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Mathematical Properties (mathematical + property)
Selected AbstractsMultidimensional FEM-FCT schemes for arbitrary time steppingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003D. Kuzmin Abstract The flux-corrected-transport paradigm is generalized to finite-element schemes based on arbitrary time stepping. A conservative flux decomposition procedure is proposed for both convective and diffusive terms. Mathematical properties of positivity-preserving schemes are reviewed. A nonoscillatory low-order method is constructed by elimination of negative off-diagonal entries of the discrete transport operator. The linearization of source terms and extension to hyperbolic systems are discussed. Zalesak's multidimensional limiter is employed to switch between linear discretizations of high and low order. A rigorous proof of positivity is provided. The treatment of non-linearities and iterative solution of linear systems are addressed. The performance of the new algorithm is illustrated by numerical examples for the shock tube problem in one dimension and scalar transport equations in two dimensions. Copyright © 2003 John Wiley & Sons, Ltd. [source] Coordinated Capacitated Lot-Sizing Problem with Dynamic Demand: A Lagrangian HeuristicDECISION SCIENCES, Issue 1 2004E. Powell Robinson Jr. ABSTRACT Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed-integer programming formulation and Lagrangian relaxation solution procedure for the single-family coordinated capacitated lot-sizing problem with dynamic demand. The problem extends both the multi-item capacitated dynamic demand lot-sizing problem and the uncapacitated coordinated dynamic demand lot-sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual-based heuristic over linear programming-based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs. [source] The exponentiated Gumbel distribution with climate applicationENVIRONMETRICS, Issue 1 2006Saralees Nadarajah Abstract The Gumbel distribution is perhaps the most widely applied statistical distribution for climate modeling. In this article we introduce a distribution that generalizes the standard Gumbel distribution in the same way the exponentiated exponential distribution generalizes the standard exponential distribution. We refer to this new distribution as the exponentiated Gumbel distribution. We provide a comprehensive treatment of the mathematical properties of this new distribution and illustrate its use for modeling rainfall data from Orlando, Florida. Among the mathematical properties, we derive the analytical shapes of the corresponding probability density function and the hazard rate function, calculate expressions for the nth moment and the asymptotic distribution of the extreme order statistics, and investigate the variation of the skewness and kurtosis measures. We also discuss estimation by the method of maximum likelihood. Copyright © 2005 John Wiley & Sons, Ltd. [source] Feedforward networks in financial predictions: the future that modifies the presentEXPERT SYSTEMS, Issue 3 2000Massimo Budcema The main goal of this paper is to show how relatively minor modifications of well-known algorithms (in particular, back propagation) can dramatically increase the performance of an artificial neural network (ANN) for time series prediction. We denote our proposed sets of modifications as the 'self-momentum', 'Freud' and 'Jung' rules. In our opinion, they provide an example of an alternative approach to the design of learning strategies for ANNs, one that focuses on basic mathematical conceptualization rather than on formalism and demonstration. The complexity of actual prediction problems makes it necessary to experiment with modelling possibilities whose inherent mathematical properties are often not well understood yet. The problem of time series prediction in stock markets is a case in point. It is well known that asset price dynamics in financial markets are difficult to trace, let alone to predict with an operationally interesting degree of accuracy. We therefore take financial prediction as a meaningful test bed for the validation of our techniques. We discuss in some detail both the theoretical underpinnings of the technique and our case study about financial prediction, finding encouraging evidence that supports the theoretical and operational viability of our new ANN specifications. Ours is clearly only a preliminary step. Further developments of ANN architectures with more and more sophisticated 'learning to learn' characteristics are now under study and test. [source] Pressure relaxation procedures for multiphase compressible flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005M.-H. Lallemand Abstract This paper deals with pressure relaxation procedures for multiphase compressible flow models. Such models have nice mathematical properties (hyperbolicity) and are able to solve a wide range of applications: interface problems, detonation physics, shock waves in mixtures, cavitating flows, etc. The numerical solution of such models involves several ingredients. One of those ingredients is the instantaneous pressure relaxation process and is of particular importance. In this article, we present and compare existing and new pressure relaxation procedures in terms of both accuracy and computational efficiency. Among these procedures we enhance an exact one in the particular case of fluids governed by the stiffened gas equation of state, and approximate procedures for general equations of state, which are particularly well suited for problems with large pressure variations. We also present some generalizations of these procedures in the context of multiphase flows with an arbitrary number of fluids. Some tests are provided to illustrate these comparisons. Copyright © 2005 John Wiley & Sons, Ltd. [source] Performance characterization of a non-linear system as both an adaptive notch filter and a phase-locked loopINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 1 2004M. Karimi-Ghartemani Abstract The behaviour of a non-linear dynamical system is described. The system may be characterized as an adaptive notch filter, or alternatively, as a phase-locked loop. Either way, the system has the inherent capability of directly providing estimates of the parameters of the extracted sinusoidal component of its input signal, namely its amplitude, phase and frequency. The structure and mathematical properties of the system are presented for two cases of fixed-frequency and varying-frequency operation. The effects of parameter setting of the system on its performance are studied in detail using computer simulations. Transient and steady-state behaviour of the system are studied in the presence of noise. Simplicity of structure, high noise immunity and robustness and the capability of direct estimation of amplitude, phase and frequency are the salient features of the system when envisaged as an adaptive notch filter or a phase-locked loop. Copyright © 2004 John Wiley & Sons, Ltd. [source] Performance optimization of object comparisonINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 10 2009Axel Hallez Comparing objects can be considered as a hierarchical process. Separate aspects of objects are compared to each other, and the results of these comparisons are combined into a single result in one or more steps by aggregation operators. The set of operators used to compare the objects and the way these operators are related with each other is called the comparison scheme. If a threshold is applied to the final result of the object comparison, the mathematical properties of the operators in the comparison scheme can be used to derive thresholds on the intermediate results. These derived threshold can be used to break of a comparison early, thus offering a reduction of the comparison cost. Using this information, we show that the order in which the operators are evaluated has an influence on the average cost of comparing two objects. Next, we proceed with a study of the properties that allow us to find an optimal order, such that this average cost is minimized. Finally, we provide an algorithm that calculates an optimal order efficiently. Although specifically developed for object comparison, the algorithm can be applied to all kinds of selection processes that involve the combination of several test results. © 2009 Wiley Periodicals, Inc. [source] Degeneracy of confined D -dimensional harmonic oscillatorINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2007H. E. Montgomery Jr. Abstract Using the mathematical properties of the confluent hypergeometric functions, the conditions for the incidental, simultaneous, and interdimensional degeneracy of the confined D -dimensional (D > 1) harmonic oscillator energy levels are derived, assuming that the isotropic confinement is defined by an infinite potential well and a finite radius Rc. Very accurate energy eigenvalues are obtained numerically by finding the roots of the confluent hypergeometric functions that confirm the degeneracy conditions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Analysis of scattering from polydisperse structure using Mellin convolutionJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 2 2006Norbert Stribeck This study extends a mathematical concept for the description of heterogeneity and polydispersity in the structure of materials to multiple dimensions. In one dimension, the description of heterogeneity by means of Mellin convolution is well known. In several papers by the author, the method has been applied to the analysis of data from materials with one-dimensional structure (layer stacks or fibrils along their principal axis). According to this concept, heterogeneous structures built from polydisperse ensembles of structural units are advantageously described by the Mellin convolution of a representative template structure with the size distribution of the templates. Hence, the polydisperse ensemble of similar structural units is generated by superposition of dilated templates. This approach is particularly attractive considering the advantageous mathematical properties enjoyed by the Mellin convolution. Thus, average particle size, and width and skewness of the particle size distribution can be determined from scattering data without the need to model the size distributions themselves. The present theoretical treatment demonstrates that the concept is generally extensible to dilation in multiple dimensions. Moreover, in an analogous manner, a representative cluster of correlated particles (e.g. layer stacks or microfibrils) can be considered as a template on a higher level. Polydispersity of such clusters is, again, described by subjecting the template structure to the generalized Mellin convolution. The proposed theory leads to a simple pathway for the quantitative determination of polydispersity and heterogeneity parameters. Consistency with the established theoretical approach of polydispersity in scattering theory is demonstrated. The method is applied to the best advantage in the field of soft condensed matter when anisotropic nanostructured materials are to be characterized by means of small-angle scattering (SAXS, USAXS, SANS). [source] On hybrid quantum,classical transport modelsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2004Naoufel Ben Abdallah Abstract This paper contains a review on the coupling between classical models and quantum models for electron transport in semiconductors. Starting from the quantum analogue of the boundary value problem for the Vlasov equation, the coupling with the Boltzmann equation in the one-dimensional stationary situation is reviewed for the stationary and time-dependent problems. Then a numerical scheme based on the characteristics method is applied to the stationary hybrid model. Some mathematical properties of the scheme are proven and illustrated in some numerical experiments. Copyright © 2004 John Wiley & Sons, Ltd. [source] Probability density of the multipole vectors for a Gaussian cosmic microwave backgroundMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2008Mark R. Dennis ABSTRACT We review Maxwell's multipole vectors, and elucidate some of their mathematical properties, with emphasis on the application of this tool to the cosmic microwave background (CMB). In particular, for a completely random function on the sphere (corresponding to the statistically isotropic Gaussian model of the CMB), we derive the full probability density function of the multipole vectors. This function is used to analyse the internal configurations of the third-year Wilkinson Microwave Anisotropy Probe quadrupole and octopole, and we show that the observations are consistent with the Gaussian prediction. A particular aspect is the planarity of the octopole, which we find not to be anomalous. [source] THE FISCAL THEORY OF THE PRICE LEVEL: A CRITIQUE*THE ECONOMIC JOURNAL, Issue 481 2002Willem H. Buiter This paper argues that the `fiscal theory of the price level' (FTPL) has feet of clay. The source of the problem is a fundamental economic misspecification. The FTPL confuses two key building blocks of a model of a market economy: budget constraints, which must be satisfied identically, and market clearing or equilibrium conditions. The FTPL asssumes that the government's intertemporal budget constraint needs to be satisfied only in equilibrium. This economic misspecification has far-reaching implications for the mathematical properties of the equilibria supported by models that impose the structure of the FTPL. It produces a rash of contradictions and anomalies. [source] A new class of coherent risk measures based on p -norms and their applicationsAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 1 2007Zhiping Chen Abstract To exercise better control on the lower tail of the loss distribution and to easily describe the investor's risk attitude, a new class of coherent risk measures is proposed in this paper by taking the minimization of p -norms of lower losses with respect to some reference point. We demonstrate that the new risk measure has satisfactory mathematical properties such as convexity, continuity with respect to parameters included in its definition, the relations between two new risk measures are also examined. The application of the new risk measures for optimal portfolio selection is illustrated by using trade data from the Chinese stock markets. Empirical results not only support our theoretical conclusions, but also show the practicability of the portfolio selection model with our new risk measures. Copyright © 2006 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||