The (1+1) Dimensional Dirac Equation With Pseudoscalar Potentials: Path Integral Treatment

The supersymetric path integrals in solving the problem of relativistic spinning particle interacting with pseudoscalar potentials is examined. The relative propagator is presented by means of path integral, where the spin degrees of freedom are described by odd Grassmannian variables and the gauge invariant part of the effective action has a form similar to the standard pseudoclassical action given by Berezin and Marinov. After integrating over fermionic variables (Grassmannian variables), the problem is reduced to a nonrelativistic one with an effective supersymetric potential. Some explicit examples are considered, where we have extracted the energy spectrum of the electron and the wave functions. PACS numbers: 03.65. Ca-Formalism, 03.65. Db-Functional analytical methods, 03.65. Pm-Relativistic wave equations.     

On a certain nonlocal problem for a hyperbolic equation

The author proves the existence and uniqueness of a generalized solution of a nonlocal problem with an integral condition for a hyperbolic equation with n spatial variables. This work is a continuation of the studies started in [3–5], where the solvability problem of nonlocal problems with an integral condition was studied for hyperbolic equations on the plane. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.     

Differentiation of species of the Baccharis genus by HPLC and chemometric methods.

Phytochemical investigation of the aerial parts of three Baccharis species (Asteraceae family) was performed using HPLC and chemometric methods, with the objective of distinguishing between three morphologically very similar species: Baccharis genistelloides Persoon var. trimera (Less.) DC, B. milleflora (Less.) DC and B. articulata (Lam.) Persoon. With the help of Principal Component Analysis (PCA) and variance weights, it was possible to characterize the chromatographic profiles of the alcoholic extracts of the three species. Application of Soft Independent Modeling of Class Analogy (SIMCA) and K-Nearest Neighbor (KNN) methods on a training set of 74 extracts resulted in models that correctly classified all eight samples in an independent test set.     

Diffuse x-ray scattering study of the formation of microdefects in heat-treated dislocation-free large-diameter silicon wafers

Diffuse x-ray scattering (DXS) is used to study the formation of microdefects (MDs) in heat-treated dislocation-free large-diameter silicon wafers with vacancies. The DXS method is shown to be efficient for investigating MDs in silicon single crystals. Specific defects, such as impurity clouds, are found to form in the silicon wafers during low-temperature annealing at 450°C. These defects are oxygen-rich regions in the solid solution with diffuse coherent interfaces. In the following stages of decomposition of the supersaturated solid solution, oxide precipitates form inside these regions and the impurity clouds disappear. As a result of the decomposition of the supersaturated solid solution of oxygen, interstitial MDs form in the silicon wafers during multistep heat treatment. These MDs lie in the {110} planes and have nonspherical displacement fields. The volume density and size of MDs forming in the silicon wafers at various stages of the decomposition are determined.     

Convergence of optimal controls in some optimization problems

We consider the behavior of bundles of optimal controls when the initial state of the system goes to some given vector. We investigate three types of optimization problems: problems with fixed process length and a free right endpoint; problems with fixed process length and a fixed right endpoint; time-optimal problems. The article is a review of recent results obtained by the author. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 301–314, 2004.     

Graphitic nanofillers in PMMA nanocomposites—An investigation of particle size and dispersion and their influence on nanocomposite properties

Mechanical, thermal, and electrical properties of graphite/PMMA composites have been evaluated as functions of particle size and dispersion of the graphitic nanofiller components via the use of three different graphitic nanofillers: “as received graphite” (ARG), “expanded graphite,” (EG) and “graphite nanoplatelets” (GNPs) EG, a graphitic materials with much lower density than ARG, was prepared from ARG flakes via an acid intercalation and thermal expansion. Subsequent sonication of EG in a liquid yielded GNPs as thin stacks of graphitic platelets with thicknesses of ～10 nm. Solution‐based processing was used to prepare PMMA composites with these three fillers. Dynamic mechanical analysis, thermal analysis, and electrical impedance measurements were carried out on the resulting composites, demonstrating that reduced particle size, high surface area, and increased surface roughness can significantly alter the graphite/polymer interface and enhance the mechanical, thermal, and electrical properties of the polymer matrix. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2097–2112, 2007     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007