Discrete commutative difference operator theory

The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis

Efficient implementation of discrete Pascal transform using difference operators

An alternative way is provided to define the discrete Pascal transform using difference operators to reveal the fundamental concept of the transform, in both one- and two-dimensional cases, which is extended to cover non-square two-dimensional applications. Efficient modularised implementations are proposed.

Coarse-grid higher order finite-difference time-domain algorithm with low dispersion errors

Higher order (2,4) FDTD schemes used for numerical solutions of Maxwell`s equations are focused on diminishing the truncation errors caused by the Taylor series expansion of the spatial derivatives. These schemes use a larger computational stencil, which generally makes use of the two constant coefficients, C-1 and C-2, for the four-point central-difference operators. In this paper we propose a novel way to diminish these truncation errors, in order to obtain more accurate numerical solutions of Maxwell`s equations. For such purpose, we present a method to individually optimize the pair of coefficients, C-1 and C-2, based on any desired grid size resolution and size of time step. Particularly, we are interested in using coarser grid discretizations to be able to simulate electrically large domains. The results of our optimization algorithm show a significant reduction in dispersion error and numerical anisotropy for all modeled grid size resolutions. Numerical simulations of free-space propagation verifies the very promising theoretical results. The model is also shown to perform well in more complex, realistic scenarios.

On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Quantum current algebra for the AdS(5) x S(5) superstring

The sigma model describing the dynamics of the superstring in the AdS(5) x S(5) background can be constructed using the coset PSU(2, 2 vertical bar 4)/SO(4, 1) x SO(5). A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE`s is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE`s. We also compute the OPE`s of the left invariant currents with the energy momentum tensor at tree level and one loop.

Equações de diferenças: aplicações no ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Demo: Using RapidMiner for Text Mining

In this demo the basic text mining technologies by using RapidMining have been reviewed. RapidMining basic characteristics and operators of text mining have been described. Text mining example by using Navie Bayes algorithm and process modeling have been revealed.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

Education and knowledge: basic pillars of changing production patterns with social equity

Includes bibliography

Norm and difference : Stone Age dietary practice in the Baltic region

Stone Age research on Northern Europe frequently makes gross generalizations about the Mesolithic and Neolithic, although we still lack much basic knowledge on how the people lived. The transition from the Mesolithic to the Neolithic in Europe has been described as a radical shift from an economy dominated by marine resources to one solely dependent on farming. Both the occurrence and the geographical extent of such a drastic shift can be questioned, however. It is therefore important to start out at a more detailed level of evidence in order to present the overall picture, and to account for the variability even in such regional or chronological overviews. Fifteen Stone Age sites were included in this study, ranging chronologically from the Early Mesolithic to the Middle or Late Neolithic, c. 8300–2500 BC, and stretching geographically from the westernmost coast of Sweden to the easternmost part of Latvia within the confines of latitudes 55–59° N. The most prominent sites in terms of the number of human and faunal samples analysed are Zvejnieki, Västerbjers and Skateholm I–II. Human and faunal skeletal remains were subjected to stable carbon and nitrogen isotope analysis to study diet and ecology at the sites. Stable isotope analyses of human remains provide quantitative information on the relative importance of various food sources, an important addition to the qualitative data supplied by certain artefacts and structures or by faunal or botanical remains. A vast number of new radiocarbon dates were also obtained. In conclusion, a rich diversity in Stone Age dietary practice in the Baltic Region was demonstrated. Evidence ranging from the Early Mesolithic to the Late Neolithic show that neither chronology nor location alone can account for this variety, but that there are inevitably cultural factors as well. Food habits are culturally governed, and therefore we cannot automatically assume that people at similar sites will have the same diet. Stable isotope studies are very important here, since they tell us what people actually consumed, not only what was available, or what one single meal contained. We should not be deceived in inferring diet from ritually deposited remains, since things that were mentally important were not always important in daily life. Thus, although a ritual and symbolic norm may emphasize certain food categories, these may in fact contribute very little to the diet. By the progress of analysis of intra-individual variation, new data on life history changes have been produced, revealing mobility patterns, breastfeeding behaviour and certain dietary transitions. The inclusion of faunal data has proved invaluable for understanding the stable isotope ecology of a site, and thereby improve the precision of the interpretations of human stable isotope data. The special case of dogs, though, demonstrates that these animals are not useful for inferring human diet, since, due to the number of roles they possess in human society, dogs could deviate significantly from humans in their diet, and in several cases have been proved to do so. When evaluating radiocarbon data derived from human and animal remains from the Pitted-Ware site of Västerbjers on Gotland, the importance of establishing the stable isotope ecology of the site before making deductions on reservoir effects was further demonstrated. The main aim of this thesis has been to demonstrate the variation and diversity in human practices, challenging the view of a “monolithic” Stone Age. By looking at individuals and not only at populations, the whole range of human behaviour has been accounted for, also revealing discrepancies between norm and practice, which are frequently visible both in the archaeological record and in present-day human behaviour.