: a reference film photocatalyst?

Pilkington Glass Activ™ represents a possible suitable successor to P25 TiO₂, especially as a benchmark photocatalyst film for comparing other photocatalyst or PSH self-cleaning films. Activ™ is a glass product with a clear, colourless, effectively invisible, photocatalytic coating of titania that also exhibits PSH. Although not as active as a film of P25 TiO₂, Activ™ vastly superior mechanical stability, very reproducible activity and widespread commercial availability makes it highly attractive as a reference photocatalytic film. The photocatalytic and photo-induced superhydrophilitic (PSH) properties of Activ™ are studied in some detail and the results reported. Thus, the kinetics of stearic acid destruction (a 10⁴ electron process) are zero order over the stearic acid range 4–129 monolayers and exhibit formal quantum efficiencies (FQE) of 0.7×10⁻⁵ and 10.2×10⁻⁵ molecules per photon when irradiated with light of 365±20 and 254 nm, respectively; the latter appears also to be the quantum yield for Activ™ at 254 nm. The kinetics of stearic acid destruction exhibit Langmuir–Hinshelwood-like saturation type kinetics as a function of oxygen partial pressure, with no destruction occurring in the absence of oxygen and the rate of destruction appearing the same in air and oxygen atmospheres. Further kinetic work revealed a Langmuir adsorption type constant for oxygen of 0.45±0.16 kPa⁻¹ and an activation energy of 19±1 kJ mol⁻¹. A study of the PSH properties of Activ™ reveals a high water contact angle (67°) before ultra-bandgap irradiation reduced to 0° after prolonged irradiation. The kinetics of PSH are similar to those reported by others for sol–gel films using a low level of UV light. The kinetics of contact angle recovery in the dark appear monophasic and different to the biphasic kinetics reported recently by others for sol–gel films [J. Phys. Chem. B 107 (2003) 1028]. Overall, Activ™ appears a very suitable reference material for semiconductor film photocatalysis.     

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.     

Self-consistent modelling of argon microwave discharge sustained by electromagnetic wave in dipole mode

Microwave discharges produced by travelling/standing electromagnetic waves have drawn considerable attention in recent years due to their wide application in microelectronic industry. Here are presented the axial distributions of the electrons and ions as well as those of excited atoms in an argon microwave discharge at a low gas pressure (400 mTorr) sustained by a 2.45 GHz travelling dipolar electromagnetic wave. The numerical calculations are based on a self-consistent kinetic-electrodynamic model and the results obtained are in a good agreement with the experimental data. The model yields also the magnitude of the wave power sustaining the discharge and the axial profiles of all electromagnetic-wave characteristics and the axial distribution of the neutral gas temperature.     

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.     

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.     

On the computation of scaling coefficients of Daubechies' wavelets

In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.     

Equivalence between mixed finite element and multi-point finite volume methods

We consider the lowest-order Raviart–Thomas mixed finite element method for elliptic problems on simplicial meshes in two or three space dimensions. This method produces saddle-point type problems for scalar and flux unknowns. We show how to easily eliminate the flux unknowns, which implies an equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. We describe the stencil of the final matrix and give sufficient conditions for its symmetry and positive definiteness. We present a numerical example illustrating the performance of the proposed method. To cite this article: M. Vohralík, C. R. Acad. Sci. Paris, Ser. I 339 (2004).