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Peter Jones' theorem on the factorization of Ap weights is sharpened for weights with bounds near 1, allowing the factorization to be performed continuously near the limiting, unweighted case. When 1 < p < infinite and omega is an Ap weight with bound Ap(omega) = 1 + epsilon, it is shown that there exist Asub1 weights u, v such that both the formula omega = uv(1-p) and the estimates A1 (u), A1 (v) = 1 + Omikron (√epsilon) hold. The square root in these estimates is also proven to be the correct asymptotic power as epsilon -> 0.
The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator.
In the paper we study the possibility to represent the index formula for spectral boundary value problems as a sum of two terms, the first one being homotopy invariant of the principal symbol, while the second depends on the conormal symbol of the problem only. The answer is given in analytical, as well as in topological terms.
The paper deals with a non-linear singular partial differential equation: (E) t∂/∂t = F(t, x, u, ∂u/∂x) in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by Gérard-Tahara [2]. In this paper, under the assumption that (E) is of totally characteristic type, the authors give a sufficient condition for (E) to have a unique holomorphic solution. The result is extended to higher order case.
The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. Concerning the geometry we even admit a more general behaviour, namely oscillating cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges.
Inhalt: Leitartikel Kongreß für Jüdische Studien - Sektion beim Deutschen Orientalistentag / Selbstkritik, Selbstverpflichtung oder Selbstzweck? / 16. DGfE-Kongreß, Der osteuropäische Chassidismus - neuere Forschungen / Schließung der Israelwissenschaft in der Humboldt-Universität / Einführung in das Fach Jüdische Studien / Notizen / Aus der jüdischen Welt / Veröffentlichungen unserer Mitglieder / Verbandsnachrichten
The nonlinear interaction of waves excited by the modified two-stream instability (Farley-Buneman instability) is considered. It is found that, during the linear stage of wave growth, the enhanced pressure of the high-frequency part of the waves locally generates a ponderomotive force. This force acts on the plasma particles and redistributes them. Thus an additional electrostatic polarization field occurs, which influences the low-frequency part of the waves. Then, the low-frequency waves also cause a redistribution of the high-frequency waves. In the paper, a self-consistent system of equations is obtained, which describes the nonlinear interaction of the waves. It is shown that the considered mechanism of wave interaction causes a nonlinear stabilization of the high-frequency waves’ growth and a formation of local density structures of the charged particles. The density modifications of the charged particles during the non-linear stage of wave growth and the possible interval of aspect angles of the high-frequency waves are estimated.
We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.
This paper deals with the electrical conductivity problem in geophysics. It is formulated as an elliptic boundary value problem of second order for a large class of bounded and unbounded domains. A special boundary condition, the so called "Complete Electrode Model", is used. Poincaré inequalities are formulated and proved in the context of weighted Sobolev spaces, leading to existence and uniqueness statements for the boundary value problem. In addition, a parameter-to-solution operator arising from the inverse conductivity problem in medicine (EIT) and geophysics is investigated mathematically and is shown to be smooth and analytic.
The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.
Contents: 1 Introduction 2 Formation and destruction of sporadic E-layers 3 Temporal variations of parameters of sporadic E-layers during earthquake preparation 3.1 Temporal variations of fbEs with time-scales of a few hours 3.2 Study of fbEs variations with characteristic time-scales of 0.5-3 hours 3.3 Variations of the parameters of sporadic E-layers with characteristic time-scales of 15-45 minutes 3.4 Sporadic E-layer variations with characteristic time-scales of 2-15 minutes 4 On the spatial scales of sporadic E-layer disturbances related to seismic activity 5 Complex experimental researches of the ionosphere, electromagnetic noise and the geomagnetic field 5.1 Ionospheric and electromagnetic phenomena of the Kayraccum earthquake in 1985 5.2 Comparison of anomalies with characteristic time-scales of 2-3 hours for ionospheric E- and F-layers, and temporal behaviour of electromagnetic noise emission intensity 5.3 Night airglow emissions in the E-region before earthquakes and sporadic E-layer variations 6 Physical models of lithosphere-ionosphere links 6.1 Lithosphere-ionosphere links due to AGW 6.2 Electromagnetic models for the lithosphere-ionosphere coupling 6.3 Sporadic E-layers as current generators 7 Discussion and conclusion
In single photon emission computed tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. The data gathered suffer from attenuation due to the tissue density µ. Each imaged slice incorporates noisy sample values of the nonlinear attenuated Radon transform (formular at this place in the original abstract) Traditional theory for SPECT reconstruction treats µ as a known parameter. In practical applications, however, µ is not known, but either crudely estimated, determined in costly additional measurements or plainly neglected. We demonstrate that an approximation of both f and µ from SPECT data alone is feasible, leading to quantitatively more accurate SPECT images. The result is based on nonlinear Tikhonov regularization techniques for parameter estimation problems in differential equations combined with Gauss-Newton-CG minimization.
The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.
Inhalt: Wolfgang Thiem Lehrerbildung in Ländern gesellschaftlicher Transformation auf dem Prüfstand vergleichender Betrachtung : Resümee einer Tagung Wladimir I. Andreev Zum Problem der pädagogischen Ausbildung von Lehrern in der Republik Belarus : Konzeptionen und Realität Wassili A. Bondar; Adam A. Grimot Tendenzen der Entwicklung pädagogischer Bildung in der Republik Belarus Maria Jakowicka; Kazimierz Uzdzicki Standards der Ausbildung von Fachlehrern in Polen Zenon Jasinski Berufskompetenzen der Lehrer Maria Molnar Reform der Lehrerbildung in der Folge der politischen und gesellschaftlichen Transformationen in Ungarn Magdalena Piorunek Qualitative Aspekte der Änderungen in der Lehrerbildung in Polen Ludmilla Regusch Thesen zur psychologischen Ausbildung des Lohrers an der Pädagogischen Universität A. I. Herzen in St. Petersburg (Rußland) Lech Salacinski Stereotype bei der pädagogischen Ausbildung von Lehrern in Polen : Versuche zu ihrer Überwindung Eleonora Sapia-Drewniak Der Lehrer im Antlitz gesellschaftlicher Veränderungen in Polen Andreas Seidel Zum Stellenwert praktischer Ausbildung Wolfgang Thiem Aktuelle Materialien und Diskussionen zur Weiterentwicklung der Lehrerbildung in Deutschland Frank Tosch: Lehrerbildung in Potsdam Ein Modell auf dem Prüfstand zwischen Hoffen und Realität Krystina Zielinska Strukturelle und bildungspolitische Aspekte der Lehrerbildung in Polen
Antike Epik : zur Geschichte narrativer metrischer Großtexte in oralen und semioralen Gesellschaften
(1998)
Inhalt: 0 Einführung 0.1 Literatur 0.2 Epos 0.3 Gattung 0.4 Aufgabe der Vorlesung 1 Anfänge griechischer Epik 1.1 Homer 1.2 Das Problem 1.3 Der Text 1.4 Medienwechsel 1.4.1 Oralpoetry 1.4.2 Schriftlichkeit 1.4.3 Leistungen der Verschriftlichung 1.5 Das Publikum 1.6 Die ersten Epen 1.7 Ilias 1.7.1 Inhalt 1.7.2 Struktur 1.7.3 Charakteristika 1.7.4 Troia und die Quellenfrage 1.8 Odyssee 1.8.1 Inhalt 1.8.2 Struktur 1.9 Wirkungsgeschichte 2 Anfänge römischer Epik 2.0 Griechische Einflüsse in der vorliterarischen Epoche 2.1 Der Befund 2.2 Das Problem 2.3 Methodisches Vorgehen 2.4 Inventar und Verortung mündlicher Literatur 2.5 Ergänzungen zum Sitz im Leben 2.6 Kristallisationskerne des Verschriftlichungsprozesses 2.7 Epos 2.8 Veränderungen im Gesamtsystem literarischer Kommunikation 2.9 Die Leistung des verschriftlichten Epos 3 Entwicklungen des zweiten und ersten Jahrhunderts v. Chr 3.1 Ennius 3.1.1 Zu Person und Werk 3.1.2 Die Annales 3.1.3 Kontext 3.2 Die weitere römische Entwicklung 3.3 Hellenistische griechische Epik 3.4 Rom 4 Vergils Aeneis 4.1 Biographie 4.2 Grundentscheidungen 4.3 Inhalt 4.4 Rezeption 4.4.1 Vergil und die europäische Literaturgeschichte 4.4.2 Zeitgenössische Rezeption 4.5 Leistung 4.5.1 Hauptperson der Aeneis ist Vergil 4.5.2 Gegenstand der Aeneis ist das zeitgenössische Rom 4.5.3 Kein Götter-, sondern ein Menschenapparat in der Aeneis 4.5.4 Die Aeneis nicht Helden-, sondern Proletarierepos 5 Das antike Lehrgedicht: Lukrez 5.1 Expositorische Dichtung 5.2 Der Epikureer Lukrez 5.3 Werkübersicht 5.4 Aussage 6 Ovid 6.1 Einführung: Ovidrezeption 6.2 Zur Person 6.3 Metamorphosen: Ein erster Zugang 6.4 Augusteische Epik 6.5 Die Metamorphosen als Epos-Parodie 6.5.1 Metamorphosen 6.5.2 Großepos 6.5.3 Systematisierung 6.5.4 Handlungsführung 6.5.5 Ovid und seine Vorgänger 6.5.6 Erzählen im Epos 6.5.7 Einzelmotive 6.5.8 Gelebte Parodie 7 Historische Epik der Prinzipatszeit 7.1 Allgemeines 7.2 Lukan 7.3 Die Pharsalia 7.3.1 Titel und Quellen 7.3.2 Inhalt 7.3.3 Gehalt 7.4 Silius Italicus 7.5 Ausblick 8 Mythologische Epik 8.1 Einführung 8.2 Valerius Flaccus 8.3 Statius 8.3.1 Zur Person 8.3.2 Thebais: Inhalt 8.3.3 Komposition 8.3.4 Einheitlichkeit 8.4 Manierismus 9 Die spätantike Epik 9.1 Überblick 9.1.1 Historischer Überblick 9.1.2 Der literaturgeschichtliche Einschnitt 9.1.3 Präzisierung 1: Christentum 9.1.4 Präzisierung 2: Ausnahmen 9.1.5 Präzisierung 3: Griechische Epik 9.1.6 Entwicklungsstränge 9.2 Panegyrisch-historische Dichtung 9.2.1 Allgemeines 9.2.2 Claudius Claudianus 9.3 Christliche Dichtung 9.3.1 Anfangsphase 9.3.2 Hauptphase 10 Epilog
Der dritte Band der Potsdamer Textbücher befasst sich mit gesellschaftlichen Entwicklungen im konfliktreichen Nahen Osten. Die Zusammenstellung der Texte erfolgte sowohl mit Blick auf die anhaltende Kulturkreisdiskussion als auch hinsichtlich der Bemühungen um Stabilität in dieser Region. Hinzu kommen Analysen zur wirtschaftlichen Entwicklung und den politischen Regimes in Israel, Palästina, Ägypten, im Jemen und Iran. Auszüge aus Verfassungen arabischer Staaten, statistische Angaben und eine Bibliographie vervollständigen das Textbuch.
Die Anwendung von optischen Parametern zur Stoffcharakterisierung wird diskutiert. Dabei ist der Schwerpunkt der Diskussion auf absorptions- und fluoreszenzspektroskopische Methoden gesetzt. Beide Methoden können schnell und zuverlässig – auch im on-line Betrieb – eingesetzt werden. Der Beitrag soll einen Überblick über die grundlegenden Möglichkeiten der Anwendung beider Methoden geben.
The fiscal reform of 1994 was introduced to strengthen the redistributive function of central government. In the aftermath of the reform it turned out, however, that the dominating cleavage is not necessarily the rivalry between "centre" and "regions", mainly because of the very complex relationships within the provinces. Though taxation itself is highly centralized there is a growing tendency of expensation of "extra-budget revenues". That is why the share of the central government concerning all revenues fell to 27%, falling considerably short of the purpose of the fiscal reform to increase the rate of central redistribution to 60% of the national fiscal ressources. Local communities have turned out to be rather successful in collecting non-tax revenues, concentrating on the non-state sectors of the economy. The problem is not so much the threat of fiscal decentralization but the definition of rules and procedures in the relationship between centre, provinces and local administrations.
Nowadays the term "technocracy", which means the elimination of politics by the rule of scientific reasoning, is most often used with a quite negative overtone. Technocrats are described as experts without morals, able to function in any kind of political system. Nevertheless one should remember that the technocratic idea contained from the very beginning a strong ethic element: conventional political power as an instrument of repression should be replaced by the rule of sciences as an instrument to improve human life. Although the idea of eliminating politics by "science-based" decisions of an autocratic leadership has been widely used to legitimate totalitarian rule, it is obvious, that clear technocratic reasoning and decision making do not go conform with the functioning of a totalitarian system. On the contrary, technic and technologic innovation accelerated the breakdown of totalitarianism. The complex character of modern societies calls for regulation by markets and pluralistic political systems. The evolution of our technical civilization improved the conditions for democratic selforganisation.
The economic reforms in the German Democratic Republic during the 60s, known as "New Economic System" (NES) or "Economic System of Socialism" (ESS) have been characterised by historians as truly technocratic. What is often not known is the fact, that during the first debate on economic reform in Eastern Germany in 1954-1958 the idea of democratic reform was prominent thanks to the role and writing of the outstanding GAR economist Fritz Behrens, who favoured a diminished role of the state in the economy and the self-rule of the workers in the factories. Behrens and his followers were denounced by party leader Walter Ulbricht as "revisionist". Together with his economic advisor, Wolfgang Berger, originally a scholar of Behrens’, he started the NES and ESS in the 60s. Behrens remained barred from the management of the reform, in which Berger plaid a prominent role. When Behrens began again to publish his demands for a democratic reform in 1967, thus intervening in the progress of the reform, he was forced to leave his academic job into retirement. In 1971, Erich Honekker succeeded Ulbricht. The economic reform was stopped. And Berger lost his job, too.
Since 1989 the German-Czech relationship has been burdened by the problem of a just assessment of World War II and the following forced transfer of the Sudeten Germans. Why are democrats on both sides who acknowledge the same values and principles unable to reach an agreement about crucial events in the past? The political and legal differences imply a moral dissent which is not being discussed systematically. The article tries to investigate the deficits of the moral arguments on both sides.
In August 1997 the Australian Government released the first White Paper ever issued on its foreign policy. As one important element, this essay tries to delineate the pro Asia-Pacific shift of Australia’s international economic and security orientations, particularly since the early 1970s - a foreign policy which could rest upon an certain bipartisan basis. The recently launched White Paper represents a new reflection upon Australia’s national interests and a soft relativisation of the strong emphasis on regional and multilateral foreign policy performances of former governments. According to a least the author’s judgement, the fundamental legacy of Australia’s international relations remain: a certain (a definite?) contradiction between the country’s predominant cultural and ethnic (!) heritage on the one hand and its geographical location on the other.
Auf der Suche nach einem neuen Ideal : zu Theorie, Norm und Praxis des Rechtsstaats in der VR China
(1998)
Besides establishing a legal system for the needs of economic construction, legal theory and legislation in China are extending their concern from an instrumental concept of law to a more value based notion, thus supplementing "rule by laws" by elements of the "Rechtsstaat" (rule of law). Whereas legal and constitutional theory take more and more bold views concerning integrating structures of checks and balances and division of powers into the legal system, urging for statutory control of the ruling party, for reforming the National People’s Congress into a responsible legislative body based on real representation of the people, providing for constitutionality of legal norms by a system of judicial review etc., legislation has started to deal with certain aspects of the Rechtsstaat in fields as administrative, criminal and criminal procedure law. In view of grave problems of implementation, this legislation may partly be regarded more to be an expression of intention to develop gradually a new ideal and a new legitimation for the political system than well established actual practice.
In 1988, the Government of the People’s Republic of China established the island of Hainan as a province and made it a Special Economic Zone. While the hope for a spectecular economic take off was the main driving force behind this decision, it provided China with an area where far reaching trial-and-error politics could be. Hence the new provincial government was granted the privilege of setting its own legal framework for administering the special economic policies and establishing a governmental structure guided by the principle of "Small government, big society". Although some of the efforts to reduce the administration in terms of scope and resources, to develop and strengthen non-governmental organizations and provide economic actors with a minimum of freedom and reliability proved successful, the overall results are mixed: While well-being and opportunities for self-fulfillment clearly grew, political participation is still confined to areas defined by the Communist Party.
Projekt: Nachhaltiges Brandenburg ; Projekt: Nachhaltige, umweltgerechte Regionalentwicklung in Ostprignitz-Ruppin ; Projekt: Entwicklung nachhaltiger Landnutzung; Projekt: Integrierte Umweltberatung und ökologische Zielsetzungen im Landkreis; Projekt: Fachinformationssystem Naturschutz und Landschaftspflege des Landesumweltamtes Brandenburg ; Projekt: Umweltverträglichkeitsprüfung ; Projekt: Planung und Projektierung der Abwasserentsorgung im Land Brandenburg (1990-1994)
Brandenburgisches Umweltforschungszentrum e.V.:
Arbeitsgruppe: Nachhaltigkeit ; Arbeitsgruppe: Umwelt- und Biotechnologie ; Arbeitsgruppe: Umweltmanagement ; Arbeitsgruppe: Umweltsoziologie ;
Zentrum für Umweltwissenschaften:
Arbeitsgruppe: Betriebliches Umweltmanagement/Umweltbewußtes Konsumentenverhalten ; Arbeitsgruppe: Grüne Bioraffinerie ; Arbeitsgruppe: Integrierter Arten- und Biotopschutz ; Arbeitsgruppe: LIDAR-Inversionen ; Arbeitsgruppe: FG Ökotechnologie ; Arbeitsgruppe: Regenerative Energien ; Arbeitsgruppe: Stoffdynamik in Geosystemen ; Arbeitsgruppe: Umweltbildung
Betrachtungen zur Rolle von Frequenzmodulationen in der sozialen Kommunikation bei Tier und Mensch
(1998)
Ethologie und Umweltbildung
(1998)
Zur Nahrungswahl der Schleiereule (Tyto alba guttata) im Landkreis Potsdam-Mittelmark (Brandenburg)
(1998)
The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.
We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.
We discuss the Cauchy problem for the Dolbeault cohomology in a domain of C n with data on a part of the boundary. In this setting we introduce the concept of a Carleman function which proves useful in the study of uniqueness. Apart from an abstract framework we show explicit Carleman formulas for the Dolbeault cohomology.
Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.
Der Weltstrafgerichtshof
(1998)
Menschenrechte in Mosambik
(1998)
The stability of the quiescent ground state of an incompressible, viscous and electrically conducting fluid sheet, bounded by stress-free parallel planes and driven by an external electric field tangential to the boundaries, is studied numerically. The electrical conductivity varies as cosh–2(x1/a), where x1 is the cross-sheet coordinate and a is the half width of a current layer centered about the midplane of the sheet. For a <~ 0.4L, where L is the distance between the boundary planes, the ground state is unstable to disturbances whose wavelengths parallel to the sheet lie between lower and upper bounds depending on the value of a and on the Hartmann number. Asymmetry of the configuration with respect to the midplane of the sheet, modelled by the addition of an externally imposed constant magnetic field to a symmetric equilibrium field, acts as a stabilizing factor.
The bifurcations in a three-dimensional incompressible, electrically conducting fluid with an external forcing of the Roberts type have been studied numerically. The corresponding flow can serve as a model for the convection in the outer core of the Earth and is realized in an ongoing laboratory experiment aimed at demonstrating a dynamo effect. The symmetry group of the problem has been determined and special attention has been paid to symmetry breaking by the bifurcations. The nonmagnetic, steady Roberts flow loses stability to a steady magnetic state, which in turn is subject to secondary bifurcations. The secondary solution branches have been traced until they end up in chaotic states.
Aller Anfang ist schwer
(1998)
Linear and non-linear analogues of the Black-Scholes equation are derived when shocks can be described by a truncated Lévy process. A linear equation is derived under the perfect correlation assumption on returns for a derivative security and a stock, and its solutions for European put and call options are obtained. It is also shown that the solution violates the perfect correlation assumption unless a process is gaussian. Thus, for a family of truncated Lévy distributions, the perfect hedging is impossible even in the continuous time limit. A second linear analogue of the Black-Scholes equation is obtained by constructing a portfolio which eliminates fluctuations of the first order and assuming that the portfolio is risk-free; it is shown that this assumption fails unless a process is gaussian. It is shown that the di erence between solutions to the linear analogues of the Black-Scholes equations and solutions to the Black-Scholes equations are sizable. The equations and solutions can be written in a discretized approximate form which uses an observed probability distribution only. Non-linear analogues for the Black-Scholes equation are derived from the non-arbitrage condition, and approximate formulas for solutions of these equations are suggested. Assuming that a linear generalization of the Black-Scholes equation holds, we derive an explicit pricing formula for the perpetual American put option and produce numerical results which show that the difference between our result and the classical Merton's formula obtained for gaussian processes can be substantial. Our formula uses an observed distribution density, under very weak assumptions on the latter.
We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction.
On a compact closed manifold with edges live pseudodifferential operators which are block matrices of operators with additional edge conditions like boundary conditions in boundary value problems. They include Green, trace and potential operators along the edges, act in a kind of Sobolev spaces and form an algebra with a wealthy symbolic structure. We consider complexes of Fréchet spaces whose differentials are given by operators in this algebra. Since the algebra in question is a microlocalization of the Lie algebra of typical vector fields on a manifold with edges, such complexes are of great geometric interest. In particular, the de Rham and Dolbeault complexes on manifolds with edges fit into this framework. To each complex there correspond two sequences of symbols, one of the two controls the interior ellipticity while the other sequence controls the ellipticity at the edges. The elliptic complexes prove to be Fredholm, i.e., have a finite-dimensional cohomology. Using specific tools in the algebra of pseudodifferential operators we develop a Hodge theory for elliptic complexes and outline a few applications thereof.
We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.
Generalizing an idea of I. Vekua [1] who, in order to construct theory of plates and shells, fields of displacements, strains and stresses of threedimensional theory of linear elasticity expands into the orthogonal Fourier-series by Legendre Polynomials with respect to the variable along thickness, and then leaves only first N + 1, N = 0, 1, ..., terms, in the bar model under consideration all above quantities have been expanded into orthogonal double Fourier-series by Legendre Polynomials with respect to the variables along thickness, and width of the bar, and then first (Nsub(3) + 1)(Nsub(2) + 1), Nsub(3), Nsub(2) = 0, 1,..., terms have been left. This case will be called (Nsub(3), Nsub(2)) approximation. Both in general (Nsub(3), Nsub(2)) and in particular (0,0) (1,0) cases of approximation, the question of wellposedness of initial and boundary value problems, existence and uniqueness of solutions have been investigated. The cases when variable cross-section turns into segments of straight line, and points have been also considered. Such bars will be called cusped bars (see also [2]).
Soit (A, H, F) un module de Fredholm p-sommable, où l'algèbre A = CT est engendrée par un groupe discret Gamma d'éléments unitaires de L(H) qui est de croissance polynomiale r. On construit alors un triplet spectral (A, H, D) sommabilité q pour tout q > p + r + 1 avec F = signD. Dans le cas où (A, H, F) est (p, infini)-sommable on obtient la (q, infini)-sommabilité de (A, H, D)pour tout q > p + r + 1.