Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Growth and differentiation on a trypanosome of the subgenus Schizotrypanum from the bat Phyllostomus hastatus

The effects of temperature, pH, osmolarity and aeration on the growth and differentiation of a trypanosome ofthe subgenus Schizotrypanum isolatedfrom the bat Phyllostomus hastatus were studied. In general, the growth characteristics ofthe flagellate were similar to those of Trypanosoma (Schizotrypanum) cruzi. However, the parasite did not growth at 33 or 37C. Increase in the osmolarity and aeration promoted growth at 33C. Significant metacyclogenesis was detected only in the growth condition where maximal growth occured (28C, pH 7.3, 380m0s/kg, in tissue cullure flasks), at the end ofthe exponential growth phase. The begining of the metacyclogenesis process was coincident with most glucose utilization and lowest pH. During metacyclogenesis both culture medium pH and osmolarity increased steadly.

The Technology Gap and the Growth of the Firm: A Case Study of China's Mobile-phone Handset Industry

We have examined the way in which local Chinese firms confronted with a technology gap have achieved growth, using the Chinese handset industry as a case study. Chinese local firms have lacked technology, and have therefore turned to outside firms for development, design, and manufacturing, while they themselves have focused on sales and marketing, using their advantage of familiarity with the Chinese market. Consequently, by establishing a growth condition in which their selection of boundaries counterbalances the technology gap they have been able to expand their market share in comparison with foreign firms.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

The impact of carbon source in Candida albicans virulence: participation of RLM1 in pathogen host interaction

Dissertação de mestrado em Genética Molecular

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Dissecting carotenoid from structural components of carotenoid-based coloration: a field experiment with great tits (Parus major).

Carotenoid-based yellowish to red plumage colors are widespread visual signals used in sexual and social communication. To understand their ultimate signaling functions, it is important to identify the proximate mechanism promoting variation in coloration. Carotenoid-based colors combine structural and pigmentary components, but the importance of the contribution of structural components to variation in pigment-based colors (i.e., carotenoid-based colors) has been undervalued. In a field experiment with great tits (Parus major), we combined a brood size manipulation with a simultaneous carotenoid supplementation in order to disentangle the effects of carotenoid availability and early growth condition on different components of the yellow breast feathers. By defining independent measures of feather carotenoid content (absolute carotenoid chroma) and background structure (background reflectance), we demonstrate that environmental factors experienced during the nestling period, namely, early growth conditions and carotenoid availability, contribute independently to variation in yellow plumage coloration. While early growth conditions affected the background reflectance of the plumage, the availability of carotenoids affected the absolute carotenoid chroma, the peak of maximum ultraviolet reflectance, and the overall shape, that is, chromatic information of the reflectance curves. These findings demonstrate that environment-induced variation in background structure contributes significantly to intraspecific variation in yellow carotenoid-based plumage coloration.

Théorèmes d'existence pour des systèmes d'équations différentielles et d'équations aux échelles de temps.

Nous présentons dans cette thèse des théorèmes d’existence pour des systèmes d’équations différentielles non-linéaires d’ordre trois, pour des systèmes d’équa- tions et d’inclusions aux échelles de temps non-linéaires d’ordre un et pour des systèmes d’équations aux échelles de temps non-linéaires d’ordre deux sous cer- taines conditions aux limites. Dans le chapitre trois, nous introduirons une notion de tube-solution pour obtenir des théorèmes d’existence pour des systèmes d’équations différentielles du troisième ordre. Cette nouvelle notion généralise aux systèmes les notions de sous- et sur-solutions pour le problème aux limites de l’équation différentielle du troisième ordre étudiée dans [34]. Dans la dernière section de ce chapitre, nous traitons les systèmes d’ordre trois lorsque f est soumise à une condition de crois- sance de type Wintner-Nagumo. Pour admettre l’existence de solutions d’un tel système, nous aurons recours à la théorie des inclusions différentielles. Ce résultat d’existence généralise de diverses façons un théorème de Grossinho et Minhós [34]. Le chapitre suivant porte sur l’existence de solutions pour deux types de sys- tèmes d’équations aux échelles de temps du premier ordre. Les résultats d’exis- tence pour ces deux problèmes ont été obtenus grâce à des notions de tube-solution adaptées à ces systèmes. Le premier théorème généralise entre autre aux systèmes et à une échelle de temps quelconque, un résultat obtenu pour des équations aux différences finies par Mawhin et Bereanu [9]. Ce résultat permet également d’obte- nir l’existence de solutions pour de nouveaux systèmes dont on ne pouvait obtenir l’existence en utilisant le résultat de Dai et Tisdell [17]. Le deuxième théorème de ce chapitre généralise quant à lui, sous certaines conditions, des résultats de [60]. Le chapitre cinq aborde un nouveau théorème d’existence pour un système d’in- clusions aux échelles de temps du premier ordre. Selon nos recherches, aucun résultat avant celui-ci ne traitait de l’existence de solutions pour des systèmes d’inclusions de ce type. Ainsi, ce chapitre ouvre de nouvelles possibilités dans le domaine des inclusions aux échelles de temps. Notre résultat a été obtenu encore une fois à l’aide d’une hypothèse de tube-solution adaptée au problème. Au chapitre six, nous traitons l’existence de solutions pour des systèmes d’équations aux échelles de temps d’ordre deux. Le premier théorème d’existence que nous obtenons généralise les résultats de [36] étant donné que l’hypothèse que ces auteurs utilisent pour faire la majoration a priori est un cas particulier de notre hypothèse de tube-solution pour ce type de systèmes. Notons également que notre définition de tube-solution généralise aux systèmes les notions de sous- et sur-solutions introduites pour les équations d’ordre deux par [4] et [55]. Ainsi, nous généralisons également des résultats obtenus pour des équations aux échelles de temps d’ordre deux. Finalement, nous proposons un nouveau résultat d’exis- tence pour un système dont le membre droit des équations dépend de la ∆-dérivée de la fonction.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Caracterização sistêmica de alterações em redes fisiológicas de plantas C3 e C4 submetidas à deficiência hídrica

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analysis of the biofilm proteome of Xylella fastidiosa

Abstract Background Xylella fastidiosa is limited to the xylem of the plant host and the foregut of insect vectors (sharpshooters). The mechanism of pathogenicity of this bacterium differs from other plant pathogens, since it does not present typical genes that confer specific interactions between plant and pathogens (avr and/or hrp). The bacterium is injected directly into the xylem vessels where it adheres and colonizes. The whole process leads to the formation of biofilms, which are considered the main mechanism of pathogenicity. Cells in biofilms are metabolically and phenotypically different from their planktonic condition. The mature biofilm stage (phase of higher cell density) presents high virulence and resistance to toxic substances such as antibiotics and detergents. Here we performed proteomic analysis of proteins expressed exclusively in the mature biofilm of X. fastidiosa strain 9a5c, in comparison to planktonic growth condition. Results We found a total of 456 proteins expressed in the biofilm condition, which correspond to approximately 10% of total protein in the genome. The biofilm showed 37% (or 144 proteins) different protein than we found in the planktonic growth condition. The large difference in protein pattern in the biofilm condition may be responsible for the physiological changes of the cells in the biofilm of X. fastidiosa. Mass spectrometry was used to identify these proteins, while real-time quantitative polymerase chain reaction monitored expression of genes encoding them. Most of proteins expressed in the mature biofilm growth were associated with metabolism, adhesion, pathogenicity and stress conditions. Even though the biofilm cells in this work were not submitted to any stress condition, some stress related proteins were expressed only in the biofilm condition, suggesting that the biofilm cells would constitutively express proteins in different adverse environments. Conclusions We observed overexpression of proteins related to quorum sensing, proving the existence of communication between cells, and thus the development of structuring the biofilm (mature biofilm) leading to obstruction of vessels and development of disease. This paper reports a first proteomic analysis of mature biofilm of X. fastidiosa, opening new perspectives for understanding the biochemistry of mature biofilm growth in a plant pathogen.

Dissecting Carotenoid from Structural Components of Carotenoid-Based Coloration: A Field Experiment with Great Tits (Parus major)

Carotenoid-based yellowish to red plumage colors are widespread visual signals used in sexual and social communication. To understand their ultimate signaling functions, it is important to identify the proximate mechanism promoting variation in coloration. Carotenoid-based colors combine structural and pigmentary components, but the importance of the contribution of structural components to variation in pigment-based colors (i.e., carotenoid-based colors) has been undervalued. In a field experiment with great tits (Parus major), we combined a brood size manipulation with a simultaneous carotenoid supplementation in order to disentangle the effects of carotenoid availability and early growth condition on different components of the yellow breast feathers. By defining independent measures of feather carotenoid content (absolute carotenoid chroma) and background structure (background reflectance), we demonstrate that environmental factors experienced during the nestling period, namely, early growth conditions and carotenoid availability, contribute independently to variation in yellow plumage coloration. While early growth conditions affected the background reflectance of the plumage, the availability of carotenoids affected the absolute carotenoid chroma, the peak of maximum ultraviolet reflectance, and the overall shape, that is, chromatic information of the reflectance curves. These findings demonstrate that environment-induced variation in background structure contributes significantly to intraspecific variation in yellow carotenoid-based plumage coloration.

Cis-acting elements and developmental regulators govern toxin gene expression in Bacillus anthracis

Expression of the structural genes for the anthrax toxin proteins is coordinately controlled by host-related signals such as elevated CO2 , and the trans-acting positive regulator, AtxA. No specific binding of AtxA to the toxin gene promoters has been demonstrated and no sequence-based similarities are apparent in the promoter regions of toxin genes. We hypothesized that the toxin genes possess common structural features that are required for positive regulation. To test this hypothesis, I performed an extensive characterization of the toxin gene promoters. I determined the minimal sequences required for atxA-mediated toxin gene expression and compared these sequences for structural similarities. In silico modeling and in vitro experiments indicated significant curvature within these regions. Random mutagenesis revealed that point mutations associated with reduced transcriptional activity, mostly mapped to areas of high curvature. This work enabled the identification of two potential cis-acting elements implicated in AtxA-mediated regulation of the toxin genes. In addition to the growth condition requirements and AtxA, toxin gene expression is under growth phase regulation. The transition state regulator AbrB represses atxA expression to influence toxin synthesis. Here I report that toxin gene expression also requires sigH, a gene encoding the RNA polymerase sigma factor associated with development in B. subtilis. In the well-studied B. subtilis system, σH is part of a feedback control pathway that involves AbrB and the major response regulator of sporulation initiation, Spo0A. My data indicate that in B. anthracis, regulatory relationships exist between these developmental regulators and atxA . Interestingly, during growth in toxin-inducing conditions, sigH and abrB expression deviates from that described for B. subtilis, affecting expression of the atxA gene. These findings, combined with previous observations, suggest that the steady state level of atxA expression is critical for optimal toxin gene transcription. I propose a model whereby, under toxin-inducing conditions, control of toxin gene expression is fine-tuned by the independent effects of the developmental regulators on the expression of atxA . The growth condition-dependent changes in expression of these regulators may be crucial for the correct timing and uninterrupted expression of the toxin genes during infection. ^