About the Stabilization of a Nonlinear Perturbed Difference Equation

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

La enfermedad tuberculosa en Bilbao al inicio del siglo XXI (1993-2002)

La Tuberculosis es una enfermedad cuya presencia ha sido constante en la historia de la humanidad. Como toda enfermedad infectocontagiosa no respeta fronteras, ni edades, ni sexos, ni razas, ni tampoco clases sociales. La tuberculosis que actualmente padecemos no es nueva; representa el final de una onda epidémica secular que alcanzó su máxima incidencia en Europa entre 1780 y 1880. Cien años marcados por el desplazamiento masivo de campesinos a las ciudades en busca de trabajo en las fábricas. Históricamente la epidemiología de la tuberculosis ha demostrado la existencia de un declive natural. Dicho declive se inició ya, incluso antes del descubrimiento de su agente causal, debido a la mejoría de las condiciones socio-económicas de la población. La aparición de la quimioterapia específica aceleró su ritmo de descenso anual. Hasta la aparición del SIDA, ningún otro factor ha modificado substancialmente su natural declinar. Tan importante son las condiciones socioeconómicas y sociopolíticas de la población en la expresión epidemiológica de ésta y otras muchas enfermedades, que en 1910, cuando no existían remedios para la tuberculosis, Holanda alcanzó el llamado punto de ruptura. Dicho punto es aquel en que se considera que la tuberculosis camina hacia su erradicación espontánea. Corresponde al momento en que cada enfermo bacilífero no puede infectar al número suficiente de personas para que se origine otro nuevo enfermo bacilífero. Evidentemente el SIDA ha supuesto una inyección de gasolina en la llama de la enfermedad tuberculosa que ha desbaratado los programas de prevención y control puestos en marcha en 1982 en nuestra Comunidad Autónoma. Como decía Napoleón Bonaparte, las batallas se ganan con organización y dinero. La batalla del SIDA aún continúa y con más ahínco en nuestro País Vasco donde esta enfermedad es especialmente prevalente. Afortunadamente los nuevos tratamientos han convertido una enfermedad mortal de necesidad en una enfermedad crónica con una mejora substancial en las expectativas de vida. Sin embargo, la gran secuela de la coinfección SIDA/Tuberculosis ha sido la aparición de multirresistencias a los fármacos por tratamientos incorrectos o falta de adherencia del paciente a los mismos. Parece que el devenir de la tuberculosis, al margen de los factores políticos, culturales y económicos, ligados a la globalización y al desarrollo sostenible dentro de un modelo neoliberal; de los movimientos de masas: inmigrantes y refugiados; del racismo; de las desigualdades de género; de la diferente accesibilidad, cobertura y eficacia en los Sistemas Públicos de Salud, etc., al margen de todo esto, la tuberculosis va a quedar condicionada a cuatro factores de índole biomédica: a) A la evolución de las multirresistencias. b) A la subordinación con la coinfección VIH. c) Al establecimiento de los denominados "nichos ecológicos", en donde la enfermedad alcanzará su máxima progresión (mayores de 65 años, sobre todo los de bajo nivel económico; inmigrantes procedentes de zonas de endemia elevada; personal sanitario y trabajadores expuestos; colectivos con adicción a drogas por vía parenteral (ADVP); alcohólicos; personas con padecimientos crónicos; pacientes en tratamientos prolongados con corticoides e inmunosupresores). En estos nichos ecológicos es donde hay que mantener un elevado índice de sospecha y establecer las estrategias adecuadas para la detección precoz de la enfermedad. d) Al éxito que se obtenga con la nueva vacuna terapéutica contra la TB creada por Joan Pere Cardona. La epidemiología de la tuberculosis estará próximamente ligada a la biología molecular y a la genética. En efecto, ya no bastará con identificar al bacilo de Koch en un paciente. Será imprescindible saber qué cepas están actuando en una determinada colectividad, así como su grado de sensibilidad frente a los tuberculostáticos. Acabó el siglo XX, hemos iniciado la segunda década del siglo XXI y la pelota aún sigue en el tejado. Estamos ante un problema de primera magnitud que hace mucho tiempo que dejó de seducir a los románticos. Como señala Bignall, comparando a la tuberculosis con lo que en su día supuso la viruela como problema de Salud Pública: La viruela se erradicó porque no sólo se disponía de una vacuna eficaz, sino además porque no requería habilidad en las relaciones humanas. Sin embargo, en la tuberculosis, la lucha ya no es contra el bacilo sino contra la mentalidad y las miserias humanas; por ello será larga, muy larga. Por todo esto y visto lo previamente descrito concluimos: 1. En la década 1993 a 2002 se diagnosticaron 847 casos de tuberculosis, 548 varones y 299 mujeres; 364 con SIDA y 483 sin demostración de VIH. 2. Si agrupamos las características medias de todos los casos recogidos, definiríamos al paciente tipo como a un varón con serología VIH negativa, una edad de 46,6 años y una afección tuberculosa de localización extrapulmonar, atendida en el Servicio de Enfermedades Infecciosas del Hospital. 3. Si el paciente tuberculoso que escogiéramos tuviera 31 años, la edad con más casos acumulados de la serie, al igual que los de 30 y 32 años, lo más frecuente que observaríamos, sería un paciente varón con SIDA y adicción a drogas por vía parenteral. 4. Aunque el sexo predominante es el varón entre los enfermos de tuberculosis, este predominio se atenúa al prescindir de los pacientes que asociaron SIDA. 5. El principal factor de riesgo para contraer el VIH en los tísicos con SIDA fue la ADVP. 6. El número de casos totales anuales viene descendiendo desde 1991, fundamentalmente a expensas del declive entre los casos que asociaron SIDA. 7. Es necesario disminuir el tiempo de demora 2 consistente en el número de días que transcurren desde que el paciente manifiesta sus primeros síntomas hasta que éste recibe el tratamiento. Puesto que el tiempo de demora 1 (que va desde que el paciente es visto en el hospital hasta que se instaura el tratamiento) cumple con los objetivos marcados en el Programa de control y prevención del Gobierno Vasco, deducimos que la Atención Primaria tiene la máxima importancia en acelerar este acortamiento del tiempo de demora disminuyendo así el periodo de riesgo de transmisión de la enfermedad. 8. La tuberculosis es una enfermedad que tiende a su natural declinar pero haciéndolo muy lentamente. Actualmente, la encontramos en zonas periféricas de la ciudad donde el VIH hace estragos en pacientes jóvenes con estilos de vida nada saludables. A estas zonas deprimidas se las denominan "nichos ecológicos". 9. La lucha contra esta enfermedad deberá ser enfocada hacia estos "nichos ecológicos". La condición necesaria para que consigamos acelerar la eliminación de la enfermedad consistirá en que diagnostiquemos y tratemos los casos afectados junto a la búsqueda de sus contactos. Pero en la tuberculosis, esto no es suficiente. Estamos luchando frente a un bacilo que se aprovecha de los más débiles, los inmunodeprimidos, edades extremas de la vida, drogodependientes, alcohólicos, zonas deprimidas económica y socialmente, que podemos delimitar en un plano y concentrar en él las medidas de control pertinentes. No olvidemos que estamos frente a un bacilo que se enclaustra en una caverna, que infecta a la tercera parte de la humanidad y espera. La tuberculosis desaparecerá en la medida en que la sociedad prospere.

Istoria delle guerre del Regno del Brasile : accadute tra la corona di Portogallo e la Republica di Olanda, composta, ed offerta alla sagra reale maesda di Pietro Secondo, Re di Portogallo & C. dal P. F. Gio. Gioseppe di S. Teresa Carmelitano Scalzo : Parte prima e Parte seconda

As negociações entre Portugal e Holanda a respeito da devolução dos territórios portugueses ocupados se desenvolveram ao longo de um decênio. As propostas iniciais de Portugal referiam-se aos territórios ocupados pelos holandeses na África e no Maranhão. Estão no raríssimo folheto.

Annaes historicos do Estado do Maranhão, em que se dá noticia do seu descobrimento, e tudo o mais que nelle tem succedido desde o anno em que foy descuberto até o de 1718offerecidos ao Augustissimo Monarca D. João V, Nosso Senhorescritos por Bernardo Pereira de Berredo

Os reis, tanto portugueses como espanhóis, variaram muito na determinação de impedir o cativeiro dos índios, até que, em 1741, o Papa Benedito XIV expediu uma bula proibindo terminantemente que qualquer pessoa, secular ou eclesiástica, possuísse como escravos os índio, sob pena de excomunhão latae sentiae.

若干流体力学问题的数学性质研究

该文利用高智的扩散抛物化方程组理论及流体力学基本方程组的特征次特征理论,流体大小尺度（LSS）方程组理论以及摄动有限差分（PFD）方法,研究若干流体力学问题的数学性质.该文得到的主要结论有：1.利用湍流大小尺度（LSS）方程组推导出湍流大小尺度涡量（LSSV）方程组,并证明两个关于湍流大小尺度涡量的命题,从而得到湍流封闭大小尺度涡量（CLSSV）方程组,并对已有的近程相互作用命题进行推广.2.根据扩散抛物化方程组理论和流体力学层次结构方程组的特征和次特征方法,研究了抛物化稳定性方程组（PSE）的特征和次特征以及消除PSE的剩余椭圆特性的问题.3.利用摄动有限差分（PFD）方法得到对流扩散反应方程的变步长摄动有限差分格式,是等步长摄动有限差分格式的推广.

Pumped double quantum dot with spin-orbit coupling

We study driven by an external electric field quantum orbital and spin dynamics of electron in a one-dimensional double quantum dot with spin-orbit coupling. Two types of external perturbation are considered: a periodic field at the Zeeman frequency and a single half-period pulse. Spin-orbit coupling leads to a nontrivial evolution in the spin and orbital channels and to a strongly spin-dependent probability density distribution. Both the interdot tunneling and the driven motion contribute into the spin evolution. These results can be important for the design of the spin manipulation schemes in semiconductor nanostructures.

Formation Mechanism Of Lamellar Chips During Machining Of Bulk Metallic Glass

The uniqThe unique lamellar chips formed in turning–machining of a Vit 1 bulk metallic glass (BMG) are found to be due to repeated shearband formation in the primary shear zone (PSZ). A coupled thermomechanical orthogonal cutting model, taking into account force, free volume and energy balance in the PSZ, is developed to quantitatively characterize lamellar chip formation. Its onset criterion is revealed through a linear perturbation analysis. Lamellar chip formation is understood as a self-sustained limit-cycle phenomenon: there is autonomous feedback in stress, free volume and temperature in the PSZ. The underlying mechanism is the symmetry breaking of free volume flow and source, rather than thermal instability. These results are fundamentally useful for machining BMGs and even for understanding the physical nature of inhomogeneous flow in BMGs.ue lamellar chips formed in turning–machining of a Vit 1 bulk metallic glass (BMG) are found to be due to repeated shearband.

On the origin of shear banding instability in metallic glasses

To uncover the physical origin of shear-banding instability in metallic glass (MG), a theoretical description of thermo-mechanical deformation of MG undergoing one-dimensional simple shearing is presented. The coupled thermo-mechanical model takes into account the momentum balance, the energy balance and the dynamics of free volume. The interplay between free-volume production and temperature increase being two potential causes for shear-banding instability is examined on the basis of the homogeneous solution. It is found that the free-volume production facilitates the sudden increase in the temperature before instability and vice versa. A rigorous linear perturbation analysis is used to examine the inhomogeneous deformation, during which the onset criteria and the internal length and time scales for three types of instabilities, namely free-volume softening, thermal softening and coupling softening, are clearly revealed. The shear-banding instability originating from sole free-volume softening takes place easier and faster than that due to sole thermal softening, and dominates in the coupling softening. Furthermore, the coupled thermo-mechanical shear-band analysis does show that an initial slight distribution of local free volume can incur significant strain localization, producing a shear band. During such a localization process, the local free-volume creation occurs indeed prior to the increase in local temperature, indicating that the former is the cause of shear localization, whereas the latter is its consequence. Finally, extension of the above model to include the shear-induced dilatation shows that such dilatation facilitates the shear instability in metallic glasses.

摄动有限体积算法及其在两相流中应用

采用一种全新的摄动有限体积(PFV)算法和水平集(Level Set)技术对液液两相系统中液滴坠落进行数值模拟,数值结果表明,PFV新算法具有节点少、精度高,效率高,编程方便等优点,能成功模拟液液两相流动,为两相流动数值模拟提供了一种新的途径.

A Continuation Method Applied to the Study of Thermocapillary Instabilities in Liquid Bridges

A continuation method is applied to investigate the linear stability of the steady, axisymmetric thermocapillary flows in liquid bridges. The method is based upon an appropriate extended system of perturbation equations depending on the nature of transition of the basic flow. The dependence of the critical Reynolds number and corresponding azimuthal wavenumber on serval parameters is presented for both cylindrical and non-cylindrical liquid bridges.

Dimensionless Analysis of the Simulation of Bucket Foundations under Dynamic Load

Firstly, the main factors are obtained by use of dimensionless analysis. Secondly, the time scaling factors in centrifuge modeling of bucket foundations under dynamic load are analyzed based on dimensionless analysis and control- ling equation. A simplified method for dealing with the conflict of scaling factors of the inertial and the percolation in sand foundation is presented. The presented method is that the material for experiments is not changed while the effects are modified by perturbation method. Thirdly, the characteristic time of liquefaction state and the characteristic scale of affected zone are analyzed.

Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.

The stochastic exit problem for dynamical systems

The problem of "exit against a flow" for dynamical systems subject to small Gaussian white noise excitation is studied. Here the word "flow" refers to the behavior in phase space of the unperturbed system's state variables. "Exit against a flow" occurs if a perturbation causes the phase point to leave a phase space region within which it would normally be confined. In particular, there are two components of the problem of exit against a flow:

i) the mean exit time

ii) the phase-space distribution of exit locations.

When the noise perturbing the dynamical systems is small, the solution of each component of the problem of exit against a flow is, in general, the solution of a singularly perturbed, degenerate elliptic-parabolic boundary value problem.

Singular perturbation techniques are used to express the asymptotic solution in terms of an unknown parameter. The unknown parameter is determined using the solution of the adjoint boundary value problem.

The problem of exit against a flow for several dynamical systems of physical interest is considered, and the mean exit times and distributions of exit positions are calculated. The systems are then simulated numerically, using Monte Carlo techniques, in order to determine the validity of the asymptotic solutions.

Periodic solutions of integro-differential equations which arise in population dynamics

The problem of the existence and stability of periodic solutions of infinite-lag integra-differential equations is considered. Specifically, the integrals involved are of the convolution type with the dependent variable being integrated over the range (- ∞,t), as occur in models of population growth. It is shown that Hopf bifurcation of periodic solutions from a steady state can occur, when a pair of eigenvalues crosses the imaginary axis. Also considered is the existence of traveling wave solutions of a model population equation allowing spatial diffusion in addition to the usual temporal variation. Lastly, the stability of the periodic solutions resulting from Hopf bifurcation is determined with aid of a Floquet theory.

The first chapter is devoted to linear integro-differential equations with constant coefficients utilizing the method of semi-groups of operators. The second chapter analyzes the Hopf bifurcation providing an existence theorem. Also, the two-timing perturbation procedure is applied to construct the periodic solutions. The third chapter uses two-timing to obtain traveling wave solutions of the diffusive model, as well as providing an existence theorem. The fourth chapter develops a Floquet theory for linear integro-differential equations with periodic coefficients again using the semi-group approach. The fifth chapter gives sufficient conditions for the stability or instability of a periodic solution in terms of the linearization of the equations. These results are then applied to the Hopf bifurcation problem and to a certain population equation modeling periodically fluctuating environments to deduce the stability of the corresponding periodic solutions.

Steady capillary-gravity waves on deep water

The properties of capillary-gravity waves of permanent form on deep water are studied. Two different formulations to the problem are given. The theory of simple bifurcation is reviewed. For small amplitude waves a formal perturbation series is used. The Wilton ripple phenomenon is reexamined and shown to be associated with a bifurcation in which a wave of permanent form can double its period. It is shown further that Wilton's ripples are a special case of a more general phenomenon in which bifurcation into subharmonics and factorial higher harmonics can occur. Numerical procedures for the calculation of waves of finite amplitude are developed. Bifurcation and limit lines are calculated. Pure and combination waves are continued to maximum amplitude. It is found that the height is limited in all cases by the surface enclosing one or more bubbles. Results for the shape of gravity waves are obtained by solving an integra-differential equation. It is found that the family of solutions giving the waveheight or equivalent parameter has bifurcation points. Two bifurcation points and the branches emanating from them are found specifically, corresponding to a doubling and tripling of the wavelength. Solutions on the new branches are calculated.