Regra de Sinais de Descartes para polinômios ortogonais

Pós-graduação em Matematica Aplicada e Computacional - FCT

A moment symbolic representation of Lévy processes with applications

By using a symbolic method, known in the literature as the classical umbral calculus, a symbolic representation of Lévy processes is given and a new family of time-space harmonic polynomials with respect to such processes, which includes and generalizes the exponential complete Bell polynomials, is introduced. The usefulness of time-space harmonic polynomials with respect to Lévy processes is that it is a martingale the stochastic process obtained by replacing the indeterminate x of the polynomials with a Lévy process, whereas the Lévy process does not necessarily have this property. Therefore to find such polynomials could be particularly meaningful for applications. This new family includes Hermite polynomials, time-space harmonic with respect to Brownian motion, Poisson-Charlier polynomials with respect to Poisson processes, Laguerre and actuarial polynomials with respect to Gamma processes , Meixner polynomials of the first kind with respect to Pascal processes, Euler, Bernoulli, Krawtchuk, and pseudo-Narumi polynomials with respect to suitable random walks. The role played by cumulants is stressed and brought to the light, either in the symbolic representation of Lévy processes and their infinite divisibility property, either in the generalization, via umbral Kailath-Segall formula, of the well-known formulae giving elementary symmetric polynomials in terms of power sum symmetric polynomials. The expression of the family of time-space harmonic polynomials here introduced has some connections with the so-called moment representation of various families of multivariate polynomials. Such moment representation has been studied here for the first time in connection with the time-space harmonic property with respect to suitable symbolic multivariate Lévy processes. In particular, multivariate Hermite polynomials and their properties have been studied in connection with a symbolic version of the multivariate Brownian motion, while multivariate Bernoulli and Euler polynomials are represented as powers of multivariate polynomials which are time-space harmonic with respect to suitable multivariate Lévy processes.

Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

Optimal beam forming for laser beam propagation through random media

Focusing optical beams on a target through random propagation media is very important in many applications such as free space optical communica- tions and laser weapons. Random media effects such as beam spread and scintillation can degrade the optical system's performance severely. Compensation schemes are needed in these applications to overcome these random media effcts. In this research, we investigated the optimal beams for two different optimization criteria: one is to maximize the concentrated received intensity and the other is to minimize the scintillation index at the target plane. In the study of the optimal beam to maximize the weighted integrated intensity, we derive a similarity relationship between pupil-plane phase screen and extended Huygens-Fresnel model, and demonstrate the limited utility of maximizing the average integrated intensity. In the study ofthe optimal beam to minimize the scintillation index, we derive the first- and second-order moments for the integrated intensity of multiple coherent modes. Hermite-Gaussian and Laguerre-Gaussian modes are used as the coherent modes to synthesize an optimal partially coherent beam. The optimal beams demonstrate evident reduction of scintillation index, and prove to be insensitive to the aperture averaging effect.

Introductory Mathematics for Quantum Chemistry

An elementary discussion of some of the mathematics employed in studying Quantum Chemistry in a style appropriate for persons who have not taken advanced mathematical instruction.

Aislamiento y caracterización de bacterias endosimbióticas procedentes de suelos contaminados por cobre en Chile

El uso intensivo de compuestos de cobre como herbicidas y fungicidas provoca la contaminación de suelos de uso agrícola debido a la acumulación de este metal en las capas más superficiales del suelo. Se sabe que la presencia de cobre y otros metales pesados afecta negativamente a las interacciones simbióticas que se establecen entre bacterias diazotróficas de los géneros Rhizobium, Sinorhizobium y Bradyrhizobium y leguminosas de interés agrícola (Laguerre et al., 2006). El objetivo de este trabajo es estudiar la diversidad de cepas endosimbióticas de leguminosas en suelos agrícolas chilenos que presentan un elevado contenido en cobre como resultado de la contaminación con residuos de extracciones mineras. Además, se pretende caracterizar el nivel de resistencia a cobre en las cepas aisladas con objeto de identificar aquellas altamente eficientes que puedan ser utilizadas como inoculantes microbianos. Para ello, se han prospectado 9 suelos agrícolas de las regiones III, V y VI de Chile con contenidos muy variables de metales. Utilizando estos suelos como inóculos de plantas trampa de leguminosas se ha obtenido una colección de 362 cepas aisladas de nódulos de guisante (Pisum sativum), judía (Phaseolus vulgaris) y alfalfa (Medicago sativa). Los análisis filogenéticos y los ensayos de resistencia a cobre realizados han permitido caracterizar y seleccionar aquellas cepas con mayores niveles de resistencia a este metal. Los resultados demuestran que los suelos altamente contaminados por cobre poseen una menor diversidad de bacterias endosimbióticas; las cepas más resistentes han sido aisladas de los suelos con niveles de contaminación intermedia. Los análisis fenotípicos y moleculares realizados sobre las cepas más resistentes han demostrado la existencia de sistemas de resistencia a cobre inducibles por este metal y potencialmente implicados en su homeostasis.

Metagenomic Anlaysis of microsymbiont selection by the legume plant host

Rhizobium leguminosarum bv.viciae is able to establish nitrogen-fixing symbioses with legumes of the genera Pisum, Lens, Lathyrus and Vicia. Classic studies using trap plants (Laguerre et al., Young et al.) provided evidence that different plant hosts are able to select different rhizobial genotypes among those available in a given soil. However, these studies were necessarily limited by the paucity of relevant biodiversity markers. We have now reappraised this problem with the help of genomic tools. A well-characterized agricultural soil (INRA Bretennieres) was used as source of rhizobia. Plants of Pisum sativum, Lens culinaris, Vicia sativa and V. faba were used as traps. Isolates from 100 nodules were pooled, and DNA from each pool was sequenced (BGI-Hong Kong; Illumina Hiseq 2000, 500 bp PE libraries, 100 bp reads, 12 Mreads). Reads were quality filtered (FastQC, Trimmomatic), mapped against reference R. leguminosarum genomes (Bowtie2, Samtools), and visualized (IGV). An important fraction of the filtered reads were not recruited by reference genomes, suggesting that plant isolates contain genes that are not present in the reference genomes. For this study, we focused on three conserved genomic regions: 16S-23S rDNA, atpD and nodDABC, and a Single Nucleotide Polymorphism (SNP) analysis was carried out with meta / multigenomes from each plant. Although the level of polymorphism varied (lowest in the rRNA region), polymorphic sites could be identified that define the specific soil population vs. reference genomes. More importantly, a plant-specific SNP distribution was observed. This could be confirmed with many other regions extracted from the reference genomes (data not shown). Our results confirm at the genomic level previous observations regarding plant selection of specific genotypes. We expect that further, ongoing comparative studies on differential meta / multigenomic sequences will identify specific gene components of the plant-selected genotypes

Genomics of host specificity in the Rhizobium-legume simbiosis

Most Rhizobium leguminosarum bv. viciae isolates are able to specifically nodulate plants of any of four different legume genera: Pisum, Lens, Vicia, and Lathyrus. However, previous evidence suggests that some genotypes are more adapted to a given plant host than others, and that the plant host can select specific genotypes among those present in a given soil population. We have used a population genomics approach to confirm that this is indeed the case, and to analyze the specific genotypic characteristics that each plant host selects

Agriculture de département de la Meuse.

At head of title: Ouvrage récomponsé par la Société d'encouragement pour l'industrie nationale.

ha-Milḥamah ṿeha-matsor : ṿe-hi lahaṭ ha-ḥerev ha-mithapekhet ben Tsarfat ṿe-Ashḳenaz ṿe-sikhsukhe Tsarfatim be-Tsarfatim.

Added t.p.: Ha-milchama we-ha-mazor; laguerre franco-allemande et les deux siéges de Paris (1870-71)

The novels, stories and sketches of F. Hopkinson Smith.

[v.1] Laguerre's and Well-worn roads.--[v.2] A white umbrella in Mexico and Other lands.--[v.3] Colonel Carter and other tales of the South.--[v.4] Tom Grogan.--[v.5] Gondola days.--[v.6] Caleb West, master diver.--[v.7] The other fellow and Tile club stories.--[v.8-9] The fortunes of Oliver Horn.--[v.10] The under dog.--[v.11] At close range.--[v.12] The wood fire in no.3.--[v.13] The tides of Barnegat.--[v.14] The veiled lady and other men and women.--[v.15] Colonel Carter's Christmas. The romance of an old-fashioned gentleman.--[v.16-17] Peter.

Recherches sur la géométrie de direction; méthodes de transformation; anticaustiques.

Available on demand as hard copy or computer file from Cornell University Library.

Essai sur le café.

Mode of access: Internet.

Mémoires de la Société des lettres, sciences et arts de Bar-le-Duc.

Ser. 2, v. 1-10 called also v. 11-20; ser. 3, v. 1-10 called also v. 21-30; ser. 4, v. 1-10 called also v. 31-40; ser. 5, v. 1- called also v. 41-