Controllability and stabilizability of linear time-varying distributed hereditary control systems

This paper is concerned with the controllability and stabilizability problem for control systems described by a time-varyinglinear abstract differential equation with distributed delay in the state variables. An approximate controllability propertyis established, and for periodic systems, the stabilization problem is studied. Assuming that the semigroup of operatorsassociated with the uncontrolled and non delayed equation is compact, and using the characterization of the asymptoticstability in terms of the spectrum of the monodromy operator of the uncontrolled system, it is shown that the approximatecontrollability property is a sufficient condition for the existence of a periodic feedback control law that stabilizes thesystem. The result is extended to include some systems which are asymptotically periodic. Copyright © 2014 John Wiley &Sons, Ltd.

Condições de otimidade para problemas de controle ótimo com condições de contorno funcionais

Pós-graduação em Matemática - IBILCE

The role of oxygen vacancies and their location in the magnetic properties of Ce1-xCuxO2-delta nanorods

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Development of a synbiotic low-calorie beverage made from soy and yacon extracts

The objective of this study was to develop a new low-calorie symbiotic beverage made from yacon (prebiotic source) and soy extracts, containing probiotic Bifidobacterium animalis ssp. lactis BB-12. The synbiotic beverage was first produced with a range of sucrose concentrations in order to determine ideal sweetness by an acceptance test using a “just-about-right scale”. Sucrose was then replaced by sucralose or aspartame to produce sugar-free beverages. Characteristics including viable cell numbers, physicochemical properties, sensorial characteristics and fructooligosaccharides content were investigated. The ideal sweetness of the beverages with sucrose, aspartame and sucralose were 7.28%, 0.0486% and 0.0167%, respectively. Sucralose exhibited higher scores in acceptance test and was used to replace sucrose in the low-calorie symbiotic beverage. The synbiotic beverage exhibited counts of Bifidobacterium spp. of 108 CFU·mL-1 , sufficient condition to be considered probiotic. The chemical composition of the product was (g/100 g): 2.91 of protein, 1.41 of fat, 2.41 of total carbohydrate; 0.82 of FOS and 148.22 Kj of energy value. The synbiotic beverage developed in this study may be successful in health applications, due to their functional ingredients (soy, probiotic bacteria and yacon prebiotics) that can afford benefits to health or can present disease-preventing properties, beyond their inherent nutritional value. In addition this low-calorie beverage can be consumed by diabetic individuals and people concerned about the ingestion of calories.

Location-price competition with externality: an application to the Tenerife tram

[EN] This paper presents a location–price equilibrium problem on a tree. A sufficient condition for having a Nash equilibrium in a spatial competition model that incorporates price, transport, and externality costs is given. This condition implies both competitors are located at the same point, a vertex that is the unique median of the tree. However, this is not an equilibrium necessary condition. Some examples show that not all medians are equilibria. Finally, an application to the Tenerife tram is presented.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Weighted Inequalities and Lipschitz Spaces

In this thesis I have characterized the trace measures for particular potential spaces of functions defined on R^n, but "mollified" so that the potentials are de facto defined on the upper half-space of R^n. The potential functions are kind Riesz-Bessel. The characterization of trace measures for these spaces is a test condition on elementary sets of the upper half-space. To prove the test condition as sufficient condition for trace measures, I had give an extension to the case of upper half-space of the Muckenhoupt-Wheeden and Wolff inequalities. Finally I characterized the Carleson-trace measures for Besov spaces of discrete martingales. This is a simplified discrete model for harmonic extensions of Lipschitz-Besov spaces.

An Analysis of Capacities, Moral Hierarchies, and the Moral Status of Non-Human Animals in Contemporary Animal Rights Work

The primary objective of this thesis is to demonstrate the pernicious impact that moral hierarchies have on our perception and subsequent treatment of non-human animals. Moral hierarchies in general are characterized by a dynamic in which one group is considered to be fundamentally superior to a lesser group. This thesis focuses specifically on the moral hierarchies that arise when humans are assumed to be superior to non-human animals in virtue of their advanced mental capabilities. The operative hypothesis of this thesis is essentially that moral hierarchies thwart the provision of justice to non-human animals in that they function as a justification for otherwise impermissible actions. When humans are assumed to be fundamentally superior to non-human animals then it becomes morally permissible for humans to kill non-human animals and utilize them as mere instrumentalities. This thesis is driven primarily by an in-depth analysis of the approaches to animal rights that are provided by Peter Singer, Tom Regan, and Gary Francione. Each of these thinkers claim that they overcome anthropocentrism and provide approaches that preclude the establishment of a moral hierarchy. One of the major findings of this thesis, however, is that Singer and Regan offer approaches that remain highly anthropocentric despite the fact that each thinker claims that they have overcome anthropocentrism. The anthropocentrism persists in these respective approaches in that each thinkers gives humans Regan and Singer have different conceptions of the criteria that are required to afford a being moral worth, but they both give preference to beings that have the cognitive ability to form desires regarding the future.. As a result, a moral hierarchy emerges in which humans are regarded to be fundamentally superior. Francione, however, provides an approach that does not foster a moral hierarchy. Francione creates such an approach by applying the principle of equal consideration of interests in a consistent manner. Moreover, Francione argues that mere sentience is both a necessary and sufficient condition for being eligible and subsequently receiving moral consideration. The upshot of this thesis is essentially that the moral treatment of animals is not compatible with the presence of a moral hierarchy. As a result, this thesis demonstrates that future approaches to animal rights must avoid the establishment of moral hierarchies. The research and analysis within this thesis demonstrates that this is not a possibility, however, unless all theories of justice that are to accommodate animals abandon the notion that cognition matters morally.

From hierarchies to well-foundedness

We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies (of various complexity) have been extensively studied, we point out that (if parameters are allowed) well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting (Π01−CA0)α⊢wf(α)where(Π01−CA0)α stands for the iteration of Π01 comprehension (with parameters) along some ordinal α and wf(α) stands for the well-foundedness of α.

Sensitive Questions in Online Surveys: An Experimental Evaluation of the Randomized Response Technique and the Crosswise Model

Self-administered online surveys provide a higher level of privacy protection to respondents than surveys administered by an interviewer. Yet, studies indicate that asking sensitive questions is problematic also in self-administered surveys. Because respondents might not be willing to reveal the truth and provide answers that are subject to social desirability bias, the validity of prevalence estimates of sensitive behaviors from online surveys can be challenged. A well-known method to overcome these problems is the Randomized Response Technique (RRT). However, convincing evidence that the RRT provides more valid estimates than direct questioning in online surveys is still lacking. A new variant of the RRT called the Crosswise Model has recently been proposed to overcome some of the deficiencies of existing RRT designs. We therefore conducted an experimental study in which different implementations of the RRT, including two implementations of the crosswise model, were tested and compared to direct questioning. Our study is a large-scale online survey (N = 6,037) on sensitive behaviors by students such as cheating in exams and plagiarism. Results indicate that the crosswise-model RRT---unlike the other variants of RRT we evaluated---yields higher prevalence estimates of sensitive behaviors than direct questioning. Whether higher estimates are a sufficient condition for more valid results, however, remains questionable.

A Simple Model of Credit Rationing with Information Externalities

Credit-rationing model similar to Stiglitz and Weiss [1981] is combined with the information externality model of Lang and Nakamura [1993] to examine the properties of mortgage markets characterized by both adverse selection and information externalities. In a credit-rationing model, additional information increases lenders ability to distinguish risks, which leads to increased supply of credit. According to Lang and Nakamura, larger supply of credit leads to additional market activities and therefore, greater information. The combination of these two propositions leads to a general equilibrium model. This paper describes properties of this general equilibrium model. The paper provides another sufficient condition in which credit rationing falls with information. In that, external information improves the accuracy of equity-risk assessments of properties, which reduces credit rationing. Contrary to intuition, this increased accuracy raises the mortgage interest rate. This allows clarifying the trade offs associated with reduced credit rationing and the quality of applicant pool.

Helium isotope concentrations and ratios in sediments from ODP Hole 130-806B

We have determined the helium abundance and isotopic composition of seafloor carbonate sediments from the flanks of the Ontong Java Plateau, western equatorial Pacific Ocean (ODP Site 806). These results provide a two million year record of the burial flux of extraterrestrial 3He, which we believe is a proxy for the terrestrial accretion rate of interplanetary dust particles. The 3He burial flux prior to ~700 ka was relatively low, ~0.5 pcc/cm**2/kyr, but from 700 ka to the present, the burial flux gradually increased to a value of ~1.0 pcc/cm**2/kyr. 100 kyr periodicity in the 3He burial flux is apparent over the last 700 kyr and correlates with the oxygen isotope record of global climate, with high 3He burial fluxes associated with interglacial periods. This periodicity and phase are consistent with previous 3He measurements in North Atlantic sediments. Although 100 kyr periodicity in 3He burial flux is in agreement with recent predictions of the accretion rate of interplanetary dust based on a model of the orbital evolution of asteroidal debris, the measurements and predictions differ by one half cycle in phase. Nevertheless, our observations suggest the terrestrial accretion rate of interplanetary dust is controlled by orbital eccentricity and/or inclination relative to the solar-system invariable plane. Such control is a necessary but not sufficient condition for the hypothesis of that variations in extraterrestrial dust accretion modulates terrestrial climate with a 100 kyr period. We also identify several brief (<25 kyr) intervals of strongly enhanced 3He burial, possibly related to random and transient fluctuations in the accretion rate of asteroidal or cometary dust particles.

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros.

Oscillatory genetic circuits: new designs and mathematical models

Introduction and motivation: A wide variety of organisms have developed in-ternal biomolecular clocks in order to adapt to cyclic changes of the environment. Clock operation involves genetic networks. These genetic networks have to be mod¬eled in order to understand the underlying mechanism of oscillations and to design new synthetic cellular clocks. This doctoral thesis has resulted in two contributions to the fields of genetic clocks and systems and synthetic biology, generally. The first contribution is a new genetic circuit model that exhibits an oscillatory behav¬ior through catalytic RNA molecules. The second and major contribution is a new genetic circuit model demonstrating that a repressor molecule acting on the positive feedback of a self-activating gene produces reliable oscillations. First contribution: A new model of a synthetic genetic oscillator based on a typical two-gene motif with one positive and one negative feedback loop is pre¬sented. The originality is that the repressor is a catalytic RNA molecule rather than a protein or a non-catalytic RNA molecule. This catalytic RNA is a ribozyme that acts post-transcriptionally by binding to and cleaving target mRNA molecules. This genetic clock involves just two genes, a mRNA and an activator protein, apart from the ribozyme. Parameter values that produce a circadian period in both determin¬istic and stochastic simulations have been chosen as an example of clock operation. The effects of the stochastic fluctuations are quantified by a period histogram and autocorrelation function. The conclusion is that catalytic RNA molecules can act as repressor proteins and simplify the design of genetic oscillators. Second and major contribution: It is demonstrated that a self-activating gene in conjunction with a simple negative interaction can easily produce robust matically validated. This model is comprised of two clearly distinct parts. The first is a positive feedback created by a protein that binds to the promoter of its own gene and activates the transcription. The second is a negative interaction in which a repressor molecule prevents this protein from binding to its promoter. A stochastic study shows that the system is robust to noise. A deterministic study identifies that the oscillator dynamics are mainly driven by two types of biomolecules: the protein, and the complex formed by the repressor and this protein. The main conclusion of this study is that a simple and usual negative interaction, such as degradation, se¬questration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations. One gene is enough and the positive transcriptional feedback signal does not need to activate a second repressor gene. At the genetic level, this means that an explicit negative feedback loop is not necessary. Unlike many genetic oscillators, this model needs neither cooperative binding reactions nor the formation of protein multimers. Applications and future research directions: Recently, RNA molecules have been found to play many new catalytic roles. The first oscillatory genetic model proposed in this thesis uses ribozymes as repressor molecules. This could provide new synthetic biology design principles and a better understanding of cel¬lular clocks regulated by RNA molecules. The second genetic model proposed here involves only a repression acting on a self-activating gene and produces robust oscil¬lations. Unlike current two-gene oscillators, this model surprisingly does not require a second repressor gene. This result could help to clarify the design principles of cellular clocks and constitute a new efficient tool for engineering synthetic genetic oscillators. Possible follow-on research directions are: validate models in vivo and in vitro, research the potential of second model as a genetic memory, investigate new genetic oscillators regulated by non-coding RNAs and design a biosensor of positive feedbacks in genetic networks based on the operation of the second model Resumen Introduccion y motivacion: Una amplia variedad de organismos han desarro-llado relojes biomoleculares internos con el fin de adaptarse a los cambios ciclicos del entorno. El funcionamiento de estos relojes involucra redes geneticas. El mo delado de estas redes geneticas es esencial tanto para entender los mecanismos que producen las oscilaciones como para diseiiar nuevos circuitos sinteticos en celulas. Esta tesis doctoral ha dado lugar a dos contribuciones dentro de los campos de los circuitos geneticos en particular, y biologia de sistemas y sintetica en general. La primera contribucion es un nuevo modelo de circuito genetico que muestra un comportamiento oscilatorio usando moleculas de ARN cataliticas. La segunda y principal contribucion es un nuevo modelo de circuito genetico que demuestra que una molecula represora actuando sobre el lazo de un gen auto-activado produce oscilaciones robustas. Primera contribucion: Es un nuevo modelo de oscilador genetico sintetico basado en una tipica red genetica compuesta por dos genes con dos lazos de retroa-limentacion, uno positivo y otro negativo. La novedad de este modelo es que el represor es una molecula de ARN catalftica, en lugar de una protefna o una molecula de ARN no-catalitica. Este ARN catalitico es una ribozima que actua despues de la transcription genetica uniendose y cortando moleculas de ARN mensajero (ARNm). Este reloj genetico involucra solo dos genes, un ARNm y una proteina activadora, aparte de la ribozima. Como ejemplo de funcionamiento, se han escogido valores de los parametros que producen oscilaciones con periodo circadiano (24 horas) tanto en simulaciones deterministas como estocasticas. El efecto de las fluctuaciones es-tocasticas ha sido cuantificado mediante un histograma del periodo y la función de auto-correlacion. La conclusion es que las moleculas de ARN con propiedades cataliticas pueden jugar el misnio papel que las protemas represoras, y por lo tanto, simplificar el diseno de los osciladores geneticos. Segunda y principal contribucion: Es un nuevo modelo de oscilador genetico que demuestra que un gen auto-activado junto con una simple interaction negativa puede producir oscilaciones robustas. Este modelo ha sido estudiado y validado matematicamente. El modelo esta compuesto de dos partes bien diferenciadas. La primera parte es un lazo de retroalimentacion positiva creado por una proteina que se une al promotor de su propio gen activando la transcription. La segunda parte es una interaction negativa en la que una molecula represora evita la union de la proteina con el promotor. Un estudio estocastico muestra que el sistema es robusto al ruido. Un estudio determinista muestra que la dinamica del sistema es debida principalmente a dos tipos de biomoleculas: la proteina, y el complejo formado por el represor y esta proteina. La conclusion principal de este estudio es que una simple y usual interaction negativa, tal como una degradation, un secuestro o una inhibition, actuando sobre el lazo de retroalimentacion positiva de un solo gen es una condition suficiente para producir oscilaciones robustas. Un gen es suficiente y el lazo de retroalimentacion positiva no necesita activar a un segundo gen represor, tal y como ocurre en los relojes actuales con dos genes. Esto significa que a nivel genetico un lazo de retroalimentacion negativa no es necesario de forma explicita. Ademas, este modelo no necesita reacciones cooperativas ni la formation de multimeros proteicos, al contrario que en muchos osciladores geneticos. Aplicaciones y futuras lineas de investigacion: En los liltimos anos, se han descubierto muchas moleculas de ARN con capacidad catalitica. El primer modelo de oscilador genetico propuesto en esta tesis usa ribozimas como moleculas repre¬soras. Esto podria proporcionar nuevos principios de diseno en biologia sintetica y una mejor comprension de los relojes celulares regulados por moleculas de ARN. El segundo modelo de oscilador genetico propuesto aqui involucra solo una represion actuando sobre un gen auto-activado y produce oscilaciones robustas. Sorprendente-mente, un segundo gen represor no es necesario al contrario que en los bien conocidos osciladores con dos genes. Este resultado podria ayudar a clarificar los principios de diseno de los relojes celulares naturales y constituir una nueva y eficiente he-rramienta para crear osciladores geneticos sinteticos. Algunas de las futuras lineas de investigation abiertas tras esta tesis son: (1) la validation in vivo e in vitro de ambos modelos, (2) el estudio del potential del segundo modelo como circuito base para la construction de una memoria genetica, (3) el estudio de nuevos osciladores geneticos regulados por ARN no codificante y, por ultimo, (4) el rediseno del se¬gundo modelo de oscilador genetico para su uso como biosensor capaz de detectar genes auto-activados en redes geneticas.

Sampling associated with resolvent-type kernels and lagrange-type interpolation series

In this paper a new class of Kramer kernels is introduced, motivated by the resolvent of a symmetric operator with compact resolvent. The article gives a necessary and sufficient condition to ensure that the associ- ated sampling formula can be expressed as a Lagrange-type interpolation series. Finally, an illustrative example, taken from the Hamburger moment problem theory, is included.