Strongly damped wave problems: Bootstrapping and regularity of solutions

The aim of the article is to present a unified approach to the existence, uniqueness and regularity of solutions to problems belonging to a class of second order in time semilinear partial differential equations in Banach spaces. Our results are applied next to a number of examples appearing in literature, which fall into the class of strongly damped semilinear wave equations. The present work essentially extends the results on the existence and regularity of solutions to such problems. Previously, these problems have been considered mostly within the Hilbert space setting and with the main part operators being selfadjoint. In this article we present a more general approach, involving sectorial operators in reflexive Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Limited liability and non-responsiveness in moral hazard and adverse selection problems

This work analyses the optimal menu of contracts offered by a risk neutral principal to a risk averse agent under moral hazard, adverse selection and limited liability. There are two output levels, whose probability of occurrence are given by agent’s private information choice of effort. The agent’s cost of effort is also private information. First, we show that without assumptions on the cost function, it is not possible to guarantee that the optimal contract menu is simple, when the agent is strictly risk averse. Then, we provide sufficient conditions over the cost function under which it is optimal to offer a single contract, independently of agent’s risk aversion. Our full-pooling cases are caused by non-responsiveness, which is induced by the high cost of enforcing higher effort levels. Also, we show that limited liability generates non-responsiveness.

The high-eccentricity asymmetric expansion of the disturbing function for non-planar resonant problems

In this paper we present an extension to the nonplanar case of the asymmetric expansion of the averaged resonant disturbing function of Ferraz-Mello & Sato (1989, A&A 225, 541-547). Comparions with the exact averaged disturbing function are also presented. The expansion gives a good approximation of the exact function in a wide region around the center of expansion.

A note on non-degenerate umbilics and the path formulation for bifurcation problems

Path formulation can be used to classify and structure efficiently multiparameter bifurcation problems around fundamental singularities: the cores. The non-degenerate umbilic singularities are the generic cores for four situations in corank 2: the general or gradient problems and the ℤ 2-equivariant (general or gradient) problems. Those categories determine an interesting 'Russian doll' type of structure in the universal unfoldings of the umbilic singularities. One advantage of our approach is that we can handle one, two or more parameters using the same framework (even considering some special parameter structure, for instance, some internal hierarchy). We classify the generic bifurcations that occur in those cases with one or two parameters.

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

On non-linear and non-ideal interactions in two vibrating problems

In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a DC motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a non-ideal problem. In this work, we considerer two non-ideal problems analyzed by using numerical simulations. The existence of the Sommerfeld effect was verified, that is, the effect of getting stuck at resonance (energy imparted to the DC motor being used to excite large amplitude motions of the supporting structure). We considered two kinds of non-ideal problem: one related to the transverse vibrations of a shaft carrying two disks and another to a piezoceramic bar transducer powered by a vacuum tube generated by a non-ideal source Copyright © 2007 by ASME.

Transposable elements: structure and dynamic of the autonomous retrotransposon R2 in Arthropoda with non-canonical reproduction

Eukaryotic ribosomal DNA constitutes a multi gene family organized in a cluster called nucleolar organizer region (NOR); this region is composed usually by hundreds to thousands of tandemly repeated units. Ribosomal genes, being repeated sequences, evolve following the typical pattern of concerted evolution. The autonomous retroelement R2 inserts in the ribosomal gene 28S, leading to defective 28S rDNA genes. R2 element, being a retrotransposon, performs its activity in the genome multiplying its copy number through a “copy and paste” mechanism called target primed reverse transcription. It consists in the retrotranscription of the element’s mRNA into DNA, then the DNA is integrated in the target site. Since the retrotranscription can be interrupted, but the integration will be carried out anyway, truncated copies of the element will also be present in the genome. The study of these truncated variants is a tool to examine the activity of the element. R2 phylogeny appears, in general, not consistent with that of its hosts, except some cases (e.g. Drosophila spp. and Reticulitermes spp.); moreover R2 is absent in some species (Fugu rubripes, human, mouse, etc.), while other species have more R2 lineages in their genome (the turtle Mauremys reevesii, the Japanese beetle Popilia japonica, etc). R2 elements here presented are isolated in 4 species of notostracan branchiopods and in two species of stick insects, whose reproductive strategies range from strict gonochorism to unisexuality. From sequencing data emerges that in Triops cancriformis (Spanish gonochoric population), in Lepidurus arcticus (two putatively unisexual populations from Iceland) and in Bacillus rossius (gonochoric population from Capalbio) the R2 elements are complete and encode functional proteins, reflecting the general features of this family of transposable elements. On the other hand, R2 from Italian and Austrian populations of T. cancriformis (respectively unisexual and hermaphroditic), Lepidurus lubbocki (two elements within the same Italian population, gonochoric but with unfunctional males) and Bacillus grandii grandii (gonochoric population from Ponte Manghisi) have sequences that encode incomplete or non-functional proteins in which it is possible to recognize only part of the characteristic domains. In Lepidurus couesii (Italian gonochoric populations) different elements were found as in L. lubbocki, and the sequencing is still in progress. Two hypothesis are given to explain the inconsistency of R2/host phylogeny: vertical inheritance of the element followed by extinction/diversification or horizontal transmission. My data support previous study that state the vertical transmission as the most likely explanation; nevertheless horizontal transfer events can’t be excluded. I also studied the element’s activity in Spanish populations of T. cancriformis, in L. lubbocki, in L. arcticus and in gonochoric and parthenogenetic populations of B. rossius. In gonochoric populations of T. cancriformis and B. rossius I found that each individual has its own private set of truncated variants. The situation is the opposite for the remaining hermaphroditic/parthenogenetic species and populations, all individuals sharing – in the so far analyzed samples - the majority of variants. This situation is very interesting, because it isn’t concordant with the Muller’s ratchet theory that hypothesizes the parthenogenetic populations being either devoided of transposable elements or TEs overloaded. My data suggest a possible epigenetic mechanism that can block the retrotransposon activity, and in this way deleterious mutations don’t accumulate.

Sensitivity analysis of a parabolic-elliptic problem

We consider the heat flux through a domain with subregions in which the thermal capacity approaches zero. In these subregions the parabolic heat equation degenerates to an elliptic one. We show the well-posedness of such parabolic-elliptic differential equations for general non-negative L-infinity-capacities and study the continuity of the solutions with respect to the capacity, thus giving a rigorous justification for modeling a small thermal capacity by setting it to zero. We also characterize weak directional derivatives of the temperature with respect to capacity as solutions of related parabolic-elliptic problems.

Direct and inverse transient eddy current problems

Die vorliegende Arbeit behandelt Vorwärts- sowie Rückwärtstheorie transienter Wirbelstromprobleme. Transiente Anregungsströme induzieren elektromagnetische Felder, welche sogenannte Wirbelströme in leitfähigen Objekten erzeugen. Im Falle von sich langsam ändernden Feldern kann diese Wechselwirkung durch die Wirbelstromgleichung, einer Approximation an die Maxwell-Gleichungen, beschrieben werden. Diese ist eine lineare partielle Differentialgleichung mit nicht-glatten Koeffizientenfunktionen von gemischt parabolisch-elliptischem Typ. Das Vorwärtsproblem besteht darin, zu gegebener Anregung sowie den umgebungsbeschreibenden Koeffizientenfunktionen das elektrische Feld als distributionelle Lösung der Gleichung zu bestimmen. Umgekehrt können die Felder mit Messspulen gemessen werden. Das Ziel des Rückwärtsproblems ist es, aus diesen Messungen Informationen über leitfähige Objekte, also über die Koeffizientenfunktion, die diese beschreibt, zu gewinnen. In dieser Arbeit wird eine variationelle Lösungstheorie vorgestellt und die Wohlgestelltheit der Gleichung diskutiert. Darauf aufbauend wird das Verhalten der Lösung für verschwindende Leitfähigkeit studiert und die Linearisierbarkeit der Gleichung ohne leitfähiges Objekt in Richtung des Auftauchens eines leitfähigen Objektes gezeigt. Zur Regularisierung der Gleichung werden Modifikationen vorgeschlagen, welche ein voll parabolisches bzw. elliptisches Problem liefern. Diese werden verifiziert, indem die Konvergenz der Lösungen gezeigt wird. Zuletzt wird gezeigt, dass unter der Annahme von sonst homogenen Umgebungsparametern leitfähige Objekte eindeutig durch die Messungen lokalisiert werden können. Hierzu werden die Linear Sampling Methode sowie die Faktorisierungsmethode angewendet.