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In this paper we study the space-time asymptotic behavior of the solutions and derivatives to th incompressible Navier-Stokes equations. Using moment estimates we obtain that strong solutions to the Navier-Stokes equations which decay in \(L^2\) at the rate of \(||u(t)||_2 \leq C(t+1)^{-\mu}\) will have the following pointwise space-time decay \[|D^{\alpha}u(x,t)| \leq C_{k,m} \frac{1}{(t+1)^{ \rho_o}(1+|x|^2)^{k/2}} \]
where \( \rho_o = (1-2k/n)( m/2 + \mu) + 3/4(1-2k/n)\), and \(|a |= m\). The dimension n is \(2 \leq n \leq 5\) and \(0\leq k\leq n\) and \(\mu \geq n/4\)
Das Problem der Integration heterogener Softwaresysteme stellt sich auch auf dem Gebiet der CAx-Systeme, wie sie in vielfältigen Ausprägungen etwa in der Automobilbranche für die Fahrzeugentwicklung eingesetzt werden. Zunächst werden die heute in diesem Bereich
praktizierten Lösungen und die dabei auftretenden Probleme kurz dargestellt. Danach werden der neue Standard für Produktdaten, STEP, und der Standard für die Interoperabilität heterogener Softwaresysteme, CORBA, sowie einige CORBA-Entwurfsmuster erläutert. Als nächstes wird eine auf diesen beiden Standards basierende CAx-Integrationsarchitektur, die im Projekt ANICA entwickelt wurde, vorgestellt und die prinzipielle Vorgehensweise bei
ihrer Realisierung beschrieben. Daran anschließend wird über eine erste Umsetzung dieser Architektur in die Praxis berichtet. Zum Abschluß wird kurz auf die gewonnenen Erfahrungen eingegangen und ein Ausblick auf zukünftige Entwicklungen gegeben.
Die virtuelle Produktentwicklung in verteilter Umgebung erfordert eine intensive Kommunika-tion zwischen den beteiligten CAx-Systemen. Diese findet bisher in Form des dateibasierten Datenaustausches mit Hilfe von Direktkonvertern oder neutralen Schnittstellen statt. Der Datenaustausch wird hierbei meist in mehreren Iterationsschleifen durchgeführt und ist oft mit Datenverlusten sowie Unterbrechungen der Entwicklungsaktivitäten verbunden. Demgegenüber steht als neuer Ansatz für die Interoperabilität zwischen CAx-Systemen das Konzept eines CAx-Objektbusses auf Basis von CORBA und STEP. Dieser Ansatz ermög-licht eine plattformübergreifende Online-Kopplung heterogener CAx-Systeme. Im Gegensatz zum dateibasierten Datenaustausch ist hierbei ein transparenter Zugriff sowohl auf Daten als auch auf Funktionen der angebundenen Systeme möglich. Dadurch kann die Durchgängigkeit der Produktdaten in der Prozeßkette deutlich erhöht werden. Zur Beurteilung der Praxistauglichkeit wird dieser neue Ansatz dem dateibasierten Daten-austausch am Beispiel virtueller Einbauuntersuchungen gegenübergestellt. Dabei werden für unterschiedliche praxisrelevante Modellgrößen die für die Übertragung von Geometrie und Topologie erforderlichen Zeiten analysiert und verglichen. Weiterhin werden die generellen Vor- und Nachteile der beiden Lösungen dargestellt. Abschließend wird auf die Potentiale des neuen Ansatzes für den Einsatz in anderen Bereichen eingegangen.
Interoperability between different CAx systems involved in the development process of cars is presently one of the most critical issues in the automotive industry. None of the existing CAx systems meets all requirements of the very complex process network of the lifecycle of a car. With this background, industrial engineers have to use various CAx systems to get an optimal support for their daily work. Today, the communication between different CAx systems is done via data files using special direct converters or neutral system independent standards like IGES, VDAFS, and recently STEP, the international standard for product data description. To reduce the dependency on individual CAx s ystem vendors, the German automotive industry developed an open CAx system architecture based on STEP as guiding principle for CAx system development. The central component of this architecture is a common, system-independent access interface to CAx functions and data of all involved CAx systems, which is under development in the project ANICA. Within this project, a CAx object bus has been developed based on a STEP data description using CORBA as an integration platform. This new approach allows a transparent access to data and functions of the integrated CAx systems without file-based data exchange. The product development process with various CAx systems concerns objects from different CAx systems. Thus, mechanisms are needed to handle the persistent storage of the CAx objects distributed over the CAx object bus to give the developing engineers a consistent view of the data model of their product. The following paper discusses several possibilities to guarantee consistent data management and storage of distributed CAx models. One of the most promising approaches is the enhancement of the CAx object bus by a STEP-based object-oriented data server to realise a central data management.
Simultaneous quantifier elimination in sequent calculus is an improvement over the well-known skolemization. It allows a lazy handling of instantiations as well as of the order of certain reductions. We prove the soundness of a sequent calculus which incorporates a rule for simultaneous quantifier elimination. The proof is performed by semantical arguments and provides some insights into the dependencies between various formulas in a sequent.
Monomial representations and operations for Gröbner bases computations are investigated from an implementation point of view. The technique ofvectorized monomial operations is introduced and it is shown how it expedites computations of Gröbner bases. Furthermore, a rank-based monomialrepresentation and comparison technique is examined and it is concluded that this technique does not yield an additional speedup over vectorizedcomparisons. Extensive benchmark tests with the Computer Algebra System SINGULAR are used to evaluate these concepts.
The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)< 0), and a natural number n (n>=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.
The first observation of spatiotemporal self-focusing of spin waves is reported. The experimental results are obtained for dipolar spin waves in yttrium-iron-garnet films by means of a newly developed space- and time-resolved Brillouin light scattering technique. They demonstrate self-focusing of a moving wave pulse in two spatial dimensions, and formation of localized two-dimensional wave packets, the collapse of which is stopped by dissipation. The experimental results are in good qualitative agreement with numerical simulations.
Wavelet transform originated in 1980's for the analysis of seismic signals has seen an explosion of applications in geophysics. However, almost all of the material is based on wavelets over Euclidean spaces. This paper deals with the generalization of the theory and algorithmic aspects of wavelets to a spherical earth's model and geophysically relevant vector fields such as the gravitational, magnetic, elastic field of the earth.A scale discrete wavelet approach is considered on the sphere thereby avoiding any type of tensor-valued 'basis (kernel) function'. The generators of the vector wavelets used for the fast evaluation are assumed to have compact supports. Thus the scale and detail spaces are finite-dimensional. As an important consequence, detail information of the vector field under consideration can be obtained only by a finite number of wavelet coefficients for each scale. Using integration formulas that are exact up to a prescribed polynomial degree, wavelet decomposition and reconstruction are investigated for bandlimited vector fields. A pyramid scheme for the recursive computation of the wavelet coefficients from level to level is described in detail. Finally, data compression is discussed for the EGM96 model of the earth's gravitational field.