Partielle Differentialgleichungen und deren Anwendung auf physikalische Fragen.

Available on demand as hard copy or computer file from Cornell University Library.

Versuch einer kurzen, gründlichen und deutlichen auch nichtmathematikern verständlichen anweisung 10-14 jährige knaben ... zu einem leichten, gründlichen und wissenschaftlichen studium der mathematik fähig zu machen ...

Mode of access: Internet.

Praktischer abriss des fischereywesens. Für oekonomen, cameralisten und liebhaber der fischereyen.

Mode of access: Internet.

Trio in C moll für 2 Violinen, Violoncell und Pianoforte /

"Partitur von der Hand J. S. Bachs datiert 30.Aug.1742."

Ausgewählte Werke /

Vol. 1: edited by Alfred Einstein and Adolf Sandberger; continuo realized by Franz Bennat. Vols. 2-3 (Bd. 1-2 of the opera) edited by Hugo Riemann.

Partielle differentialgleichungen und deren anwendung auf physikalische fragen.

Mode of access: Internet.

Trio in D for two violins and violoncello : concerto no. IV, op. 2 /

For two violins, violoncello, and piano.

Von Goethe zum Expressionismus; Dichtung und Geistesleben Deutschlands seit 1800,

Mode of access: Internet.

Geschichte der musiktheorie im IX.-XIX. jahrhundert.

Reprint of 2d ed., 1921. Bibliographical footnotes.

Catechism of musical instruments...

At head of title: Augener's edition. no.9201.

Effective cell-centred time-domain Maxwell's equations numerical solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed. © 2004 Elsevier Inc. All rights reserved.

Maple tools for the Kurzweil integral

Riemann sums based on delta fine partitions are illustrated with a Maple procedure

A formal object-oriented approach to defining consistency constraints for UML models

We discuss how integrity consistency constraints between different UML models can be precisely defined at a language level. In doing so, we introduce a formal object-oriented metamodeling approach. In the approach, integrity consistency constraints between UML models are defined in terms of invariants of the UML model elements used to define the models at the language-level. Adopting a formal approach, constraints are formally defined using Object-Z. We demonstrate how integrity consistency constraints for UML models can be precisely defined at the language-level and once completed, the formal description of the consistency constraints will be a precise reference of checking consistency of UML models as well as for tool development.

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

The JNR Property and the Borel Structure of a Banach Space

Research partially supported by a grant of Caja de Ahorros del Mediterraneo.