Integral Representations of Functional Series with Members Containing Jacobi Polynomials

MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

Monogenic polynomials of four variables with binomial expansion

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.

Clifford-Hermite polynomials in fractional Clifford analysis

In this paper we generalize radial and standard Clifford-Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann-Liouville derivative in a symbolic way. As main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven.

Lire à l’ère du numérique « Le nénuphar et l’araignée » de Claire Legendre

Cet article se veut exploratoire en deux temps : une piste de réflexion sur l’impact du numérique sur les sciences humaines, et une lecture de l’essai « Le nénuphar et l’araignée » de Claire Legendre, publié le 4 février 2015 chez Les Allusifs. Notre hypothèse est qu’il est nécessaire de jeter les bases d’une théorie et d’une pensée du numérique, comme de poursuivre et de favoriser l’implémentation de nouveaux outils de recherche conçus par et pour les humanités, en lien direct avec les questions d’édition, de diffusion, d’encodage, de fouille, de curation, ou encore de visualisation et de représentation des données textuelles, sonores et visuelles. Cet article propose ainsi une première piste d’exploration de l’usage de ces nouvelles possibilités pour la littérature québécoise.

Lire à l’ère du numérique « Le nénuphar et l’araignée » de Claire Legendre

Cet article se veut exploratoire en deux temps : une piste de réflexion sur l’impact du numérique sur les sciences humaines, et une lecture de l’essai « Le nénuphar et l’araignée » de Claire Legendre, publié le 4 février 2015 chez Les Allusifs. Notre hypothèse est qu’il est nécessaire de jeter les bases d’une théorie et d’une pensée du numérique, comme de poursuivre et de favoriser l’implémentation de nouveaux outils de recherche conçus par et pour les humanités, en lien direct avec les questions d’édition, de diffusion, d’encodage, de fouille, de curation, ou encore de visualisation et de représentation des données textuelles, sonores et visuelles. Cet article propose ainsi une première piste d’exploration de l’usage de ces nouvelles possibilités pour la littérature québécoise.

On polynomials with given Hilbert function and applications

Using Macaulay's correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.

Modeling and Design of Phase Shifted Full Bridge Isolated DC-DC ZVS Converter with Peak Current Mode Control

Nowadays, there is a boom in the use of electrification. Electric vehicles are gaining interest worldwide due to various factors, including climate and environmental awareness. In this thesis, a step-down isolated power supply for electric tractors is investigated, specifically the phase-shifted full-bridge (PSFB) DC-DC with synchronous rectification and zero-voltage switching (ZVS). This converter was selected for its high-power capacity with high efficiency. A 3500 W PSFB converter with peak current control (PCCM) is designed and modeled in MATLAB. The input voltage range is from 550 V to 820 V and the output voltage range is limited to 9 V to 16 V with a maximum output current of 250 A. All components were commercially designed and selected, including magnetics for the high-frequency transformer and inductors, taking into account loss calculations. Zero voltage switching for the lagging leg is achieved at 13% to 100% load. The proven efficiency of the converter is around 90

Silk Fibroin And Sodium Alginate Blend: Miscibility And Physical Characteristics.

Films of silk fibroin (SF) and sodium alginate (SA) blends were prepared by solution casting technique. The miscibility of SF and SA in those blends was evaluated and scanning electron microscopy (SEM) revealed that SF/SA 25/75 wt.% blends underwent microscopic phase separation, resulting in globular structures composed mainly of SF. X-ray diffraction indicated the amorphous nature of these blends, even after a treatment with ethanol that turned them insoluble in water. Thermal analyses of blends showed the peaks of degradation of pristine SF and SA shifted to intermediate temperatures. Water vapor permeability, swelling capacity and tensile strength of SF films could be enhanced by blending with SA. Cell viability remained between 90 and 100%, as indicated by in vitro cytotoxicity test. The SF/SA blend with self-assembled SF globules can be used to modulate structural and mechanical properties of the final material and may be used in designing high performance wound dressing.

Transmission Of Intra-cellular Genetic Information: A System Proposal.

One of the great challenges of the scientific community on theories of genetic information, genetic communication and genetic coding is to determine a mathematical structure related to DNA sequences. In this paper we propose a model of an intra-cellular transmission system of genetic information similar to a model of a power and bandwidth efficient digital communication system in order to identify a mathematical structure in DNA sequences where such sequences are biologically relevant. The model of a transmission system of genetic information is concerned with the identification, reproduction and mathematical classification of the nucleotide sequence of single stranded DNA by the genetic encoder. Hence, a genetic encoder is devised where labelings and cyclic codes are established. The establishment of the algebraic structure of the corresponding codes alphabets, mappings, labelings, primitive polynomials (p(x)) and code generator polynomials (g(x)) are quite important in characterizing error-correcting codes subclasses of G-linear codes. These latter codes are useful for the identification, reproduction and mathematical classification of DNA sequences. The characterization of this model may contribute to the development of a methodology that can be applied in mutational analysis and polymorphisms, production of new drugs and genetic improvement, among other things, resulting in the reduction of time and laboratory costs.

Emergent Antiferromagnetism Out Of The Hidden-order" State In Uru2si2: High Magnetic Field Nuclear Magnetic Resonance To 40 T."

Very high field (29)Si-NMR measurements using a fully (29)Si-enriched URu(2)Si(2) single crystal were carried out in order to microscopically investigate the hidden order (HO) state and adjacent magnetic phases in the high field limit. At the lowest measured temperature of 0.4 K, a clear anomaly reflecting a Fermi surface instability near 22 T inside the HO state is detected by the (29)Si shift, (29)K(c). Moreover, a strong enhancement of (29)K(c) develops near a critical field H(c) ≃ 35.6 T, and the ^{29}Si-NMR signal disappears suddenly at H(c), indicating the total suppression of the HO state. Nevertheless, a weak and shifted (29)Si-NMR signal reappears for fields higher than H(c) at 4.2 K, providing evidence for a magnetic structure within the magnetic phase caused by the Ising-type anisotropy of the uranium ordered moments.

Orientação do corpo humano como um todo a partir do seu elipsoide central de inercia

Universidade Estadual de Campinas . Faculdade de Educação Física

Neural networks and statistical analysis for classification of corneal videokeratography maps based on Zernike coefficients: a quantitative comparison

PURPOSE: The main goal of this study was to develop and compare two different techniques for classification of specific types of corneal shapes when Zernike coefficients are used as inputs. A feed-forward artificial Neural Network (NN) and discriminant analysis (DA) techniques were used. METHODS: The inputs both for the NN and DA were the first 15 standard Zernike coefficients for 80 previously classified corneal elevation data files from an Eyesys System 2000 Videokeratograph (VK), installed at the Departamento de Oftalmologia of the Escola Paulista de Medicina, São Paulo. The NN had 5 output neurons which were associated with 5 typical corneal shapes: keratoconus, with-the-rule astigmatism, against-the-rule astigmatism, "regular" or "normal" shape and post-PRK. RESULTS: The NN and DA responses were statistically analyzed in terms of precision ([true positive+true negative]/total number of cases). Mean overall results for all cases for the NN and DA techniques were, respectively, 94% and 84.8%. CONCLUSION: Although we used a relatively small database, results obtained in the present study indicate that Zernike polynomials as descriptors of corneal shape may be a reliable parameter as input data for diagnostic automation of VK maps, using either NN or DA.

Low temperature synthesis of CdSiO3 nanostructures

We report the synthesis of single-phase, crystalline CdSiO3 nanostructures at 580ºC; to the best of our knowledge, this is the lowest temperature at which this material is reported to form. The desired phase does not form below 580ºC, since the diffraction peaks are shifted to lower angles in the material treated at 570ºC when compared to JDPDS Card No. 85-0310. The source of silicon has strong influence on the product morphology: Na2SiO3 yields single-phase CdSiO3 in needle-shaped nanostructures, while high surface area mesostructured SiO2 yields coralloid-shaped particles. Low angle X-ray diffractometry reveals that the mesostructured nature of the silica precursor is not maintained in the resulting CdSiO3. Scanning electron microscopy suggests that in this case a transition occurs between the spherical morphology of the precursor and the needle-shape morphology of the material prepared from Na2SiO3. The surface area of the silica precursor has a strong influence in the reaction, since the use of commercial silica with a lower surface area does not yield the desired product.