WSEAS CONFERENCES. WSEAS, Unifying the Science

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 Volume 7,  2008
Print ISSN: 1109-2769
E-ISSN: 2224-2880








Issue 1, Volume 7, January 2008

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


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


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


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. Their 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, Poincare-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


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


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


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


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


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


Authors: Constantin Udriste, Paul Popescu, 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


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


Authors: Milos Arsenijevic, Miodrag Kapetanovic

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


Authors: M. Isabel Garcia-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


Authors: S. Abdullah, M. D. Ibrahim, A. Zaharim, 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


Authors: Azami Zaharim, Ibrahim Mohamed, Shahrum Abdullah, 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


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


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


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


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 (0β, 0β−1) of nonstandard numbers and to establish the existence of infinitesimals (0β > Lβ−2 > xβ > 0β−2). An invariant logarithmic definition of coordinate is presented and the concept of “measureless” or “dimensionless” numbers (L’β, λβ, 0β) = (Lβ, 1β, 0β) 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 vm = 350 m/s, gravitational waves that propagate at the speed of light vt = c, and gravitational radiation that propagates at superluminal speeds vg > 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


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


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


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


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


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


Authors: Andres Fraguela, Juan–Antonio Infante, Angel Manuel Ramos, Jose Maria 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: Fast Algorithms and MATLAB Software for Solution of the Dirichlet Boundary Value Problems for Elliptic Partial Differential Equations in Domains with Complicated Geometry


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


Authors: Singa Wang Chiu, Jyh-Chau Yang, 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


Authors: Rafael Alvarez, Francisco-Miguel Martinez, Jose-Francisco Vicent, 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


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

: 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


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 Mobius Cubes


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


Authors: Asu Inan, 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


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


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 Holder Norm for Solutions to (∂/∂t-L)(u)=divf on Bounded Domains


Authors: Caroline Sweezy

Abstract: The rate of change of u, a solution to Lu=divf in a bounded, rough domain ΩT, u=g on ∂T , is investigated using a local Hölder norm of u and different measures on ΩT and on ∂T. 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


Authors: Jun Wang, 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


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


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


Authors: Hamid Shamloo, 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


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


Authors: Shi-Ling Wu, 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

Issue 6, Volume 7, June 2008

Title of the Paper: Function Approximation using Artificial Neural Networks


Authors: Zarita Zainuddin, Ong Pauline

Abstract: Function approximation, which finds the underlying relationship from a given finite input-output data is the fundamental problem in a vast majority of real world applications, such as prediction, pattern recognition, data mining and classification. Various methods have been developed to address this problem, where one of them is by using artificial neural networks. In this paper, the radial basis function network and the wavelet neural network are applied in estimating periodic, exponential and piecewise continuous functions. Different types of basis functions are used as the activation function in the hidden nodes of the radial basis function network and the wavelet neural network. The performance is compared by using the normalized square root mean square error function as the indicator of the accuracy of these neural network models.

Keywords: function approximation, artificial neural network, radial basis function network, wavelet neural network.

Title of the Paper: Two Congruence Classes for Symmetric Binary Matrices over F2


Authors: Yong-Hyuk Kim, Keomkyo Seo

Abstract: We provide two congruence classes for symmetric binary matrices over a finite field of characteristic 2. We use standard methods of matrix analysis to prove directly that there exist two congruence classes. Our proof gives explicit algorithms to compute the congruence classes.

Keywords: congruence of matrices, binary matrices, finite field of characteristic 2.

Title of the Paper: The Matrix Padé Approximation in Systems of Differential Equations and Partial Differential Equations


Authors: C. Pestano-Gabino, C. Gonzalez-Concepcion, M. C. Gil-Farina

Abstract: In [3] we presented a technique to study the existence of rational solutions for systems of linear firstorder ordinary differential equations. The method is based on a rationality characterization that involves Matrix Padé Approximants. Moreover the main ideas were only applied in the numerical resolution of a particular partial differential equation. This paper may be considered as an extension of [3], in the sense that we propose fundamental matrices directly for linear m-order ordinary differential equations without making a transformation to an equivalent system of first order. In addition, we increase its field of applications to particular solutions of the mentioned systems and to Partial Differential Equations.

Keywords: Systems of Differential Equations, Partial Differential Equations (PDE), Matrix Padé Approximation (MPA), rational solutions, minimum degrees (m.d.)

Title of the Paper: A Functional Approximation Comparison between Neural Networks and Polynomial Regression


Authors: Ong Hong Choon, Leong Chee Hoong, Tai Sheue Huey

Abstract: Multi-layered perceptron (MLP) neural networks are well known as universal approximators. They are often used as estimation tools in place of the classical statistical methods. The focus of this study is to compare the approximation ability of MLP with a traditional statistical regression model, namely the polynomial regression. Comparison among the single hidden layer MLP, double hidden layer MLP and polynomial regression is carried out on the basis of similar number of weights or parameters. The performance of these three categories is measured using fraction of variance unexplained (FVU). The closer the FVU value is to zero, the better the estimation result and this is associated with a higher degree of accuracy. From the empirical results obtained in this study, we conclude that overall polynomial regression performs slightly better than MLP for a similar number of parameter except for the complicated interaction function. Meanwhile, double hidden layer MLP outperforms single hidden layer MLP. The MLP is more appropriate than the polynomial regression in approximating the complicated interaction function.

Keywords: Artificial neural network, Multi-layered perceptrons, Polynomial regression

Title of the Paper: Exact Test Critical Values for Correlation Testing with Application


Authors: Ching-Hui Chang, Jyh-Jiuan Lin, Nabendu Pal

Abstract: Tables of critical values for the exact test method based on the maximum likelihood estimator (MLE) have been obtained to test a hypothesis on the correlation coefficient between the components of a bivariate normal random vector. The exact test is then compared, in terms of size and power, with the other popular methods, namely - the ‘z - test’, the ‘modified z - test’ and the ‘t - test’. While these popular methods have almost identical size and power to the exact test for large samples, their small sample performance is far from satisfactory as evident from our extensive numerical computations. Thus, our tables of critical values are useful when sample size is not large (i.e., ≤ 30 ). Also, it is demonstrated through a real-life dataset how the tables of critical values can be used for interval estimation.

Keywords: Asymptotic variance, confidence interval, size, power.

Title of the Paper: Improving Probability Education Through Statistical Experiments


Authors: Saeed Al-Hajjar

Abstract: This study analyze some hypothesis on the difficulties facing the teaching of probabilities, and see how models of probability are useful to solve any confusion. This will be clarified by formulating questions that can be addressed with data, collect , organize, and display relevant data to answer them. In this part we will see the solution of the problem ” who will win the million ”, which is a good example of improving probability education through statistical experiments.

Keywords: Hazard, Confirmed, Change, Probability, Modeling, Random Experiment, Equiprobable

Title of the Paper: The Local analytic Solution to Some Nonlinear Diffusion-Reaction Problems


Authors: Gabriella Bognar, Erika Rozgonyi

Abstract: -The positive radially symmetric solutions to the nonlinear problem

are considered. We examine the existence of local solutions and give a method for the determination of power series solutions. The comparison of the local analytic and entire solutions is given for some special values of parameters p, n, γ, and δ.

Keywords: Nonlinear partial differential equations, p-Laplacian, non-Newtonian fluid, polytrophic gas, local analytic solutions

Title of the Paper: Stress Strain Modeling by Transformed Equations of Ultrasonic Wave


Authors: Arash Ziaie, Kaveh Kumarci, Arash Kyioumarsi

Abstract: The equations of ultrasonic wave propagation in Cartesian coordinates are functions of 27 partial displacement derivatives, which first derived and then transformed into cylindrical coordinates. The new obtained functions are functions of 27 partial displacements of first and second order derivatives in cylindrical coordinates too and they will be linearized using a perturbation method based on the Taylor series expansion. A displacement wave, which propagates in a body, composed of two general part; static displacement part, and also small dynamic displacement part. Happening of the small dynamic displacement of a particle around its static situation, Taylor series expansion can be written around this point. Using this determined static situation and considering only the two first components of Taylor series expansion, the equations of motion will be linearized. Tremendously lengthy algebraic operations involved in the derivation and linearization process, all of the mathematical manipulations are performed using Mathematica.

Keywords: perturbation- acoustoelasticity- strained cylindrical solids- ultrasonic- wave propagation- Mathematica

Title of the Paper: On the Ratio Processes Induced from the Mean-Field Bouchaud-Mezard Model


Authors: Feng-Rung Hu

Abstract: In this article, we develop the ratio processes  i= 1,2,...,n induced from the meanfield Bouchaud-Mezard model. The limit i m of the long-time average of the ratio process  is studied and compared with all others. We shows that a strictly increasing sequence of the investment volatilities implies a strictly decreasing sequence of the limits, given appropriate J, based on both theoretical and numerical analyses. It reveals a negative correlation between the investment volatilities and the ratio processes. As an empirical application, this negative correlation can be employed to characterize the mean-field Bouchaud-Mezard model. Our main result also indicates that an agent whose spontaneous growth or decrease in wealth due to investment in stock markets is always small will eventually become rich in the meanfield Bouchaud-Mezard model.

Keywords: Mean-field Bouchaud-Mezard model, Wealth distribution, Ratio process, Volatility, Ergodic, Long-time average

Title of the Paper: The Influence of the Geometry and the Material Properties on the Behavior of the Human Knee


Authors: Valerica Mosnegutu, Veturia Chiroiu Lucian Capitanu, Mihai Popescu

Abstract: In this paper, the motion of the knee joint during flexion and extension is investigated. It is developed a mathematical model of the knee joint that describes motion in 12 generalized coordinates as a function of the externally motion. The model is based on the patellar track geometry experimental data. The surface of the patellar track is modeled by using the n-ellipsoid model. The inverse problem is restricted to slow motions, so we consider that static optimization is good enough for our goal.

Keywords: knee joint motion, surface modeling, n-ellipsoid model, patellar track geometry, geometric and natural compatibilities.

Issue 7, Volume 7, July 2008

Title of the Paper: Stress Strain Modeling by Transformed Equations of Ultrasonic Wave


Authors: Arash Ziaie, Kaveh Kumarci, Arash Kyioumarsi

Abstract: The equations of ultrasonic wave propagation in Cartesian coordinates are functions of 27 partial displacement derivatives, which first derived and then transformed into cylindrical coordinates. The new obtained functions are functions of 27 partial displacements of first and second order derivatives in cylindrical coordinates too and they will be linearized using a perturbation method based on the Taylor series expansion. A displacement wave, which propagates in a body, composed of two general part; static displacement part, and also small dynamic displacement part. Happening of the small dynamic displacement of a particle around its static situation, Taylor series expansion can be written around this point. Using this determined static situation and considering only the two first components of Taylor series expansion, the equations of motion will be linearized. Tremendously lengthy algebraic operations involved in the derivation and linearization process, all of the mathematical manipulations are performed using Mathematica.

Keywords: perturbation- acoustoelasticity- strained cylindrical solids- ultrasonic- wave propagation- Mathematica

Title of the Paper: An Algorithm for Clustering Tendency Assessment


Authors: Yingkang Hu, Richard J. Hathaway

Abstract: The visual assessment of tendency (VAT) technique, developed by J.C. Bezdek, R.J. Hathaway and J.M. Huband, uses a visual approach to find the number of clusters in data. In this paper, we develop a new algorithm that processes the numeric output of VAT programs, other than gray level images as in VAT, and produces the tendency curves. Possible cluster borders will be seen as high-low patterns on the curves, which can be caught not only by human eyes but also by the computer. Our numerical results are very promising. The program caught cluster structures even in cases where the visual outputs of VAT are virtually useless.

Keywords: Clustering, similarity measures, data visualization, clustering tendency

Title of the Paper: Computing Exact Symmetries of Dynamical Systems from their Reduced System of Equations can be Interesting II


Authors: Festus I. Arunaye

Abstract: The symmetry analysis of differential equations in the context of Lie point and nonlocal symmetries is rich in the literature. In this paper we present the computation of the exact symmetry transformations of dynamical systems from their reduced systems in three dimensions, using the Kepler problem as vehicle. We also note that this computational technique is applicable to systems that can be reduced to couple oscillator(s) and a conservation law.

Keywords: Exact, symmetries, Dynamical, systems, infinitesimal, generators, flow, Kepler, Lie.

Title of the Paper: Solving the Problem of the Compressible Fluid Flow around Obstacles by an Indirect Approach with Vortex Distribution and Linear Boundary Elements


Authors: Luminita Grecu

Abstract: In the present paper there is presented a solution with linear boundary elements of lagrangean type for the singular boundary integral equation obtained by an indirect technique with vortex distribution for the bidimensional compressible fluid flow around bodies. The singular boundary integral equation the problem is reduced at is formulated in terms of primary variables-the components of the velocity on the boundary. Numerical solutions for the components of the velocity and the local pressure coefficient are obtained, for different types of obstacles, with some computer codes made in MATHCAD, based on the method exposed. For some particular cases, when analytical solutions exist a comparison study between the numerical solutions and the exact ones is also done. It can be seen, from the graphics obtained, that the numerical solutions are in good agreement with the exact solutions of the problem. The paper is also focused on a comparison study between the numerical solutions obtained when the indirect method with sources distribution is used and the numerical solution presented in this paper when boundary elements of same type are used for solving both singular boundary integral equations.

Keywords: Compressible fluid flow, boundary element method, vortex distribution, linear boundary elements

Title of the Paper: The Role of Predictability of Financial Series in Emerging Market Applications


Authors: Gabriela Prelipcean, Mircea Boscouanu, Nicolae Popoviciu

Abstract: A new metric that quantifies the predictability of financial time series is proposed. Time series predictability provides a measure of how well a time series can be modeled by a particular method, or how well a prediction can be made. This new time series predictability metric is developed based on the Kaboudan η –metric. The new metrics, based on Genetic Programming (GP) and Artificial Neural Networks (ANN) overcomes the stationarity problem presented in the pure η -metric and provides a new feature, which shows how the predictability changes over different subsequences in a time series. Timing detection and portfolio balancing should be based on trading strategies that evolved to optimize buy/sell decisions. The interest is to explore new trading rules based on an automated security trading decision support system triggered by both quantitative and qualitative factors. The focus is to develop quantitative metrics that characterize time series according to their ability to be modeled by a particular method, such as the predictability of a time series using the GP approach or an ANN.

Keywords: quantitative metrics, predictability, timing detection, portfolio selection, Genetic Programming (GP), Artificial Neural Networks (ANN).

Title of the Paper: Mathematical Models that Coordinate the Movement through Obstacles of the Dynamic Systems Endowed with Artificial Sight


Authors: Ovidiu Ilie Sandru

Abstract: This paper proposes two kinds of geometrical models meant to coordinate the movement through obstacles of the automatons endowed with artificial sight. Besides the novelty of theoretical nature that accompanies them, it is important to underline the fact that these models have been adapted to the possibilities of computer based management.

Keywords: Mathematical modeling, dynamical system, artificial sight, motion through obstacles, Euclidean distance, Riemann space, geodesics, Dirichlet problem, numerical discretization.

Title of the Paper: Multiple Regression Models of the Volumetric Stem Biomass


Authors: Noraini Abdullah, Zainodin Jubok, Nigel Jonney J. B.

Abstract: The development of a simple model was presented for obtaining the volumetric stem biomass of a tropical tree species. To model the volumetric stem biomass, Cinnamomum of family Lauracea was chosen. Mensuration data were collected based on two volumetric equations, namely, the Huber’s and Newton’s equations. During data collection, the variables considered were height of stem or trunk, height of tree, diameter at breast height, diameter at middle and diameter at top of the stem before the crown. Possible variables with their interactions were screened with spearman correlation tests and values greater than 0.95 were selected. The best model was determined using the process of eight selection criteria (8SC). However, the best model was found to be in the form of multiple regressions (MR) up to the fourth order interactions.

Keywords: stem volume, volumetric equations, best model, correlation tests, interactions, selection criteria, multiple regression.

Title of the Paper: Analytical Solutions for a Nonlinear Coupled Pendulum


Authors: Ligia Munteanu, Veturia Chiroiu, Stefania Donescu

Abstract: In this paper, the motion of two pendulums coupled by an elastic spring is studied. By extending the linear equivalence method (LEM), the solutions of its simplified set of nonlinear equations are written as a linear superposition of Coulomb vibrations. The inverse scattering transform is applied next to exact set of equations. By using the Θ - function representation, the motion of pendulum is describable as a linear superposition of cnoidal vibrations and additional terms, which include nonlinear interactions among the vibrations. Comparisons between the LEM and cnoidal solutions and comparisons with the solutions obtained by the fourth-order Runge-Kutta scheme are performed. Finally, an interesting phenomenon is put into evidence with consequences for dynamic of pendulums.

Keywords: cnoidal method, linear equivalence method, cnoidal vibrations, Coulomb vibrations, coupled pendulum.

Issue 8, Volume 7, August 2008

Title of the Paper: The Polynomial Roots Repartition and Minimum Roots Separation


Authors: Muresan Alexe Calin

Abstract: It is known that, if all the roots of a polynomial are real, they can be localised, using a set of intervals, which contain the arithmetic average of the roots. The aim of this paper is to present an original method for giving other distributions of the roots/ modules of the roots on real axis, a method for evaluating and improving the “polynomial minimum root separation” results, a method for the complex polynomials and for polynomials having all roots real. We use the discriminant, Hadamard’s inequality, Mahler’s measure and new original inequalities. Also we will make some considerations about the cost for isolate the polynomial real roots. Our method is based on the successive splitting for the interval which contains all roots.

Keywords: Roots repartition, Isolating the roots, Mahler’s measure

Title of the Paper: New Analytical Cavitation Erosion Models


Authors: Constantin Patrascoiu

Abstract: Cavitation erosion prediction for the hydraulic machines is very important in the hydraulics research because that cavitation erosion is a source of failure of pumps water turbine blade, pipelines and other hydraulic devices. In this paper new kinds of theoretical volume loss rate curve of erosion cavitation progress is proposed. The analytical models describing this new kind of erosion curves give a new vision of the volume loss rate curve and produce a good concordance between the experimental and theoretical data if there is a good choice of theoretical model. Instead of using a unique analytical (universal) model for all materials, we give the possibility of a good choice between the proposed models. There may also appear some open problem such as optimally correlating this analytical cavitation erosion models with the properties of the implied materials.

Keywords: Cavitation, Erosion, Mathematical model, Differential equations, Bessel’s equations.

Title of the Paper: Fully Implicit Moving Boundary Model with Liquid Phase Perfect Mixing for CO2 Diffusion into n-Decane


Authors: Damelys Zabala, Aura L. Lopez De Ramos

Abstract: - Carbon dioxide diffusion into n-decane inside cylindrical and square glass capillary tubes has been modeled [1,2], with two different models for each tube and the convective model for the square tube depended on the results of the cylindrical one. For those models, the liquid phase density was always considered constant and its value was adjusted from the experimental data of gas-liquid interface position. This approach was done using the diffusivities obtained by correlations which modify the infinite dilution diffusion coefficient using a thermodynamical factor. Now, the liquid phase density is considered variable on time with perfect mixing inside the phase and an effective diffusivity can be determined. This effective diffusivity involves the molecular and convective contributions to the global mass transfer. Both interface displacements (inside cylindrical and square tubes) can be modeled using the same model without dependency between their results. The terms inside the finite difference matrix for the liquid phase are not constant, because they depend on the solute concentration and on the liquid density then an iterative calculation for the matrix coefficients must be done in each timestep. A partially implicit model considers this iterative calculation keeping the liquid density value for the previous time (j). A fully implicit model considers this iterative calculation keeping the liquid density value for the present time (j+1). It was showed that the model results, adjusted to the experimental interface position values, predicted effective diffusivities which are variable on time. The simulation time (76 min) for the fully implicit numerical model is higher than the simulation time (62 min) for the partially implicit numerical model. It was found that the type of numerical solution scheme affects the results (up to 5% deviation) for the square capillary model but it doesn’t change the cylindrical capillary model results.

Key-Words: - Capillary tube, Free boundary, Mass transfer, Numerical Modeling, Diffusion.

Issue 9, Volume 7, September 2008

Title of the Paper: An Algorithm for Creation of an Optimized Adaptive Grid for Improved Explicit Finite Difference Scheme


Authors: Raka Jovanovic, Milan Tuba, Dana Simian

Abstract: This paper deals with the two main shortcomings of explicit finite difference schemes: the use of a discretization grid with the same resolution over the entire problem space, and low level of precision and stability. We present a combination of two improvements. Their application is illustrated with the numerical simulation of the propagation of a light beam in a photonic lattice. The discretization problem is avoided by using a multi-resolution grid. An algorithm for the grid creation is developed and that algorithm is optimized for software implementation and parallelization. The efficiency of the algorithm is increased by further improving the precision of the explicit method by use of a multidimensional generalization of the Runge-Kutta scheme. Due to the multidimensionality and nonlinearity of the considered problem, our improved explicit finite difference gave better results than Crank-Nicholson scheme.

Keywords: Adaptive grid algorithm, Multi-resolution, Finite differences, Simulation, Numerical optimization

Title of the Paper: Interval-Valued Intuitionistic Fuzzy Ideals of K-Algebras


Authors: Muhammad Akram, Karamat H. Dar, Biao Long Meng, K. P. Shum

Abstract: The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-algebras and investigate some interesting properties. We characterize Artinian and Noetherian K-algebras by considering IIFIs of a K-algebra K: Characterization theorems of fully invariant and characteristic IIFIs are also discussed.

Keywords: K-algebras, Interval-valued intuitionistic fuzzy sets, Equivalence relations, Artinian and Noetherian K-algebras

Title of the Paper: The Optimal Stopping Times of American Call Options with Dividend-paying and Placing Stocks


Authors: Guangqin Li

Abstract: American options can be exercised at any time during their lifetime. This paper addresses the optimal stopping time of several kinds of American call options.

Keywords: Stopping time, American call option, martingale, equivalent martingale measure, dividend-paying and placing rate

Title of the Paper: Some Preconditioning Techniques for Linear Systems


Authors: Qingbing Liu

Abstract: New convergence intervals of parameters i are derived and applied for solving the modified linear systems, which enables a better understanding of how parameters should be chosen. The convergence theorem for H-matrix is given. Meanwhile, we discuss the convergence results for M-matrices linear systems and give some new preconditioners. Numerical examples are used to illustrate our results.

Keywords: Convergence, H-matrix, M-matrix, Preconditioner, Gauss-Seidel method

Issue 10, Volume 7, October 2008

Title of the Paper: The Number “6” in Planar Tilings


Authors: Hao Li

Abstract: This paper obtains some important properties of planar normal tiling and proves purely combinatorially Grünbaum’s Theorem. Moreover, we give the six-neighbor-theorem and definite “relative density” to describe the increase of tiles with some special properties. Finally, Γpm - tilings are classified by their adjacent types.

Keywords: Normal tiling, Adjacent, Neighbor, Adjacent-graph, Relative density, Adjacent-type

Title of the Paper: On Very True Operators and υ-Filters


Authors: Xuejun Liu, Zhudeng Wang

Abstract: In this paper, based on Hajek, Vychodil, Rachunek and Salounova’s works, we study the concept of υ-filters of residuated lattices with weak υt-operators, axiomatize very true operators, discuss filters and v-filters of residuated lattices with weak υt-operator, give the formulas for calculating the υ-filters generated by subsets, and show that lattice of υ-filters of a commutative residuated lattice with υt-operator is a complete Brouwerian lattice.

Keywords: Fuzzy logic, Residuated lattice, Very true, Weak υt-operator, υ-Filter

Title of the Paper: Optimal Control of a Spin System Acting on a Single Quantum Bit


Authors: Evgenia Kirillova, Thomas Hoch, Karlheinz Spindler

Abstract: We study a quantum spin system acting on a single quantum bit. The evolution of this system is governed by the Schroedinger equation which takes the form of a right-invariant system on the special unitary group SU(2) with two control inputs. Using a suitable version of Pontryagin's Principle which is tailor-made for control problems on Lie groups, the optimal controls are derived in two cases: the energy-optimal case (in which the control effort is minimized for a specified end time)and the time-optimal case (in which the control duration is minimized for given constraints on the size of the controls).

Keywords: Nonlinear control, optimal control, quantum spin systems

Title of the Paper: Convergence Analysis of a Streamline Diffusion Method for a Singularly Perturbed Convection-diffusion Problem


Authors: Zhongdi Cen, Lifeng Xi

Abstract: A streamline diffusion finite element method (SDFEM) is applied to a singularly perturbed convection-diffusion two-point boundary value problem in conservative form. The stability and accuracy of the SDFEM on arbitrary grids are studied. We derive the pointwise error estimates and the approximation of derivatives. These bounds are then made explicit for the particular cases of Shishkin-type meshes. Numerical experiments support our theoretical results.

Keywords: Convection-diffusion, singular perturbation, streamline diffusion, Shishkin-type mesh

Issue 11, Volume 7, November 2008

Title of the Paper: Oscillation and Non-oscillation Criteria for Quasi-linear Second Order Differential Equations


Authors: Wei Dong, Tieguo Ji, Xueting Zhao

Abstract: Some oscillation and non-oscillation criteria for quasi-linear second order equations are obtained. These results are extensions of earlier results of C.Huang(J.Math Anal. Appl.210(1997), 712-723), A. Elbert(J.Math.Anal.Apll.226(1998), 207-219) and J.Wong(J.Math.Anal.Apll.291(2004), 180-188) which are all about oscillation and non-oscillation criteria of the solution of the second order linear equation. After the proof of the main theorem, two examples are given as the additional remarks of the criteria. At last a special case is discussed. And the uniqueness and periodic criteria of the special case are obtained further by using comparison theorem and Leray-Schauder degree approach.

Keywords: Quasi-linear equation, oscillation, non-oscillations, periodic solution, Leray-Schauder degree

Title of the Paper: Uniqueness of Positive Solutions For Neumann Problems in Unbounded Domain


Authors: Wei Dong, Nianpeng Wang, Chenghua Dang


Keywords: Sub-super solution, Neumann problem, Comparison principle, Positive solution, Squeezing method

Title of the Paper: Reliability Mathematics Analysis on Traction Substation Operation


Authors: Hongsheng Su

Abstract: In electrified railway traction power supply systems, the operational qualities and reliabilities of the main traction transformer loop is higher, but ones of bus output units is comparatively low. The traction transformer loop still works when output loops are in failure, and the output loop interrupts working when the main transformer is in failure, and only has residual life when restoring working, the connection formation between them is in series. Traditional reliability analysis methods let their lifetime follow exponential distribution, and reliability is investigated based on the minimal path sets, which lead to a comparatively rough result, consequently. According to Markov theory, in this paper the main loop life is considered as mixed Erlang distribution with order n, and the output unit life follows generic distribution. As compared with conventional series systems, the acquired results are proved to be reliable and sound.

Keywords: Transformer, Erlang distribution, Life, Markov theory, Reliability, Traction substation

Title of the Paper: Indeterminate Forms and their Behaviours


Authors: Saeed Al-Hajjar

Abstract: This study shows that there exist solutions to the seven main indeterminate forms that are raised in the world of mathematics. Some limits of functions are said to be indeterminate when merely knowing the limiting behaviour of individual parts of expression is not sufficient to actually determine the overall limit. There will be a study of a certain typical number whereas, if a variable x tends to a certain value α (eventually equal to +∞ or -+∞) , a certain function Γ(x) does not have an apparent limit from the first view. To eliminate the indetermination (or looking for the right value of Γ(α), is to find this limit if it exists.

Keywords: Infinity , indeterminate, equivalent infinitely large principal, equivalent infinitely small principal, limit, function

Title of the Paper: Particle Swarm Optimization – Tabu Search Approach to Constrained Engineering Optimization Problems


Authors: Ritchie Mae Gamot, Armacheska Mesa

Abstract: Constraint handling is one of the most difficult parts encountered in practical engineering design optimizations. Different kinds of methods were proposed for handling constraints namely, genetic algorithm, self-adaptive penalty approach and other evolutionary algorithms. Particle Swarm Optimization (PSO) efficiently solved most nonlinear optimization problems with inequity constraints. This study hybridizes PSO with a meta-heuristic algorithm called Tabu Search (TS) to solve the same engineering design problems. The algorithm starts with a population of particles or solution generated randomly and is updated using the update equations of PSO. The updated particles are then subjected to Tabu Search for further refinement. The PSO algorithm handles the global search for the solution while TS facilitates the local search. With embedded hyrbridization, this study which we call PSO-TS, showed better results compared to algorithms reported in Hu et al's study as applied to four benchmark engineering problems. Specifically, this study beat the results of Coello, Deb and Hu.

Keywords: Constrained engineering optimization problems, particle swarm optimization, tabu search

Issue 12, Volume 7, December 2008

Title of the Paper: Optimal Control of a Spin System Acting on a Single Quantum Bit


Authors: Evgenia Kirillova, Thomas Hoch, Karlheinz Spindler

Abstract: We study a quantum spin system acting on a single quantum bit. The evolution of this system is governed by the Schr¨odinger equation which takes the form of a right-invariant system on the special unitary group SU(2) with two control inputs. Using a suitable version of Pontryagin’s Principle which is tailor-made for control problems on Lie groups, the optimal controls are derived in two cases: the energy-optimal case (in which the control effort is minimized for a specified end time) and the time-optimal case (in which the control duration is minimized for given constraints on the size of the controls).

Keywords: Nonlinear control, optimal control, quantum spin systems

Title of the Paper: Peak-Valley Segmentation Algorithm for Fatigue Time Series Data


Authors: Z. M. Nopiah, M. I. Khairir, S. Abdullah, C. K. E. Nizwan

Abstract: This paper presents the peak-valley (PV) segmentation algorithm for the purpose of producing a reliable method of fatigue time series segmentation and statistical segment-by-segment analysis of fatigue damage. The time series were segmented using a piecewise linear representation (PLR) based segmentation algorithm and consecutively the peak-valley (PV) segmentation algorithm. Statistical analysis and fatigue damage calculations were made on each segment and scatter plots were produced based on the relationship between segmental damage and its corresponding kurtosis value. Observations were made on the scatter plots produced by the PV segmentation algorithm to determine the reliability of the data scattering for fatigue data clustering prospects.

Keywords: Time series, segmentation, peak-valley, data scattering, kurtosis, fatigue damage

Title of the Paper: Abrupt Changes Detection in Fatigue Data Using the Cumulative Sum Method


Authors: Z. M. Nopiah, M. N.Baharin, S. Abdullah, M. I. Khairir, C. K. E. Nizwan

Abstract: The detection of abrupt changes refers to a time instant at which properties suddenly change, but before and after which properties are constant in some sense. CUSUM (Cumulative Sum) is a sequential analysis technique that is used in the detection of abrupt changes. The objective in this study is to apply CUSUM technique in analysing fatigue data for detection of abrupt changes. For the purpose of this study, a collection of nonstationary data that exhibits a random behavior was used. This random data was measured in the unit of microstrain on the lower suspension arm of a car. Experimentally, the data was collected for 60 seconds at a sampling rate of 500 Hz, which gave 30,000 discrete data points. By using CUSUM method, a CUSUM plot was constructed in monitoring the mean changes for fatigue data. Global signal statistical value indicated that the data were non Gaussian distribution in nature. The result of the study indicates that CUSUM method is only applicable for certain type of data with mixed high amplitude in a random background data.

Keywords: Abrupt changes, CUSUM, nonstationary data, mean changes, global statistics

Title of the Paper: The Suitability of Statistical Distribution in Fitting Wind Speed Data


Authors: Azami Zaharim, Siti Khadijah Najid, Ahmad Mahir Razali, Kamaruzzaman Sopian

Abstract: Wind energy has been used for navigation and agriculture. Recently, wind energy is given a lot of attention because of the focus on renewable energy. Wind energy growth in Asia is currently on the rise. Both India and China are leading with more installed capacity and manufacturing facilities. In Malaysia, wind energy conversion is also given a serious consideration. The potential for wind energy generation in Malaysia depends on the availability of the wind resource that varies with specific location. This paper deals with how to model or how to fit several probability distribution models to Malaysia wind speed data available. As usually described in the literature concerning efforts to develop an adequate statistical model for wind speed, there are a few statistical models discussed such as Weibull Distribution and Rayleigh Distribution. In the literature, it is a common procedure to compare these functions to determine which one fits the measured distribution best. The result from a simple descriptive statistics shows that Weibull distribution might be the probability distribution that can fit the data well.

Keywords: Wind speed, wind speed distribution, Weibull

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