Book rewiev

Howard Anton and Robert C. Busby, John Wiley & Sons, Inc., 2002.     

RSOS Models and Jantzen–Seitz Representations of Hecke Algebras at Roots of Unity

A special family of partitions occurs in two apparently unrelated contexts: the evaluation of one-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras H_m. We provide an explanation of this coincidence by showing how the irreducible H_m-modules which remain irreducible under restriction to H_{m_1} (Jantzen–Seitz modules) can be determined from the decomposition of a tensor product of representations sl_n.     

A two-fraction model for the calculation of the resonance spectra of the complex permittivity of ice in the far infrared

A two-fraction model that makes it possible to calculate analytically the complex dielectric permittivity of ice in the far infrared and submillimeter wavelength ranges is proposed. The librational and vibrational fractions are considered. The first fraction, consisting of rigid dipoles executing anharmonic reorientations in defects of the structure, gives rise to the librational band of ice at 800 cm^?1. The second fraction consists of elastically vibrating oppositely charged H-bonded molecules. This fraction describes two bands of ice in the range 100–300 cm^?1, and the nonresonant background of dielectric losses in the submillimeter wavelength range. The dielectric permittivity spectra of ice calculated for the temperature of ?7°C are consistent with the experimental spectra. The spectra of ice at the temperature ?30°C are predicted.     

Realization of an OpenMath Server for REDUCE

Various approaches and standards for transferring mathematical objects between different computer programs in multimedia environment in the framework of the OpenMath project are described. The use of these standards might revolutionize the exchange of mathematical information caused by the development of computer algebra tools and telecommunication possibilities. The standards make it possible to create databases and easily save and use mathematical objects obtained in different applications, e.g., to exchange the data obtained in different computer algebra systems and place information on the Internet. Bibliography: 9 titles.     

Une méthode de calcul des coefficients de réflexion et de transmission d'une houle bidimensionnelle en milieu confinéA new method for the calculation of transmission and reflection coefficients for water waves in a small basin

This paper presents a method to estimate reflected and transmitted wave amplitude spectra in a bounded domain such as a wave tank, when available data signals must be shortened due to interferences and wall effects. This paper extends the well known Goda and Suzuki two-probe method to three probes. The paper also suggests solutions to compute reliable transmission and reflection coefficients in spite of problems linked to higher harmonics and to the interference between different wave trains propagating in the tank. To cite this article: G. Duclos, A.H. Clément, C. R. Mecanique 331 (2003).     

Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

Structure of 18-cyanoprogesterone,C22H29O2N

The crystal structure of 18-cyanoprogesterone was determined by X-ray diffraction methods:P2₁2₁2₁ a=7.436(2),b=11.322(2),c=22.642(2) Å. The structure was solved usingShelx-86. Final conventionalR=0.054.R _w =0.051 for 1841 reflections. TheA ring has an intermediate sofa-half-chair conformation with asymmetry parameters C _s ^/1 =11.0, C ₂ ^3,4 =14.9. The steroid skeleton exhibits a flattening of theA ring relative to the rest of the molecule. The progesterone side chain has a typical conformation, and the C16-C17-C20-O20 torsion angle is –19.0(6)°.     

Influence of the pyridine methyl substituent position on the chemical changes of the NCS groups in the thermal decomposition of coordination compounds of the type Cu(NCS)2L2

The influence of the position of the CH₃ group in picoline and lutidine ligands on the degree of chemical change of the NCS groups in coordination compounds of the type Cu(NCS)₂L₂ (whereL=2-, 3- and 4-picoline, and 2,3-, 2,4-, 2,5-, 2,6-, 3,4- and 3,5-lutidine) is dealt with. The most marked effect of the CH₃ group is found to be exerted in position 4. This effect of the methyl group on the degree of chemical change points to the mutual influence of the ligands in coordination compounds of Cu(II).

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Zusammenfassung Der Artikel befaßt sich mit dem Einfluß der Lage der CH₃ Gruppe in Pikolinen und Lutidinen als Liganden auf den Grad der chemischen Änderungen der Gruppen NSC in Koordinationsverbindungen des Typs Cu(NCS)₂L₂ (L=2-, 3- und 4-Pikoline, 2,3-, 2,4-, 2,5-, 2,6-, 3,4- und 3,5-Lutidine). Der ausgeprägteste Effekt der CH₃ Gruppe wurde in der Position 4 beobachtet. Dieser Einfluß der Methylgruppe auf das Ausmaß der chemischen Änderungen deutet auch auf die gegenseitige Wirkung der Liganden in Koordinationsverbindungen von Cu(II).

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Résumé L'article a trait à l'influence de la position du groupe CH₂ dans les picolines et lutidines, en tant que ligands, sur le degré des changements chimiques des groupes SCN dans les composés de coordination du type Cu(SCN)₂L₂ (L=2-, 3 et 4-picoline, 2,3-, 2,4-,2,5-, 2,6-, 3,4- et 3,6-lutidine). L'effet le plus prononcé du groupe CH₃ s'observe en position 4. Cette influence du groupe méthyle sur le degré des changements chimiques indique aussi l'influence mutuelle des ligands dans les composés de coordination du Cu(II).

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- , , NCS Cu(NCS)₂,L₂, L=2-, 3- 4- , 2.3-, 2.4-, 2.5-, 2.6-, 3.4- 3.5-. , 4. Cu(II).

     

Pion multiplicity in nuclear collisions

Data on the mean multiplicity of ^- produced in minimum bias proton-proton, proton-neutron and proton-nucleus interactions as well as central nucleus-nucleus collisions at momenta of 1.4–400 GeV/c per nucleon have been compiled and studied. The results for neutron-neutron and nucleon-nucleon interactions were then constructed. The dependence of the mean pion multiplicity in proton-nucleus interactions and central collisions of identical nuclei are studied as a function of the collision energy and the nucleus mass number. The number of produced pions per participant nucleon in central collisions of identical nuclei is found to be independent of the number of participants at a fixed incident momentum per nucleon. The mean multiplicity of negatively charged hadrons per participant nucleon for central nucleus-nucleus collisions is lower by about 0.12 than the corresponding multiplicity for nucleon-nucleon interactions atp _LAB 15 A·GeV/c, whereas the result at 200 A·GeV/c is above the corresponding nucleon-nucleon multiplicity. This may indicate change of the collision dynamics at high energy.