Foundational, First-Order, and Second-Order Classification Theory

Both basic and applied research on the construction, implementation, maintenance, and evaluation of classification schemes is called classification theory. If we employ Ritzer’s metatheoretical method of analysis on the over one-hundred year-old body of literature, we can see categories of theory emerge. This paper looks at one particular part of knowledge organization work, namely classification theory, and asks 1) what are the contours of this intellectual space, and, 2) what have we produced in the theoretical reflection on con- structing, implementing, and evaluating classification schemes? The preliminary findings from this work are that classification theory can be separated into three kinds: foundational classification theory, first-order classification theory, and second-order classification theory, each with its own concerns and objects of study.

The Galilean turn in population ecology

The standard mathematical models in population ecology assume that a population's growth rate is a function of its environment. In this paper we investigate an alternative proposal according to which the rate of change of the growth rate is a function of the environment and of environmental change. We focus on the philosophical issues involved in such a fundamental shift in theoretical assumptions, as well as on the explanations the two theories offer for some of the key data such as cyclic populations. We also discuss the relationship between this move in population ecology and a similar move from first-order to second-order differential equations championed by Galileo and Newton in celestial mechanics.

A mechanistic approach to methylene blue sorption on two vegetable wastes: Cork bark and grape stalks

Two vegetable wastes, cork bark and grape stalks, were investigated for the removal of methylene blue from aqueous solution. The effects of contact time, dye concentration, pH, and temperature on sorption were studied relative to adsorption on a commercially-activated carbon. The highest adsorption yield was obtained within the pH range 5 to 10 for grape stalks and 7 to 10 for cork bark. The sorption kinetics of dye onto activated carbon and grape stalks was very fast. Kinetics data were fitted to the pseudo-first and second order kinetic equations, and the values of the pseudo-second-order initial rate constants were found to be 1.69 mg g-1 min-1 for activated carbon, 2.24 mg g-1 min-1 for grape stalks, and 0.90 mg g-1 min-1 for cork bark. Langmuir maximum sorption capacities for activated carbon, grape stalks, and cork bark for methylene blue estimated by the Orthogonal Distance Regression method (ODR) were 157.5 mg g-1, 105.6 mg g-1, and 30.52 mg g-1, respectively. FTIR spectra indicated that carboxylic groups and lignin play a significant role in the sorption of methylene blue. Electrostatic forces, n-p interactions, cation-p, and p-p stacking interactions contribute to methylene blue sorption onto grape stalks and cork bark. Grape stalks can be considered an efficient biosorbent and as a viable alternative to activated carbon and ion-exchange resins for the removal of methylene blue

A comprehensive investigation of the synthesis of prebiotic galactooligosaccharides by whole cells of Bifidobacterium bifidum NCIMB 41171

The synthesis of galactooligosaccharides (GOS) by whole cells of Bifidobacterium bifidum NCIMB 41171 was investigated by developing a set of mathematical models. These were second order polynomial equations, which described responses related to the production of GOS constituents, the selectivity of lactose conversion into GOS, and the relative composition of the produced GOS mixture, as a function of the amount of biocatalyst, temperature, initial lactose concentration, and time. The synthesis reactions were followed for up to 36 h. Samples were withdrawn every 4 h, tested for β-galactosidase activity, and analysed for their carbohydrate content. GOS synthesis was well explained by the models, which were all significant (P < 0.001). The GOS yield increased as temperature increased from 40 °C to 60 °C, as transgalactosylation became more pronounced compared to hydrolysis. The relative composition of GOS produced changed significantly with the initial lactose concentration (P < 0.001); higher ratios of tri-, tetra-, and penta-galactooligosaccharides to transgalactosylated disaccharides were obtained as lactose concentration increased. Time was a critical factor, as a balanced state between GOS synthesis and hydrolysis was roughly attained in most cases between 12 and 20 h, and was followed by more pronounced GOS hydrolysis than synthesis.

Teorema de Sturm e zeros de polinômios ortogonais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelos descritos por equações diferenciais ordinárias

Pós-graduação em Matemática Universitária - IGCE

Soluções quase automórficas para equações diferenciais abstratas de segunda ordem

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

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The Feynman-Kac formula and applications to PDEs

The thesis presents a probabilistic approach to the theory of semigroups of operators, with particular attention to the Markov and Feller semigroups. The first goal of this work is the proof of the fundamental Feynman-Kac formula, which gives the solution of certain parabolic Cauchy problems, in terms of the expected value of the initial condition computed at the associated stochastic diffusion processes. The second target is the characterization of the principal eigenvalue of the generator of a semigroup with Markov transition probability function and of second order elliptic operators with real coefficients not necessarily self-adjoint. The thesis is divided into three chapters. In the first chapter we study the Brownian motion and some of its main properties, the stochastic processes, the stochastic integral and the Itô formula in order to finally arrive, in the last section, at the proof of the Feynman-Kac formula. The second chapter is devoted to the probabilistic approach to the semigroups theory and it is here that we introduce Markov and Feller semigroups. Special emphasis is given to the Feller semigroup associated with the Brownian motion. The third and last chapter is divided into two sections. In the first one we present the abstract characterization of the principal eigenvalue of the infinitesimal generator of a semigroup of operators acting on continuous functions over a compact metric space. In the second section this approach is used to study the principal eigenvalue of elliptic partial differential operators with real coefficients. At the end, in the appendix, we gather some of the technical results used in the thesis in more details. Appendix A is devoted to the Sion minimax theorem, while in appendix B we prove the Chernoff product formula for not necessarily self-adjoint operators.

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual o-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving nonclassical damping is proposed. An example of modal control sucessfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving non-classical damping is proposed. An example of modal control successfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.

On the suboptimality of the p-version interior penalty discontinuous Galerkin method

We address the question of the rates of convergence of the p-version interior penalty discontinuous Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with respect to the polynomial degree (in the Hilbertian Sobolev space setting). An example for which the suboptimal rate of convergence with respect to the polynomial degree is both proven theoretically and validated in practice through numerical experiments is presented. Moreover, the performance of p- IPDG on the related problem of p-approximation of corner singularities is assessed both theoretically and numerically, witnessing an almost doubling of the convergence rate of the p-IPDG method.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Some experiments with high order compact methods using a computer algebra software - Part I

We consider a procedure for obtaining a compact fourth order method to the steady 2D Navier-Stokes equations in the streamfunction formulation using the computer algebra system Maple. The resulting code is short and from it we obtain the Fortran program for the method. To test the procedure we have solved many cavity-type problems which include one with an analytical solution and the results are compared with results obtained by second order central differences to moderate Reynolds numbers. (c) 2005 Elsevier B.V. All rights reserved.