The Knizhnik-Zamolodchikov equations associated with the root system <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript>

At the end of the twentieth century, in mathematical physics, the Knizhnik-Zamolodchikov equations for the root systems A _n and their generalizations for the root systems of types B _n , C _n , and D were constructed. For the root system of type G ₂, the vector version of the Knizhnik-Zamolodchikov equations was obtained by M. P. Zamakhovskii and V. P. Leksin. However, the tensor version of these equations has remained unstudied. In this paper, the Knizhnik-Zamolodchikov equations associated with the root system of type G ₂ are considered. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.     

Peritectic phase growth in directionally solidified Cu-70% Sn alloy

The growth mechanism of the peritectic η phase involving the peritectic reaction and peritectic transformation in Cu-70%Sn alloy was investigated under directional solidification. The results show that a major growth mechanism in thickening of the peritectic η-layer is not the peritectic reaction but the peritectic transformation. The transformation temperature and isothermal time play crucial roles in determining the volume fraction and the thickness of the peritectic η phase. With the increase of the temperature and isothermal time, the volume fraction of the peritectic η phase increases. The regressed data show that the relationship between the thickness of η phase (Δx) and the transformation temperature (T) meets the following equation In Δx=6.5−1673 1 / T. Additionally, there exists a relationship between the thickness of the η phase (Δx) and the isothermal time (t) at the 9 mm solidification distance below the peritectic reaction interface, Δx=0.72t ^1/2, which is consistent with the theoretical model. Supported by the National Science Foundation of China (Grant No. 50395102)     

Characterization and Thermal Behaviour of Garnets from Almandine–Pyrope Series at 1200°C

Hyperfine Interactions - The natural garnets from almandine (Fe3Al2Si3O12)–pyrope (Mg3Al2Si3O12) series with the iron to magnesium atomic ratio ranging from 0.2 to 1 were characterised and...     

The fracture energy of materials under pulse microsecond-scale loading

Based on the results of fracture in polymethyl methacrylate and a spheroplastic using a magnetic-pulse setup, the specific work of the formation of a new surface is estimated, which is similar to Griffith’s surface energy for quasi-static tests. The value obtained is greater than the corresponding value determined from the quasi-static tests by an order of magnitude and tends to increase as the loading time decreases.     

New isothermal equation of state of solids applied to high pressures

In the present paper, a new two-parameter inverted equation of state (EOS) is developed which is found to be working very well in the high-pressure region. To check its success and validity, this EOS has been applied in a number of solids. The computed volume compression is found to be in very good agreement with the experimental data in the whole range of pressure in all the solids. The minimum and the maximum pressure range used in the present study is 0–320 kbar and 0–3000 kbar, respectively.     

Vanishing of local homology

 We study the vanishing properties of local homology of complexes of modules without assuming that its homology is artinian. Using vanishing results for local homology and cohomology we prove new vanishing results for Ext- and Tor-modules. Received: 1 August 2002; in final form: 23 September 2002 / Published online: 16 May 2003 Mathematics Subject Classification (1991): 13C12, 13D07, 13D45.     

Investigation of anode and cathode jets influence on electric arc properties with current up to 500 kA

A number of phenomena connected with the formation of electrode jets in discharges in hydrogen at a current of 10/sup 5/-10/sup 6/ A, a current growth rate of 10/sup 10/ A/s, an initial pressure 0.1-4.0 MPa, and a discharge gap length of 5-40 mm were studied. After the secondary breakdown, the jets are observed through a discharge semitransparent channel, widening with velocity (4-7) /spl middot/ 10/sup 2/ m/s. Shockwave formation was detected at the interaction of jets with the surrounding gas and the opposite electrode. Plasma vapor pressure of metal near the end of the tungsten cathode 70 /spl mu/s after initiation of a discharge was 180 MPa. Thus, magnitude of brightness temperature was 59 /spl middot/ 10/sup 3/ K, with an average charge of ions-m~=3.1, and a concentration of metal vapors n=5.3/spl middot/10/sup 19/ cm/sup -3/. While those at the end of the anode 90 /spl mu/s after initiation of discharge: m~=2.6, n=7.4/spl middot/10/sup 19/ cm/sup -3/. Probable reasons of high-voltage drops near the electrodes (the summarized magnitude of which is /spl sim/1 kV) are discussed on the basis of experimental data. For the first time, the shadow method registered symmetric ejection of material from the all-cathode surface the maximum discharge current was observed.     

A column generation approach for the timetabling problem of Greek high schools

A column generation (CG) approach for the solution of timetabling problems is presented. This methodology could be used for various instances of the timetabling problem, although in this paper the solution of the high-school situation in Greece is presented. The results obtained show clearly that the CG approach that has been extremely successful in recent years in the solution of airline crew scheduling problems could also be very efficient and robust for the solution of timetabling problems. Several large timetabling problems corresponding to real problems have been successfully solved, with the solutions obtained feasible and of very high quality in accordance with the problem definition. In addition, none of the solutions contained any idle hour for any of the teachers, which was one of the main goals of this optimization effort.     

Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem. Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311.