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  • Articles  (24)
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  • 60H15  (14)
  • artificial intelligence
  • Springer  (24)
  • 1995-1999  (14)
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  • 1955-1959
  • 1995  (14)
  • 1988  (10)
  • Mathematics  (24)
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  • Articles  (24)
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  • Springer  (24)
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  • 1995-1999  (14)
  • 1985-1989  (10)
  • 1955-1959
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  • 1
    Electronic Resource
    Electronic Resource
    On non-degenerate quasi-linear stochastic partial differential equations (1995)
    Springer
    Potential analysis 4 (1995), S. 157-171 
    Details
    ISSN: 1572-929X
    Keywords: 60H15 ; 35R30 ; Stochastic partial differential equations ; space-time white noise
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove a limit theorem for non-degenerate quasi-linear parabolic SPDEs driven by space-time white noise in one space-dimension, when the diffusion coefficient is Lipschitz continuous and the nonlinear drift term is only measurable. Hence we obtain an existence and uniqueness and a comparison theorem, which generalize those in [2], [4], [5] to the case of non-degenerate SPDEs with measurable drift and Lipschitz continuous diffusion coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01275588
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  • 2
    Electronic Resource
    Electronic Resource
    Stochastic partial differential equations in M-type 2 Banach spaces (1995)
    Springer
    Potential analysis 4 (1995), S. 1-45 
    Details
    ISSN: 1572-929X
    Keywords: 35R60 ; 60H15 ; 46E35 ; 47F05 ; 47D06 ; Stochastic parabolic equations ; M-type 2 and UMD Banach spaces ; real and complex interpolation ; Sobolev and Besov spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study abstract stochastic evolution equations in M-type 2 Banach spaces. Applications to stochastic partial differential equations inL p spaces withp⩾2 are given. For example, solutions of such equations are Hölder continuous in the space variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048965
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  • 3
    Electronic Resource
    Electronic Resource
    The pressure equation for fluid flow in a stochastic medium (1995)
    Springer
    Potential analysis 4 (1995), S. 655-674 
    Details
    ISSN: 1572-929X
    Keywords: 60H15 ; 35J25 ; 76S05 ; Pressure equation ; stochastic permeability ; Wick product ; stochastic distribution ; stochastic PDE
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An equation modelling the pressurep(x) =p(x, w) atx ∈D ⊂R d of an incompressible fluid in a heterogeneous, isotropic medium with a stochastic permeabilityk(x, w) ≥ 0 is the stochastic partial differential equation $$\left\{ {\begin{array}{*{20}c} {div(k(x,{\mathbf{ }}\omega )\diamondsuit \nabla p(x,\omega )){\mathbf{ }} = {\mathbf{ }}--f(x);{\mathbf{ }}x \in D} \\ {\begin{array}{*{20}c} {p(x,{\mathbf{ }}\omega ){\mathbf{ }} = {\mathbf{ }}0;} & {x \in \partial D} \\ \end{array} } \\ \end{array} } \right.$$ wheref is the given source rate of the fluid, ◊ denotes Wick product. We representk as the positive noise given by the Wick exponential of white noise, and we find an explicit formula for the (unique) solutionp(x, w), which is proved to belong to the space (S)−1 of generalized white noise distributions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02345830
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  • 4
    Electronic Resource
    Electronic Resource
    A prolog-based decision support system for computer capacity planning (1988)
    Springer
    Annals of operations research 12 (1988), S. 337-357 
    Details
    ISSN: 1572-9338
    Keywords: Decision support systems ; logic programming ; prolog ; artificial intelligence ; computer capacity planning ; planning for resource acquisition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper describes a project to implement a decision support system for computer capacity planning. The system provides an intelligent interface to the various models needed for this type of planning by assisting the user in model formulation, data manipulation, model execution, interpretation and manipulation of results. The implementation strategy is based on the integration of relational model and database management with logic. A modified version of a Prolog interpreter is utilized as the vehicle for this integrated strategy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186375
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  • 5
    Electronic Resource
    Electronic Resource
    A knowledge-based approach to scheduling in an F.M.S. (1988)
    Springer
    Annals of operations research 12 (1988), S. 109-134 
    Details
    ISSN: 1572-9338
    Keywords: Flexible manufacturing system ; production scheduling ; artificial intelligence ; predicate calculus ; state-operator framework ; knowledge-based system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper reports the development of a computer-based system for production scheduling in a dedicated FMS. The system is based on the state-operator framework commonly used in artificial intelligence. Such a system consists of three components: (i) a knowledge base of states, which describes both the current task domain situation and the goal to be achieved; (ii) a set of operators that are used to manipulate the knowledge base; and (iii) a control strategy to decide which operators to apply next and to resolve conflicts. Some of the interesting features of the scheduling system include: (i) the ability to detect resource conflicts; (ii) the ability to determine alternate routes for a given part in the event of a resource conflict; and (iii) the ability to amend plans if an alternate route is found. These features allow the system to take advantage of the flexible routing for parts that an FMS allows. The system has been implemented using the XLISP programming language. Implementation considerations are discussed. A small but comprehensive example is presented. Further research directions are suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186363
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  • 6
    Electronic Resource
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    Generalized resolution and cutting planes (1988)
    Springer
    Annals of operations research 12 (1988), S. 217-239 
    Details
    ISSN: 1572-9338
    Keywords: Propositional logic ; resolution ; integer programming ; theorem proving ; artificial intelligence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper illustrates how the application of integer programming to logic can reveal parallels between logic and mathematics and lead to new algorithms for inference in knowledge-based systems. If logical clauses (stating that at least one of a set of literals is true) are written as inequalities, then the resolvent of two clauses corresponds to a certain cutting plane in integer programming. By properly enlarging the class of cutting planes to cover clauses that state that at least a specified number of literals are true, we obtain a generalization of resolution that involves both cancellation-type and circulant-type sums. We show its completeness by proving that it generates all prime implications, generalizing an early result by Quine. This leads to a cutting-plane algorithm as well as a generalized resolution algorithm for checking whether a set of propositions, perhaps representing a knowledge base, logically implies a given proposition. The paper is intended to be readable by persons with either an operations research or an artificial intelligence background.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186368
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  • 7
    Electronic Resource
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    A knowledge-based system for tactical situation assessment (1988)
    Springer
    Annals of operations research 12 (1988), S. 285-296 
    Details
    ISSN: 1572-9338
    Keywords: Situation assessment ; human-machine interface ; intelligent assistant ; intelligent interface ; human-machine system ; artificial intelligence ; operations research ; knowledge-based systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract To perform tactical situation assessment effectively, a system must be capable of performing tactical information integration, interpretation, and threat evaluation. This paper describes a prototype system for naval surface warfare which incorporates a human operator for integration, an artificial intelligence-based subsystem for interpretation, and an operations research-based system for evaluation. The system provides the operator with an interactive environment for displaying and managing tactical information and tools for interpreting and evaluating it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186371
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  • 8
    Electronic Resource
    Electronic Resource
    User-model interaction in decision support systems for risk management (1988)
    Springer
    Annals of operations research 16 (1988), S. 185-197 
    Details
    ISSN: 1572-9338
    Keywords: risk management ; decision analysis ; expert systems ; artificial intelligence ; operations research
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper describes and evaluates three different approaches to building decision support systems: the Operations Research/Management Science approach, the Decision Analysis/Multiattribute Utility approach, and the Artificial Intelligence/Expert Systems approach. It evaluates the usefulness of the three approaches for risk management. In particular, it defines evaluation objectives of risk analysts, risk managers, and laypeople and provides a subjective assessment how the three approaches stack up against their objectives. The paper concludes that for most risk management applications a combination of the three approaches would be most desirable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02283744
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  • 9
    Electronic Resource
    Electronic Resource
    Alternative formulations of mixed integer programs (1988)
    Springer
    Annals of operations research 12 (1988), S. 241-276 
    Details
    ISSN: 1572-9338
    Keywords: Mixed-integer programming ; logic ; representability ; artificial intelligence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We study the formation of mixed-integer programming (MIP) constraints through the development of constructions which syntactically parallel the set operations of union, intersection, Cartesian product, and linear affine transformation. In this manner, we are able to both modularize the work of constructing representations (as the representations for base sets of a composite construction need not be disjunctively derived) and to make connections to certain of the logic-based approaches to artificial intelligence which utilize the intersection (“and”) and union (“or”) operations. We provide results which allow one to “calculate” the linear relaxation of a composite construction, in terms of set operations on the relaxation of the base sets. We are also able to compare the size of the relaxations for different formulations of the same MIP set, when these different formulations arise from one another through distributive laws. Utilizing these results, we generalize the Davis-Putnam algorithm of propositional logic to an MIP form, and answer a question regarding the relative efficiency of two versions of this algorithm. In this context, the subroutines of the logic algorithm correspond to list processing subroutines for MIP to be used prior to running linear programs. They are similar in nature to preprocessing routines, wherein entire MIP constraint sets are manipulated as formal symbols of logic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186369
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  • 10
    Electronic Resource
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    The scaling limit for a stochastic PDE and the separation of phases (1995)
    Springer
    Probability theory and related fields 102 (1995), S. 221-288 
    Details
    ISSN: 1432-2064
    Keywords: 60H15 ; 60K35 ; 35R60 ; 82C24
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We investigate the problem of singular perturbation for a reaction-diffusion equation with additive noise (or a stochastic partial differential equation of Ginzburg-Landau type) under the situation that the reaction term is determined by a potential with double-wells of equal depth. As the parameter ε (the temperature of the system) tends to 0, the solution converges to one of the two stable phases and consequently the phase separation is formed in the limit. We derive a stochastic differential equation which describes the random movement of the phase separation point. The proof consists of two main steps. We show that the solution stays near a manifoldM ε of minimal energy configurations based on a Lyapunov type argument. Then, the limit equation is identified by introducing a nice coordinate system in a neighborhood ofM ε.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213390
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  • 11
    Electronic Resource
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    Itô correction terms for the radial parts of semimartingales on manifolds (1995)
    Springer
    Probability theory and related fields 101 (1995), S. 133-146 
    Details
    ISSN: 1432-2064
    Keywords: 58G32 ; 60H15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider functions,F, of a semimartingale,X, on a complete manifold which fail to beC 2 only on, and are sufficiently well-behaved near, a codimension 1 subset ℒ. We obtain an extension of the Itô formula which is valid for all time by adding a continuous predictable process given explicitly in terms of two geometric local times ofX on ℒ and the Gâteaux derivative ofF. We then examine the cut locus of a point of the manifold in sufficient detail to show that this result applies to give a corresponding expression for the radial part of the semimartingale.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01192198
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  • 12
    Electronic Resource
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    Convergence to equilibrium for classical and quantum spin systems (1995)
    Springer
    Probability theory and related fields 103 (1995), S. 529-552 
    Details
    ISSN: 1432-2064
    Keywords: 60H15 ; 60K35 ; 35K55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper is devoted to stochastic equations describing the evolution of classical and quantum unbounded spin systems on discrete lattices and on Euclidean spaces. Existence and asymptotic properties of the corresponding transition semigroups are studied in a unified way using the theory of dissipative operators on weighted Hilbert and Banach spaces. This paper is an enlarged and rewritten version of the paper [7].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01246338
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  • 13
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    Martingale and stationary solutions for stochastic Navier-Stokes equations (1995)
    Springer
    Probability theory and related fields 102 (1995), S. 367-391 
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    ISSN: 1432-2064
    Keywords: 60H15 ; 76D05 ; 35Q10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We prove the existence of martingale solutions and of stationary solutions of stochastic Navier-Stokes equations under very general hypotheses on the diffusion term. The stationary martingale solutions yield the existence of invariant measures, when the transition semigroup is well defined. The results are obtained by a new method of compactness.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01192467
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  • 14
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    Ergodicity of stochastic plates (1995)
    Springer
    Probability theory and related fields 102 (1995), S. 19-44 
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    ISSN: 1432-2064
    Keywords: 60H15 ; 60F10 ; 73K12
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We prove the stabilization of plates subject to a stochastic evolution of Ginzburg Landa type. We study the asymptotic behaviour of the rate of stabilization when the intensity of the noise vanishes. An approximate simulated annealing property is also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01295219
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  • 15
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    A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation (1995)
    Springer
    Probability theory and related fields 102 (1995), S. 159-188 
    Details
    ISSN: 1432-2064
    Keywords: 60H15 ; 81G99 ; 35K55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A system ofN particles inR d with mean field interaction and diffusion is considered. Assuming adiabatic elimination of the momenta the positions satisfy a stochastic ordinary differential equation driven by Brownian sheets (microscopic equation), where all coefficients depend on the position of the particles and on the empirical mass distribution process. This empirical mass distribution process satisfies a quasilinear stochastic partial differential equation (SPDE). This SPDE (mezoscopic equation) is solved for general measure valued initial conditions by “extending” the empirical mass distribution process from point measure valued initial conditions with total mass conservation. Starting with measures with densities inL 2(R d ,dr), wheredr is the Lebesgue measure, the solution will have densities inL 2(R d ,dr) and strong uniqueness (in the Itô sense) is obtained. Finally, it is indicated how to obtain (macroscopic) partial differential equations as limits of the so constructed SPDE's.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213387
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  • 16
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    Large time behavior of interface solutions to the heat equation with Fisher-Wright white noise (1995)
    Springer
    Probability theory and related fields 102 (1995), S. 289-311 
    Details
    ISSN: 1432-2064
    Keywords: 60H15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The one-dimensional heat equation driven by Fisher-Wright white noise is studied. From initial conditions with compact support, solutions retain this compact support and die out in finite time. There exist interface solutions which change from the value 1 to the value 0 in a finite region. The motion of the interface location is shown to approach that of a Brownian motion under rescaling. Solutions with a finite number of interfaces are approximated by a system of annihilating Brownian motions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01192463
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  • 17
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    Existence, uniqueness and invariant measures for stochastic semilinear equations on Hilbert spaces (1995)
    Springer
    Probability theory and related fields 102 (1995), S. 331-356 
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    ISSN: 1432-2064
    Keywords: 60H15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of stochastic evolution equations with additive noise and weakly continuous drift is considered. First, regularity properties of the corresponding Ornstein-Uhlenbeck transition semigroupR t are obtained. We show thatR t is a compactC 0-semigroup in all Sobolev spacesW n,p which are built on its invariant measure μ. Then we show the existence, uniqueness, compactness and smoothing properties of the transition semigroup for semilinear equations inL p(μ) spaces and spacesW 1,p . As a consequence we prove the uniquencess of martingale solutions to the stochastic equation and the existence of a unique invariant measure equivalent to μ. It is shown also that the density of this measure with respect to μ is inL p(μ) for allp≧1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01192465
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  • 18
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    Stochastic evolution equations in Hilbert spaces (1995)
    Springer
    Applied mathematics & optimization 32 (1995), S. 255-279 
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    ISSN: 1432-0606
    Keywords: Stochastic PDEs ; Nonlinear monotone operators ; Difference approximations ; 60H15 ; 35R60 ; 47H17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we consider Ito's stochastic differential equation in Hilbert spaces. A strong solution is generated by the difference approximation. A regularity result is obtained for solutions to a class of parabolic stochastic partial differential equations. Hyperbolic stochastic evolution equations are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01187902
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  • 19
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    Effective equations of two-phase flow in random media (1995)
    Springer
    Calculus of variations and partial differential equations 3 (1995), S. 385-406 
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    ISSN: 1432-0835
    Keywords: 35B27 ; 76T05 ; 35Q35 ; 60H15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Abstract We consider the behavior of incompressible two-phase flow in heterogeneous reservoirs with randomly placed heterogeneities; that is, in media with permeabilityA and porosityΦ which are stationary random fields. We assume both Darcy velocity and the diffusion flux being given nonlinear functions of the concentration. Using the tools of stochastic homogenization we get the nonlinear effective equations which govern the flow behavior in a homogeneous medium, being equivalent in the sense of homogenization theory, to the original one. Whenε is small the randomly heterogeneous porous medium behaves like a deterministic medium with effective permeability tensor Ao. It is shown how to calculate the effective permeability tensor Ao by solving auxiliary stochastic problems. Using the rescaling parameterε, corresponding to the characteristic scale of heterogeneities, we prove the convergence of the homogenization process forε → 0. Furthermore, by using regularity results for the nonlinear effective equations we construct the correctors and establish strong convergence.
    Notes: Résumé On considère le comportement des écoulements diphasiques incompressibles dans un réservoir hétérogène avec les hétérogénéités placées aléatoirement; c'est-à-dire, dans un milieux où la permeabilitéA et la porositéΦ sont des champs aléatoires stochastiquement homogénes. On suppose à la fois que le vecteur flux de diffusion et la vitesse de Darcy sont des fonctions nonlinéaires de la concentration. En utilisant les techniques d'homogénéisation stochastique on obtient à grande échelle des équations nonlinéaires „efficaces“ décrivants un écoulement en milieux poreux equivalent à l'écoulement original dans le sens de la théorie de l'homogénéisation. Le milieu poreux aléatoire se comporte à grande échelle comme un milieux deterministe avec un tenseur „efficace“ de permeabilité A o , pourɛ suffisemment petit. Ce tenseur de perméabilité „efficace“ est calculé en resolvant des problèmes stochastiques auxilliaires. Lorsque le paramétreε, correspondant à l'échelle caractéristique des hétérogénéités, tend vers zero, nous montrons la convergence du processus d'homogénéisation. Finalement, en utilisant des résultats de régularité pour les équations „efficaces“ nonlineaires obtenues, nous construisons les correcteurs et démontrons la convergence forte.
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    URL: http://dx.doi.org/10.1007/BF01189397
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  • 20
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    Knowledge-based geographic information systems (KBGIS): New analytic and data management tools (1988)
    Springer
    Mathematical geology 20 (1988), S. 1021-1035 
    Details
    ISSN: 1573-8868
    Keywords: geographic information system ; geography ; geology ; earth science data ; spatial data ; artificial intelligence ; data analysis ; data bases ; data management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract In its simplest form, a geographic information system (GIS) may be viewed as a data base management system in which most of the data are spatially indexed, and upon which sets of procedures operate to answer queries about spatial entities represented in the data base. Utilization of artificial intelligence (AI) techniques can enhance greatly the capabilities of a GIS, particularly in handling very large, diverse data bases involved in the earth sciences. A KBGIS has been developed by the U.S. Geological Survey which incorporates AI techniques such as learning, expert systems, new data representation, and more. The system, which will be developed further and applied, is a prototype of the next generation of GIS's, an intelligent GIS, as well as an example of a general-purpose intelligent data handling system. The paper provides a description of KBGIS and its application, as well as the AI techniques involved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00892977
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  • 21
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    Experiments with microcomputer-based artificial intelligence environments (1988)
    Springer
    Mathematical geology 20 (1988), S. 1037-1047 
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    ISSN: 1573-8868
    Keywords: artificial intelligence ; data bases ; microcomputer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The U.S. Geological Survey (USGS) has been experimenting with the use of relatively inexpensive microcomputers as artificial intelligence (AI) development environments. Several AI languages are available that perform fairly well on desk-top personal computers, as are low-to-medium cost expert system packages. Although performance of these systems is respectable, their speed and capacity limitations are questionable for serious earth science applications foreseen by the USGS. The most capable artificial intelligence applications currently are concentrated on what is known as the “artificial intelligence computer,” and include Xerox D-series, Tektronix 4400 series, Symbolics 3600, VAX, LMI, and Texas Instruments Explorer. The artificial intelligence computer runs expert system shells and Lisp, Prolog, and Smalltalk programming languages. However, these AI environments are expensive. Recently, inexpensive 32-bit hardware has become available for the IBM/AT microcomputer. USGS has acquired and recently completed Beta-testing of the Gold Hill Systems 80386 Hummingboard, which runs Common Lisp on an IBM/AT microcomputer. Hummingboard appears to have the potential to overcome many of the speed/capacity limitations observed with AI-applications on standard personal computers. USGS is a Beta-test site for the Gold Hill Systems GoldWorks expert system. GoldWorks combines some high-end expert system shell capabilities in a medium-cost package. This shell is developed in Common Lisp, runs on the 80386 Hummingboard, and provides some expert system features formerly available only on AI-computers including frame and rule-based reasoning, on-line tutorial, multiple inheritance, and object-programming.
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    URL: http://dx.doi.org/10.1007/BF00892978
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  • 22
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    Generalized bochner theorems and the spectrum of complete manifolds (1988)
    Springer
    Acta applicandae mathematicae 12 (1988), S. 1-33 
    Details
    ISSN: 1572-9036
    Keywords: 58G11 ; 58G32 ; 60H15 ; Bochner's theorem ; Brownian motion and heat flow ; spectrum of the Laplacian ; hyperbolic manifolds ; cohomology with compact support
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Bochner's theorem that a compact Riemannian manifold with positive Ricci curvature has vanishing first cohomology group has various extensions to complete noncompact manifolds with Ricci possibly negative. One still has a vanishing theorem for L 2 harmonic one-forms if the infimum of the spectrum of the Laplacian on functions is greater than minus the infimum of the Ricci curvature. This result and its analogues for p-forms yield vanishing results for certain infinite volume hyperbolic manifolds. This spectral condition also imposes topological restrictions on the ends of the manifold. More refined results are obtained by taking a certain Brownian motion average of the Ricci curvature; if this average is positive, one has a vanishing theorem for the first cohomology group with compact supports on the universal cover of a compact manifold. There are corresponding results for L 2 harmonic spinors on spin manifolds.
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    URL: http://dx.doi.org/10.1007/BF00047567
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  • 23
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    Linear programming based decomposition approach in evaluating priorities from pairwise comparisons and error analysis (1995)
    Springer
    Journal of optimization theory and applications 84 (1995), S. 207-234 
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    ISSN: 1573-2878
    Keywords: Pairwise comparisons ; eigenvectors ; analytic hierarchy process ; linear programming ; fuzzy sets ; membership values ; artificial intelligence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract One of the most difficult issues in many real-life decisionmaking problems is how to estimate the pertinent data. An approach which uses pairwise comparisons was proposed by Saaty and is widely accepted as an effective way of determining these data. Suppose that two matrices with pairwise comparisons are available. Furthermore, suppose that there is an overlapping of the elements compared in these two matrices. The problem examined in this paper is how to combine the comparisons of the two matrices in order to derive the priorities of the elements considered in both matrices. A simple approach and a linear programming approach are formulated and analyzed in solving this problem. Computational results suggest that the LP approach, under certain conditions, is an effective way for dealing with this problem. The proposed approach is of critical importance because it can also result in a reduction of the total required number of comparisons.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02191743
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  • 24
    Electronic Resource
    Electronic Resource
    A new sequential cluster algorithm for optical lens design (1988)
    Springer
    Journal of optimization theory and applications 59 (1988), S. 165-172 
    Details
    ISSN: 1573-2878
    Keywords: Cluster theory ; artificial intelligence ; decision rules ; optical lens systems ; nonlinear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optical lens design problems are solved by numerical optimization. If we describe an optical lens system by constructive parameters, we may identify such a system by a vectorx ∈ ℝ n . To find an adequate system for a given problem, we have to organize the optimization process in a parameter space with a fixed dimensionn. Often, such an optimization leads to inadequate results. For this reason, we have to alter the number of lenses contained in the system. Consequently, we have to change the dimension of the space for the parametric description of the lens system. This paper describes a special sequential cluster algorithm to realize the move from one parameter space to another by computation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938306
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