Perturbations on the antidiagonals of Hankel matrices

Given a strongly regular Hankel matrix, and its associated sequence of moments which defines a quasi-definite moment linear functional, we study the perturbation of a fixed moment, i.e., a perturbation of one antidiagonal of the Hankel matrix. We define a linear functional whose action results in such a perturbation and establish necessary and sufficient conditions in order to preserve the quasi-definite character. A relation between the corresponding sequences of orthogonal polynomials is obtained, as well as the asymptotic behavior of their zeros. We also study the invariance of the Laguerre-Hahn class of linear functionals under such perturbation, and determine its relation with the so-called canonical linear spectral transformations. © 2013 Elsevier Ltd. All rights reserved.

A Characterization of L-orthogonal Polynomials from Three Term Recurrence Relations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function

This paper presents a new method for producing a functional-structural plant model that simulates response to different growth conditions, yet does not require detailed knowledge of underlying physiology. The example used to present this method is the modelling of the mountain birch tree. This new functional-structural modelling approach is based on linking an L-system representation of the dynamic structure of the plant with a canonical mathematical model of plant function. Growth indicated by the canonical model is allocated to the structural model according to probabilistic growth rules, such as rules for the placement and length of new shoots, which were derived from an analysis of architectural data. The main advantage of the approach is that it is relatively simple compared to the prevalent process-based functional-structural plant models and does not require a detailed understanding of underlying physiological processes, yet it is able to capture important aspects of plant function and adaptability, unlike simple empirical models. This approach, combining canonical modelling, architectural analysis and L-systems, thus fills the important role of providing an intermediate level of abstraction between the two extremes of deeply mechanistic process-based modelling and purely empirical modelling. We also investigated the relative importance of various aspects of this integrated modelling approach by analysing the sensitivity of the standard birch model to a number of variations in its parameters, functions and algorithms. The results show that using light as the sole factor determining the structural location of new growth gives satisfactory results. Including the influence of additional regulating factors made little difference to global characteristics of the emergent architecture. Changing the form of the probability functions and using alternative methods for choosing the sites of new growth also had little effect. (c) 2004 Elsevier B.V. All rights reserved.

Theory and Analysis of Classic Heavy Metal Harmony

This thesis explores melodic and harmonic features of heavy metal, and while doing so, explores various methods of music analysis; their applicability and limitations regarding the study of heavy metal music. The study is built on three general hypotheses according to which 1) acoustic characteristics play a significant role for chord constructing in heavy metal, 2) heavy metal has strong ties and similarities with other Western musical styles, and 3) theories and analytical methods of Western art music may be applied to heavy metal. It seems evident that in heavy metal some chord structures appear far more frequently than others. It is suggested here that the fundamental reason for this is the use of guitar distortion effect. Subsequently, theories as to how and under what principles heavy metal is constructed need to be put under discussion; analytical models regarding the classification of consonance and dissonance and chord categorization are here revised to meet the common practices of this music. It is evident that heavy metal is not an isolated style of music; it is seen here as a cultural fusion of various musical styles. Moreover, it is suggested that the theoretical background to the construction of Western music and its analysis can offer invaluable insights to heavy metal. However, the analytical methods need to be reformed to some extent to meet the characteristics of the music. This reformation includes an accommodation of linear and functional theories that has been found rather rarely in music theory and musicology.

VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.

Semigrupos de operadores lineares e equações diferenciais em espaços de Banach

Pós-graduação em Matemática Universitária - IGCE

Semigrupos de operadores lineares e aplicações

Pós-graduação em Matemática Universitária - IGCE

Análise estrutural de juntas rebitadas de uso aeronaútico

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Pore structure and column efficiency of silica monoliths in high performance liquid chromatography (HPLC)

Five different methods were critically examined to characterize the pore structure of the silica monoliths. The mesopore characterization was performed using: a) the classical BJH method of nitrogen sorption data, which showed overestimated values in the mesopore distribution and was improved by using the NLDFT method, b) the ISEC method implementing the PPM and PNM models, which were especially developed for monolithic silicas, that contrary to the particulate supports, demonstrate the two inflection points in the ISEC curve, enabling the calculation of pore connectivity, a measure for the mass transfer kinetics in the mesopore network, c) the mercury porosimetry using a new recommended mercury contact angle values. rnThe results of the characterization of mesopores of monolithic silica columns by the three methods indicated that all methods were useful with respect to the pore size distribution by volume, but only the ISEC method with implemented PPM and PNM models gave the average pore size and distribution based on the number average and the pore connectivity values.rnThe characterization of the flow-through pore was performed by two different methods: a) the mercury porosimetry, which was used not only for average flow-through pore value estimation, but also the assessment of entrapment. It was found that the mass transfer from the flow-through pores to mesopores was not hindered in case of small sized flow-through pores with a narrow distribution, b) the liquid penetration where the average flow-through pore values were obtained via existing equations and improved by the additional methods developed according to Hagen-Poiseuille rules. The result was that not the flow-through pore size influences the column bock pressure, but the surface area to volume ratio of silica skeleton is most decisive. Thus the monolith with lowest ratio values will be the most permeable. rnThe flow-through pore characterization results obtained by mercury porosimetry and liquid permeability were compared with the ones from imaging and image analysis. All named methods enable a reliable characterization of the flow-through pore diameters for the monolithic silica columns, but special care should be taken about the chosen theoretical model.rnThe measured pore characterization parameters were then linked with the mass transfer properties of monolithic silica columns. As indicated by the ISEC results, no restrictions in mass transfer resistance were noticed in mesopores due to their high connectivity. The mercury porosimetry results also gave evidence that no restrictions occur for mass transfer from flow-through pores to mesopores in the small scaled silica monoliths with narrow distribution. rnThe prediction of the optimum regimes of the pore structural parameters for the given target parameters in HPLC separations was performed. It was found that a low mass transfer resistance in the mesopore volume is achieved when the nominal diameter of the number average size distribution of the mesopores is appr. an order of magnitude larger that the molecular radius of the analyte. The effective diffusion coefficient of an analyte molecule in the mesopore volume is strongly dependent on the value of the nominal pore diameter of the number averaged pore size distribution. The mesopore size has to be adapted to the molecular size of the analyte, in particular for peptides and proteins. rnThe study on flow-through pores of silica monoliths demonstrated that the surface to volume of the skeletons ratio and external porosity are decisive for the column efficiency. The latter is independent from the flow-through pore diameter. The flow-through pore characteristics by direct and indirect approaches were assessed and theoretical column efficiency curves were derived. The study showed that next to the surface to volume ratio, the total porosity and its distribution of the flow-through pores and mesopores have a substantial effect on the column plate number, especially as the extent of adsorption increases. The column efficiency is increasing with decreasing flow through pore diameter, decreasing with external porosity, and increasing with total porosity. Though this tendency has a limit due to heterogeneity of the studied monolithic samples. We found that the maximum efficiency of the studied monolithic research columns could be reached at a skeleton diameter of ~ 0.5 µm. Furthermore when the intention is to maximize the column efficiency, more homogeneous monoliths should be prepared.rn

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Non-centrosymmetric crystals of new N-benzylideneaniline derivatives as potential materials for non-linear optics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A linear O(N) model: a functional renormalization group approach for flat and curved space

In questa tesi sono state applicate le tecniche del gruppo di rinormalizzazione funzionale allo studio della teoria quantistica di campo scalare con simmetria O(N) sia in uno spaziotempo piatto (Euclideo) che nel caso di accoppiamento ad un campo gravitazionale nel paradigma dell'asymptotic safety. Nel primo capitolo vengono esposti in breve alcuni concetti basilari della teoria dei campi in uno spazio euclideo a dimensione arbitraria. Nel secondo capitolo si discute estensivamente il metodo di rinormalizzazione funzionale ideato da Wetterich e si fornisce un primo semplice esempio di applicazione, il modello scalare. Nel terzo capitolo è stato studiato in dettaglio il modello O(N) in uno spaziotempo piatto, ricavando analiticamente le equazioni di evoluzione delle quantità rilevanti del modello. Quindi ci si è specializzati sul caso N infinito. Nel quarto capitolo viene iniziata l'analisi delle equazioni di punto fisso nel limite N infinito, a partire dal caso di dimensione anomala nulla e rinormalizzazione della funzione d'onda costante (approssimazione LPA), già studiato in letteratura. Viene poi considerato il caso NLO nella derivative expansion. Nel quinto capitolo si è introdotto l'accoppiamento non minimale con un campo gravitazionale, la cui natura quantistica è considerata a livello di QFT secondo il paradigma di rinormalizzabilità dell'asymptotic safety. Per questo modello si sono ricavate le equazioni di punto fisso per le principali osservabili e se ne è studiato il comportamento per diversi valori di N.

A Functional-Based Distribution Diagnostic for a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed modesl and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. Linear functions or the resulting "rotated" residuals are used to construct an empirical cumulative distribution function (ECDF), whose stochastic limit is characterized. We describe a resampling technique that serves as a computationally efficient parametric bootstrap for generating representatives of the stochastic limit of the ECDF. Through functionals, such representatives are used to construct global tests for the hypothesis of normal margional errors. In addition, we demonstrate that the ECDF of the predicted random effects, as described by Lange and Ryan (1989), can be formulated as a special case of our approach. Thus, our method supports both omnibus and directed tests. Our method works well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series).