Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

LIPSCHITZ CLASSIFICATION OF FUNCTIONS ON A HOLDER TRIANGLE

The problem of semialgebraic Lipschitz classification of quasihomogeneous polynomials on a Holder triangle is studied. For this problem, the ""moduli"" are described completely in certain combinatorial terms.

On S-asymptotically omega-periodic functions on Banach spaces and applications

This paper is devoted to the study of the class of continuous and bounded functions f : [0, infinity] -> X for which exists omega > 0 such that lim(t ->infinity) (f (t + omega) - f (t)) = 0 (in the sequel called S-asymptotically omega-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically omega-periodic functions. We also study the existence of S-asymptotically omega-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

A New Family of Distance Functions for Perceptual Similarity Retrieval of Medical Images

A long-standing challenge of content-based image retrieval (CBIR) systems is the definition of a suitable distance function to measure the similarity between images in an application context which complies with the human perception of similarity. In this paper, we present a new family of distance functions, called attribute concurrence influence distances (AID), which serve to retrieve images by similarity. These distances address an important aspect of the psychophysical notion of similarity in comparisons of images: the effect of concurrent variations in the values of different image attributes. The AID functions allow for comparisons of feature vectors by choosing one of two parameterized expressions: one targeting weak attribute concurrence influence and the other for strong concurrence influence. This paper presents the mathematical definition and implementation of the AID family for a two-dimensional feature space and its extension to any dimension. The composition of the AID family with L (p) distance family is considered to propose a procedure to determine the best distance for a specific application. Experimental results involving several sets of medical images demonstrate that, taking as reference the perception of the specialist in the field (radiologist), the AID functions perform better than the general distance functions commonly used in CBIR.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

Exact time-dependent solutions for a self-regulating gene

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

UNIQUENESS AND NONUNIQUENESS RESULTS FOR A CERTAIN CLASS OF ALMOST PERIODIC DISTRIBUTIONS

We consider distributions u is an element of S'(R) of the form u(t) = Sigma(n is an element of N) a(n)e(i lambda nt), where (a(n))(n is an element of N) subset of C and Lambda = (lambda n)(n is an element of N) subset of R have the following properties: (a(n))(n is an element of N) is an element of s', that is, there is a q is an element of N such that (n(-q) a(n))(n is an element of N) is an element of l(1); for the real sequence., there are n(0) is an element of N, C > 0, and alpha > 0 such that n >= n(0) double right arrow vertical bar lambda(n)vertical bar >= Cn(alpha). Let I(epsilon) subset of R be an interval of length epsilon. We prove that for given Lambda, (1) if Lambda = O(n(alpha)) with alpha < 1, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (2) if Lambda = O(n) is uniformly discrete, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (3) if alpha > 1 and. is uniformly discrete, then for all epsilon > 0, u vertical bar I(epsilon) = 0 double right arrow u = 0. Since distributions of the above mentioned form are very common in engineering, as in the case of the modeling of ocean waves, signal processing, and vibrations of beams, plates, and shells, those uniqueness and nonuniqueness results have important consequences for identification problems in the applied sciences. We show an identification method and close this article with a simple example to show that the recovery of geometrical imperfections in a cylindrical shell is possible from a measurement of its dynamics.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Active Dendrites Enhance Neuronal Dynamic Range

Since the first experimental evidences of active conductances in dendrites, most neurons have been shown to exhibit dendritic excitability through the expression of a variety of voltage-gated ion channels. However, despite experimental and theoretical efforts undertaken in the past decades, the role of this excitability for some kind of dendritic computation has remained elusive. Here we show that, owing to very general properties of excitable media, the average output of a model of an active dendritic tree is a highly non-linear function of its afferent rate, attaining extremely large dynamic ranges (above 50 dB). Moreover, the model yields double-sigmoid response functions as experimentally observed in retinal ganglion cells. We claim that enhancement of dynamic range is the primary functional role of active dendritic conductances. We predict that neurons with larger dendritic trees should have larger dynamic range and that blocking of active conductances should lead to a decrease in dynamic range.

Simplified Mathematical Model for an Anaerobic Sequencing Batch Biofilm Reactor Treating Lipid-Rich Wastewater Subject to Rising Organic Loading Rates

This study proposes a simplified mathematical model to describe the processes occurring in an anaerobic sequencing batch biofilm reactor (ASBBR) treating lipid-rich wastewater. The reactor, subjected to rising organic loading rates, contained biomass immobilized cubic polyurethane foam matrices, and was operated at 32 degrees C +/- 2 degrees C, using 24-h batch cycles. In the adaptation period, the reactor was fed with synthetic substrate for 46 days and was operated without agitation. Whereas agitation was raised to 500 rpm, the organic loading rate (OLR) rose from 0.3 g chemical oxygen demand (COD) . L(-1) . day(-1) to 1.2 g COD . L(-1) . day(-1). The ASBBR was fed fat-rich wastewater (dairy wastewater), in an operation period lasting for 116 days, during which four operational conditions (OCs) were tested: 1.1 +/- 0.2 g COD . L(-1) . day(-1) (OC1), 4.5 +/- 0.4 g COD . L(-1) . day(-1) (OC2), 8.0 +/- 0.8 g COD . L(-1) . day(-1) (OC3), and 12.1 +/- 2.4 g COD . L(-1) . day(-1) (OC4). The bicarbonate alkalinity (BA)/COD supplementation ratio was 1:1 at OC1, 1:2 at OC2, and 1:3 at OC3 and OC4. Total COD removal efficiencies were higher than 90%, with a constant production of bicarbonate alkalinity, in all OCs tested. After the process reached stability, temporal profiles of substrate consumption were obtained. Based on these experimental data a simplified first-order model was fit, making possible the inference of kinetic parameters. A simplified mathematical model correlating soluble COD with volatile fatty acids (VFA) was also proposed, and through it the consumption rates of intermediate products as propionic and acetic acid were inferred. Results showed that the microbial consortium worked properly and high efficiencies were obtained, even with high initial substrate concentrations, which led to the accumulation of intermediate metabolites and caused low specific consumption rates.

Avaliação de modelos geoidais gravimétricos determinados com funções covariâncias planas e esféricas (Estudo de Caso: Estado de São Paulo e adjacências)

The least squares collocation is a mathematical technique which is used in Geodesy for representation of the Earth's anomalous gravity field from heterogeneous data in type and precision. The use of this technique in the representation of the gravity field requires the statistical characteristics of data through covariance function. The covariances reflect the behavior of the gravity field, in magnitude and roughness. From the statistical point of view, the covariance function represents the statistical dependence among quantities of the gravity field at distinct points or, in other words, shows the tendency to have the same magnitude and the same sign. The determination of the covariance functions is necessary either to describe the behavior of the gravity field or to evaluate its functionals. This paper aims at presenting the results of a study on the plane and spherical covariance functions in determining gravimetric geoid models.