We show that the reduced mesh root systems and mesh geometries of roots for each of the simply-laced Dynkin diagrams can be classified by applying symbolic computer algebra computations and numeric algorithmic computa...
详细信息
ISBN:
(纸本)9780769546308
We show that the reduced mesh root systems and mesh geometries of roots for each of the simply-laced Dynkin diagrams can be classified by applying symbolic computer algebra computations and numeric algorithmic computations in Maple, C++ and Linux. Results of our computing experiences are presented in a table of Section 2 and in Section 6.
We present a denotational semantics designed with metric spaces and continuations for an abstract concurrent language embodying two new features: the semantics of parallel composition is based on the concept of maxima...
详细信息
ISBN:
(纸本)9780769546308
We present a denotational semantics designed with metric spaces and continuations for an abstract concurrent language embodying two new features: the semantics of parallel composition is based on the concept of maximal parallelism, and computations are specified by means of multiset rewriting rules. To the best of our knowledge, this is the first paper that presents a metric denotational semantics for this combination of features, encountered also in membrane computing.
symbolic Computation (Mathematics Subject Classification 2000, 68W30) is often treated as just another subject in the wide field of special topics within mathematics;on the same level as mesh generation (65L50) or qua...
详细信息
ISBN:
(纸本)9780769546308
symbolic Computation (Mathematics Subject Classification 2000, 68W30) is often treated as just another subject in the wide field of special topics within mathematics;on the same level as mesh generation (65L50) or quasi-Frobenius rings (16L60). Here we want to argue that actually symbolic Compuation is not so much a topic in mathematics, but a relatively novel approach to mathematical epistemology;a different and, as we believe, fruitful way of looking at mathematics and the acquisition of knowledge in mathematics.
We continue and complete a Coxeter spectral study (presented in our talk given in SYNASC11, Timisoara, September 2011 [6]) of the root systems in the sense of Bourbaki [4], the mesh geometries Gamma(R-Delta, phi(A)) o...
详细信息
ISBN:
(纸本)9780769549347;9781467350266
We continue and complete a Coxeter spectral study (presented in our talk given in SYNASC11, Timisoara, September 2011 [6]) of the root systems in the sense of Bourbaki [4], the mesh geometries Gamma(R-Delta, phi(A)) of roots of Delta in the sense of [20], and matrix morsifications A is an element of Mor (Delta), for simply-laced Dynkin diagrams Delta is an element of {A(n), D-n, E-6, E-7, E-8}. One of the main aims of the talk is to present a progress obtained during the last year in solving the problems stated in our talk [6]. We show that the reduced mesh root systems and mesh geometries of roots for each of the Dynkin diagrams Delta can be classified for n <= 9 by applying symbolic computer algebra computations and numeric algorithmic computations. We also compute the isotropy group Gl(n, Z)(Delta) of Delta defined in [22]-[23], determine its structure and compute the Gl(n, Z)(Delta)-orbits of the morsifications A is an element of Mor (Delta), for Delta is an element of {A(n), D-m}, with n <= 9 and 4 <= m <= 8. Results of our computing experiences are presented in three tables of Section 4.
In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and disc...
详细信息
ISBN:
(纸本)9780769546308
In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. the main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting. Keywords: computer algebra, differential equation, branch cut
Solving a linear system of equations is a common task performed for most of the scientific experiments. Everyday, these applications increase their demands, pushing the computational capacity to the limits. At a certa...
详细信息
ISBN:
(纸本)9780769549347;9781467350266
Solving a linear system of equations is a common task performed for most of the scientific experiments. Everyday, these applications increase their demands, pushing the computational capacity to the limits. At a certain point, our systems, running common algorithms, become unable to process such massive amounts of information. the paper analyses and modifies the standard Gaussian reduction so that a huge array may be handled by almost any distributed system. Moreover, the paper focuses on providing a decent level of fault tolerance in order to comply with a real, heterogeneous distributed system and on becoming a solution for sensitive applications.
the proceedings contain 81 papers. the topics discussed include: the gradual computerisation of mathematics on MathLang;P2P open agent networks for decision making;some applications of weakly Picard operators;function...
ISBN:
(纸本)0769530788
the proceedings contain 81 papers. the topics discussed include: the gradual computerisation of mathematics on MathLang;P2P open agent networks for decision making;some applications of weakly Picard operators;functional-based comparison between two special classes of uni- and bidirectional systolic arrays;parallel multiple polynomials quadratic sieve on multi-core architectures;structural properties and observability in membrane systems;approximation of attractors by a variable time-stepping algorithm for Runge-Kutta methods;customized reflection lines for surface interrogation in car body design;invariance in the class of weighted power means;the CMDS medical diagnosis system;adaptive negotiation based on rewards and regret in a multi-agent environment;strong convergence of the projection method in convex feasibility problems;proposal of business process and rules modeling withthe XTT method.
Grids became a commonplace for the computation of expensive numerical simulations. this work addresses the problem of searching for relevant simulations and for their results in a grid. this is challenging especially ...
详细信息
ISBN:
(纸本)9780769546308
Grids became a commonplace for the computation of expensive numerical simulations. this work addresses the problem of searching for relevant simulations and for their results in a grid. this is challenging especially due to the large number of existing simulations, the small semantic differences between them, and the distributed nature of the grid environment. We propose a solution that addresses simultaneously these three challenges by integrating a latent semantic indexing algorithm a linguistic processing module with a grid application framework. this resulted in a novel prototype, ELSIGExplorer, capable of retrieving relevant scenarios computed with GridSFEA on heterogeneous grids. We evaluated our approach on benchmark datasets from the medical domain and on a set of scenarios for simulating dynamic behavior of biological neural microcircuits in grid.
We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all of them when seen as isomorp...
详细信息
ISBN:
(纸本)9780769549347;9781467350266
We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all of them when seen as isomorphic withthe set of natural numbers. Constructors and deconstructors seen through an initial algebra semantics are generalized to recursively defined functions obeying similar laws. Implementations using GHC's view construct are discussed, based on the free algebra of rooted ordered binary trees.
暂无评论