Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

Limit between stages I and II of a seed imbibition curve

O conhecimento das fases de absorção de água das diferentes espécies é importante em pesquisas objetivando melhorar a qualidade das sementes, utilizando tratamentos como condicionamento osmótico, pré-hidratação e uso de bioreguladores. O objetivo do presente trabalho foi estabelecer uma metodologia para determinar o limite entre a primeira e a segunda fase do processo, considerando o modelo W = f(t) - (a - w0)exp(-kt), utilizando testes estatísticos. O limite entre as duas primeiras fases do processo de absorção de água pelas sementes, foi determinado utilizando-se a distribuição assintótica de uma função de estimadores. O ponto a partir do qual esta diferença (W*) deixa de ser significativa foi determinado utilizando-se o teste estatístico T de Student. Para os dados utilizados como exemplo, tem-se o modelo ou =(0,434 + 0,00162 t) - (0,434 - w o)exp(-0,121 t), com r² = 0,98 e W* = (0,434 - w o) exp(-0,121 t). O valor de t encontrado (27,2 horas) é menor do que o valor determinado, considerando-se como critério para mudança de fase a diferença de 1% entre a assíntota e o valor estimado pelo modelo ajustado. Essa diferença de duas horas corresponde a 0,28% de água absorvida.

GROUND-STATE-ENERGY OF SINGULAR POTENTIALS

It is shown that for singular potentials of the form lambda/r(alpha),the asymptotic form of the wave function both at r --> infinity and r --> 0 plays an important role. Using a wave function having the correct asymptotic behavior for the potential lambda/r(4), it is, shown that it gives the exact ground-state energy for this potential when lambda --> 0, as given earlier by Harrell [Ann. Phys. (NY) 105, 379 (1977)]. For other values of the coupling parameter X, a trial basis;set of wave functions which also satisfy the correct boundary conditions at r --> infinity and r --> 0 are used to find the ground-state energy of the singular potential lambda/r(4) It is shown that the obtained eigenvalues are in excellent agreement with their exact ones for a very large range of lambda values.

Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Some results on stability of retarded functional differential equations using dichotomic map techniques

This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation x′(t) = -b(t)x(t - r) and of its nonlinear generalization x′(t) = b(t) f (x(t - r)) are established. © 1998 Kluwer Academic Publishers.

Electrodynamics of helium with retardation and self-interaction effects

We show that an extra constant of motion with an analytic form can exist in the neighborhood of some discrete circular orbits of helium when one includes retardation and self-interaction effects. The energies of these discrete stable circular orbits are in the correct atomic magnitude. The highest frequency in the stable manifold of one such orbit agrees with the highest frequency sharp line of parahelium to within 2%. The generic term of the frequency in the stable manifold to higher orbits is also in agreement with the asymptotic form of quantum mechanics for helium.

Nonmodal energetics of electromagnetic drift waves

The linear properties of an electromagnetic drift-wave model are examined. The linear system is non-normal in that its eigenvectors are not orthogonal with respect to the energy inner product. The non-normality of the linear evolution operator can lead to enhanced finite-time growth rates compared to modal growth rates. Previous work with an electrostatic drift-wave model found that nonmodal behavior is important in the hydrodynamic limit. Here, similar behavior is seen in the hydrodynamic regime even with the addition of magnetic fluctuations. However, unlike the results for the electrostatic drift-wave model, nonmodal behavior is also important in the adiabatic regime with moderate to strong magnetic fluctuations. © 2000 American Institute of Physics.

Effects of long-term cyclosporin therapy on gingiva of rats--analysis by stereological and biochemical estimation.

Cyclosporin A (CsA) is used as an immunosuppressive agent and its prominent side effect is the induction of gingival overgrowth, which remains a significant problem. The risk factors appraised include the duration of treatment. However, there are no stereological and biochemical studies exploring the effects of long-term CsA therapy on gingival tissue. The purpose of the present study was to investigate the level of TGF-beta1 in saliva and describe the densities of fibroblasts and collagen fibers in the gingival tissue of rats treated with CsA for long periods. Rats were treated for 60, 120, 180 and 240 days with a daily subcutaneous injection of 10 mg/kg of body weight of CsA. At the end of the experimental periods, saliva was collected for the determination of TGF-beta1 levels. After histological processing, the oral epithelium and the connective tissue area were measured as well as the volume densities of fibroblasts (Vf) and collagen fibers (Vcf). After 60 and 120 days of CsA treatment, there was a significant increase in Vf and Vcf as well as a significant increase in TGF-beta1 levels. After 180 and 240 days, reduction in the gingival overgrowth associated with significant decreases in the level of TGF-beta1, and also decreased Vf and Vcf, were observed. The data presented here suggest that after long-term therapy, a decrease in TGF-beta1 levels occurs, which might contribute to an increase in the proteolytic activity of fibroblasts in the gingiva, favoring the normality of extracellular matrix synthesis.

Effects of the density, aviary type, breed, and age on the behaviors of laying hens kept in cages

An experiment was carried out in order to investigate the behaviors of laying hens due to the environmental factors of: density inside of the cage, aviary type, breed, and age. The experiment was configured as a factorial 4x2x2x2 study, with treatments being four different ages, two different breeds, two different cage densities, and two different aviaries. The birds' behaviors were recorded using video cameras installed in the cages, using samples of 15 minutes recorded from 12 PM to 4 PM. The observed behaviors, frequency and duration of behaviors (measured in seconds) were identified and noted related to each bird. The study was initiated in March 2007, during four non-consecutive weeks. The observed behaviors were: opening wings, stretching, threatening, ruffling feathers, drinking water, aggressive pecking, eating, running, lying down, stretching head out of the cage, preening, mounting, prostrating, and doing nothing (inactivity). Due to the non-normality of the data recorded, the Kruskal-Wallis statistical test of the MINITAB Statistical Software® was used to compare the medians of the variables. For breed factor, only the durations of the eating presented significant differences (p-value< 0.05). For cage density, there was a significant median difference (p-value< 0.05) for almost all behaviors observed. The average length of time of behaviors was higher for the lowest cage density. However, the frequency of behaviors was lmerfor the lowest cage density. The frequency of the behaviors to preen feathers, to lie down, to drink water and to stretch the head were higher in the aviary, where the groups of birds were smaller. The observed behaviors were particularly affected by experimental factors cage density, and aviary type, which directly affects the available space for each bird.

Stability of the null solution of the equation ẋ(t) = -a(t)x(t) + b(t)x([t])

The asymptotic stability of the null solution of the equation ẋ(t) = -a(t)x(t)+b(t)x([t]) with argument [t], where [t] designates the greatest integer function, is studied by means of dichotomic maps. © 2010 Academic Publications.

On stability of differential equations with piecewise constant argument using dichotomic maps

This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.

Spin and pseudospin symmetries of the Dirac equation with confining central potentials

We derive the node structure of the radial functions which are solutions of the Dirac equation with scalar S and vector V confining central potentials, in the conditions of exact spin or pseudospin symmetry, i.e., when one has V=±S+C, where C is a constant. We show that the node structure for exact spin symmetry is the same as the one for central potentials which go to zero at infinity but for exact pseudospin symmetry the structure is reversed. We obtain the important result that it is possible to have positive energy bound solutions in exact pseudospin symmetry conditions for confining potentials of any shape, including naturally those used in hadron physics, from nuclear to quark models. Since this does not occur for potentials going to zero at large distances, which are used in nuclear relativistic mean-field potentials or in the atomic nucleus, this shows the decisive importance of the asymptotic behavior of the scalar and vector central potentials on the onset of pseudospin symmetry and on the node structure of the radial functions. Finally, we show that these results are still valid for negative energy bound solutions for antifermions. © 2013 American Physical Society.

The effects of different styles of musical auditory stimulation on cardiac autonomic regulation in healthy women

The literature investigated the effects of chronic baroque music auditory stimulation on the cardiovascular system. However, it lacks in the literature the acute effects of different styles of music on cardiac autonomic regulation. To evaluate the acute effects of baroque and heavy metal music on heart rate variability (HRV) in women. The study was performed in 21 healthy women between 18 and 30 years old. We excluded persons with previous experience with music instrument and those who had affinity with the song styles. All procedures were performed in the same sound-proof room. We analyzed HRV in the time (standard deviation of normal-to-normal respiratory rate (RR) intervals, root-mean square of differences between adjacent normal RR intervals in a time interval, and the percentage of adjacent RR intervals with a difference of duration greater than 50 ms) and frequency (low frequency [LF], high frequency [HF], and LF/HF ratio) domains. HRV was recorded at rest for 10 min. Subsequently they were exposed to baroque or heavy metal music for 5 min through an earphone. After the first music exposure they remained at rest for more 5 min and them they were exposed again to baroque or heavy metal music. The sequence of songs was randomized for each individual. The power analysis provided a minimal number of 18 subjects. Shapiro-Wilk to verify normality of data and analysis of variance for repeated measures followed by the Bonferroni test for parametric variables and Friedman's followed by the Dunn's post-test for non-parametric distributions. During the analysis of the time-domain indices were not changed. In the frequency-domain analysis, the LF in absolute units was reduced during the heavy metal music stimulation compared to control. Acute exposure to heavy metal music affected the sympathetic activity in healthy women.

Reduction of infinite dimensional systems to finite dimensions: Compact convergence approach

We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics can be reduced to finite dimensions via the invariant manifolds technique. Some practical models are considered to show wide applicability of the theory. © 2013 Society for Industrial and Applied Mathematics.