# Applied Mathematics and Computation

Published by Elsevier

Print ISSN: 0096-3003

Published by Elsevier

Print ISSN: 0096-3003

Publications

Biosensor measurement of transdermal alcohol oncentration in perspiration exhibits significant variance from subject to subject and device to device. Short duration data collected in a controlled clinical setting is used to calibrate a forward model for ethanol transport from the blood to the sensor. The calibrated model is then used to invert transdermal signals collected in the field (short or long duration) to obtain an estimate for breath measured blood alcohol concentration. A distributed parameter model for the forward transport of ethanol from the blood through the skin and its processing by the sensor is developed. Model calibration is formulated as a nonlinear least squares fit to data. The fit model is then used as part of a spline based scheme in the form of a regularized, non-negatively constrained linear deconvolution. Fully discrete, steepest descent based schemes for solving the resulting optimization problems are developed. The adjoint method is used to accurately and efficiently compute requisite gradients. Efficacy is demonstrated on subject field data.

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High gradient magnetic field separators have been widely used in a variety of biological applications. Recently, the use of magnetic separators to remove malaria-infected red blood cells (pRBCs) from blood circulation in patients with severe malaria has been proposed in a dialysis-like treatment. The capture efficiency of this process depends on many interrelated design variables and constraints such as magnetic pole array pitch, chamber height, and flow rate. In this paper, we model the malaria-infected RBCs (pRBCs) as paramagnetic particles suspended in a Newtonian fluid. Trajectories of the infected cells are numerically calculated inside a micro-channel exposed to a periodic magnetic field gradient. First-order stiff ordinary differential equations (ODEs) governing the trajectory of particles under periodic magnetic fields due to an array of wires are solved numerically using the 1(st) -5(th) order adaptive step Runge-Kutta solver. The numerical experiments show that in order to achieve a capture efficiency of 99% for the pRBCs it is required to have a longer length than 80 mm; this implies that in principle, using optimization techniques the length could be adjusted, i.e., shortened to achieve 99% capture efficiency of the pRBCs.

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A method advanced by Milito and Houck (1992) to compute the
sojourn time distribution of the n<sup>th</sup> arrival to a single
server queue is expanded to study a) the “marking”
probability of the “leaky bucket” policing mechanism; b) the
cell delay when the “leaky bucket” is used as a traffic
shaper; c) a class of admission control problems not addressable by
standard Markovian decision models; d) queues with abandonments; e)
queues with correlated arrivals modeled as AR processes

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This paper describes a design approach to nonlinear adaptive control system with unknown parameters and applies it to the excitation control of power systems. The adaptive control strategy is formed by recursive method without involving transformation of linearization. The characteristic of the controller is that it involves a dynamic estimator of parameters. A general expression of nonlinear adaptive decentralized excitation control strategy for multimachine systems is acquired, in which all of the feedback variables are local measurements. Simulation results on a 6-machines, 22-buses system manifests the validity of the nonlinear adaptive controllers

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A new algorithm is presented for the determination of the generalized inverse and the Drazin inverse of a polynomial matrix. The proposed algorithm is based on the discrete Fourier transform and thus is computationally fast in contrast to other known algorithms. The above algorithm is implemented in the Mathematica programming language and illustrated via examples.

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The first-order necessary conditions for the extremum of typical optimal control problems lead to boundary-value problems in differential-algebraic equations (BVP-DAE). This paper presents a procedure for the numerical solution of these BVP-DAE. Here, the algebraic equations are nonlinear and not easily eliminated from the boundary-value problem. The solution method presented is based on the multiple shooting technique. In this approach the time domain is divided into subintervals. By requiring that the differential-algebraic equations be continuous from one interval to the next, and satisfy the boundary conditions leads to a set of shooting equations. Efficient techniques for integrating the differential-algebraic equations, and solving the shooting equations are discussed

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In the usual design of linear quadratic optimal control systems, the regulator performance is obtained for several different values of the constant Lagrange multiplier q. The Lagrange multiplier determines the amount of control energy expended. If the energy is to be constrained, then the value of q must be found such that the energy constraint is satisfied. In this paper a method is described for determining simultaneously the optimal trajectory and the value of q which satisfies the energy constraint.

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This paper studies a fluid model driven by an M/G/1 queue with multiple exponential vacations. By introducing various vacation strategies to the fluid model, we can provide greater flexibility for the design and control of input rate and output rate. The Laplace transform of the steady-state distribution of the buffer content is expressed through the minimal positive solution to a crucial equation. Then the performance measure-mean buffer content, which is independent of the vacation parameter, is obtained. Finally, with some numerical examples, the parameter effect on the mean buffer content is presented.

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In this paper, a frequency domain method is developed for plant set estimation. The estimation of a plant "set" rather than a point estimate is required to support many methods of modern robust control design. The approach here is based on using a Schroeder-phased multisinusoid input design which has the special property of placing input energy only at the discrete frequency points used in the computation. A detailed analysis of the statistical properties of the frequency domain estimator is given leading to exact expressions for the probability distribution of the estimation error, and many important properties. It is shown that for any nominal parametric plant estimate, one can use these results to construct an overbound on the additive uncertainty to any prescribed statistical confidence. The "soft" bound thus obtained can be used to replace "hard" bounds presently used in many robust control analysis and synthesis methods.

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The rate equations of narrow-stripe semiconductor lasers are
considered. These equations represent the dynamics of the photon number
and the electron densities in the active and absorbing regions. Having
the rate equations, (i) it is shown that the laser is the bounded-input
bounded-state (BIBS) and the bounded-input bounded-output (BIBO) stable;
(ii) the amplitudes of step inputs are determined for which all
equilibrium points of the laser are unstable. The boundedness of the
laser output and the instability of its equilibrium points imply that
the laser can have a periodic, a quasi-periodic, or a chaotic output.
When the output is periodic, the laser is self-pulsating, which is the
desirable behavior of the laser. Moreover, a procedure is given to
determine the values of laser parameters for which the laser
self-pulsates

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However we deny naive realism, it is difficult to describe the form of life in a Newtonian paradigm. Because any formal descriptions of biological systems inevitably include the concept of “function,” they entail the problem of self-reference. The description of function can be compared to that of meaning of a word, and in philosophy we no longer understand that there exists meaning inherent in a word of a language. As well as the problem of meaning, we cannot describe the aspect resulting from the function, because we cannot identify the specific function of a shape or morphology with the relationship between the shape itself and its environment. Therefore, even if we construct a new formal language in which the self-contradiction resulting from the self-reference is alleviated, that language is just one of various possible ones. In this sense, the form of life in formal description is possible but not necessary. The phrase “not necessary” just refers to the outside of the formal description. In this paper reference to the outside of a formal system is discussed in the context of time-space complementarity, and it is strongly related to the origin of irreversible time. We have to introduce both forward and backward time, as proposed previously by the author and coworkers, even in this context.

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In ACM conference on electronic commerce (EC’03), Han et al. [Identity-based confirmer signatures from pairings over elliptic curves, in: Proceedings of ACM Conference on Electronic Commerce Citation 2003, San Diego, CA, USA, June 09–12, 2003, pp. 262–263] proposed an ID-based confirmer signature scheme using pairings (the scheme is in fact an ID-based undeniable signature scheme). In this paper, we show that this signature scheme is not secure and the signer can deny any signature, even if it is a valid signature, and any one can forge a valid confirmer signature of a signer with identity ID on an arbitrary message and confirm this signature to the verifier.

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In this paper, by using the extremal ranks of generalized Schur complements, we study the mixed-type reverse-order laws for (AB)(1,2,3) and (AB)(1,2,4), and the sufficient and necessary conditions are established for these two reverse-order laws. Finally, two numerical examples are given to illustrate our results.

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Streamer discharges are important both in theory and industry applications.
This paper proposed a local discontinuous Galerkin method to simulate the
convection dominated fluid model of streamer discharges. To simulate the rapid
transient streamer discharge process, a method with high resolution and high
order accuracy is highly desired. Combining the advantages of finite volume and
finite element method, local discontinuous Galerkin method is such a choice. In
this paper, a simulation of a double-headed streamer discharge in nitrogen was
performed by using 1.5-dimensional fluid model. The preliminary results
indicate the potential of extending the method to general streamer simulations
in complex geometries.

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An adaptive conjugate gradient learning algorithm has been developed for training of multilayer feedforward neural networks. The problem of arbitrary trial-and-error selection of the learning and momentum ratios encountered in the momentum backpropagation algorithm is circumvented in the new adaptive algorithm. Instead of constant learning and momentum ratios, the step length in the inexact line search is adapted during the learning process through a mathematical approach. Thus, the new adaptive algorithm provides a more solid mathematical foundation for neural network learning. The algorithm has been implemented in C on a SUN-SPARCstation and applied to two different domains: engineering design and image recognition. It is shown that the adaptive neural networks algorithm has superior convergence property compared with the momentum backpropagation algorithm.

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Multiserver retrial systems arise in telecommunication and computer networks areas. It is of basic importance to study performance and reliability of retrial systems with unreliable servers, because of limited ability of repairs and heavy influence of the breakdowns on the performance of the system. However, so far the repairable retrial systems are analyzed only by queueing theory and almost works assumed that service station consists of one single server. In this paper, we give a detailed analysis of finite-source retrial systems with multiple servers subject to random breakdowns and repairs using generalized stochastic petri nets model. We show how this high level model allows us to cope with the complexity of such retrial systems involving the unreliability of the servers, under the different breakdowns disciplines. The main steady-state performance and reliability indices are derived and several numerical calculations were performed to show the effect of servers number, retrial, failure and repair rates on the performability measures of the system.

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The assignment problem is to find the total costs optimal jobs assignment schedule where n jobs are allocated to n workers, and each worker receives exactly just one job, such that the total cost is optimal. The quadratic assignment problem with penalty takes three types of costs into consideration: direct cost, interactive cost an penalty. In this paper, the fuzzy quadratic assignment problem with penalty is formulated as expected value model, chance-constrained programming and dependent-chance programming according to various decision criteria, and the crisp equivalents are given. Furthermore, hybrid genetic algorithm is designed for solving the proposed fuzzy programming models.

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In this paper, we have applied restrictive Pade approximation classical implicit finite difference method to the Burgers’ equation with a set of initial and boundary conditions to obtain its numerical solution. The stability region and truncation error of the new method are discussed. The accuracy of the proposed method is demonstrated by the two test problems. The numerical results obtained by this method for various values of viscosity have been compared with the exact solution to show the efficiency of the method. The numerical results are found in good agreement with the exact solutions.

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General curvilinear coordinate systems are considered along with the error induced by coordinate systems, basic differential models for coordinate generation, elliptic grid generation, conformal grid generation, algebraic grid generation, orthogonal grid generation, patched coordinate systems, and solid mechanics applications of boundary fitted coordinate systems. Attention is given to coordinate system control and adaptive meshes, the application of body conforming curvilinear grids for finite difference solution of external flow, the use of solution adaptive grids in solving partial differential equations, adaptive gridding for finite difference solutions to heat and mass transfer problems, and the application of curvilinear coordinate generation techniques to the computation of internal flows. Other topics explored are related to the solution of nonlinear water wave problems using boundary-fitted coordinate systems, the numerical modeling of estuarine hydrodynamics on a boundary-fitted coordinate system, and conformal grid generation for multielement airfoils.

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In this paper we use Adomian decomposition method to solve systems of nonlinear fractional differential equations and a linear multi-term fractional differential equation by reducing it to a system of fractional equations each of order at most unity. We begin by showing how the decomposition method applies to a class of nonlinear fractional differential equations and give two examples to illustrate the efficiency of the method. Moreover, we show how the method can be applied to a general linear multi-term equation and solve several applied problems.

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During the past decade, hybrid algorithms combining evolutionary computation and constraint-handling techniques have shown to be effective to solve constrained optimization problems. For constrained optimization, the penalty function method has been regarded as one of the most popular constraint-handling technique so far, whereas its drawback lies in the determination of suitable penalty factors, which greatly weakens the efficiency of the method. As a novel population-based algorithm, particle swarm optimization (PSO) has gained wide applications in a variety of fields, especially for unconstrained optimization problems. In this paper, a hybrid PSO (HPSO) with a feasibility-based rule is proposed to solve constrained optimization problems. In contrast to the penalty function method, the rule requires no additional parameters and can guide the swarm to the feasible region quickly. In addition, to avoid the premature convergence, simulated annealing (SA) is applied to the best solution of the swarm to help the algorithm escape from local optima. Simulation and comparisons based on several well-studied benchmarks demonstrate the effectiveness, efficiency and robustness of the proposed HPSO. Moreover, the effects of several crucial parameters on the performance of the HPSO are studied as well.

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As competition from emerging economies such as China and India puts pressure on global supply chains and as new constraints emerge, it presents opportunities for approaches such as game theory for solving the transshipment problem. In this paper we use the well-known Shapley value concept from cooperative game theory as an approach to solve the transshipment problem for maintaining stable conditions in the logistics network. A numerical example is presented to show the usefulness of this approach.

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This paper presents a new algorithm called probabilistic global search lausanne (PGSL). PGSL is founded on the assumption that optimal solutions can be identified through focusing search around sets of good solutions. Tests on benchmark problems having multi-parameter non-linear objective functions revealed that PGSL performs better than genetic algorithms and advanced algorithms for simulated annealing in 19 out of 23 cases studied. Furthermore as problem sizes increase, PGSL performs increasingly better than these other approaches. Empirical evidence of the convergence of PGSL is provided through its application to Lennard–Jones cluster optimisation problem. Finally, PGSL has already proved to be valuable for engineering tasks in areas of design, diagnosis and control.

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This paper includes a reply to the comment suggested by Kahya [Emin Kahya, Comment on titled “An improvement on Fibonacci search method in optimization theory”]. Kahya claims that he proposes some corrections for some deficiencies of the paper [Murat Subasi, Necmettin Yildirim, Bünyamin Yildiz, An improvement on Fibonacci search method in optimization theory, Applied Mathematics and Computation 147 (2004) 893–901]. Here, we prove that in Kahya’s suggestions there is no novelty and so, they are not contributional.

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A powerful, easy-to-use analytic tool for nonlinear problems in general, namely the homotopy analysis method, is further improved and systematically described through a typical nonlinear problem, i.e. the algebraically decaying viscous boundary layer flow due to a moving sheet. Two rules, the rule of solution expression and the rule of coefficient ergodicity, are proposed, which play important roles in the frame of the homotopy analysis method and simplify its applications in science and engineering. An explicit analytic solution is given for the first time, with recursive formulas for coefficients. This analytic solution agrees well with numerical results and can be regarded as a definition of the solution of the considered nonlinear problem.

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This paper tries to extend the Adomian decomposition method for solving fully fuzzy linear systems (shown as FFLS). For finding a positive fuzzy vector that satisfies , where and are respectively a fuzzy matrix and a fuzzy vector, we employ Dubois and Prade’s approximate arithmetic operators on LR fuzzy numbers. We also transform the FFLS and use the Adomian decomposition method for solving an FFLS. Then, we compare this method with the Jacobi iterative technique. Additionally, we give some numerical examples.

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In this paper, a new method using radial basis function (RBF) networks is presented for solving the linear second kind integral equations of Fredholm and Volterra types. This method employs a growing neural network as the approximate solution of the integral equations, whose the activation functions are RBFs. The parameters (weights, centers and widths) of the approximate solution are adjusted by using an unconstrained optimization problem. Numerical results show that our method has the potentiality to become an efficient approach for solving integral equations.

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Vehicle routing problem is concerned with finding efficient routes, beginning and ending at a central depot, for a fleet of vehicles to serve a number of customers with demands for some commodity. This paper considers the vehicle routing problem in which the travel times are assumed to be fuzzy variables. A fuzzy optimization model is designed for fuzzy vehicle routing problem with time window. Moreover, fuzzy simulation and genetic algorithm are integrated to design a hybrid intelligent algorithm to solve the fuzzy vehicle routing model. Finally, a numerical example is given to show the effectiveness of the algorithm.

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In this article a model of the linear thermo-elastic theory without energy dissipation is employed to study radially symmetric thermo-elastic wave propagation in an infinitely extended thin plate with a circular hole when the inner boundary of the hole is subjected to (i) zero stress and a step-input of temperature rise and (ii) a step-input of stress and zero temperature change. The analytical expressions for short-time solutions for displacement, temperature and stresses are derived. The results derived are compared with earlier results derived by using other generalized thermo-elasticity theories. Numerical results applicable to a copper-like material are presented to illustrate the analytical result.

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We present and illustrate the simulation results of a cellular automata model describing the dynamics of a forest fire spread on a mountainous landscape taking into account factors such as the type and density of vegetation, the wind speed and direction and the spotting phenomenon. The model is used to simulate the wildfire that broke up on Spetses in August of 1990 and destroyed a major part of the Island’s forest. We used a black-box non-linear optimization approach to fine-tune some of the model’s parameters based on a geographical information system incorporating available data from the real forest fire. The comparison between the simulation and the actual-observed results showed that the proposed model predicts in a quite adequate manner the evolution characteristics in space and time of the real incident and as such could be potentially used to develop a fire risk-management tool for heterogeneous landscapes.

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We investigate the global character of solutions of the equation in the title with nonnegative parameters and positive initial conditions. We give a detailed description of the semicycles of solutions and prove that the equilibrium of the equation is globally asymptotically stable.

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In this paper, a new gradient regularization algorithm is introduced and applied to solve an inverse problem of determining source terms in one-dimensional advection–dispersion equation with final observations. By functional approximations, the algorithm is reduced to find an optimal perturbation for a given source parameter involving computations of gradient vectors. In the case of using accurate data, the optimal perturbation can be directly worked out by the least square method; in the case of with random noisy data, regularization strategy may be useful to the realization of the algorithm. As compared with ordinary gradient regularization algorithm, the new gradient regularization algorithm gives a possible approach to the precise choices of optimal regularization parameters. Several numerical simulations under different conditions are carried out showing that the algorithm is feasible and efficient. Furthermore, the algorithm is successfully applied to solve a real life example of determining an average magnitude of groundwater pollution sources.

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An auxiliary elliptic equation method is presented for constructing exact solitary and periodic travelling-wave solutions of the K(2,2) equation (defocusing branch). Some known results in the literature are recovered more efficiently, and some new exact travelling-wave solutions are obtained. Also, new stationary-wave solutions are obtained.

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In this paper, by using bifurcation method, we successfully find the K(2,2) equation with osmosis dispersion ut+(u2)x-(u2)xxx=0 possess two new types of travelling wave solutions called kink-like wave solutions and antikink-like wave solutions. They are defined on some semifinal bounded domains and possess properties of kink waves and anti-kink waves. Their implicit expressions are obtained. For some concrete data, the graphs of the implicit functions are displayed, and the numerical simulation of travelling wave system is made by Maple. The results show that our theoretical analysis agrees with the numerical simulation.

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It has been recently showed in [M.E. Alexander, S.M. Moghadas, Periodicity in an epidemic model with a generalized non-linear incidence, Math. Biosci. 189 (2004) 75–96] that one of the possible causes of unexpected failures of some vaccination campaigns may be the nonlinearity of the force of infection. The aim of this paper is to give a simple and biologically meaningful sufficient condition for the globally stable eradication of diseases whose spreading is described via a generic class of SIR and SEIR epidemic models ruled by nonlinear force of infection. We consider a scenario in which there are both traditional and pulse vaccination strategies.

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The aim of this paper is to discuss the new class of epidemic models proposed by Satsuma et al., which are characterized by incidence rates which are nonlinearly dependent on the number of susceptibles as follows: infection rate (S, I) = g(S)I. By adding the biologically plausible constraint g′(S) > 0, we study the SIR and the SEIR models with vital dynamics with such infection rate, and results are done on the global asymptotic stability of the disease free and of the endemic equilibria, similarly to the ones of the classical models, also in presence of traditional and pulse vaccination strategies. Relaxing the constraint g′(S) > 0, we show that the epidemic system may exhibit multiple endemic equilibria.

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In this paper, we consider an epidemic model with the nonlinear incidence of a sigmoidal function. By mathematical analysis, it is shown that the model exhibits the bistability and undergoes the Hopf bifurcation and the Bogdanov–Takens bifurcation. By numerical simulations, it is found that the incidence rate can induce multiple limit cycles, and a little change of the parameter could lead to quite different bifurcation structures.

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We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material’s behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We derive a variational formulation for the problem and then, under a smallness assumption on the data, we prove the existence of a unique weak solution to the model. We also investigate the behavior of the solution with respect the electric data on the contact surface and prove a continuous dependence result. Then, we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the contact by using a penalized approach and a version of Newton’s method. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of two-dimensional test problems. These simulations provide a numerical validation of our continuous dependence result and illustrate the effects of the conductivity of the foundation, as well.

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Dual numbers, split-quaternions, split-octonions, and other number systems with nilpotent spaces have received sporadic yet persistent interest, beginning from their roots in the 19th century, to more recent attention in connection with supersymmetry in physics. In this paper, a number system in the 2D plane is investigated, where the squares of its basis elements p and q each map into the coordinate origin. Modeled similarly to an original concept by C. Musès, this new system will be termed “PQ space” and presented as a generalization of nilpotence and zero. Compared to the complex numbers, its multiplicative group and underlying vector space are equipped with as little as needed modifications to achieve the desired properties. The locus of real powers of basis elements pα and qα resembles a four-leaved clover, where the coordinate origin at (0, 0) will not only represent the additive identity element, but also a map of “directed zeroes” from the multiplicative group. Algebraic and geometric properties of PQ space are discussed, and its naturalness advertised by comparison with other systems. The relation to Musès’ “p and q numbers” is shown and its differences defended. Next to possible applications and extensions, a new butterfly-shaped fractal is generated from a recursion algorithm of Mandelbrot type.
Preprint available at http://www.jenskoeplinger.com/P

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We study the long-time behavior of the finite difference solution to the generalized Kuramoto–Sivashinsky equation in two space dimensions with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system and the upper semicontinuity d(Ah,τ,A)→0. Finally, we obtain the long-time stability and convergence of the difference scheme. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.

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Area-perimeter ratios are often used to quantify 2D shape compactness. Shape compactness is of main importance to evaluate the effect of external disturbance on natural habitats. Reference values (Amin(p), Amax(p), Pmin(a), Pmax(a)) for area (A) and perimeter (P) are defined and proven. The calculation of these reference values is based on the characteristics of the object studied and on pixel geometry. The cases for 4- and 8-connectivity are discussed. Using these references, alternative area-perimeter ratios are composed. Examples are elaborated to illustrate the use of the indices and their performance.

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This paper introduces a finite volume unstructured algorithm for groundwater contaminant simulation. The algorithm is developed using the direct finite volume concept constructed on an unstructured grid system. The cell-centered explicit conservative scheme has been adopted in numerical simulation. An example of groundwater contaminant transport simulation on a simple geometry is presented and results are compared with an analytic solution and the solutions obtained by using a finite difference method on structured grids. The direct finite volume method applied on an arbitrary unstructured grid system is found promising for modeling groundwater contamination transport behavior.

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In this article the author constructs an effective difference scheme for the solution of coupled dynamic electroelasticity problems for finite dimensional solids. Such a construction is based on the energy conservation law for the electromechanical system and the definition of generalised solutions for the corresponding differential problem. Results of computational experiments are presented for hollow piezoceramic cylinders in the two-dimensional case. Key words: piezoelectrics, discrete conservation laws for coupled systems, electro-mechanical interactions, generalised solutions. 1 Introduction: Piezoceramic Applications and Coupled Field Theory Piezoelectricity is an example of phenomena where coupling two physical fields of different natures (namely mechanical and electrical fields) is a key factor to be taken into account in a variety of applications. It is just one of many important examples where two theories, originally developed independently of each other (in this case the t...

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In this paper we present a method for estimating unknown parameter that
appear in a two dimensional nonlinear reaction-diffusion model of cancer
invasion. This model considers that tumor-induced alteration of
microenvironmental pH provides a mechanism for cancer invasion. A coupled
system reaction-diffusion describing this model is given by three partial
differential equations for the 2D non-dimensional spatial distribution and
temporal evolution of the density of normal tissue, the neoplastic tissue
growth and the excess concentration of H+ ions. Each of the model parameters
has a corresponding biological interpretation, for instance, the growth rate of
neoplastic tissue, the diffusion coefficient, the re-absorption rate and the
destructive influence of H+ ions in the healthy tissue. After solving the
direct problem, we propose a model for the estimation of parameters by fitting
the numerical solution with real data, obtained via in vitro experiments and
fluorescence ratio imaging microscopy. We define an appropriate functional to
compare both the real data and the numerical solution using the adjoint method
for the minimization of this functional. We apply a splitting strategy joint
with Adaptive Finite Element Method (AFEM) to solve the direct problem and the
adjoint problem. The minimization problem (the inverse problem) is solved by
using a trust-region-reflective method including the computation of the
derivative of the functional.

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In this paper, we investigate a generalized two-dimensional Lotka–Volterra system which has a center. We give an inductive algorithm to compute polynomials of periodic coefficients, find structures of solutions for systems of algebraic equation corresponding to isochronous centers and weak centers of finite order, and derive conditions on parameters under which the considered equilibrium is an isochronous center or a weak center of finite order. We show that with appropriate perturbations at most two critical periods bifurcate from the center.

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Two dimensional singularly perturbed convection–diffusion problem with discontinuous coefficients is considered. The problem is discretized using an inverse-monotone finite volume method on Shishkin meshes. We established first-order global pointwise convergence that is uniform with respect to the perturbation parameter. Numerical experiments that support the theoretical results are given.

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In this paper, we propose a face recognition method using a fusion method based on bidirectional 2DPCA. While the previous PCA method computes the covariance matrix by using a one-dimensional vector, 2DPCA method computes the covariance matrix by directly using a direct two-dimensional image, and extracts the feature vectors by solving an eigenvalue problem. The proposed method recognizes the faces by applying the modified 2DPCA obtaining a linear transformation matrix using two covariance matrices which are the row and column covariance matrices. The experimental results indicate that the proposed method shows a higher and more stable recognition rate than the conventional methods.

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This paper investigates the existence of positive solutions for 2nth-order singular sub-linear m-point boundary value problems. Firstly, we establish a comparison theorem, then we define a partial ordering in C2n-2 [a, b] boolean AND C-2n(a, b) and construct lower and upper solutions to give a necessary and sufficient condition for the existence of C2n-2[0, 1] as well as C2n-1[0,1] positive solutions. Our nonlinearity f(t, x(1), x(2),...., x(n)) may be singular at x(i) = 0, i = 1, 2,..., n, t = 0 and/or t = 1. (c) 2006 Elsevier Inc. All rights reserved.

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In this paper, we obtain the existence of multiple positive solutions of a boundary value problem for 2nth-order singular nonlinear integro-differential equations in a Banach space by means of fixed point index theory of completely continuous operators.

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