Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the zeros of a class of generalized hypergeometric polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Lê–Greuel type formula for the Euler obstruction and applications

The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we establish several Lê–Greuel type formulas for germs f:(X,0)→(C,0) and g:(X,0)→(C,0). We give applications when g is a generic linear form and when f and g have isolated singularities.

Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Affine Hall-Littlewood Functions for A(1)((1)) And Some Constant Term Identities of Cherednik-Macdonald-Mehta Type

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A(1)((1)). We obtain closed form formulas for certain t-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher level generalizations of Cherednik's Macdonald and Macdonald-Mehta constant term identities.

On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

Evaluation of bond covalency and bond valence in Sr-doped perovskite-type compounds

Formulas for decomposing of complex crystals to a sum of binary crystals are described and applied to the study of bond covalency in La1-xSrxFeO3 (0.0 less than or equal to x less than or equal to 0.9) and Ca1-xSrxMnO3 (0.0 less than or equal to x less than or equal to 0.5). The bond valence is treated by bond-valence sums scheme. The results indicate that, for both compounds, with the increasing doping level, the bond covalency and bond valence show the same trend, namely, larger bond covalency corresponds to higher bond valence. For La1-xSrxFeO3, with the increase of doping level, the bond covalency of La-O, Ca-O decreases in the orthorhombic (0.0 less than or equal to x less than or equal to 0.2) and rhombohedral (0.4 less than or equal to x less than or equal to 0.7) systems, then increases slightly for the cubic (0.8 less than or equal to x less than or equal to 0.9) system, but that of Fe-O increases for all crystal systems. A sharp decrease in bond covalency was observed where the crystal changes from orthorhombic to rhombohedral, while a smooth trend was seen for the rhombohedral-to-cubic transition. On the other hand, for orthorhombic Ca1-xSrxMnO3, the bond covalency of Ca-O, Sr-O, and Mn-O (4-coordinate site) decreases with the increasing doping level, that of Mn-O (2-coordinate site) increases.

AN ALGEBRAIC METHOD TO ESTIMATE GENERAL TYPE OF PHASES OF STRUCTURE FACTORS

The algebraic formulas of 1.5 and 2.5 rank are given for four space groups P2(1), Pn, Pna2(1), P2(1)2(1)2(1). It is better that the results of applying them to estimating general type of phases for four correspondent crystal structures. And a method of transforming algebraic formulas from 1.5(2.5) rank is proposed.

THE ALGEBRAIC-METHOD ESTIMATING +/-PI/2 TYPE OF PHASES OF STRUCTURE FACTORS

The algebraic formulas of 1.5 and 2.5 rank which can be applied to estimating +/- pi/2 type of phases for P2(1)2(1)2(1) space group were derived using the method of structure factor algebra. Both types of the formulas are satisfactory for two known crystal structures in estimating their +/- pi/2 type of phases.

Determination of fractional energy loss of waves in nearshore waters using an improved high-order Boussinesq-type model

Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.

Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

We study the Riemann boundary value problem , for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent. We consider both the case when the coefficient is piecewise continuous and it may be of a more general nature, admitting its oscillation. The explicit formulas for solutions in the variable exponent setting are given. The related singular integral equations in the same setting are also investigated. As an application there is derived some extension of the Szegö-Helson theorem to the case of variable exponents.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Composition and structural formulas of ODP Site 200-1224 Eocene ferrobasalt minerals

The ~46-m.y.-old igneous basement cored during Leg 200 in the North Pacific represents one of the few cross sections of Pacific oceanic crust with a total penetration into basalt of >100 m. The rocks, emplaced during the Eocene at a fast-spreading rate (~14 cm/yr; full rate) are strongly differentiated tholeiitic basalts (ferrobasalts) with 7-4.5 wt% MgO, relatively high TiO2 (2-3.5 wt%), and total iron as Fe2O3 (9.1-16.8 wt%). The differentiated character of these lavas is related to unusually large amounts of crystallization differentiation of plagioclase, clinopyroxene, and olivine. The lithostratigraphy of the basement (cored to ~170 meters below seafloor) is divided into three units. The deepest unit (lithologic Unit 3), is a succession of lava flows of no more that a few meters thickness each. The intermediate unit (lithologic Unit 2) is represented by intermixed thin flows and pillows, whereas the shallowest unit (lithologic Unit 1), comprises two massive flows. The rocks range from aphyric to sparsely clinopyroxene-plagioclase-phyric (phenocryst content = <3 vol%) and from holocrystalline to hypohyaline. Chilled margins of pillow fragments show holohyaline to sparsely vitrophyric textures. Site 1224 oxide minerals present a type of alteration not previously seen, where titanomagnetite is only partially destroyed and the pure magnetite component is partially removed from the mineral, leaving, in the most extreme case, a nearly pure ulvöspinel residuum. As a result of this dissolution, iron, mainly in the oxidized state, is added to the circulating solvent fluids. This means that a considerable metal source can result from low-temperature reactions throughout the upper ocean crust. The coarsest-grained lithologic Unit 1 rocks have interstitial myrmekitic intergrowths of quartz and sodic plagioclase (~An12), roughly similar in mineralogy and bulk composition to tonalite/trondhjemite veinlets in abyssal gabbros from the southwest Indian Ocean and Hess Deep, eastern equatorial Pacific. Based on idiomorphic relationships and projections into the simplified Q-Ab-Or-H2O granite ternary system, the myrmekitic intergrowths formed at the same time as, or just after, the oxide minerals coprecipitated and at low water vapor pressure (~0.5 kbar). Their compositions correspond to SiO2-oligoclase intergrowths that are considerably less potassic than dacitic glasses that erupt, although rarely, along the East Pacific Rise or that have been produced experimentally by partial melting of gabbro. Based on the crystallization history and comparison to experimental data, the original interstitial siliceous liquids resulted from late-stage immiscible separation of siliceous and iron-rich liquids. The rare andesitic lavas found along the East Pacific Rise may be hybrid rocks formed by mixing of these immiscible siliceous melts with basaltic magma.

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros.

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.