Full-relativistic calculation of electronic structure of Zr2AlC and Zr2AlN

We have employed a full-relativistic version of an all-electron full-potential linearized-augmented plane-wave method in the local density approximation to investigate the electronic structure of nanolaminate Zr₂AlX (X=C and N). The Zr 4d electrons are treated as valence electrons. We have investigated the lattice parameters, bulk moduli, band structures, total and partial densities of states and charge densities. It is demonstrated that the strength and electrical transport properties in these materials are principally governed by the metallic planes.     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

Field Theory Methods in Classical Dynamics

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger–Feynman–Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geometrical Berry phase as an example. Finally a direct integration of Hamilton's equations is shown to lead naturally to a path integral expression, as a resolution of the identity, as applied to arbitrary functions of generalized coordinates and momenta.     

Monte Carlo study of interfacial silicon suboxide layers and oxidation kinetics

A simple simulation scheme that simultaneously describes the growth kinetics of SiO₂ films at the nanometer scale and the SiO_x/Si interface dynamics (its extent, and spatial/temporal evolution) is presented. The simulation successfully applies to experimental data in the region above and below 10 nm, reproduces the Deal and Grove linear-parabolic law and the oxide growth rate enhancement in the very thin film regime (the so-called anomalous region). According to the simulation, the oxidation is governed mainly by two processes: (a) the formation of a transition suboxide layer and (b) its subsequent drift towards the silicon bulk. We found that it is the superposition of these two processes that produces the crossover from the anomalous oxidation region behavior to the linear-parabolic law.     

Metastability in the Potts model on the Cayley tree

Metastability in the ferromagneticp-state Potts model defined on the Cayley tree is discussed. It is shown that the sign of the boundary fieldH _s determines the order of the transition as well as the stability of the low-temperature phase. Lowering the temperature withH _s >0, a system withp<2 (p>2) will display a second (first)-order transition to a metastable (stable) phase. ForH _s >0 a second (first)-order transition to a metastable (stable) phase occurs ifp>2 (p<2). In this case the system also has a residual entropy which is negative forp<2.     

Some experiences in controlling contamination of environmental materials during sampling and processing for low-level actinide analysis

Selected experiences in the control of contamination and the threat it poses to the quality of analytical date are discussed in the context of the whole analytical process from collection of marine environmental samples, through handling and radiochemical separation, to the final interpretation of results. Examples include a demonstration of the contamination introduced during sediment core sectioning, contamination of sea water by a ship's pumping system, and the effect of filtration on the apparent partitioning of radionuclides between solid and liquid phases of sea water.     

Acoustic field in a closed layered shell with resonant systems

The acoustic field inside a shell excited by a spatially inhomogeneous harmonic pressure field is studied. The shell is assumed to have a finite length, a set of orthogonal stiffening ribs, two ends bounding the acoustic volume, and a sound-insulating structure, which includes layers of sound-insulating material, resonant elements, and an interior panel. The shell is considered to be orthotropic with boundary conditions corresponding to a free support. For the acoustic field in the closed volume, analytical expressions are derived with allowance for the elastoacoustic interaction of the shell with the sound-insulating layers and with the medium both inside the shell (with arbitrary impedance values at the ends) and outside it. These expressions are used to investigate the effect of different types of resonant systems on the sound field inside the shell.     

Simple, expedient methods for the determination of water and electrolyte contents of cellulose solvent systems

The concentrations of water, W, and electrolytes present in solutions of LiCl in N,N-dimethylacetamide, LiCl/DMAc, and of tetrabutylammonium fluoride. x-hydrate in DMSO, TBAF.xW/DMSO can be accurately and expediently determined by three independent methods, UV–vis, FTIR and EMF measurement. The first relies on the use of solvatochromic probes whose spectra are sensitive to solution composition. It is applicable to W/LiCl/DMAc solutions but not to TBAF.xW/DMSO, because the charge-transfer complex bands of the probes are suppressed by strong interactions with the latter electrolyte. Integration of ν_OH band of water may be employed in order to determine [W], hence [electrolyte] by weight difference. EMF measurement uses ion-selective electrodes in order to determine [electrolyte], hence [W] by weight difference. Results of the latter method were in excellent agreement with those of FTIR. The reason for the failure of Karl Fischer titration is addressed, and the relevance of the results obtained to functionalization of cellulose under homogenous solution conditions is briefly commented on.     

C- and N-Amidotrichloroethylation of Azoles

1H-Pyrazoles, triazoles, and imidazoles in reaction with ethoxycarbonylimine and arylsulfonylimines of chloral yield addition products, corresponding 1-(1-amidotrichloroethyl)azoles. Derivatives of 1-alkylpyrazoles and pyrazolones react with chloral 4-chlorophenylsulfonylimine to furnish products of C-amidotrichloroethylation into position 4 of the azole ring.