On the periodic solutions of a class of duffing differential equations

In this work we study the periodic solutions, their stability and bifurcation for the class of Duffing differential equation mathematical equation represented where C > 0, ε > 0 and Λ are real parameter, A(t), b(t) and h(t) are continuous T periodic functions and ε is sufficiently small. Our results are proved using the averaging method of first order.

On exponential stability of functional differential equations with variable impulse perturbations

We consider a class of functional differential equations subject to perturbations, which vary in time, and we study the exponential stability of solutions of these equations using the theory of generalized ordinary differential equations and Lyapunov functionals. We introduce the concept of variational exponential stability for generalized ordinary differential equations and we develop the theory in this direction by establishing conditions for the trivial solutions of generalized ordinary differential equations to be exponentially stable. Then, we apply the results to get corresponding ones for impulsive functional differential equations. We also present an example of a delay differential equation with Perron integrable right-hand side where we apply our result.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.

General method for reducing the two-body Dirac equation

A semirelativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schrödinger-type equations is also discussed. © 1992 American Institute of Physics.

Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

We define the Virasoro algebra action on imaginary Verma modules for affine and construct an analogue of the Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.

STRUCTURE AND BIFURCATION OF PULLBACK ATTRACTORS IN A NON-AUTONOMOUS CHAFEE-INFANTE EQUATION

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, u(t) = u(xx) + lambda(xx) - lambda u beta(t)u(3), and investigate the bifurcations that this attractor undergoes as A is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.

A uniqueness theorem for the determination of sources in the Germain–Lagrange plate equation

We prove a uniqueness result related to the Germain–Lagrange dynamic plate differential equation. We consider the equation {∂2u∂t2+△2u=g⊗f,in ]0,+∞)×R2,u(0)=0,∂u∂t(0)=0, where uu stands for the transverse displacement, ff is a distribution compactly supported in space, and g∈Lloc1([0,+∞)) is a function of time such that g(0)≠0g(0)≠0 and there is a T0>0T0>0 such that g∈C1[0,T0[g∈C1[0,T0[. We prove that the knowledge of uu over an arbitrary open set of the plate for any interval of time ]0,T[]0,T[, 0

Parameterschätzung in zeitdiskreten ergodischen Markov-Prozessen am Beispiel des Cox-Ingersoll-Ross-Modells

In dieser Arbeit geht es um die Schätzung von Parametern in zeitdiskreten ergodischen Markov-Prozessen im allgemeinen und im CIR-Modell im besonderen. Beim CIR-Modell handelt es sich um eine stochastische Differentialgleichung, die von Cox, Ingersoll und Ross (1985) zur Beschreibung der Dynamik von Zinsraten vorgeschlagen wurde. Problemstellung ist die Schätzung der Parameter des Drift- und des Diffusionskoeffizienten aufgrund von äquidistanten diskreten Beobachtungen des CIR-Prozesses. Nach einer kurzen Einführung in das CIR-Modell verwenden wir die insbesondere von Bibby und Sørensen untersuchte Methode der Martingal-Schätzfunktionen und -Schätzgleichungen, um das Problem der Parameterschätzung in ergodischen Markov-Prozessen zunächst ganz allgemein zu untersuchen. Im Anschluss an Untersuchungen von Sørensen (1999) werden hinreichende Bedingungen (im Sinne von Regularitätsvoraussetzungen an die Schätzfunktion) für die Existenz, starke Konsistenz und asymptotische Normalität von Lösungen einer Martingal-Schätzgleichung angegeben. Angewandt auf den Spezialfall der Likelihood-Schätzung stellen diese Bedingungen zugleich lokal-asymptotische Normalität des Modells sicher. Ferner wird ein einfaches Kriterium für Godambe-Heyde-Optimalität von Schätzfunktionen angegeben und skizziert, wie dies in wichtigen Spezialfällen zur expliziten Konstruktion optimaler Schätzfunktionen verwendet werden kann. Die allgemeinen Resultate werden anschließend auf das diskretisierte CIR-Modell angewendet. Wir analysieren einige von Overbeck und Rydén (1997) vorgeschlagene Schätzer für den Drift- und den Diffusionskoeffizienten, welche als Lösungen quadratischer Martingal-Schätzfunktionen definiert sind, und berechnen das optimale Element in dieser Klasse. Abschließend verallgemeinern wir Ergebnisse von Overbeck und Rydén (1997), indem wir die Existenz einer stark konsistenten und asymptotisch normalen Lösung der Likelihood-Gleichung zeigen und lokal-asymptotische Normalität für das CIR-Modell ohne Einschränkungen an den Parameterraum beweisen.

Preconditioning strategies for the numerical solution of convection-diffusion partial differential equations

Il trattamento numerico dell'equazione di convezione-diffusione con le relative condizioni al bordo, comporta la risoluzione di sistemi lineari algebrici di grandi dimensioni in cui la matrice dei coefficienti è non simmetrica. Risolutori iterativi basati sul sottospazio di Krylov sono ampiamente utilizzati per questi sistemi lineari la cui risoluzione risulta particolarmente impegnativa nel caso di convezione dominante. In questa tesi vengono analizzate alcune strategie di precondizionamento, atte ad accelerare la convergenza di questi metodi iterativi. Vengono confrontati sperimentalmente precondizionatori molto noti come ILU e iterazioni di tipo inner-outer flessibile. Nel caso in cui i coefficienti del termine di convezione siano a variabili separabili, proponiamo una nuova strategia di precondizionamento basata sull'approssimazione, mediante equazione matriciale, dell'operatore differenziale di convezione-diffusione. L'azione di questo nuovo precondizionatore sfrutta in modo opportuno recenti risolutori efficienti per equazioni matriciali lineari. Vengono riportati numerosi esperimenti numerici per studiare la dipendenza della performance dei diversi risolutori dalla scelta del termine di convezione, e dai parametri di discretizzazione.

Monodromy calculations for some differential equations

In vielen Teilgebieten der Mathematik ist es w"{u}nschenswert, die Monodromiegruppe einer homogenen linearen Differenzialgleichung zu verstehen. Es sind nur wenige analytische Methoden zur Berechnung dieser Gruppe bekannt, daher entwickeln wir im ersten Teil dieser Arbeit eine numerische Methode zur Approximation ihrer Erzeuger.rnIm zweiten Abschnitt fassen wir die Grundlagen der Theorie der Uniformisierung Riemannscher Fl"achen und die der arithmetischen Fuchsschen Gruppen zusammen. Auss erdem erkl"aren wir, wie unsere numerische Methode bei der Bestimmung von uniformisierenden Differenzialgleichungen dienlich sein kann. F"ur arithmetische Fuchssche Gruppen mit zwei Erzeugern erhalten wir lokale Daten und freie Parameter von Lam'{e} Gleichungen, welche die zugeh"origen Riemannschen Fl"achen uniformisieren. rnIm dritten Teil geben wir einen kurzen Abriss zur homologischen Spiegelsymmetrie und f"uhren die $widehat{Gamma}$-Klasse ein. Wir erkl"aren wie diese genutzt werden kann, um eine Hodge-theoretische Version der Spiegelsymmetrie f"ur torische Varit"aten zu beweisen. Daraus gewinnen wir Vermutungen "uber die Monodromiegruppe $M$ von Picard-Fuchs Gleichungen von gewissen Familien $f:mathcal{X}rightarrow bbp^1$ von $n$-dimensionalen Calabi-Yau Variet"aten. Diese besagen erstens, dass bez"uglich einer nat"urlichen Basis die Monodromiematrizen in $M$ Eintr"age aus dem K"orper $bbq(zeta(2j+1)/(2 pi i)^{2j+1},j=1,ldots,lfloor (n-1)/2 rfloor)$ haben. Und zweitens, dass sich topologische Invarianten des Spiegelpartners einer generischen Faser von $f:mathcal{X}rightarrow bbp^1$ aus einem speziellen Element von $M$ rekonstruieren lassen. Schliess lich benutzen wir die im ersten Teil entwickelten Methoden zur Verifizierung dieser Vermutungen, vornehmlich in Hinblick auf Dimension drei. Dar"uber hinaus erstellen wir eine Liste von Kandidaten topologischer Invarianten von vermutlich existierenden dreidimensionalen Calabi-Yau Variet"aten mit $h^{1,1}=1$.

Social cognition as a mediator variable between neurocognition and functional outcome in schizophrenia: empirical review and new results by structural equation modeling

Cognitive impairments are currently regarded as important determinants of functional domains and are promising treatment goals in schizophrenia. Nevertheless, the exact nature of the interdependent relationship between neurocognition and social cognition as well as the relative contribution of each of these factors to adequate functioning remains unclear. The purpose of this article is to systematically review the findings and methodology of studies that have investigated social cognition as a mediator variable between neurocognitive performance and functional outcome in schizophrenia. Moreover, we carried out a study to evaluate this mediation hypothesis by the means of structural equation modeling in a large sample of 148 schizophrenia patients. The review comprised 15 studies. All but one study provided evidence for the mediating role of social cognition both in cross-sectional and in longitudinal designs. Other variables like motivation and social competence additionally mediated the relationship between social cognition and functional outcome. The mean effect size of the indirect effect was 0.20. However, social cognitive domains were differentially effective mediators. On average, 25% of the variance in functional outcome could be explained in the mediation model. The results of our own statistical analysis are in line with these conclusions: Social cognition mediated a significant indirect relationship between neurocognition and functional outcome. These results suggest that research should focus on differential mediation pathways. Future studies should also consider the interaction with other prognostic factors, additional mediators, and moderators in order to increase the predictive power and to target those factors relevant for optimizing therapy effects.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Kinetic study of thermal 1,3-dipolar cycloaddition of azomethine ylides using differential scanning calorimetry as monitoring window

Kinetics of 1,3-dipolar cycloaddition involving azomethine ylides, generated from thermal [1,2]-prototropy of the corresponding imino ester, employing differential scanning calorimetry (DSC), is surveyed. Glycine and phenylalanine derived imino esters have different behavior. The first one prefers reacting with itself at 75 ºC, rather than with the dipolarophile. However, the α-substituted imino ester gives the cycloadduct at higher temperatures. The thermal dynamic analysis by 1H NMR of the neat reaction mixture of the glycine derivative reveals the presence of signals corresponding to the dipole in very small proportion. The non-isothermal and isothermal DSC curves of the cycloaddition of phenylalaninate and diisobutyl fumarate are obtained from freshly prepared samples. The application of known kinetic models and mathematical multiple non-linear regressions (NLR) allow to determine and to compare Ea, lnA, reaction orders, and reaction enthalpy. Finally a rate equation for each different temperature can be established for this particular thermal cycloaddition.

Iterative and direct methods for solving Poisson's equation and their adaptability to ILLIAC IV,

Includes bibliography.

Automatic detection and treatment of oscillatory and/or stiff ordinary differential equations /

"Presented at the Differential Equation Workshop, Center for Interdisciplinary Research (Zif), University of Bielefeld, West Germany, April 21, 1980."