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Discrete Set (discrete + set)
Selected AbstractsQuantitative Comparison of Approximate Solution Sets for Bi-criteria Optimization Problems,DECISION SCIENCES, Issue 1 2003W. Matthew Carlyle ABSTRACT We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near-pareto-optimal solutions to bi-criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives. [source] hp -Mortar boundary element method for two-body contact problems with frictionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2008Alexey Chernov Abstract We construct a novel hp -mortar boundary element method for two-body frictional contact problems for nonmatched discretizations. The contact constraints are imposed in the weak sense on the discrete set of Gauss,Lobatto points using the hp -mortar projection operator. The problem is reformulated as a variational inequality with the Steklov,Poincaré operator over a convex cone of admissible solutions. We prove an a priori error estimate for the corresponding Galerkin solution in the energy norm. Due to the nonconformity of our approach, the Galerkin error is decomposed into the approximation error and the consistency error. Finally, we show that the Galerkin solution converges to the exact solution as ,,((h/p)1/4) in the energy norm for quasiuniform discretizations under mild regularity assumptions. We solve the Galerkin problem with a Dirichlet-to-Neumann algorithm. The original two-body formulation is rewritten as a one-body contact subproblem with friction and a one-body Neumann subproblem. Then the original two-body frictional contact problem is solved with a fixed point iteration. Copyright © 2008 John Wiley & Sons, Ltd. [source] Resonance phenomena in compound cylindrical waveguidesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2006Günter Heinzelmann Abstract We study the large time asymptotics of the solutions u(x,t) of the Dirichlet and the Neumann initial boundary value problem for the wave equation with time-harmonic right-hand side in domains , which are composed of a finite number of disjoint half-cylinders ,1,,,,r with cross-sections ,,1,,,,,r and a bounded part (,compound cylindrical waveguides'). We show that resonances of orders t and t1/2 may occur at a finite or countable discrete set of frequencies ,, while u(x,t) is bounded as t,, for the remaining frequencies. A resonance of order t occurs at , if and only if ,2 is an eigenvalue of the Laplacian ,, in , with regard to the given boundary condition u=0 or ,u/,n=0, respectively. A resonance of order t1/2 occurs at , if and only if (i) ,2 is an eigenvalue of at least one of the Laplacians for the cross-sections ,,1,,,,r, with regard to the respective boundary condition and (ii) the respective homogeneous boundary value problem for the reduced wave equation ,U+,2U=0 in , has non-trivial solutions with suitable asymptotic properties as | x | ,, (,standing waves'). Copyright © 2006 John Wiley & Sons, Ltd. [source] PRESENTISM: THROUGH THICK AND THINPACIFIC PHILOSOPHICAL QUARTERLY, Issue 3 2008H. SCOTT HESTEVOLD Without defending Presentism, I argue first that Presentists should be Time -Free Presentists , Presentists whose views do not imply that there exist irreducible times. Second, I argue that Presentists should accept Limited Thick Presentism, the view that ,the present' has some extension and is thereby neither durationlessly thin nor unlimitedly ,thick'. Third, before addressing several objections to Limited Time-Free Thick Presentism [LTFTP], I argue that defenders of LTFTP should accept that ,temporal becoming' involves an overlapping succession of present entities, not a ,skipping' from one set of present entities to the next discrete set. [source] Growth model on (1 + 1) dimensions with local relaxation and discrete number of orientationsPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 5 2004W. L. Cavalcanti Abstract We introduced in this work a simple model for studying the texture formation during the electrodeposition process. Monte Carlo simulations were used to describe the formation of the deposits, and scaling concepts were also employed to characterize their growth and roughness properties. Particles are randomly deposited on a substrate, and their main axis can be aligned in a discrete set of possible directions. The final orientation of the deposited particle is determined by the interaction energy with its first neighboring particles and substrate temperature. Particle interactions are chosen according to the q -state ferromagnetic Potts model hamiltonian. Simulations were performed on (1 + 1) dimensions, for different values of temperature and substrate size. We have found different behaviors at low and high temperatures. Only at zero temperature the system reaches an absorbing state with all the layers occupied by particles oriented in the same direction. At this temperature we found the dynamic, roughness and growth exponents of the model, which satisfies the well known Family,Vicsek scaling relation for the self-affine interfaces. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Ionic and electronic defects in a-BaTiO3 thin films studied by transient and steady state conductivity measurementsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 3 2007F. El Kamel Abstract Conduction mechanisms in BaTiO3 films deposited at low temperatures on Cu-electrodes have been investigated in transient and steady regimes as a function of temperatures and electric field. This work aims to identify possible defects which govern the leakage current. Electrical measurements reveal that Space Charge Limited Current (SCLC) constitutes the main leakage mechanism in both the transient and the steady regimes. Based on the theory of SCLC, two types of defects can be detected. At higher temperatures, oxygen vacancies constitute the main defects which migrate across the film to generate an ionic leakage current. Diffusion of these defects is thermally activated with an activation energy around 1 eV. Moreover, at lower temperatures the J - E measurements reveals the presence of a discrete set of shallow traps at 0.45 eV below the conduction band with an effective density of 4 × 1022 m,3. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A scenario-based stochastic programming model for the control or dummy wafers downgrading problemAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2009Shu-Hsing Chung Abstract The subject of this paper is to study a realistic planning environment in wafer fabrication for the control or dummy (C/D) wafers problem with uncertain demand. The demand of each product is assumed with a geometric Brownian motion and approximated by a finite discrete set of scenarios. A two-stage stochastic programming model is developed based on scenarios and solved by a deterministic equivalent large linear programming model. The model explicitly considers the objective to minimize the total cost of C/D wafers. A real-world example is given to illustrate the practicality of a stochastic approach. The results are better in comparison with deterministic linear programming by using expectation instead of stochastic demands. The model improved the performance of control and dummy wafers management and the flexibility of determining the downgrading policy. Copyright © 2008 John Wiley & Sons, Ltd. [source] Analysis of lattice-translocation disorder in the layered hexagonal structure of carboxysome shell protein CsoS1CACTA CRYSTALLOGRAPHICA SECTION D, Issue 9 2009Yingssu Tsai Lattice-translocation or crystal order,disorder phenomena occur when some layers or groups of molecules in a crystal are randomly displaced relative to other groups of molecules by a discrete set of vectors. In previous work, the effects of lattice translocation on diffraction intensities have been corrected by considering that the observed intensities are the product of the intensities from an ideal crystal (lacking disorder) multiplied by the squared magnitude of the Fourier transform of the set of translocation vectors. Here, the structure determination is presented of carboxysome protein CsoS1C from Halothiobacillius neapolitanus in a crystal exhibiting a lattice translocation with unique features. The diffraction data are fully accounted for by a crystal unit cell composed of two layers of cyclic protein hexamers. The first layer is fully ordered (i.e. has one fixed position), while the second layer randomly takes one of three alternative positions whose displacements are related to each other by threefold symmetry. Remarkably, the highest symmetry present in the crystal is P3, yet the intensity data (and the Patterson map) obey 6/m instead of symmetry; the intensities exceed the symmetry expected from combining the crystal space group with an inversion center. The origin of this rare phenomenon, known as symmetry enhancement, is discussed and shown to be possible even for a perfectly ordered crystal. The lattice-translocation treatment described here may be useful in analyzing other cases of disorder in which layers or groups of molecules are shifted in multiple symmetry-related directions. [source] Spatial Multistate Transitional Models for Longitudinal Event DataBIOMETRICS, Issue 1 2008F. S. Nathoo Summary Follow-up medical studies often collect longitudinal data on patients. Multistate transitional models are useful for analysis in such studies where at any point in time, individuals may be said to occupy one of a discrete set of states and interest centers on the transition process between states. For example, states may refer to the number of recurrences of an event, or the stage of a disease. We develop a hierarchical modeling framework for the analysis of such longitudinal data when the processes corresponding to different subjects may be correlated spatially over a region. Continuous-time Markov chains incorporating spatially correlated random effects are introduced. Here, joint modeling of both spatial dependence as well as dependence between different transition rates is required and a multivariate spatial approach is employed. A proportional intensities frailty model is developed where baseline intensity functions are modeled using parametric Weibull forms, piecewise-exponential formulations, and flexible representations based on cubic B-splines. The methodology is developed within the context of a study examining invasive cardiac procedures in Quebec. We consider patients admitted for acute coronary syndrome throughout the 139 local health units of the province and examine readmission and mortality rates over a 4-year period. [source] Vestigial expression in the Drosophila embryonic central nervous systemDEVELOPMENTAL DYNAMICS, Issue 9 2008Kirsten A. Guss Abstract The Drosophila central nervous system is an excellent model system in which to resolve the genetic and molecular control of neuronal differentiation. Here we show that the wing selector vestigial is expressed in discrete sets of neurons. We track the axonal trajectories of VESTIGIAL-expressing cells in the ventral nerve cord and show that these cells descend from neuroblasts 1-2, 5-1, and 5-6. In addition, along the midline, VESTIGIAL is expressed in ventral unpaired median motorneurons and cells that may descend from the median neuroblast. These studies form the requisite descriptive foundation for functional studies addressing the role of vestigial during interneuron differentiation. Developmental Dynamics 237:2483,2489, 2008. © 2008 Wiley-Liss, Inc. [source] Lateral magnocellular nucleus of the anterior neostriatum (LMAN) in the zebra finch: Neuronal connectivity and the emergence of sex differences in cell morphologyMICROSCOPY RESEARCH AND TECHNIQUE, Issue 6 2001Barbara E. Nixdorf-Bergweiler Abstract The song system of birds provides a model system to study basic mechanisms of neuronal plasticity and development underlying learned behavior. Song learning and production involve discrete sets of interconnected nuclei in the avian brain. One of these nuclei, the lateral magnocellular nucleus of the anterior neostriatum (LMAN), is the output of the so-called anterior forebrain pathway known to be essential for learning and maintenance of song, both processes depending on auditory feedback. In zebra finches, only males sing and this sexually dimorphic behavior is mirrored by sexual dimorphism in neuronal structure that develops during ontogeny. Female zebra finches are not able to sing and nuclei of the song system are strongly reduced in size or even lacking, when compared to male brains. Only LMAN can be delineated as easily in females as in males. Since female zebra finches, despite being unable to sing, recognize song just as males do and form a memory for song (model acquisition) early in life, LMAN is a putative candidate for song acquisition in both sexes. Therefore, development of LMAN was studied at the cellular and ultrastructural level in both male and female zebra finches. Regressive development of dendritic spines, enlargement of neuronal cell body and nuclei size, as well as changes at the nucleolar level are events all occurring exclusively in males, when song learning progresses. The decline in synapse number and the augmentation in synaptic contact length at synapses in LMAN in males are indicative for synaptic plasticity, whereas in females synapse number and synaptic contact length remain unchanged. Microsc. Res. Tech. 54:335,353, 2001. © 2001 Wiley-Liss, Inc. [source] | |||||||||||||