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Effective and ef cient modelling of in nite media is important for the production of accurate and useful solutions for many scienti c and engineering problems invo- ing in nite domains (Bettess 1977, 1980, Chow and Smith 1981, Medina and Taylor 1983, Zhang and Zhao 1987, Zhao et al. 1989, Zhao and Valliappan 1993a, b, c, d, Astley 1996, 1998, Yang et al. 1996, Yang and Huang 2001, Yun et al. 2000, 2007, Wang et al. 2006). Some typical examples involving in nite domains are as follows: (1) earthquake wave propagation within the upper crust of the Earth in the elds of geophysics and seismology, (2) dynamic structure foundation interaction in the elds of geotechnical, civil and dam engineering, and (3) transient pore- uid ow, heat transfer and mass transport within the interior of the Earth in the elds of g- science and geoenvironmental engineering. Although the solid Earth is viewed as a bounded domain at the terrestrial scale, it can be treated as an unbounded domain at the human scale. For instance, in the case of predicting possible property damages caused by an earthquake, only a limited region around the epicentre is of interest because the earthquake wave energy is signi cantly reduced as the distance from the epicentre is increased.

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To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions, wind ing numbers and degrees of mappings, fixed-point theorems, appli cations such as the Jordan curve theorem, invariance of domain, in dices of vector fields and Euler characteristics, fundamental groups

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While in geometry attempts to square the circle never succeeded, the UML has achieved it: states canbeimplementedasclasses. '{Wehavemade much progressfrom thetime cloudswere used. ' The Uni ed Modeling Language is described as a language for specifying, - sualizing, constructing, and documenting the artifacts of software systems' and for business modeling (OMG UML V1. x documents). The UML re?ects some of the best experiences in object-oriented modeling, thus it has the potential to become a widely-used standard object-oriented modeling language. As a generally-applicable standard the UML has to be both ?exible (ext- sible, adaptable, modia ble) and precise. Flexibility is needed if the UML is to be used in a variety of application domains. Tailoring of UML syntax and adaptation of UML semantics to system domains is highly desirable. Incor- rating domain-specic concepts into the language will yield modeling languages that more e ectively support system development in these domains. Tailoring may involve determining a subset of the UML that is applicable to the domain, extending or modifying existing language elements, or den ing new language elements. One can envisage UML variants that are tailored to specic domains, for example, UML for real-time systems, multimedia systems, and for intern- based systems. Furthermore, one can also de ne UML variants that determine levels of sophistication in the use of the UML.

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To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

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Reasoning under uncertainty is always based on a specified language or for malism, including its particular syntax and semantics, but also on its associated inference mechanism. In the present volume of the handbook the last aspect, the algorithmic aspects of uncertainty calculi are presented. Theory has suffi ciently advanced to unfold some generally applicable fundamental structures and methods. On the other hand, particular features of specific formalisms and ap proaches to uncertainty of course still influence strongly the computational meth ods to be used. Both general as well as specific methods are included in this volume. Broadly speaking, symbolic or logical approaches to uncertainty and nu merical approaches are often distinguished. Although this distinction is somewhat misleading, it is used as a means to structure the present volume. This is even to some degree reflected in the two first chapters, which treat fundamental, general methods of computation in systems designed to represent uncertainty. It has been noted early by Shenoy and Shafer, that computations in different domains have an underlying common structure. Essentially pieces of knowledge or information are to be combined together and then focused on some particular question or domain. This can be captured in an algebraic structure called valuation algebra which is described in the first chapter. Here the basic operations of combination and focus ing (marginalization) of knowledge and information is modeled abstractly subject to simple axioms.

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Anbieter: Thalia AT

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