This book examines the basic mathematical properties of solutions to boundary integral equations and details the variational methods for the boundary integral equations arising in elasticity, fluid ...mechanics and acoustic scattering theory.
The Henstock–Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new ...integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock–Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.
•We make a revision of recent generalizations of the Choquet integral that appear in the literature.•We show some of the most relevant theoretical features of these extensions.•We also discuss some ...applications where these extensions have provided good results.
In 2013, Barrenechea et al. used the Choquet integral as an aggregation function in the fuzzy reasoning method (FRM) of fuzzy rule-based classification systems. After that, starting from 2016, new aggregation-like functions generalizing the Choquet integral have appeared in the literature, in particular in the works by Lucca et al. Those generalizations of the Choquet integral, namely CT-integrals (by t-norm T), CF-integrals (by a fusion function F satisfying some specific properties), CC-integrals (by a copula C), CF1F2-integrals (by a pair of fusion functions (F1, F2) under some specific constraints) and their generalization gCF1F2-integrals, achieved excellent results in classification problems. The works by Lucca et al. showed that the aggregation task in a FRM may be performed by either aggregation, pre-aggregation or just ordered directional monotonic functions satisfying some boundary conditions, that is, it is not necessary to have an aggregation function to obtain competitive results in classification. The aim of this paper is to present and discuss such generalizations of the Choquet integral, offering a general panorama of the state of the art, showing the relations and intersections among such five classes of generalizations. First, we present them from a theoretical point of view. Then, we also summarize some applications found in the literature.
Bridging the divide between engineers and physicists for whom fractional calculus facilitates numerous applications, this book concentrates on the Caputo operators, providing a self-contained and ...mathematically rigorous study of their properties and equations.
The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and ...illustrates them with numerous examples.
To derive a less conservative stability criterion via Lyapunov-Krasovskii functional (LKF) method, in previous literature, multiple integral terms are usually introduced into the construction of ...LKFs. This article generalizes the results of previous literature by proposing a polynomial-type LKF, which contains the LKFs with multiple integral terms as special cases. In addition, a Jacobi-Bessel inequality is presented to bound the derivative of such LKF. As a result, an improved stability criterion of time-delay systems is established. Finally, two numerical examples are given to illustrate the effectiveness, and advantages of our method.
No estado do Amazonas, o sistema de educação integral está constituído por dois subsistemas: um, das Escolas Estaduais de Tempo Integral – EETIs e, outro, dos Centros Estaduais de Tempo Integral – ...CETIs. Este artigo resulta de uma pesquisa realizada, em 2014, em três Escolas Estaduais de Tempo Integral – EETIs, com o objetivo de verificar em que condições de trabalho, a práxis da gestão escolar concorre para alcançar os fins instituídos em lei e por quais experiências pedagógicas em educação integral, além disso, quais seus desafios? A metodologia consistiu numa revisão histórica sobre as principais experiências pedagógicas com educação integral no Brasil: tempo integral, educação integral liberal e educação integral politécnica; aplicação de survey multifatorial às escolas da base empírica e análise dos resultados por meio do materialismo histórico. Chegou-se à conclusão: por mais que a gestão escolar tenha apresentado uma tendência a práticas democráticas, dois obstáculos precisam ser superados: o espontaneísmo afetivo e o gerencialismo burocrático. Além disso, aplicar os princípios da LDB pela perspectiva do movimento sindical e pôr em prática uma gestão democrática superadora da educação integral, sob a forma de tempo integral.
In this paper, an improvement is made to an efficient direct method for numerical evaluation of high order singular curved boundary integrals. Then this improved singular integral evaluation method ...is employed to solve the strongly and hypersingular integrals involved in the dual boundary element method (Dual BEM), which combine the use of displacement and traction boundary integral equations to solve crack problems in a single domain formulation. The singular integral evaluation method is carried out based on a parameter plane expansion and radial integral approach, this paper proposed a new strategy for treating the singular radial integral, which plays a vital role in this method. In isoparametric coordinate system, the singular curved boundary integral is mapped into a singular square plane integral in intrinsic coordinates, then the radial integration method (RIM) is employed to transform the singular square plane integral into a regular line integral over the contour of intrinsic square plane and a singular radial integral over the path from source point to the contour of intrinsic square plane. A singularity isolation technique is utilized to divide the singular radial integral into two parts, the regular radial integral can be evaluated normally using Gauss quadrature and the singular radial that can be evaluated analytically by expanding the non-singular part of the integrand function into a power series. Compared with conventional local interpolation approach to deal with the singular radial integral, the newly proposed method has a more rigorous mathematical derivation, and can achieve more stable and precise results. Based on the successful implementation of direct evaluation of singular boundary integrals, Dual BEM is successfully applied to solve two- and three-dimensional elastic crack problems including straight and curved crack paths with continuous or discontinuous elements. Two different approaches, geometrical extrapolation method and J-integral method are used in the evaluation of stress intensity factors. Several numerical examples are given to validate effectiveness of the presented method.
•Based on singularity isolation, an efficient 2D and 3D singular curved boundary integral evaluation method is proposed.•Continuous elements are used in the discretization of straight or curved crack surfaces.
This monograph introduces an investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson's type before ...turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations.
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