Hermite Calculus

We develop a new method of umbral nature to treat blocks of Her mite and of Hermite like poly- nomials as independent algebraic quantities. The Calculus we propose allows the formulation of a number of ”practical rules” allowing significant simplific ations in computational problem

Integrals of Special Functions and Umbral Methods

We derive integrals of combination of Gauss and Bessel functions, by the use of umbral techniques. We show that the method allows the possibility of pursuing new and apparently fruitful avenues in the theory of special functions, displaying interesting links with the theory and the formalism of integral transforms

Integrals of Special Functions and Umbral Methods

AbstractWe derive integrals of combination of Gauss and Bessel functions, by the use of umbral techniques. We show that the method allows the possibility of pursuing new and apparently fruitful avenues in the theory of special functions, displaying interesting links with the theory and the formalism of integral transforms

Q-functions and distributions, operational and umbral methods

The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logical context. Methods of Umbral and operational calculus have been embedded in a powerful and efficient analytical tool, which will be applied to the study of the properties of distributions such as Tsallis, Weibull and Student’s. We state that they can be viewed as standard Gaussian distributions and we take advantage of the relevant properties to infer those of the aforementioned distributions

Umbral methods and harmonic numbers

The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals

Primary Effusion Lymphoma in a HIV Infected Patient

O linfoma primário das cavidades é um subtipo de linfoma não-Hodgkin (LNH), de ocorrência rara, prognóstico muito reservado, mais frequentemente descrito em indivíduos imunodeprimidos, em particular no contexto de infecção pelo vírus da imunodeficiência humana (VIH), no qual as células malignas proliferam exclusivamente nas cavidades serosas e que está associado ao vírus herpes humano tipo 8 (VHH8). Os autores apresentam o caso de um doente com infecção VIH, internado por febre e queixas constitucionais e que desenvolveu, enquanto decorria estudo etiológico da síndrome febril, ascite volumosa e, ainda, derrame pleural direito e derrame pericárdico. O líquido ascítico mostrou a presença de células grandes linfóides com fenótipo não B e não T. Não foram evidenciadas massas tumorais, linfadenopatias ou envolvimento da medula óssea. O doente morreu 41 dias após o diagnóstico, sem ter iniciado quimioterapia. Ainda que não tenha sido possível a demonstração de infecção pelo VHH-8 nas células linfóides, os dados clínicos, citológicos e imunofenotípicos apontam para um diagnóstico altamente provável de linfoma primário das cavidades

Sheffer and Non-Sheffer Polynomial Families

By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials

Phase Transitions And Spatially Ordered Counterion Association In Ionic-lipid Membranes: A Statistical Model.

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types--each one associated, respectively, with the polar-headgroup and the acyl-chain states--which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.8403190

The supernova-regulated ISM. II. The mean magnetic field

The origin and structure of the magnetic fields in the interstellar medium of spiral galaxies is investigated with 3D, non-ideal, compressible MHD simulations, including stratification in the galactic gravity field, differential rotation and radiative cooling. A rectangular domain, 1x1x2 kpc^{3} in size, spans both sides of the galactic mid-plane. Supernova explosions drive transonic turbulence. A seed magnetic field grows exponentially to reach a statistically steady state within 1.6 Gyr. Following Germano (1992) we use volume averaging with a Gaussian kernel to separate magnetic field into a mean field and fluctuations. Such averaging does not satisfy all Reynolds rules, yet allows a formulation of mean-field theory. The mean field thus obtained varies in both space and time. Growth rates differ for the mean-field and fluctuating field and there is clear scale separation between the two elements, whose integral scales are about 0.7 kpc and 0.3 kpc, respectively.Comment: 5 pages, 10 figures, submitted to Monthly Notices Letter