Dynamical changes from harmonic vibrations of a limited power supply driving a Duffing oscillator

The harmonic oscillations of a Duffing oscillator driven by a limited power supply are investigated as a function of the alternative strength of the rotor. The semi-trivial and non-trivial solutions are derived. We examine the stability of these solutions and then explore the complex behaviors associated with the bifurcations sequences. Interestingly, a 3D diagram provides a global view of the effects of alternate strength on the appearance of chaos and hyperchaos on the system.

ON THE RADICAL OF A FREE MALCEV ALGEBRA

We prove that the prime radical rad M of the free Malcev algebra M of rank more than two over a field of characteristic not equal 2 coincides with the set of all universally Engelian elements of M. Moreover, let T(M) be the ideal of M consisting of all stable identities of the split simple 7-dimensional Malcev algebra M over F. It is proved that rad M = J(M) boolean AND T(M), where J(M) is the Jacobian ideal of M. Similar results were proved by I. Shestakov and E. Zelmanov for free alternative and free Jordan algebras.

Multiparameter twisted Weyl algebras

We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the multiparameter quantized Weyl algebra and Hayashi's q-analog of the Weyl algebra are special cases of this construction. We classify all simple weight modules over any multiparameter twisted Weyl algebra. Extending results by Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over a class of twisted generalized Weyl algebras which includes the multiparameter twisted Weyl algebras. (C) 2011 Elsevier Inc. All rights reserved.

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

A model and an algebra for semi-structured and full-text queries

The need for a convergence between semi-structured data management and Information Retrieval techniques is manifest to the scientific community. In order to fulfil this growing request, W3C has recently proposed XQuery Full Text, an IR-oriented extension of XQuery. However, the issue of query optimization requires the study of important properties like query equivalence and containment; to this aim, a formal representation of document and queries is needed. The goal of this thesis is to establish such formal background. We define a data model for XML documents and propose an algebra able to represent most of XQuery Full-Text expressions. We show how an XQuery Full-Text expression can be translated into an algebraic expression and how an algebraic expression can be optimized.

Bestimmung des elektrischen Formfaktors des Neutrons G en in der Reaktion 3 He (e,e'n) bei einem Impulsübertrag Q 2 =0.67 (GeV/c) 2

In der Überprüfung von Kernmodellen stellt der elektrische Formfaktor des Neutrons Gen eine wichtige Eingangsgröße dar. Im Rahmen dieser Arbeit wurde am polarisierten Elektronenstrahl des Mainzer Mikrotrons MAMI der elektrische Formfaktor des Neutrons in der Reaktion 3He(e,e'n) bestimmt. Aus dem Verhältnis der Asymmetrien respektive der Helizitätsumkehr der Elektronenpolarisation mit Targetspin senkrecht und parallel zum Impulsübertrag konnte in einer integralen Analyse Gen bestimmt werden. Zusammengefasst ergab sich Gen(Q2=0.67 (GeV/c)2) = 0.0468 +- 0.0064(stat} +- 0.0027(syst}. Um den Einfluß von Kernbindungseffekten, die z. Zt. von der Gruppe um Prof. Glöckle in Bochum theoretisch gerechnet werden, auch experimentell abzusichern, wurden parallel zur Gen-Messung die Targetasymmetrie Ay0 3He(e,e'n) und Protonenasymmetrie 3He(e,e'p) bestimmt. Die Empfindlichkeit dieser Observablen auf FSI und D-Wellenbeiträge schafft Redundanzen, aus denen auf die Eigenschaften des freien Neutrons im gebundenen System geschlossen werden kann.

Strukturen und Phasen des beta-Eukryptits sowie die Sammlung von Beugungsdaten mit axialen q-Scans

Der 'gestopfte Hochquarz' ß-Eukryptit (LiAlSiO4) ist bekannt für seine außergewöhnliche anisotrope Li-Ionenleitfähigkeit und die nahe Null liegende thermische Ausdehnung.Untersucht wurde die temperaturabhängige ß-Eukryptit-Phasenabfolge, insbesondere die modulierte Phase. Deren Satellitenreflexe sind gegenüber den normalen Reflexen erheblich verbreitert, überlappen miteinander sowie mit den dazwischen liegenden 'a-Reflexen' zu Tripletts. Für die Separation der Triplett-Intensitäten waren bisherige Standardverfahren zur Beugungsdatensammlung ungeeignet. Mit 'axialen q-Scans' wurde ein neuartiges Verfahren entwickelt. Intensitäten wurden mit dem neu-entwickelten least squares-Programm GKLS aus 2000 Profilen seriell und automatisch gewonnen und erfolgreich auf Standarddaten skaliert. Die Verwendung verbreiterter Reflexprofile erwies sich als zulässig.Die Verbreiterung wurde auf eine verminderte Fernordnung der Modulation von 11 bis 16 Perioden zurückgeführt (Analyse mit der Gitterfunktion), womit ein ungewöhnliches beugungswinkelabhängiges Verhalten der Reflexbreiten korrespondiert und mit typischen Antiphasendomänendurchmessern (andere Autoren) korreliert.Eine verminderte Si-/ Al-Ordnung wird als ursächlich für geringe Domänengrößen und Fernordnung angesehen, sowie für Eigenschaften wie z.B. a/c-Verhältnisse, Ausdehnungskoeffizienten, Ionenleitfähigkeit, Strukturtyp und Umwandlungstemperaturen. Änderungen des SiO2-Gehaltes, der Temperatur oder der Si- /Al-Ordnung zeitigen für einige Eigenschaften ähnliche Wirkungen.Die gemittelte Struktur der modulierten Phase wurde erstmals zuverlässig bestimmt, die Rolle des Li charakterisiert, Zweifel an der hexagonalen Symmetrie des ß-Eukryptits wurden ausgeräumt und die Bestimmung der modulierten Struktur wurde weitgehend vorbereitet.

Use of computer algebra in the calculation of Feynman diagrams

The increasing precision of current and future experiments in high-energy physics requires a likewise increase in the accuracy of the calculation of theoretical predictions, in order to find evidence for possible deviations of the generally accepted Standard Model of elementary particles and interactions. Calculating the experimentally measurable cross sections of scattering and decay processes to a higher accuracy directly translates into including higher order radiative corrections in the calculation. The large number of particles and interactions in the full Standard Model results in an exponentially growing number of Feynman diagrams contributing to any given process in higher orders. Additionally, the appearance of multiple independent mass scales makes even the calculation of single diagrams non-trivial. For over two decades now, the only way to cope with these issues has been to rely on the assistance of computers. The aim of the xloops project is to provide the necessary tools to automate the calculation procedures as far as possible, including the generation of the contributing diagrams and the evaluation of the resulting Feynman integrals. The latter is based on the techniques developed in Mainz for solving one- and two-loop diagrams in a general and systematic way using parallel/orthogonal space methods. These techniques involve a considerable amount of symbolic computations. During the development of xloops it was found that conventional computer algebra systems were not a suitable implementation environment. For this reason, a new system called GiNaC has been created, which allows the development of large-scale symbolic applications in an object-oriented fashion within the C++ programming language. This system, which is now also in use for other projects besides xloops, is the main focus of this thesis. The implementation of GiNaC as a C++ library sets it apart from other algebraic systems. Our results prove that a highly efficient symbolic manipulator can be designed in an object-oriented way, and that having a very fine granularity of objects is also feasible. The xloops-related parts of this work consist of a new implementation, based on GiNaC, of functions for calculating one-loop Feynman integrals that already existed in the original xloops program, as well as the addition of supplementary modules belonging to the interface between the library of integral functions and the diagram generator.

Le matrici e la loro algebra

In questa tesi ci si propone lo studio dell'anello delle matrici quadrate di ordine n, su un campo, per arrivare a dimostrare che ha solo ideali banali pur non essendo un campo. Allo scopo si introducono le operazioni elementari e il procedimento di traduzione di tali operazioni con opportune moltiplicazioni per matrici dette elementari. Si considera inoltre il gruppo generale lineare arrivando a dimostrare che un particolare sottoinsieme delle matrici elementari è un generatore di tale gruppo.

Synthesis and characterization of metal-chalcogenide MQ 2-Nanoparticles (M = Mo, W, Zr; Q = S, O)

Here, we present the adaptation and optimization of (i) the solvothermal and (ii) the metal-organic chemical vapor deposition (MOCVD) approach as simple methods for the high-yield synthesis of MQ2 (M=Mo, W, Zr; Q = O, S) nanoparticles. Extensive characterization was carried out using X-ray diffraction (XRD), scanning and transmission electron micros¬copy (SEM/TEM) combined with energy dispersive X-ray analysis (EDXA), Raman spectroscopy, thermal analyses (DTA/TG), small angle X-ray scattering (SAXS) and BET measurements. After a general introduction to the state of the art, a simple route to nanostructured MoS2 based on the decomposition of the cluster-based precursor (NH4)2Mo3S13∙xH2O under solvothermal conditions (toluene, 653 K) is presented. Solvothermal decomposition results in nanostructured material that is distinct from the material obtained by decomposition of the same precursor in sealed quartz tubes at the same temperature. When carried out in the presence of the surfactant cetyltrimethyl¬ammonium bromide (CTAB), the decomposition product exhibits highly disordered MoS2 lamellae with high surface areas. The synthesis of WS2 onion-like nanoparticles by means of a single-step MOCVD process is discussed. Furthermore, the results of the successful transfer of the two-step MO¬CVD based synthesis of MoQ2 nanoparticles (Q = S, Se), comprising the formation of amorphous precursor particles and followed by the formation of fullerene-like particles in a subsequent annealing step to the W-S system, are presented. Based on a study of the temperature dependence of the reactions a set of conditions for the formation of onion-like structures in a one-step reaction could be derived. The MOCVD approach allows a selective synthesis of open and filled fullerene-like chalcogenide nanoparticles. An in situ heating stage transmission electron microscopy (TEM) study was employed to comparatively investigate the growth mechanism of MoS2 and WS2 nanoparticles obtained from MOCVD upon annealing. Round, mainly amorphous particles in the pristine sample trans¬form to hollow onion-like particles upon annealing. A significant difference between both compounds could be demonstrated in their crystallization conduct. Finally, the results of the in situ hea¬ting experiments are compared to those obtained from an ex situ annealing process under Ar. Eventually, a low temperature synthesis of monodisperse ZrO2 nanoparticles with diameters of ~ 8 nm is introduced. Whereas the solvent could be omitted, the synthesis in an autoclave is crucial for gaining nano-sized (n) ZrO2 by thermal decomposition of Zr(C2O4)2. The n-ZrO2 particles exhibits high specific surface areas (up to 385 m2/g) which make them promising candidates as catalysts and catalyst supports. Co-existence of m- and t-ZrO2 nano-particles of 6-9 nm in diameter, i.e. above the critical particle size of 6 nm, demonstrates that the particle size is not the only factor for stabilization of the t-ZrO2 modification at room temperature. In conclusion, synthesis within an autoclave (with and without solvent) and the MOCVD process could be successfully adapted to the synthesis of MoS2, WS2 and ZrO2 nanoparticles. A comparative in situ heating stage TEM study elucidated the growth mechanism of MoS2 and WS2 fullerene-like particles. As the general processes are similar, a transfer of this synthesis approach to other layered transition metal chalcogenide systems is to be expected. Application of the obtained nanomaterials as lubricants (MoS2, WS2) or as dental filling materials (ZrO2) is currently under investigation.