954 resultados para Lie algebra
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Two original poems
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We describe the C*-algebras of " ax+b" -like groups in terms of algebras of operator fields defined over their dual spaces.
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Driven by the requirements of the bionic joint or tracking equipment for the spherical parallel manipulators (SPMs) with three rotational degrees-of-freedom (DoFs), this paper carries out the topology synthesis of a class of three-legged SPMs employing Lie group theory. In order to achieve the intersection of the displacement subgroups, the subgroup characteristics and operation principles are defined in this paper. Mainly drawing on the Lie group theory, the topology synthesis procedure of three-legged SPMs including four stages and two functional blocks is proposed, in which the assembly principles of three legs are defined. By introducing the circular track, a novel class of three-legged SPMs is synthesized, which is the important complement to the existing SPMs. Finally, four typical examples are given to demonstrate the finite displacements of the synthesized three-legged SPMs.
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Radiation induced bystander effects are secondary effects caused by the production of chemical signals by cells in response to radiation. We present a Bio-PEPA model which builds on previous modelling work in this field to predict: the surviving fraction of cells in response to radiation, the relative proportion of cell death caused by bystander signalling, the risk of non-lethal damage and the probability of observing bystander signalling for a given dose. This work provides the foundation for modelling bystander effects caused by biologically realistic dose distributions, with implications for cancer therapies.
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Cost-effective semantic description and annotation of shared knowledge resources has always been of great importance for digital libraries and large scale information systems in general. With the emergence of the Social Web and Web 2.0 technologies, a more effective semantic description and annotation, e.g., folksonomies, of digital library contents is envisioned to take place in collaborative and personalised environments. However, there is a lack of foundation and mathematical rigour for coping with contextualised management and retrieval of semantic annotations throughout their evolution as well as diversity in users and user communities. In this paper, we propose an ontological foundation for semantic annotations of digital libraries in terms of flexonomies. The proposed theoretical model relies on a high dimensional space with algebraic operators for contextualised access of semantic tags and annotations. The set of the proposed algebraic operators, however, is an adaptation of the set theoretic operators selection, projection, difference, intersection, union in database theory. To this extent, the proposed model is meant to lay the ontological foundation for a Digital Library 2.0 project in terms of geometric spaces rather than logic (description) based formalisms as a more efficient and scalable solution to the semantic annotation problem in large scale.
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Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.
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This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.
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Collection : Théâtre contemporain illustré ; 121e et 122e livraisons
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Collection : Théâtre contemporain illustré ; 121e et 122e livraisons