Interaction-induced adiabatic cooling and antiferromagnetism of cold fermions in optical lattices

We propose an interaction-induced cooling mechanism for two-component cold fermions in an optical lattice. It is based on an increase of the spin entropy upon localization, an analogue of the Pomeranchuk effect in liquid helium 3. We discuss its application to the experimental realization of the antiferromagnetic phase. We illustrate our arguments with dynamical mean-field theory calculations.     

Applications of elliptic functions to ion-acoustic plasma waves

New several classes of exact solutions are obtained in terms of the Weierstrass elliptic function for some nonlinear partial differential equations modeling ion-acoustic waves as well as dusty plasmas in laboratory and space sciences. The Weierstrass elliptic function solutions of the Schamel equation, a fifth order dispersive wave equation and the Kawahara equation are constructed. Moreover, Jacobi elliptic function solutions and solitary wave solutions of the Schamel equation are also given. The stability of some periodic wave solutions is computationally studied.     

Studies on the potentiometric thallium(III)-selective carbon paste electrode and its possible applications

Construction, performance characteristics and applications of a carbon paste thallium(III) ion-selective electrode are described. The electrode, which is based on ion-associate compounds formed between cetylpyridinium and chlorothallate(III) complexes dissolved in tricresyl phosphate as pasting liquid, showed near-Nernstian response over the concentration range of 5.8 x 10(-6) - 2.9 x 10(-3) mol/L. Potentiometric titrations of thallium(III) with cetylpyridinium chloride were affected by higher concentrations of excess halides, probably due to the formation of higher halogenothallates.     

Some Properties of Finite Morphisms on Double Points

For a finite morphism f : X Y of smooth varieties such that f maps X birationally onto X=f(X), the local equations of f are obtained at the double points which are not triple. If C is the conductor of X over X, and are the subschemes defined by C, then D and are shown to be complete intersections at these points, provided that C has the expected codimension. This leads one to determine the depth of local rings of X at these double points. On the other hand, when C is reduced in X, it is proved that X is weakly normal at these points, and some global results are given. For the case of affine spaces, the local equations of X at these points are computed.     

Effect of sulfur on the electrical conductivity of FEF-loaded SBR during swelling

Following a series of experiments on the effect of different factors of the electrical conductivity of carbon-black-loaded styrene butadiene rubber, an attempt was made to study the effect on electrical conduction of changing the sulfur content. It was found that an optimum sulfur content leads to a swelling-resistant composite with good electrical insulation. This was done for dry as well as wet specimens of rubber.     

A perturbation treatment for optimal slightly nonlinear systems with linear control and quadratic criteria

Recently, it has been discovered that symbolic algebraic manipulations can be performed on the computer with input/output data in symbolic form. Accordingly, and for slightly nonlinear two-point boundary-value problems, it is feasible to obtain approximate analytical solutions in the form of power series in a small parameter. In these solutions, the boundary values are presented in a literal form. In this paper, the Lie canonical transformation is applied to derive approximate optimal solutions for slightly nonlinear systems with quadratic criteria. The transformation generator is determined by simple partial differential equations of the first order. To determine the arbitrary constants of the transformation in terms of the two-point boundary values, inversion of a vectorial power series in a small parameter is required, and a recursive algorithm for this inversion is given. To express the final solution in terms of these boundary values, a substitution of the inverted vectorial power series into another vectorial power series is also necessary, and a recursive algorithm for this substitution is presented.The authors are indebted to Professor J. V. Breakwell for his suggestions.     

Exciton-polaritons by two-photon absorption in semiconductors

The creation of excitonic polariton states by two-photon absorption is theoretically investigated. A semi-classical approach is adopted to compute the two-photon transition probability to polariton states through an intermediate exciton state. The numerical results in CuCl show two peaks corresponding to the longitudinal exciton and transverse polariton states, respectively. These results are in good agreement with the experiment.     

O-silylated enolate phenylthioalkylation: a new synthesis of unsaturated 1,5-dicarbonyl compounds.

The O-silylated enolates of ketones and esters can be phenylthioalkylated by the chlorides (2) and (3) under ZnBr₂-catalysis; ozonolysis and subsequent sulphoxide thermolysis then gives the corresponding unsaturated 1,5-dicarbonyl compounds.