A class of simplicial restart fixed point algorithms without an extra dimension

In an earlier paper we introduced an algorithm for approximating a fixed point of a mapping on the product space of unit simplices. Ideas of that paper are used to construct a class of triangulations ofR ⁿ. More precisely, for somek, 1 k n, and positive integersm ₁ , m_k with sumn, a triangulation ofR ⁿ is obtained by triangulating the cells which are formed by taking the product of given triangulations ofR ^mj, j = 1, ,k. The triangulation of each cell will be defined in relation to an arbitrarily chosen pointv inR ⁿ, being the starting point of the algorithm. Fork = n we obtain theK triangulation originally due to Todd. Each element of the class can be used to find a simplex which approximates a fixed point of a mapping onR ⁿ by generating a unique path of adjacent simplices of variable dimension starting with the pointv. We also give convergence conditions. It is indicated how in casek = n a connected set of fixed points can be generated. Moreover, we give some computational experience.     

堪为物理学第三分支的计算物理

本文是作者1982年在中国访问时所作的讲演,论述物理学各领域的前沿工作,用许多事例说明计算物理对推动物理理论的重大意义。文中还指出计算物理在其性质、方法及需要等方面不同于和独立于解析的理论物理和实验物理,而成为物理学的第三分支。     

A Unified Fixed Point Theory for Countably P -Concentrative Multimaps

New fixed point results and Leray-Schauder alternatives are presented for countably P -concentrative multimaps. The notion of an essential map is also introduced for a wide class of maps.     

Effect of an electric field on defects in a nematic liquid crystal with variable surface anchoring

We report experimental studies on defects in a nematic liquid crystal with negative dielectric anisotropy mounted in a cell with perfluoropolymer-coated surfaces. The sample exhibits a discontinuous anchoring transition from planar to homeotropic on cooling at zero or a small electric field, and above a cross-over voltage a continuous ‘inverse Freedericksz transition’, at which the director starts tilting in opposite directions at the two surfaces. Defects of strength ±1/2 are either annihilated or expelled when the director tilts. On the other hand, disclination lines of ±1 which end in partial point defects (boojums) at the surfaces in the planar alignment regime acquire point defects of strength ±1 at the midplane of the cell when the director tilts. At a low enough temperature, the homeotropic anchoring becomes strong, and an electric field above the Freedericksz threshold generates the usual umbilic defects, which follow the dynamic scaling laws found in earlier studies.     

Vacancy-like defects in nanocrystalline SnO2: influence of the annealing treatment under different atmospheres

The study of electronic and chemical properties of semiconductor oxides is motivated by their several applications. In particular, tin oxide is widely used as a solid state gas sensor material. In this regard, the defect structure has been proposed to be crucial in determining the resulting film conductivity and then its sensitivity. Here, the characteristics of vacancy-like defects in nanocrystalline commercial high-purity tin oxide powders and the influence of the annealing treatment under different atmospheres are presented. Specifically, SnO₂ nanopowders were annealed at 330 °C under three different types of atmospheres: inert (vacuum), oxidative (oxygen) and reductive (hydrogen). The obtained experimental results are discussed in terms of the vacancy-like defects detected, shedding light to the basic conduction mechanisms, which are responsible for gas detection.     

Self-interstitial solute interaction in aluminium base alloys: Problems of data interpretation

The interpretation of electrical resistivity measurement results of Al base alloys is critically discussed. Correct numerical data evaluation with respect to the atomistic properties r_c/r_p, r_t and Pf^t/Pf is yet impossible for Al and its alloys because of the overlapping of Ic and Id recovery for those electron irradiations for which damage rate measurements exist and because of the unexplained scatter of initial damage rate data.     

First-principles study on the electronic structure and optical properties of La0.75Sr0.25MnO3-σ materials with oxygen vacancies defects

The electronic structure and optical properties of La_0.75Sr_0.25MnO_3-σ (LSMO_3-σ) materials with 1 × 1 × 4 orthorhombic perovskite structure were performed by first-principles calculation. The structural changing of LSMO₃ (ideal structure, σ = 0) was not obvious under generalized gradient approximation (GGA) and GGA + U arithmetic. On the contrary, the structural changing of LSMO_3-σ (σ = 0.25, with oxygen vacancies defects in the z = 0, c/8, c/6, c/4, and c/2) with GGA + U were more obvious than the result of ideal. This structural distortion induced distinct changing in density of states (DOS) for LSMO_3-σ materials. Oxygen vacancy defects caused a shift of the total density of states (TDOS) features toward low binding energies and LSMO_3-σ keep half-metal properties as well as LSMO₃ ideal structure. In addition, the hybridization between the Mn-e_g and O-2p orbital was weakened and the partial density of states (PDOS) of Mn indicated a strong d-d orbital interaction. By the result of oxygen vacancy formation energy, oxygen vacancy defects can be more easily formed in La-O layers (z = 0 and c/6) to compare with other layers (z = c/8, c/4 and c/2). The calculation result of optical properties suggested that the ideal LSMO could be produced strong absorption in the range of ultraviolet and visible light, while the LSMO_3-σ with oxygen vacancies defects were presented weak absorption in the range of visible light.     

“Painlevé 34” equation: Equivalence test

We give the complete solution of the Equivalence Problem for “Painlevé 34” equation.     

Density effects of heavy-ion stopping power in high temperature matter

Abstract

The stopping power and range for Xe ions in high temperature matter (partially ionized plasmas) have been calculated using the dielectric response function method. Calculations have been made for a target matter Al (Z = 13) over a wide range of temperatures and densities considering a finite temperature model. The stopping powers obtained have smaller values in comparison with those of a zero temperature model. The stopping power strongly depends on the density and temperature of the target material, and the projectile ion energy.     

Crystal structure of a cholesterol-based dimesogen

The title compound, cholesteryl 6[4-(4-pentyloxyphenylethynyl)phenoxy]hexanoate (DMT5), a cholesterol-based dimesogen, crystallizes in the monoclinic space group P2₁ with the parameters a = 9.812(3) Å, b = 9.713(2) Å, c = 24.179(2) Å, β = 92.48(1)° V = 2302.2(9) ų, Z = 2, F₀₀₀ = 836, λ(MoK_α) = 0.71069 Å, μ = 0.067 cm 1, final R = 0.0772. The structure has intermolecular hydrogen bonds; it is stabilized by the presence of intermolecular contacts whose spacings are less than van der Waals' radii.