A problem in extremal quasiconformal extensions

A constantK ₀ ^(m) (h) is introduced for every quasisymmetric mappingh of the unit circle and every integerm≥4 which contains the constantK ₀(h) (indicated by the change in module of the quadrilaterals with vertices on the circle) as a special case. A necessary and sufficient condition is established forK ₀ ^(m) (h) =K ₁(h). It is shown that there are infinitely many quasisymmetric mappings of the unit circle having the property thatK ₀ ^(m) (h)<K ₁(h), wherek ₁(h) is the maximal dilatation ofh.     

Optimale Quantisierung

Zusammenfassung. Optimale Quantisierungen oder – damit ?quivalent – minimale Summen von Momenten spielen in mehreren Zweigen der Mathematik und ihrer Anwendungen eine Rolle. Ausgehend von der Fejes Tóth'schen Ungleichung für Summen von Momenten in der euklidischen Ebene und einem zugeh?rigen Stabilit?tssatz, werden gewisse Erweiterungen auf normierte R?ume und riemannsche Mannigfaltigkeiten h?herer Dimension besprochen. Die Ergebnisse werden dann auf Probleme aus folgenden Bereichen angewendet: (i) Datenübertragung, (ii) Wahrscheinlichkeitstheorie, (iii) numerische Integration, (iv) Approximation konvexer K?rper und (v) isoperimetrische Probleme. Eingegangen am 29. Mai 2002 / Angenommen am 8. Juli 2002     

Lattice Thermal Transport in the Homogeneous Cage-Like Compounds Cu3VSe4 and Cu3NbSe4: Interplay between Phonon-Phase Space,Anharmonicity, and Atomic Mass

Understanding the correlation between crystal structure and thermal conductivity in semiconductors is very important for designing heat-transport-related devices, such as high-performance thermoelectric materials and heat dissipation in micro-nano-scale devices. In this work, the lattice thermal conductivity ( ) of the cage-like compounds Cu₃VSe₄ and Cu₃NbSe₄ was investigated by experimental measurements and first-principles calculations. The experimental of Cu₃NbSe₄ is approximately 25 % lower than that of Cu₃VSe₄ at 300 K. The relevant important physical parameters, including the sound velocity, heat capacity, weighted phonon phase space (W), and third-order force constants along with atomic mass were theoretically analyzed. It is found that W is the dominant parameter in determining the , and the other factors only play a minor role. The physical origin is the relatively “soft” lattice of Cu₃NbSe₄ with heavier atomic mass. This research provides deep insight into the correlation between the thermal conductivity and crystal structure and paves the way for discovering high-performance thermal management device and thermoelectric materials with intrinsically low .     

The anisotropic van der waals potential for He-N2

We have calculated the spherical v₀ and anisotropic radial components v₂ and v₄ in the usual Legendre expansion for the rigid rotor He-N₂ potential using the method of Tang and Toennies Potential curves covering the range of internuclear distances from 2.5 to 8.0 Å, which includes the minimum region, arc presented and compared with a recent experimental potential derived from differential total cross sections.     

Synthesis of tumor-associated glycopeptide antigens for the development of tumor-selective vaccines

In contrast to normal cells, the glycoprotein profile on epithelial tumor cells is distinctly altered. Due to an incomplete formation of the glycan side-chains resulting from a premature sialylation, additional peptide epitopes become accessible to the immune system in mucin-type glycoproteins on tumor cells. These tumor-associated structure alterations constitute the basis for a selective immunological attack on cancer cells. For the construction of immunostimulating antigens, glycopeptide partial structures from the mucins MUC1 and MUC4 carrying the tumor-associated sialyl-T(N), alpha2,6-sialyl-T and alpha2,3-sialyl-T antigens have been synthesized. Employing different linkers such as the allylic HYCRON or the fluoride-sensitive PTMSEL anchor, the antigenic glycopeptide structures were constructed on the solid phase utilizing pre-assembled glycosyl amino acid building blocks prepared in solution by convergent chemical or chemoenzymatic strategies. The proliferation of cytotoxic T cells has been induced applying a construct composed of a sialyl-T(N) MUC1-glycopeptide conjugated with a tetanus toxin T cell peptide epitope.     

Antiferromagnetic complexes involving metal---metal bonds III. Synthesis, structure and magnetic properties of heterotrinuclear complexes of the type M(CO)5L (M = Cr, Mo and w) containing [(C5H5CrSCMe3)2S] as unusual antiferromagnetic ligand L

Isostructural heterotrinuclear complexes (C₅H₅CrSCMe₃)₂S · M(CO)₅ (II–IV) were isolated from photochemical reactions between the antiferromagnetic complex (C₅H₅CrSCMe₃)₂S (I) (with the Cr---Cr bond 2.689 Å long and with the exchange parameter −2J = 430 cm⁻¹) and metal hexacarbonyls, M(CO)₆, where M is Cr, Mo, or W. According to the X-ray structural data on III and IV, complex I plays the role of an unusual antiferromagnetic ligand L bound to M through the sulphide bridge (M–S 2.58(2) Å). Its geometry remains practically unaffected by the complex formation (the Cr---Cr bond length in III and IV is 2.73(1) Å). The exchange parameter, −2J (410, 440 and 440 cm⁻¹ in II to IV, respectively), also shifts only insignificantly from that of I, which probably means that indirect exchange via the sulphide bridge in I is of minor importance compared with the direct Cr---Cr exchange. The Cr---Cr bond length may thus be correlated with the observed overall exchange coupling.     

Pressure and volume dependence of thelo-to phonons in InAs

The pressure dependence of thelo-to phonons in InAs has been investigated by Raman scattering using the diamond anvil cell. Indium arsenide transforms, presumably to the rock-salt structure at 70±1 kbar. The mode Grüneisen parameters for thelo-to phonons are γ _lo =0.99±0.03, γ _to =1.2±0.03 respectively. The effective charge,e* _T , for InAs decreases slightly with pressure and this trend is in accordance with the behaviour of other III–V zinc blende structured semiconductors: The structural phase transition is discussed in the light of theoretical calculations for phase stability of III–V compounds, as well as recent high pressure x-ray diffraction studies.     

The formation of a series of barium tungsten bronzes

The phases occurring in samples of gross composition Ba_xWO₃ (0.01 < x < 0.33) heated at temperatures between 1073 and 1373°K have been determined using X-ray diffraction and electron microscopy. At all temperatures a tetragonal tungsten bronze phase with a narrow homogeneity range of x = 0.20?0.21 was observed to form. In addition, at temperatures up to 1273°K, a series of orthorhombic intergrowth bronzes forms within a restricted composition range around x = 0.04. The latter phases are unstable at higher temperatures and were not found in preparations made at 1323°K. Similarly a new type of bronze phase forms at x = 0.14?0.16 at temperatures up to 1323°K, but not at 1373°K. The structure of this phase is unknown. Aspects of the crystal chemistry of the barium bronzes and the relationships to other bronze phases are discussed.     

AlSiP3, a compound with a novel wurtzite-pyrite intergrowth structure

AlSiP₃ is formed by heating aluminum and silicon powder with red phosphorus and adding small amounts of iodine or AlCl₃. Small, black crystals with metallic lustre grow at 1200°K. The compound crystallizes in the orthorhombic space group Pmnb (No. 62) with a = 987.2 pm, b = 586.1 pm, c = 608.8 pm and four formula units. In the structure isolated P atoms as well as P₂ pairs are present (PP = 218.2 pm). Silicon is tetrahedrally bonded (SiP = 224.2 ? 228.2 pm) whereas aluminum has octahedral coordination (AlP = 244.2 – 260.8 pm). The structure can be described as an intergrowth structure of wurtzite and pyrite type.