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An ACO-RFD hybrid method to solve NP-complete problems

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Frontiers of Computer Science 2013年第5期7卷 729-744页

作者： Pablo RABANAL Ismael RODRIGUEZ Fernando RUBIO dept. Sistemas Inforrnaiticos y computacion Facultad de Informatica Universidad Complutense de Madrid Madrid 28040 Spain

In this paper we hybridize ant colony optimiza- tion （ACt） and river formation dynamics （RFD）, two related swarm intelligence methods. In ACt, ants form paths （prob- lem solutions） by following each other＇s pheromone trails and reinforcing trails at best paths until eventually a single path is followed. On the other hand, RFD is based on copy- ing how drops form rivers by eroding the ground and de- positing sediments. In a rough sense, RFD can be seen as a gradient-oriented version of ACt. Several previous experi- ments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACt. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACt in the first exe- cution steps in general, though RFD solutions surpass ACt solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACt. We use a kind of ant-drop hybrid and consider both pheromone trails and altitudes in the environment. We apply the hybrid method, as well as ACt and RFD, to solve two NP-hard problems where ACt and RFD fit in a different manner： the traveling salesman problem （TSP） and the prob- lem of the minimum distances tree in a variable-cost graph （MDV）. We compare the results of each method and we an- alyze the advantages of using the hybrid approach in each case.

关键词： river formation dynamics ant colony optimization heuristic algorithms NP-hard problems

Morphisms and Elements of Group-like Type in Weak Multiplier Bialgebras

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Algebra Colloquium 2018年第1期25卷 107-132页

作者： Esperanza Lopez-Centella departamento de Didactica de la matematica Universidad de Granada Facultad de Educacion Economfa y Tecnologfa de Ceuta

以达到提供一个范畴的处理弱更多样地 bialgebras (由 B 介绍了 ? hm， G

关键词：样地元素类型子范畴代数学定义阳离子集合

Reiterated homogenization of a laminate with imperfect contact:gain-enhancement of effective properties

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Applied Mathematics and Mechanics(English Edition) 2018年第8期39卷 1119-1146页

作者： F.E.ALVAREZ-BORGES J.BRAVO-CASTILLERO M.E.CRUZ R.GUINOVART-DIAZ L.D.PEREZ-FERNANdeZ R.RODRIGUEZ-RAMOS F.J.SABINA facultad de matematica y computacion Departamento de MatematicaUniversidad de La HabanaSan Lazaro y LHabana 4La HabanaCP 10400Cuba departamento de matematicas y Mecanica Universidad Nacional Autonoma de MexicoInstituto de Investigaciones en Matematicas Aplicadas y en Sistemas01000 CDMXAP 20-126M′exico departamento de Engenharia Mecanica Universidade Federal do Rio de JaneiroPolitecnica/COPPECaixa Postal 68503Rio de JaneiroRJCEP 21941-972Brasil departamento de matematica e Estatistica Universidade Federal de PelotasCaixa Postal 354PelotasRio Grande do SulCEP 96010-900Brasil

A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method(RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.

关键词： reiterated homogenization method(RHM) imperfect contact variational formulation effective coefficient gain

A Diffusively Corrected Multiclass Lighthill-Whitham-Richards Traffic Model with Anticipation Lengths and Reaction Times

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Advances in Applied Mathematics and Mechanics 2013年第5期5卷 728-758页

作者： Raimund Burger Pep Mulet Luis M.Villada CI2MA and departamento de Ingenierıa matematica Facultad de Ciencias Fısicas y MatematicasUniversidad de ConcepcionCasilla 160-CConcepcionChile departament de matematica Aplicada Universitat de ValenciaAv.Dr.Moliner 50E-46100 BurjassotSpain

Multiclass Lighthill-Whitham-Richards trafficmodels[Benzoni-Gavage and Colombo,Euro.J.Appl.Math.,14(2003),pp.587–612;Wong and Wong,Transp.Res.A,36(2002),pp.827–841]give rise to first-order systems of conservation laws that are hyperbolic under usual conditions,so that their associated Cauchy problems are wellposed.Anticipation lengths and reaction times can be incorporated into these models by adding certain conservative second-order terms to these first-order conservation laws.These terms can be diffusive under certain circumstances,thus,in principle,ensuring the stability of the solutions.The purpose of this paper is to analyze the stability of these diffusively correctedmodels under varying reaction times and anticipation lengths.It is demonstrated that instabilities may develop for high reaction times and short anticipation lengths,and that these instabilities may have controlled frequencies and amplitudes due to their nonlinear nature.

关键词： Traffic flow multispecies model anticipation length reaction time diffusive correction quasilinear system of second-order Pdes stability numerical simulation

A Note on Expanding Planar Real Cellular Automata

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Acta Mathematica Sinica,English Series 2018年第9期34卷 1371-1378页

作者： Jairo GUZMAN Neptali ROMERO Universidad del Atldntico Facultad de Ciencias Bdsicas Departamento de Matematicas Km 7 antigua via Puerto Colombia Barranquilla Colombia Universidad Centroccidental Lisandro Alvarado Decanato de Ciencias y Tecnologia Departamento de Matematica Nucleo Obelisco Barquisimeto Venezuela

In this paper, we deal with one-parameter families of real cellular automata in R2. We prove that for a wide class of block functions from R2 to R, the corresponding real cellular automaton is expanding when the value... 详细信息

关键词： Real cellular automata block function expanding map

A POSTERIORI ERROR ANALySIS OF A FULLy-MIXED FINITE ELEMENT METHOD FOR A TWO-DIMENSIONAL FLUID-SOLID INTERACTION PROBLEM

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Journal of Computational Mathematics 2015年第6期33卷 606-641页

作者： Carolina Dominguez Gabriel N. Gatica salim meddahi Instituto de Ciencias Fisicas y Matemdticas facultad de ciencias universidad austral de chile Avenida Eduardo Morales Miranda - Campus isla teja valdivia chile CI2 MA and departamento de Ingenieria matematica Universidad de concapcion casilla 160 concepcion chile departamento de Matemdticas Facultad de ciencias universidad de oiede calvo satela s/n oviedo espana

In this paper we develop an a posteriori error analysis of a fully-mixed finite element method for a fluid-solid interaction problem in 2D. The media are governed by the elas-todynamic and acoustic equations in time-harmonic regime, respectively, the transmission conditions are given by the equilibrium of forces and the equality of the corresponding normal displacements, and the fluid is supposed to occupy an annular region surrounding the solid, so that a Robin boundary condition imitating the behavior of the sommerfeld condition is imposed on its exterior boundary. Dual-mixed approaches are applied in both domains, and the governing equations are employed to eliminate the displacenent a of the solid and the pressure p of the fluid. In addition, since both transmission conditions become essential, they are enforced weakly by means of two suitable lahrange multipliers The unknowns of the solid and the fluid are then approximated by a conforming galerkin scheme defined in terms of PEERS elements in the solid, Raviart-Thomas of lowest order in the fluid, and continuous piecewise linear functions on the boundary, As the main con-tribution of this work, we derive a reliable and efficient residual-based a posteriori error estimator for the aforedescribed coupled problem. Some numerical results confirming the properties of the estimator are also reported.

关键词： Mixed finite elements Helmholtz equation Elastodynamic equation A poste- riori error analysis

Strong emissions of blue-yellow-red regions of La and Ti modified KNaNbO_(3) ferroelectric ceramics

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Journal of Advanced Ceramics 2015年第3期4卷 183-189页

作者： M.D.DURRUTHy-RODRIGUEZ M.HERNANdeZ-GARCIA J.PORTELLES J.FUENTES M.A.HERNANdeZ-LANDAVERde M.RAMIREZ CARDONA J.M.yANEZ-LIMON departamento de Fisica Aplicada Instituto de CiberneticaMatematica y FisicaCITMA15#551VedadoLa HabanaCP 10400Cuba facultad de Fisica Universidad de La HabanaSan Lazaro y LVedadoLa HabanaCP 10400Cuba CINVESTAV-Unidad Queretaro IPNLibramiento Norponiente 2000Fracc.Real de JuriquillaCP 76230QueretaroMexico Centro de Investigaciones en Ciencias de la Tierra y Materiales Universidad Autonoma del Estado de HidalgoMexico

In this work,the results of the study on the optical properties of the perovskite structure ABO3 with La^(3+) substitution for ions K^(+) and Na^(+) in the A site and Ti^(4+) substitution for ion Nb^(5+) in the B site are presented.The ceramics were sintered at 1100℃ and 1190℃ and formed at 10 MPa and 80 MPa.dense ceramics were obtained with 94% of the theoretical density.The piezoresponse force microscopy(PFM)showed needle-shaped grains with a size of 30 nm for the samples formed at 10 MPa at both sintering temperatures.Apparently,the high temperature and high pressure used in formation reduced the energy of the band gap(Eg)from 3.36 to 3.09 eV.Strong emissions to 2.19,1.86,2.5,and 2.31 eV were obtained by exciting the samples at 325,373,457,and 500 nm,respectively;these emissions corresponded to blue-yellow-red regions of the visible spectrum.

关键词： emission spectra condense matter ferroelectric materials band structure X-ray diffraction(XRD)

FRACTIONAL DIFFUSION EQUATIONS WITH INTERNAL deGREES OF FREEDOM

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Journal of Computational Mathematics 2003年第4期21卷 491-494页

作者： LuisVázquez departamento de matematica Aplicada Facultad de InformaticaUniversidad ComplutenseE-28040 MadridSpain Centro de Astrobiologia CSIC-INTAE-28850 Torrejon de ArdozMadridSpain

We present a generalization of the linear one-dimensional diffusion equation by combining the fractional derivatives and the internal degrees of freedom. The solutions are constructed from those of the scalar fractional diffusion equation. We analyze the interpolation between the standard diffusion and wave equations defined by the fractional derivatives. Our main result is that we can define a diffusion process depending on the internal degrees of freedom associated to the system.

关键词： Fractional derivative DifFunors Diffusion process Generalized Dirac equation.

Numerical Approximation of Oscillatory Solutions of Hyperbolic-Elliptic Systems of Conservation Laws by Multiresolution Schemes

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Advances in Applied Mathematics and Mechanics 2009年第5期1卷 581-614页

作者： Stefan Berres Raimund Burger Alice Kozakevicius departamento de Ciencias matematicas y Fısicas Universidad Catolica de TemucoTemucoChile CI2MA and departamento de Ingenier´ıa Matem´atica Facultad de Ciencias Fısicas y Matem´aticasUniversidad de Concepci´onCasilla 160-CConcepci´onChile departamento de matematica-CCNE Universidade Federal de Santa MariaAv.Roraima1000Campus Universit´arioSanta MariaRSCEP 97105-900Brazil

The generic structure of solutions of initial value problems of hyperbolic-elliptic systems,also called mixed systems,of conservation laws is not yet fully understood.One reason for the absence of a core well-posedness theory for these equations is the sensitivity of their solutions to the structure of a parabolic regularization when attempting to single out an admissible solution by the vanishing viscosity approach.There is,however,theoretical and numerical evidence for the appearance of solutions that exhibit persistent oscillations,so-called oscillatory waves,which are(in general,measure-valued)solutions that emerge from Riemann data or slightly perturbed constant data chosen from the interior of the elliptic region.To capture these solutions,usually a fine computational grid is required.In this work,a version of the multiresolution method applied to a WENO scheme for systems of conservation laws is proposed as a simulation tool for the efficient computation of solutions of oscillatory wave type.The hyperbolic-elliptic 2×2 systems of conservation laws considered are a prototype system for three-phase flow in porous media and a system modeling the separation of a heavy-buoyant bidisperse suspension.In the latter case,varying one scalar parameter produces elliptic regions of different shapes and numbers of points of tangency with the borders of the phase space,giving rise to different kinds of oscillation waves.

关键词： Hyperbolic-elliptic system conservation law oscillation wave numerical simulation multiresolution method sedimentation model