Special Issue: Nonclassical Lagrangian Dynamics and Potential Maps

Guest Editor: Constantin Udriste

Title of the Paper: Euler-Lagrange Characterization of Area-Minimizing Graphs in Randers Spaces with Non-constant Potential

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Authors: Vladimir Balan

Abstract: Within the framework of Randers spaces with non-constant potential, the mean curvature form of hypersurfaces is determined, and the equations which characterize the area-minimizing graph surfaces are explicitly derived as associated Euler-Lagrange PDEs. By applying the extended framework to the particular case of graphs in Randers spaces with constant potential, the known result of Souza-Spruck-Tenenblat ([27]) is confirmed. It is shown that the only linear affine potentials for which the Randers metric admits all the affine planes as minimal graphs, are necessarily constant. As well, the ODE which characterizes the generating curve of surfaces of revolution is derived, this extending the result obtained by Souza-Tenenblat in [26] in the constant potential case.

Keywords: Euler-Lagrange equations, mean curvature 1-form, Finsler structure, Randers metric, hypersurfaces, minimal graphs, minimal surfaces of revolution.

Title of the Paper: Necessary Optimality Conditions for Fractional Action-Like Problems with Intrinsic and Observer Times

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Authors: Gastao S. F. Frederico, Delfim F. M. Torres

Abstract: We prove higher-order Euler-Lagrange and DuBois-Reymond stationary conditions to fractional actionlike variational problems. More general fractional action-like optimal control problems are also considered.

Keywords: calculus of variations, FALVA problems, higher-order Euler-Lagrange equations, higher-order DuBois-Reymond stationary condition, multi-time control theory.

Title of the Paper: Non-Classical Lagrangian Dynamics and Potential Maps

Authors: Constantin Udriste

Abstract: The basic theory regarding Nonclassical Lagrangian Dynamics and Potential Maps was announced in [7]. Since its mathematical impact is now at large vogue, we reinforce some arguments. Section 1 extends the theory of harmonic and potential maps in the language of differential geometry. Section 2 defines a generalized Lorentz world-force law and shows that any PDE system of order one (in particular, p-flow) generates such a law in a suitable geometrical structure. In other words, the solutions of any PDE system of order one are harmonic or potential maps, i.e., they are solutions of Euler-Lagrange prolongation PDE system of order two built via Riemann- Lagrange structures and a least squares Lagrangian. Section 3 formulates open problems regarding the geometry of semi-Riemann manifolds (J1(T,M), S1), (J2(T,M), S2). Section 4 shows that the Lorentz-Udriste world-force law is equivalent to certain covariant Hamilton PDEs on (J1(T,M), S1). Section 5 describes the maps determining a continuous group of transformations as ultra-potential maps

Keywords: ultra-harmonic map, ultra-potential map, Lagrangian, Hamiltonian, Lorentz-Udriste world force law.

Title of the Paper: Euler-Lagrange-Hamilton Dynamics with Fractional Action

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Authors: Constantin Udriste, Dumitru Opris

Abstract: Our aim is three-fold: to point out that the fractional integral actions are coming from Stieltjes actions, to find the roots and the geometry of some Euler-Lagrange or Hamilton ODEs or PDEs, to evidentiate some ideas that include the fractal theory of solids. Section 1 discusses the Euler-Lagrange ODEs associated to single-time Stieltjes actions. Teir dual Hamilton ODEs are analized in Section 2. Section 3 studies the geometry associated to singletime Euler-Lagrange or Hamilton operators. Section 4 analyzes the Euler-Lagrange PDEs associated to multitime Stieltjes actions (multiple or curvilinear integrals). Section 5 formulates the multitime perimetric problem of nonrenewable resources. Section 6 studies the Hamilton PDEs associated to multitime Stieltjes actions. Section 7 describes the geometry associated to multitime Euler-Lagrange or Hamilton operators (dynamical connection and semi-spray, Poincar´e-Cartan form, Hamilton-Poisson systems on jet bundle). Section 8 formulates a multitime Hamilton-Poisson systems theory on jet bundle.

Keywords: fractional Stieltjes action, Euler-Lagrange or Hamilton equations, dynamic connection, symplectic manifold.

Title of the Paper: Nonclassical Electromagnetic Dynamics

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Authors: Constantin Udriste, Dorel Zugravescu, Florin Munteanu

Abstract: Our paper is concerned with effects of special forces on the motion of particles. §1(§2) studies the singletime geometric dynamics induced by electromagnetic vector fields (1-forms) and by the Euclidean structure of the space. §3 defines the second-order forms or vectors. §4 (§5) describes a nonclassical electric (magnetic) dynamics produced by an ”electric (magnetic) second-order Lagrangian”, via the extremals of the energy functional. §6 generalize this dynamics for a general second-order Lagrangian, having in mind possible applications for dynamical systems coming from Biomathematics, Economical Mathematics, Industrial Mathematics, etc.

Keywords: geometric dynamics, second-order vectors, second-order Lagrangian, nonclassical dynamics.

Title of the Paper: Determining a Metric by Boundary Single-Time Flow Energy

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Authors: Ariana Pitea

Abstract: Our theory of determining a tensor by single-time flow energy is similar to those developed by Sharafutdinov. Section 1 refines the theory of potential curves determined by a flow and a Riemannian metric. Section 2 defines the boundary energy of a potential curve and proves that the problem of determining a metric from a single-time flow boundary energy cannot have a unique solution. Section 3 linearizes the above-mentioned problem and defines the notion of single-ray transform.

Keywords: potential curves, least squares Lagrangian, single-ray transform, boundary energy.

Title of the Paper: Determining a Pair of Metrics by Boundary Energy Associated to a Multitime PDE System

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Authors: Ariana Pitea, Constantin Udriste

Abstract: Our theory of determining a tensor by boundary energy of a multitime first order PDE system is similar to those developed by Sharafutdinov. Section 1 refines the theory of potential maps determined by a first order multitime PDE system and a vertical metric. Section 2 defines the boundary energy of a first order PDE system and proves that the problem of determining a vertical metric from the boundary energy of a multitime PDE system cannot have a unique solution. Section 3 linearizes the above mentioned problem and defines the notion of multi-ray transform.

Keywords: potential map, least squares Lagrangian, boundary energy, multi-ray transform, extremals.

Title of the Paper: Multitime Models of Optimal Growth

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Authors: Constantin Udriste, Massimiliano Ferrara

Abstract: Section 1 underlines the limitations of standard multi-variable variational calculus and the sense of multitime. Section 1 formulates the controllability problem for a multiple integral functional or for a path independent curvilinear integral subject to a multitime evolution of flow type. Section 2 describes a two-time optimal economic growth modelled by Euler-Lagrange PDEs associated to a double integral functional or to a path independent curvilinear integral in two dimensions. Section 3 motivates the optimal economic growth by two-time maximum principles. Section 4 studies the two-time optimal economic growth with bang-bang policy based on a curvilinear integral action.

Keywords: multitime maximum principle, multitime optimal economic growth, bang-bang policy.

Title of the Paper: A Descent Method for Nonsmooth Variational Inequalities via Regularization

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Authors: Barbara Panicucci, Massimo Pappalardo, Mauro Passacantando

Abstract: In this paper we propose a descent method for solving variational inequality problems where the underlying operator is nonsmooth, locally Lipschitz, and monotone over a closed, convex feasible set. The idea is to combine a descent method for variational inequality problems whose operators are nonsmooth, locally Lipschitz, and strongly monotone, with the Tikonov-Browder regularization technique. Finally, numerical results are presented and discussed.

Keywords: variational inequality, nonsmooth mapping, gap function, descent method, Tikhonov-Browder regularization.

Title of the Paper: Generalized Multitime Lagrangians and Hamiltonians

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Authors: Constantin Udriste, Paul Popescu and Marcela Popescu

Abstract: We establish a natural frame for affine Lagrangians and Hamiltonians. The focus is on the Hamiltonians applicable in classical fields and their generalizations. A unitary treatment of scalar and volume-valued Hamiltonians in a special class is obtained. Considering a variational problem of the action defined by a Hamiltonian in this class, one obtains informations about the multitime dynamical solutions of the classical variational problem for scalar and volume-valued Hamiltonians.

Keywords: affine lagrangian, affine hamiltonian, variational equation, jet space.

Issue 2, Volume 7, February 2008

Title of the Paper: Theoretical Analysis of Inverse Weibull Distribution

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Authors: M. Shuaib Khan, G.R Pasha, Ahmed Hesham Pasha

Abstract: In this study we present the theoretical analysis of Inverse weibull distribution. This paper presents the flexibility of the Inverse weibull distribution that approaches to different distributions. Here we compare the relevant parameters such as shape, scale parameters by using simulation analysis. Here we present the relationship between shape parameter and other properties such as mean, median, mode, variance, coefficient of variation, coefficient of skewness and coefficient of kurtosis models are shown graphically and mathematically presented.

Keywords: Inverse weibull distribution, simulation analysis, graphically analysis

Title of the Paper: An Lω1ω1 Axiomatization of the Linear Archimedean Continua as Merely Relational Structures

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Authors: Miloš Arsenijević, Miodrag Kapetanović

Abstract: We have chosen the language Lω1ω1 in which to formulate the axioms of two systems of the linear Archimedean continua – the point-based system, SP, and the stretch-based system, SI – for the following reasons: 1. It enables us to formulate all the axioms of each system in one and the same language; 2. It makes it possible to apply, without any modification, Arsenijević's two sets of rules for translating formulas of each of these systems into formulas of the other, in spite of the fact that these rules were originally formulated in a first-order language for systems that are not continuous but dense only; 3. It enables us to speak about an infinite number of elements of a continuous structure by mentioning explicitly only denumerably many of them; 4. In this way we can formulate not only Cantor's coherence condition for linear continuity but also express the large-scale and small-scale variants of the Archimedean axiom without any reference, either explicit or implicit, to a metric; 5. The models of the two axiom systems are structures that need not be relational-operational but only relational, which means that we can speak of the linear geometric continua directly and not only via the field of real numbers (numbers will occur as subscripts only, and they will be limited to the natural numbers).

Keywords: Linear continuum, L_omega_1/omega_1, point-based, stretch-based axiomatization, trivial difference, Archimedean axiom

Title of the Paper: Bifurcation diagrams of generic families of singular systems under proportional and derivative feedback

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Authors: M. Isabel Garc´Ia-Planas

Abstract: In this paper we study qualitative properties about nearby singular systems using stratification method. We construct the stratification partitioning the set of singular systems according to the complete set of discrete invariants. We show that it is a constructible stratification and that it is Whitney regular for one input regularizable systems. We give an application to the obtention of bifurcation diagrams for few parameter generic families of singular regularizable systems.

Keywords: Singular systems, Feedback and derivative feedback equivalence, stratification, canonical form, orbit, stratum.

Title of the Paper: Statistical Analysis of a Nonstationary Fatigue Data Using the ARIMA Approach

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Authors: S. Abdullah, M. D. Ibrahim, A. Zaharim and Z. Mohd Nopiah

Abstract: Auto Regressive Integrated Moving Average (ARIMA) is a broad class of time series models, and it has been achieved using the statistical differencing approach. It is normally being performed using the computational method. Thus, it is useful to choose the suitable model from a possibly large selection of the available ARIMA formulations. The ARIMA approach was then analysed with the presence of stationary behaviour in a nonstationary data. For the purpose of the random data analysis, a nonstationary data that exhibiting a random behaviour was used. This random data was measured in the unit of microstrain on the lower suspension arm or a car travelling on a country road surface. With this engineering unit, hence, the data is known as a variable amplitude fatigue loading. Experimentally, the data was collected for 225 seconds at the sampling rate of 200 Hz, which gave 45,000 discrete data points. Using the computational analysis by means of statistical software package, the ARIMA parameters were estimated by the application of the data smoothing technique in order to reduce the random variation of the fatigue data. Therefore, the significant ARIMA parameters were established and being applied in the study of the variation in nonstationary data. For this paper, finally, it is suggested that the ARIMA method provided a good platform to analyse fatigue random data, especially in the scope of the durability research.

Keywords: ARIMA, Statistical analysis, Fatigue, Nonstationary data, Statistics.

Title of the Paper: An Evaluation of Test Statistics for Detecting Level Change in BL(1,1,1,1) Models

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Authors: Azami Zaharim, Ibrahim Mohamed, Shahrum Abdullah and Mohd. Sahar Yahya

Abstract: A study is carried out to investigate the sampling properties of the outlier test statistics of a procedure developed for detecting level change in BL(1,1,1,1) processes. It is done with respect to the sample size, the type of outlier and the size of the coefficients of the BL(1,1,1,1) process. The results show that, in general, the outlier detection procedure is capable of detecting level change, although the performance is affected if ω is large.

Keywords: Level change, bilinear process, outlier test statistics, outlier detection procedure, sampling properties.

Issue 3, Volume 7, March 2008

Title of the Paper: On The Ermanno-Bernoulli and Quasi-Ermanno-Bernoulli Constants for Linearizing Dynamical Systems

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Authors: F.I. Arunaye, H. White

Abstract: It is well known that the Ermanno-Bernoulli constants derived from the Laplace-Runge-Lenz vector of dynamical systems are efficiently used to reduce them to a system of harmonic oscillator(s) and conservation law in the context of point and nonlocal symmetries of dynamical systems. In this paper, we review Ermanno-Bernoulli constants and observe that one can also use analogous constants obtained from the Hamilton vector of dynamical systems to serve the same purpose. We report the generic natural variables for reducing such dynamical systems in two-dimensions and three-dimensions to a system of one harmonic oscillator and two harmonic oscillators respectively, and a conservation law with some examples. We also note that the symmetry groups obtained from the reduced systems using the alternative constants are realizations of those obtained from Ermanno-Bernoulli constants. We also report here that the symmetries of the original dynamical systems can be obtained from symmetries of the reduced systems.

Keywords: Quasi, Constants, Symmetries, Vectors, Conservation, Oscillators, Laplace-Runge-Lenz, Hamilton, Coordinates, Dynamical.

Title of the Paper: Qualitative properties of the ice-thickness in a 3D model

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Authors: S.N. Antontsev, H.B. De Oliveira

Abstract: In this work we consider a 3D isothermal mathematical model for ice sheets flows over a horizontal bedrock. The model is derived from the mechanics and dynamics of ice sheets and experimental results carried out in Glaciology. The final formulation of the model gives rise to a degenerate quasi-linear elliptic-parabolic equation for the ice-thickness function. Under appropriated initial and Dirichlet boundary conditions, we discuss the existence and uniqueness of weak solutions for this problem. Then, we prove that the local speed of propagations of disturbances from the initial ice-thickness is finite. We prove also that the solutions of this problem have the waiting-time local behavior. To establish these properties we use here a suitable local energy method.

Keywords: ice sheet dynamics, existence, uniqueness, finite speed of propagations, waiting time.

Title of the Paper: Ultra Long Orbital Tethers Behave Highly Non-Keplerian and Unstable

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Authors: Radu D. Rugescu, Daniele Mortari

Abstract: Large twin tethers are investigated as possible competitive-cost tools for non-gasdynamic descent, landing, takeoff and return from target celestial bodies and as passive tools for debris retrieval from orbit. The particular behavior of orbiting bodies connected with long cables is a recent preoccupation in astrodynamics and proves being full of unexpected results. The investigation here presented is focused on the non-Keplerian behavior of such large tether systems, considered in a first approximation as rigid or very stiff and massless. The investigation starts with the feasibility of non-gasdynamic orbital deployment of twin tethers without any involvement of expensive rocket propulsion means. The free tether release systems are associated to a horizontal impulsive separation (HIS) and eventual friction-free deployment to the desired length. This horizontal deployment seems to supply the most productive means of continuous separation and departure of masses in orbit. The relative motion during separation is studied and the observation is made that a considerable kinetic moment of the system preserves during all eventual phases of the flight. After the friction-free deployment the extending cable is instantly immobilized at the so-called connection moment. From here after the tether length remains constant. The evolution of the deployed tether is followed in order to record the specific behavior when the length of the tether is extremely great. The motion of the two connected masses and of the mass center proves completely non-Keplerian, beginning with the libration around local vertical due to the considerable residual kinetic moment at connection. A practical application of the quasi-vertical libration is in orbital passive debris collector, when a sandwich composite large panel is orbited for long periods of time for collecting small mass, high velocity Earth orbit debris. The most promising and controversial application of such long tethers resides in the anchoring technique to achieve the skeleton of a future space elevator. The stability of motion is an important aspect which is approached my numerical simulations.

Keywords: Astrodynamics, Space tethers, Tether dynamics, Large space structures, Tether instability.

Title of the Paper: Implications of a Scale Invariant Model of Statistical Mechanics to Nonstandard Analysis and the Wave Equation

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Authors: Siavash H. Sohrab

Abstract: A scale-invariant model of statistical mechanics is applied to examine the physical foundation of nonstandard analysis and to identify the nature and the range (0_β, 0_β−1) of nonstandard numbers and to establish the existence of infinitesimals (0_β > L_β−2 > x_β > 0_β−2). An invariant logarithmic definition of coordinate is presented and the concept of “measureless” or “dimensionless” numbers (L_’β, λ_β, 0_β) = (L_β, 1_β, 0_β) is described. Also, a scale-invariant definition of fractal dimension is introduced that suggest exceedingly large values 10⁷ of fractal dimension. A scale invariant form of the wave equation is derived that applies to acoustic waves that propagate at speed of sound v_m = 350 m/s, gravitational waves that propagate at the speed of light v_t = c, and gravitational radiation that propagates at superluminal speeds v_g > 2 x10¹⁰ c.

Keywords: Nonstandard analysis; Infinitesimals; Gravitational waves; Gravitational radiation.

Title of the Paper: Fuzzy Approach to Semi-parametric of a Sample Selection Model

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Authors: L. Muhamad Safiih, A.A.Basah Kamil, M. T. Abu Osman

Abstract: The sample selection model is studied in the context of semi-parametric methods. With the deficiency of the parametric model, such as inconsistent estimators etc, the semi-parametric estimation methods provide the best alternative to handle this deficiency. Semi-parametric of a sample selection model is an econometric model and has found interesting application in empirical studies. The issue of uncertainty and ambiguity still become are still major problem and are complicated in the modelling of a semi-parametric sample selection model as well as its parametric. This study, focuses on the context of fuzzy concept as a hybrid to the semi-parametric sample selection model. The best approach of accounting for uncertainty and ambiguity is to take advantage of the tools provided by the theory of fuzzy sets. It seems particularly appropriate for modelling vague concepts. Fuzzy sets theory and its properties, through the concept of fuzzy number, provide an ideal framework in order to solve the problem of uncertain data. In this paper, we introduce a fuzzy membership function for solving uncertain data of a semi-parametric sample selection model.

Keywords: uncertainty, semi-parametric sample selection model, crisp data, fuzzy number, membership function

Title of the Paper: Fuzzy Semi-parametric Sample Selection Model Case Study for Participation of Married Women

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Authors: L. Muhamad Safiih, A.A.Basah Kamil, M. T. Abu Osman

Abstract: The sample selection model is studied in the context of semi-parametric methods. The issue of uncertainty and ambiguity are still major problems and the modelling of a semi-parametric sample selection model as well as its parametric. The best approach of accounting for uncertainty and ambiguity is to take advantage of the tools provided by the theory of fuzzy sets. The semi-parametric of a sample selection model is an econometric model that has found an interesting application in empirical studies. In this paper, the married women participants in the Malaysia labour force are studied. It comprises the analysis of a) participation equation in the wage sector and b) the wage equation in the wage sector. The data set used for this study is from the Malaysian population and family survey 1994 (MPFS-1994).

Keywords: uncertainty, semi-parametric sample selection model, participant equation, wage equation, fuzzy number.

Issue 4, Volume 7, April 2008

Title of the Paper: The Stability of Collocation Methods for Approximate Solution of Singular Integro- Differential Equations.

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Authors: Iurie Caraus, Nikos E. Mastorakis

Abstract: In this article we obtained that the collocation methods are stable in according with the small perturbations of coefficients, kernels and right part of studied equations. We proved that the condition number of the approximate operator exists and bounded. The condition number of collocation methods is appropriated with condition number for exact singular integro- differential equations.

Keywords: condition number, stability, collocation methods, singular integro- differential equations.

Title of the Paper: Optimal Operational Strategy for Hybrid Renewable Energy System Using Genetic Algorithms

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Authors: Kamaruzzaman Sopian, Azami Zaharim, Yusoff Ali,
               Zulkifli Mohd Nopiah, Juhari Ab. Razak, Nor Salim Muhammad

Abstract: Off-grid settlements require efficient, reliable and cost-effective renewable energy as alternative to the power supplied by diesel generator. Techno-economic analysis is required to find the optimum renewable energy system in the long run. This paper reviews the application of genetic algorithms in optimization of hybrid system consisting of pico hydro system, solar photovoltaic modules, diesel generator and battery sets. It is intended to maximize the use of renewable system while limiting the use of diesel generator. Daily load demand is assumed constant for derivation of annual load. Power derived from the hybrid should be able to meet the demand. Local weather data is used and analyzed to assess the technical and economic viability of utilizing the hybrid system. Optimization of the system will be based on the component sizing and the operational strategy. Genetic algorithms programming is used to evaluate both conditions in minimizing the total net present cost for optimum configuration. Manufacturer data for the hybrid components is used in calculation of sizing to represent actual power derivation. Several operation strategies will be considered while forming the vectors for optimum strategy. Random selection of sizing and strategy is used to initiate the solution for the problem which will have the lowest total net present cost. Sensitivity analysis is also performed to optimize the system at different conditions.

Keywords: Genetic algorithms; Operation strategy; Hybrid system; Renewable energy, Optimization

Title of the Paper: Improved Estimation of State of Stochastic Systems via Invariant Embedding Technique

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Authors: Nicholas A. Nechval, Gundars Berzins, Maris Purgailis,
               Konstantin N. Nechval

Abstract: In the present paper, for constructing the minimum risk estimators of state of stochastic systems, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant estimator, which has smaller risk than any of the well-known estimators. Also the problem of how to select the total number of the observations optimally when a constant cost is incurred for each observation taken is discussed. To illustrate the proposed technique, examples are given.

Keywords: Stochastic system; State; Estimation; Invariant embedding technique

Title of the Paper: Identification of a Heat Transfer Coefficient when it is a Function Depending on Temperature

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Authors: Andr’Es Fraguela, Juan–Antonio Infante,
               A’ Ngel Manuel Ramos, Jos’E Mar’Ia Rey

Abstract: This paper deals with an inverse problem concerning the identification of the heat exchange coefficientH (assumed depending on the temperature) between a certain material with the external environment (see, e.g., [12], [20] for real applications modelled with equations involving this coefficient). Only experimental measurements of the temperature are supposed to be known. The goal is to identifyH in order to get a solution for the corresponding model, approximating some given temperature measurements. The main difficulty is that we consider the case of functions H depending on the solution of the state equation. We begin by setting several scenarios for the inverse problem. For each scenario, we know the initial and ambient temperatures, we identify function H through different methods and we obtain error bounds in adequate norms (uniform and square integrable). Finally, we study the inverse problem in the framework of the classical theory for Hilbert spaces. Several methods are used (Tikhonov, Morozov, Landweber,. . . ) and the approximations obtained, as well as the one provided by our method, are shown.

Keywords: Function identification, Inverse Problems, Heat exchange, Regularization strategies.

Title of the Paper: Identification of a Heat Transfer Coefficient when it is a Function Depending on Temperature

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Authors: Alexandre Grebennikov

Abstract: New fast algorithms for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. Algorithms are based on new version of General Ray (GR) method which consists in application of the Radon transform directly to the PDE and in reduction PDE to assemblage of Ordinary Differential Equations (ODE). The class of the PDE includes the Laplace, Poisson and Helmgoltz equations. GR-method presents the solution of the Dirichlet boundary value problem for this type of equations by explicit analytical formulas that use the direct and inverse Radon transform. Proposed version of GR-method is justified theoretically, realized by MATLAB software, which quality we demonstrate by numerical experiments.

Keywords: fast algorithms, boundary value problems , partial differential equations, Radon transform, MATLAB software

Title of the Paper: Manufacturing Lot Sizing with Backordering, Scrap, and Random Breakdown Occurring in Inventory-Stacking Period

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Authors: Singa Wang Chiu, Jyh-Chau Yang and Shu-Ying Chen Kuo

Abstract: This paper is concerned with determination of optimal lot size for an economic manufacturing quantity model with backordering, scrap and breakdown occurring in inventory-stacking period. Generation of defective items and random breakdown of production equipment are inevitable in most real-life manufacturing systems. To cope with the stochastic machine failures, production planners practically calculate the mean time between failures (MTBF) and establish the robust plan accordingly, in terms of optimal lot size that minimizes total production-inventory costs for such an unreliable system. Random scrap rate is considered in this study, and breakdown is assumed to occur in inventory stacking period. Mathematical modeling and analysis is used and the renewal reward theorem is employed to cope with the variable cycle length. An optimal manufacturing lot size that minimizes the long-run average costs for such an imperfect system is derived. Numerical example is provided to demonstrate its practical usages.

Keywords: Optimization, Manufacturing systems, Production lot size, Machine breakdown, Backordering, Scrap, Inventory

Title of the Paper: A Matricial Public Key Cryptosystem with Digital Signature

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Authors: Rafael Alvarez, Francisco-Miguel Martinez, Jose-Francisco Vicent, and Antonio Zamora

Abstract: We describe a new public key cryptosystem using block upper triangular matrices with elements in Zp , based on a generalization of the discrete logarithm problem over a finite group. The proposed cryptosystem is very efficient, requiring very few operations and also allows an ElGamal based digital signature scheme. The main benefit is that the security level is higher than other algorithms for the same key size.

Keywords: Cryptography, Security, Public-Key, DLP, Finite Fields, Diffie-Hellman, Polynomial Matrices, ElGamal, Digital Signature.

Issue 5, Volume 7, May 2008

Title of the Paper: A Multistage Mean/Variance approach for Portfolio Management in the Mexican Market

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Authors: Maria A. Osorio, Ana Ballinas, Erika Jimenez, Abraham Sanchez

Abstract: This paper describes the use of Mean/Variance multistage portfolio management for building efficient frontiers. The maximization of the returns yields the maximum and the variance minimization the minimum points in the efficient frontier. The efficient frontier is the graph describing all the optimal options between these two points. The intermediate points are obtained minimizing the variance (risk measure) subject to different percentages of the maximum utility expected. According to the investor’s characteristics, a point in the graph, containing a complete set of investment strategies can be chosen. The stochastic quadratic and linear models use a scenario tree to represent the multistage discretization of the random returns. The examples are applied to the Mexican bursaries market.

Keywords: Portfolio Management, Stochastic Programming, Mean/Variance Optimization.

Title of the Paper: Incomplete Linguistic Preference Relations to Evaluate Multimedia Authoring System

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Authors: Tien-Chin Wang, Ying-Hsiu Chen, Yu-Chen Chiang

Abstract: MCMD problems with fuzzy preference information on alternatives are essential problems of the importance of weighting and ranking. In this study, the AHP method is reviewed, and then Fuzzy PreRa and incomplete linguistic preference relations methods are elucidated. This study applied above three MCDM methods to a software selection problem proposed by Lai et al. [Software selection: a case study of the application of the analytical hierarchical process to the selection of a multimedia authoring system, Information and Management, Vol.36, 1999, pp.221-232.]. The outcome obtained by Fuzzy PreRa and incomplete linguistic preference relations methods almost coincides with that produced by the AHP method, also with the least judgments. The result shows that the approach developed is simple and comprehensible in concept, efficient in computation, and robust in modeling human evaluation processes which make it of general use for solving practical qualitative multi-criteria problems.

Keywords: AHP, fuzzy preference relations, incomplete linguistic preference relations, multimedia authoring system (MAS), multi-criteria decision making (MCDM), selection

Title of the Paper: Embedding a family of 2D meshes into M¨obius cubes

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Authors: Chia-Jui Lai, Jheng-Cheng Chen

Abstract: M¨obius cubes are an important class of hypercube variants. This paper addresses how to embed a family of disjoint 2D meshes into a M¨obius cube. Two major contributions of this paper are: (1) For n ≥ 1, there exists a 2 × 2n−1 mesh that can be embedded in the n-dimensional M¨obius cube with dilation 1 and expansion 1. (2) For n ≥ 4, there are two disjoint 4 × 2n−3 meshes that can be embedded in the n-dimensional 0-type M¨obius cube with dilation 1. The results are optimal in the sense that the dilations of the embeddings are 1. The result (2) mean that a family of two 2D-mesh-structured parallel algorithms can be operated on a same crossed cube efficiently and in parallel.

Keywords: M¨obius cubes, mesh embedding, dilation, expansion, interconnection network.

Title of the Paper: Numerical Modeling of Mild Slope Equation with Finite Volume Method

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Authors: Asu İnan and Lale Balas

Abstract: When waves propagate from deep water to shallow water, they transform. Extended mild slope equation includes wave transformations such as refraction, diffraction, shoaling, reflection and dissipations due to bottom friction and wave breaking and harbour resonance. Extended mild slope equation can be applied to the rapidly varying topographies through higher order bottom effetcs. Nonlinear wave celerity and group velocity have been considered in the calculations. In this study, extended mild slope equation has been reduced to Helmholtz equation and solved with finite volume method. Numerical model has been tested on semicircular shoaling area and compared with the physical experiment measurements given in literarure. Numerical model has been applied to the Fethiye Bay in the Mediterranean Sea in Turkey.

Keywords: Extended mild slope equation, finite volume method, wave refraction, diffraction, nonlinear wave celerity and group velocity

Title of the Paper: Varadhan estimates without probability: upper bound

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Authors: Remi Leandre

Abstract: We translate in semi-group theory our proof of Varadhan estimates for subelliptic Laplacians which was using the theory of large deviations of Wentzel-Freidlin and the Malliavin Calculus of Bismut type.

Keywords: Large deviations. Subelliptic estimates.

Title of the Paper: Global Optimization Using Hybrid Approach

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Authors: Ting-Yu Chen, Yi Liang Cheng

Abstract: The paper deals with a global optimization algorithm using hybrid approach. To take the advantage of global search capability the evolution strategy (ES) with some modifications in recombination formulas and elites keeping is used first to find the near-optimal solutions. The sequential quadratic programming(SQP) is then used to find the exact solution from the solutions found by ES. One merit of the algorithm is that the solutions for multimodal problems can be found in a single run. Eight popular test problems are used to test the proposed algorithm. The results are satisfactory in quality and efficiency.

Keywords: Global optimization algorithm, hybrid approach, evolution strategy

Title of the Paper: Weights, inequalities and a local HÖlder norm for solutions to (∂/∂t-L)(u)=divf on bounded domains

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Authors: Caroline Sweezy

Abstract: The rate of change of u, a solution to Lu=divf in a bounded, rough domain ΩT, u=g on ∂pΩT , is investigated using a local Hölder norm of u and different measures on ΩT and on ∂pΩT. Results are discussed for both L a strictly elliptic operator and for L=∂/∂t-L0, with L0 a strictly parabolic divergence form operator; the coefficients are bounded and measurable, and in the case of L0 , time dependent.

Keywords: elliptic, parabolic equations, Lipschitz domains, Borel measures, kernels, Hölder norms.

Title of the Paper: The Asymptotical Behavior of Probability Measures for the Fluctuations of Stochastic Models

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Authors: Jun Wang and Cuining Wei

Abstract: We consider the fluctuations of shapes of two phases boundaries of the one-dimensional statistical mechanics models. By applying the theory of one-dimensional random walk, the models of the two phases boundaries are constructed by assuming that there is a specified value of the large area in the intermediate region of the two phases boundaries. Then we investigate the asymptotical behavior of the corresponding sequence of probability measures describing the statistical properties of the two phases boundaries. We show that the limiting probability measures coincide with some conditional probability distribution of certain Gaussian distribution. Further we discuss the properties of fluctuations of phase separation lines for the Ising model, and we obtain the asymptotic properties of the two interfaces S.O.S. model.

Keywords: Stochastic models; random phase boundaries; central limit theory; random walk; Gibbs measure; Hamiltonian

Title of the Paper: The Analysis and Correction of Factors Influencing Imaging Quality of Digital Radiographic Testing System

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Authors: Cheng Yao-yu, Li Yong-hong , Hu Yan, Liu Yan-hua

Abstract: The factors influencing imaging quality of industrial digital radiographic imaging system are analyzed detailedly. This imaging system is a new type industrial digital radiographic imaging system developed by author, The structure of ray conversion screen and its non-uniformity, the discordance analysis of scientific grade CCD and vignetting effect of the optical system are introduced. The correction method of non-uniformity for testing system is studied, the correction arithmetic is given and the methods of reducing circuit random noise and the noise produced by scatter ray are illuminated. The correction image and the one that don’t be corrected are given, the merits of this system and problem need to be more studied are illuminated.

Keywords: digital radiographic imaging, non-uniformity correction, x ray conversion, scientific grade CCD, dark current

Title of the Paper: Combinatorial Optimization: Mutual Relations among Graph Algorithms

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Authors: Eva Milkova

Abstract: The Theory of Graphs is a wonderful, practical discipline. Informatics has played a big part in its development, and these two fields are strongly interconnected. This can, perhaps, mainly be seen in the design of computer algorithms. On the one hand, there are many methods which can be used for solving the same problem, while on the other hand, using effective modifications of one algorithm, we can devise methods of solving various other tasks. To educate students in the area close connected with Graph Theory and Computer Science, called as Combinatorial or Discrete Optimization, it is important to make them familiar with certain algorithms in contexts to be able to get deeper into each problem and entirely understand it. In the paper we present just a few ideas that have proved successful in teaching and learning this quite young part of mathematics.

Keywords: Graph Algorithms, Minimum Spanning Tree Problem, Breadth-First-Search, Depth-First-Search, Dijkstra’s Algorithm, Maze Problem, Eulerian Graph

Title of the Paper: Investigation of Characteristics of Separation Zones in T-Junctions

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Authors: Hamid Shamloo and Bahareh Pirzadeh

Abstract: The river diversion, for domestic, agricultural and industrial consumption, has a vital role to make economic progress and to develop the human communities. There are different ways of river diversion which are proportional to rivers' condition and the quantity of the diversion of water. Lateral river intake is one of these ways. This paper provides detail application of FLUENT-2D software in simulation of lateral intake flows. Numerical simulations undertaken in present two dimensional work use RSM turbulent model. Results of velocity field measurement using K-e Standard model were compared with Shettar & Murthy (1966). Then using RSM turbulent model, dimensions of separation zone were measured and compared with Kasthuri & Pundarikanthan (1987). In both cases good agreement are found between numerical and experimental results.

Keywords: Open channel, Lateral Intake, Turbulence, Separation zone, Numerical modeling, Fluent

Title of the Paper: Bifuzzy ideals of K-algebras

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Authors: Muhammad Akram

Abstract: In this paper we introduce the notion of bifuzzy ideals of K-algebras and investigate some interesting properties. Then we study the homomorphisms between the ideals of K-algebras and their relationship between the domains and the co-domains of the bifuzzy ideals under these homomorphisms. Finally the Cartesian product of bifuzzy ideals is discussed.

Keywords: Bifuzzy ideals; Characteristic; Equivalence relations; Homomorphisms; Cartesian product.

Title of the Paper: A note on the modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems

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Authors: Shi-Ling Wu and Ting-Zhu Huang

Abstract: Comparing the lopsided Hermitian/skew-Hermitian splitting (LHSS) method and Hermitian/skew-Hermitian splitting (HSS) method, a new criterion for choosing the above two methods is presented, which is better than that of Li, Huang and Liu [Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems, Numerical Lin. Alg. Appl., 14 (2007): 217-235].

Keywords: non-Hermitian matrix; splitting; skew-Hermitian matrix; Hermitian matrix; iteration