Search results for "Mathematica"

showing 10 items of 7971 documents

The set of conjugacy class sizes of a finite group does not determine its solvability

2014

Abstract We find a pair of groups, one solvable and the other non-solvable, with the same set of conjugacy class sizes.

Set (abstract data type)Discrete mathematicsMathematics::Group TheoryFinite groupTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESTheoryofComputation_COMPUTATIONBYABSTRACTDEVICESAlgebra and Number TheoryConjugacy classTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONMathematicsofComputing_DISCRETEMATHEMATICSMathematicsJournal of Algebra
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Attracting sets in a deterministic discrete traffic model

2001

The fundamental diagram of the Nagel-Schreckenberg traffic model is derived analytically for the deterministic case using methods and concepts from nonlinear dynamics. It is shown that the possible states of the long-term behaviour form a globally attractive subset which can be well characterized. This attractive set of states is composed of coexisting attractors. The attractor concept is applied to a slow-to-start extension of the model. For this example it is shown that the attractive set consists of coexisting attractors with different macroscopic properties, that can be determined analytically.

Set (abstract data type)Discrete mathematicsNonlinear systemAttractorDiagramTraffic modelGeneral Physics and AstronomyApplied mathematicsStatistical and Nonlinear PhysicsExtension (predicate logic)Mathematical PhysicsMathematicsJournal of Physics A: Mathematical and General
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Words and Patterns

2002

In this paper some new ideas, problems and results on patterns are proposed. In particular, motivated by questions concerning avoidability, we first study the set of binary patterns that can occur in one infinite binary word, comparing it with the set of factors of the word. This suggests a classification of infinite words in terms of the "difference" between the set of its patterns and the set of its factors. The fact that each factor in an infinite word can give rise to several distinct patterns leads to study the set of patterns of a single finite word. This set, endowed with a natural order relation, defines a poset: we investigate the relationships between the structure of such a poset…

Set (abstract data type)Discrete mathematicsStructure (mathematical logic)Regular languageRelation (database)Binary numberComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Natural orderPartially ordered setComputer Science::Formal Languages and Automata TheoryWord (computer architecture)Mathematics
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A primal-dual algorithm for the fermat-weber problem involving mixed gauges

1987

We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions. When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set of optimal locations has nonepty interior an…

Set (abstract data type)Fermat's Last TheoremMathematical optimizationSimple (abstract algebra)General MathematicsNumerical analysisApplied mathematicsWeber problemFinite setSoftwareCounterexampleDual (category theory)MathematicsMathematical Programming
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Stochastic frontier models using R

2020

Abstract The production function is usually assumed to specify the maximum output obtainable, from a given set of inputs, describing the boundary or frontier of the obtainable output from each feasible combination of input; it relates the production process of individual units to the efficient border of the production possibilities. The measure of the distance of each unit from the border is the most immediate way to assess its (in)efficiency. However, the production function is not generally known, but it has only a set of information on each production unit and it is therefore essential to develop techniques to estimate the production frontier. Starting from the packages already developed…

Set (abstract data type)FrontierMathematical optimizationStochastic frontier analysisComputer scienceBoundary (topology)Production (economics)Production functionProduction–possibility frontierMeasure (mathematics)
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A Posteriori Methods

1998

A posteriori methods could also be called methods for generating Pareto optimal solutions. After the Pareto optimal set (or a part of it) has been generated, it is presented to the decision maker, who selects the most preferred among the alternatives. The inconveniences here are that the generation process is usually computationally expensive and sometimes in part, at least, difficult. On the other hand, it is hard for the decision maker to select from a large set of alternatives. One more important question is how to present or display the alternatives to the decision maker in an effective way. The working order in these methods is: 1) analyst, 2) decision maker.

Set (abstract data type)Generation processMultiobjective optimization problemPareto optimalMathematical optimizationWeighting coefficientOrder (exchange)Computer scienceA priori and a posterioriDecision maker
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Heuristics for the bi-objective path dissimilarity problem

2009

In this paper the path dissimilarity problem is considered. The problem has previously been studied within several contexts, the most popular of which is motivated by the need to select transportation routes for hazardous materials. The aim of this paper is to formally introduce the problem as a bi-objective optimization problem, in which a single solution consists of a set of p different paths, and two conflicting objectives arise, on one hand the average length of the paths must be kept low, and on the other hand the dissimilarity among the paths in the set should be kept high. Previous methods are reviewed and adapted to this bi-objective problem, thus we can compare the methods using th…

Set (abstract data type)Hazard (logic)Mathematical optimizationOptimization problemGeneral Computer ScienceModeling and SimulationPath (graph theory)GRASPManagement Science and Operations ResearchRouting (electronic design automation)HeuristicsMetaheuristicMathematicsComputers & Operations Research
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A Hierarchy of Twofold Resource Allocation Automata Supporting Optimal Sampling

2009

We consider the problem of allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. More specifically, the user is presented with `n ' sets of data points, S 1 , S 2 , ..., S n , where the set S i has N i points drawn from two classes {*** 1 , *** 2 }. A random sample in set S i belongs to *** 1 with probability u i and to *** 2 with probability 1 *** u i , with {u i }. i = 1, 2, ...n , being the quantities to be learnt. The problem is both interesting and non-trivial because while both n and each N i are large, the number of samples that can be drawn is bounded by a constant, c . We solve the problem by first modelling it a…

Set (abstract data type)Mathematical optimizationAsymptotically optimal algorithmHierarchy (mathematics)Learning automataComputer scienceBounded functionContinuous knapsack problemResource allocationStochastic optimization
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Fast solution of radial distribution networks with automated compensation and reconfiguration

2000

Abstract Optimal operation of radial distribution networks with automated compensation and reconfiguration requires the solution of a combinatorial optimisation problem, since the variables are the on/off status of capacitor banks and the open/close status of tie-switches. The solution approaches recently proposed use iterative algorithms such as genetic algorithms, simulated annealing and tabu search, for which the network needs to be solved in different configurations and at different compensation levels. The aim of this evaluation is that of attributing a quality index to each solution so that all the solutions can be suitably ordered. In an automated network, any configuration can be ob…

Set (abstract data type)Mathematical optimizationControl theoryComputer scienceComputationSimulated annealingEnergy Engineering and Power TechnologyControl reconfigurationPower factorElectrical and Electronic EngineeringTabu searchPower (physics)Compensation (engineering)Electric Power Systems Research
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A Maximal-Space Algorithm for the Container Loading Problem

2008

In this paper, a greedy randomized adaptive search procedure (GRASP) for the container loading problem is presented. This approach is based on a constructive block heuristic that builds upon the concept of maximal space, a nondisjoint representation of the free space in a container. This new algorithm is extensively tested over the complete set of Bischoff and Ratcliff problems [Bischoff, E. E., M. S. W. Ratcliff. 1995. Issues in the development of approaches to container loading. Omega 23 377–390], ranging from weakly heterogeneous to strongly heterogeneous cargo, and outperforms all the known nonparallel approaches that, partially or completely, have used this set of test problems. When …

Set (abstract data type)Mathematical optimizationHeuristic (computer science)Computer scienceContainer (abstract data type)GRASPGeneral EngineeringParallel algorithmAlgorithm designAlgorithmGreedy randomized adaptive search procedureBlock (data storage)INFORMS Journal on Computing
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