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Merton points out that "the most precise significance of the word function is of course found in mathematics …. " But, says Martindale, "The work of most of the recent functionalists has been at the opposite pole from this meaning." Consequently, assertions made by functionalists have not always been received with the degree of confidence that their authors might consider appropriate. It is the purpose of this paper to suggest a way in which qualitatively formulated propositions of a functional kind may be translated into a language which points to empirical referents and thus, if all goes well, leads in the end to the formulation of mathematical equations. [ABSTRACT FROM AUTHOR]

This paper proposes an iterative approximation technique of log-magnitude response for IIR filters. Minimization of the mean-square error between a desired log-frequency response and that of an IIR filter leads to a nonlinear problem. In this paper, the least squares problem on the logarithmic scale is approximated by the iteration of a weighted least squares problem on the linear scale. The weighting function is updated using the result of the previous iteration so that the weighted error on the linear scale approximates the squared error on the logarithmic scale. The filter coefficients at each iteration step can efficiently be obtained using a fast recursive algorithm for a set of linear equations. Several design examples are presented, which show that the iterative algorithm converges after one or two iterations in practice and the weighted error at convergence gives a good, estimate of the mean-square error on the logarithmic scale. An example is also presented, where both log-magnitude and phase responses are approximated simultaneously. [ABSTRACT FROM AUTHOR]

This paper presents a quantitative discussion on the stability of the second-order periodic difference equation, which characterizes the discrete periodic time-varying system. The periodic parameter discrete system, which corresponds to Mathieu's equation in the continuous system, is represented by a second-order linear difference equation with a small parameter E in the varying term. The parameter E plays an important role in the determination of the stability. By applying McLachlan's method, the expression for the boundary between the stability and the instability can be determined analytically with regard to the parameters contained in the equation. For the case where the periodic parameter of the difference equation is represented as a sum of two even functions, the boundary between stability and instability is determined. The stability can be analyzed in a similar way for the case where the periodic parameter is represented as a sum of N even functions in Fourier series. [ABSTRACT FROM AUTHOR]

In the analysis of a discrete nonlinear system, one of the important problems is to derive a steady solution for the nonlinear difference equation characterizing the system. However, the study for the solution method of the difference system has not been sufficient, and examples of the methods being applied to the parametric oscillation are few. This paper presents a method which derives the steady solution for the quasi-linear difference equation containing a periodic parametric excitation in its weakly nonlinear function with small parameter ∊. In this method the harmonic balance and the averaging methods used in the solution of the continuous nonlinear differential equation are ape plied to the discrete system. Since the non-linear term in the equation is bounded by ∊, the discrete waveform in the steady state is almost sinusoidal. This paper presents numerical examples for the solutions by the two methods, assuming the solution as the discrete oscillation corresponding to the sinusoid of the continuous system. As a result, the same solution is obtained by either method. Comparing the result with the output waveform obtained directly by the numerical calculation for the fundamental equation, the validity of the approximate solution by the proposed method was verified. [ABSTRACT FROM AUTHOR]

This article is a comment on the paper by Spirtes, Scheines, and Glymour. The problem of equivalent models is discussed. The conclusion of the authors that the automatic model modification procedure in LISREL performs poorly may be due to the fact that all equivalent models are not counted as correct models. Our own experiment based on their model 8 demonstrates that the automatic model modification procedure in LISREL indeed performs very well when all equivalent models are counted as correct. Contrary to what the authors claim, the modification index in LISREL can be used to detect equivalent models and give useful insight into the problem of model modification. [ABSTRACT FROM AUTHOR]

In electromagnetics, a numerical technique that finds immense application is the method of moments. This method reduces the boundary value problem containing integro-differential equations into the form AX = where A is a full complex matrix, that is known and X is the unknown to be solved for the given excitation Y. In this paper, the matrix equation has been solved on various computers such as the VAX 3500, VAX 8530, Multimax 320, Alliant FX/80 and IBM 3090-600E. Two of the established methods, viz. gaussian elimination and the conjugate gradient method have been used to solve the above matrix equations. A detailed timing analysis has been done to bring out the features of various computer architectures. [ABSTRACT FROM AUTHOR]

The finite difference time-domain (FDTD) method is a well known numerical technique that has been used to solve electromagnetic boundary value problems. However, the method requires large computational resources to solve a problem, restricting its use on sequential computers to small problems. This has led to the use of expensive supercomputers in the past to solve larger problems. In this paper we first discuss existing parallel implementations of the FDTD method. We then describe an approach to compute the FDTD equations based on distributed-memory computer architectures. Finally we evaluate a low-cost parallel implementation of the FDTD method that runs on a network of workstations, utilizing spare network capacity. [ABSTRACT FROM AUTHOR]

In this paper a parallel algorithm is created for solving electromagnetic wave scattering problems. The algorithm based on the finite difference time-domain (FDTD) representation of the Maxwell's equations written in 3L Parallel Fortran for use on a transputer array. The problem simulated consists of a space (air) where a spherical dielectric scatterer is located. This space is subdivided into fine equisize meshes extending throughout the 3-D domain; the excitation wave is of sinusoidal form. Geometric decomposition is used as the principal algorithm strategy. Results are presented for the performance of the classical sequential algorithm and compared with the parallel algorithm in terms of computational speed-up. [ABSTRACT FROM AUTHOR]

In the paper we apply the boundary element multiple reciprocity method to the Brinkman equation, showing that the technique yields an incomplete series representation of the corresponding fundamental solution, incompleteness that is due to a weakness in the way the method is usually applied. For the present case an additional integral relation is found that makes the series complete. Unfortunately, the relation is particular to this problem and cannot be generalized in a simple way. The result found in this work suggests that in multiple reciprocity it is necessary to have an extra relation in integral form to define the missing terms in the series representation. This extra relation has to yield zero contribution for cases when the multiple reciprocity method gives the complete series representation. [ABSTRACT FROM AUTHOR]

The paper presents a hybrid Trefftz (HT) element approach for the numerical solution of transient plate bending problems. In the proposed method, the dynamic plate equation is first discretized with respect to time and then the resulting set of elliptic equations is solved by the corresponding time independent hybrid Trefftz element approach. Two examples are considered to assess the effectiveness of the numerical method. [ABSTRACT FROM AUTHOR]

In this paper the superconvergence property of isoparametric bilinear finite elements is considered. A new superconvergence recovery method for isoparametric bilinear finite elements is discovered on the four vertices and the four midpoints of the edges of the elements for piecewise strongly regular quadrilateral subdivisions. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonlinear stability of travelling wave solutions with shock profile for a relaxation model with a nonconvex ux, which is proposed by Jin and Xin [Comm. Pure Appl. Math., 48 (1995), pp. 555-563] to approximate an original hyperbolic system numerically under the subcharacteristic condition introduced by T. P. Liu [Comm. Math. Phys., 108 (1987), pp. 153-175]. The travelling wave solutions with strong shock profile are shown to be asymptotically stable under small disturbances with integral zero using an elementary but technical energy method. Proofs involve detailed study of the error equation for disturbances using the same weight function introduced in [Comm. Math. Phys., 165 (1994), pp. 83-96]. [ABSTRACT FROM AUTHOR]

The paper establishes the existence of strong solutions for diffusion-type stochastic equations with continuous coefficients. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Cauchy problem ... where p > 1. Let Ω be a set in RN given by Ω ≡ {(r, ω) ∈ R+ x SN - 1 : r > R, d(ω, ω0) < cr 1μ} for some R > 0, c > ω0 &isin SN - 1, and 0 ≤ μ < 1, where d(., .) denotes the standard distance on SN - 1. It is shown that if u0 decays like |x|- alpha; as |x| → ∞ in Ω with 0 < α < α 2(1 - μ)/(p - 1), then the solution blows up in finite time regardless of the behavior of u0 outside Ω. Moreover the life span of such a solution with u0 = λφ is estimated from above for small λ > 0 in terms of p, α, and μ. The optimality of these results is also studied. [ABSTRACT FROM AUTHOR]

This paper addresses the qualitative behavior of a nonlinear convection-diffusion equation on a smooth bounded domain in Rn , in which the strength of the convection grows superlinearly as the density increases. While the initial-boundary value problem is guaranteed to have a local-in-time solution for smooth initial data, it is possible for this solution to be extinguished in finite time. We demonstrate that the way this may occur is through finite-time "blow up," i.e., the unboundedness of the solution in arbitrarily small neighborhoods of one or more points in the closure of the spatial domain. In special circumstances, such as the presence of radial symmetry, the set of blowup points can be identified; these points may be either on the boundary or on the interior of the domain. Furthermore, criteria can be established that guarantee that blowup occurs. In this paper, such criteria are presented, involving the dimension of the space, the growth rate of the nonlinearity, the strength of the imposed convection field, the diameter of the domain, and the mass of the initial data. Furthermore, the temporal rate of blowup is estimated. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence and the asymptotic stability of traveling waves for a model system derived from approximating the one-dimensional system of the radiating gas. We show the existence of smooth or discontinuous traveling waves and also prove the uniqueness of these traveling waves under the entropy condition, in the class of piecewise smooth functions with the first kind discontinuities. Furthermore, we show that the C3-smooth traveling waves are asymptotically stable and that the rate of convergence toward these waves is t-1/4, which looks optimal. The proof of stability is given by applying the standard energy method to the integrated equation of the original one. [ABSTRACT FROM AUTHOR]

Multidimensional positive definite advection transport algorithm (MPDATA) is an iterative process for approximating the advection equation, which uses a donor cell approximation to compensate for the truncation error of the originally specified donor cell scheme. This step may be repeated an arbitrary number of times, leading to successively more accurate solutions to the advection equation. In this paper, we show how to sum the successive approximations analytically to find a single antidiffusive velocity that represents the effects of an arbitrary number of passes. The analysis is first done in one dimension to illustrate the method and then is repeated in two dimensions. The existence of cross terms in the truncation analysis of the two-dimensional equations introduces an extra complication into the calculation. We discuss the implementation of our new antidiffusive velocities and provide some examples of applications, including a third-order accurate scheme. [ABSTRACT FROM AUTHOR]

In this paper we introduce a moving mesh method for solving PDEs in two dimensions. It can be viewed as a higher-dimensional generalization of the moving mesh PDE (MMPDE) strategy developed in our previous work for one-dimensional problems [W. Huang, Y. Ren, and R. D. Russell, SIAM J. Numer. Anal., 31 (1994), pp. 709–730]. The MMPDE is derived from a gradient flow equation which arises using a mesh adaptation functional in turn motivated from the theory of harmonic maps. Geometrical interpretations are given for the gradient equation and functional, and basic properties of this MMPDE are discussed. Numerical examples are presented where the method is used both for mesh generation and for solving time-dependent PDEs. The results demonstrate the potential of the mesh movement strategy to concentrate the mesh points so as to adapt to special problem features and to also preserve a suitable level of mesh orthogonality. [ABSTRACT FROM AUTHOR]

This paper studies the effect of multipath interference on the performance of random access techniques in which the power level of a packet depends on its time of arrival. The protocols considered are pure ALOHA and slotted ALOHA. Key performance measures such as channel throughout and mean packet delay are obtained. These results are derived partially using minislot approximation and are verified via computer simulations. For practical purposes in evaluating the successful packet reception probability the signal capture effect is also taken into consideration. How seriously the multipath interference affects the two protocols are witnessed through numerical examples. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper the Navier-Stokes equations are discretized by semi-implicit schemes and the resulting symmetric or non-symmetric systems of linear equations are treated. A number of solvers for solving generally non-symmetric systems of linear equations are tested in order to find the optimal one. Copyright © 1999 John Wiley & Sons, Ltd. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical analysis of the autoconvolution equation x × x = y restricted to the interval [0,1]. We present a discrete constrained least squares approach and prove its convergence in Lp(0,1), 1≤ p ≤ ∞, where the regularization is based on a prescribed bound for the total variation of admissible solutions. This approach includes the case of non-smooth solutions possessing jumps. Moreover, an adaptation to the Sobolev space H1(0,1) is added. A numerical case study concerning the determination of non-monotone smooth and non-smooth functions x from the autoconvolution equation with noisy data y completes the paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider the finite-dimensional approximations of Tikhonov regularization for nonlinear ill-posed problems with approximately given right-hand sides. We propose an a posteriori parameter choice strategy, which is a modified form of Morozov's discrepancy principle, to choose the regularization parameter. Under certain assumptions on the nonlinear operator, we obtain the convergence and rates of convergence for Tikhonov regularized solutions. This paper extends the results, which were developed by Plato and Vainikko in 1990 for solving linear ill-posed equations, to nonlinear problems. [ABSTRACT FROM AUTHOR]

In this paper a methodology for the transformation of a second degree equation to its canonical expression is presented. A generalized chart for knowledge (EGA) used for this transformation, as well as the interpretation of the presented canonical equation are exposed. As an example, the utilization of this methodology in the optimization of basic leaching step of sodium alginate is showed, making emphasis in the mathematical model and response surface interpretation. [ABSTRACT FROM AUTHOR]

Fast Marching Methods are numerical schemes for computing solutions to the nonlinear Eikonal equation and related static. Hamilton­Jacobi equations. Based on entropy-satisfying upwind schemes and fast sorting techniques, they yield consistent, accurate, and highly efficient algorithms. They are optimal in the sense that the computational complexity of the algorithms is O(N log N), where N is the total number of points in the domain. The schemes are of use in a variety of applications, including problems in shape offsetting, computing distance from compiles curves and surfaces, shape-from-shading, photolithographic development, computing first arrivals in seismic travel times, construction of shortest geodesies on surfaces, optimal path planning around obstacles, and visibility and reflection calculations. In this paper, were review the development of these techniques, including the theoretical and numerical underpinnings; provide details of the computational schemes, including higher order versions; and demonstrate the techniques in a collection of different areas. [ABSTRACT FROM AUTHOR]

This paper presents some known results on the approximate and null controllability of the Navier­Stokes equations. All of them can be viewed as partial answers to a conjecture of J.-L. Lions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new class of generalized nonlinear implicit quasivariational inclusions for set-valued mappings. We construct some new iterative algorithms for this generalized nonlinear implicit quasivariational inclusions for set-valued mappings without compactness. We prove the existence of solutions for this generalized nonlinear implicit quasivariational inclusions for set-valued mappings without compactness and the convergence of iterative sequences generated by the algorithms. We also give an application to generalized nonlinear implicit variational inequalities. [ABSTRACT FROM AUTHOR]

This paper is concerned with refinement equations of the type [This symbol cannot be presented in ASCII format] where f is the unknown function defined on the s-dimensional Euclidean space Rs, a is a finitely supported sequence on Zs, and M is an s × s dilation matrix with m := | det M|. The solution of a refinement equation can be obtained by using the subdivision scheme associated with the mask. In this paper we give a characterization for the convergence of the subdivision scheme when the mask is nonnegative. Our method is to relate the problem of convergence to m column-stochastic matrices induced by the mask. In this way, the convergence of the subdivision scheme can be determined in a finite number of steps by checking whether each finite product of those column-stochastic matrices has a positive row. As a consequence of our characterization, we show that the convergence of the subdivision scheme with a nonnegative mask depends only on the location of its positive coefficients. Several examples are provided to demonstrate the power and applicability of our approach. [ABSTRACT FROM AUTHOR]

In this paper linear periodic systems of difference equations are classified with respect to periodic similarity and kinematic similarity. Complete sets of invariants of periodic difference equations relative to such similarity transformations are given, and corresponding canonical forms are described. Also the irreducible periodic difference equations, i.e., those that cannot be reduced by such similarities to a nontrivial direct sum, are identified. [ABSTRACT FROM AUTHOR]

Multilevel algorithms are a successful class of optimization techniques which addresses the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimization method which refines the partition at each graph level. In this paper we present an enhancement of the technique which uses imbalance to achieve higher quality partitions. We also present a formulation of the Kernighan­Lin partition optimization algorithm which incorporates load-balancing. The resulting algorithm is tested against a different but related state-of-the-art partitioner and shown to provide improved results. [ABSTRACT FROM AUTHOR]

This paper presents a new Lagrangian approach for the two-dimensional (2-D) time-dependent Euler equations. It may be considered as a sequel to the authors' previous Lagrangian approaches for steady supersonic flow computations [C. Y. Loh and W. H. Hui, J. Comput. Phys., 89 (1990), pp. 207­240; W. H. Hui and C. Y. Loh, J. Comput. Phys., 103 (1992), pp. 450­464; W. H. Hui and C. Y. Loh, J. Comput. Phys., 103 (1992), pp. 465­471; C. Y. Loh and M. S. Liou, J. Comput. Phys., 104 (1993), pp. 150­161; C. Y. Loh and M. S. Liou, SIAM J. Sci. Comput., 15 (1994), pp. 1038­1058; C. Y. Loh and M. S. Liou, J. Comput. Phys., 113 (1994), pp. 224­248]. The theoretical background and the intrinsic flow coordinates as well as the Lagrangian conservation form are introduced based on the concept of material functions (or path functions). A TVD scheme of the Godunov type is chosen to describe the numerical procedure. Several examples are then given to justify the claimed advantages of the new methodology, namely, (a) any contact discontinuities are crisply solved and (b) grids are automatically and accurately generated following pathlines. [ABSTRACT FROM AUTHOR]

The perturbation analysis of weighted and constrained rank-deficient linear least squares is difficult without the use of the augmented system of equations. In this paper a general form of the augmented system is used to get simple perturbation identities and perturbation bounds for the general linear least squares problem both for the full-rank and rank-deficient problem. Perturbation identities for the rank-deficient weighted and constrained case are found as a special case. Interesting perturbation bounds and condition numbers are derived that may be useful when considering the stability of a solution of the rank-deficient general least squares problem. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper shows that a third grade fluid (different from the model employed by Fosdick and Rajagopal, see Tigoiu [6]) has a unique solution when experiences a weakly perturbed flow and the rest state is asymptotically stable. This result is not in contradiction with the result obtained by Joseph, but it proves the limit in the application of the representation theorem of Coleman and Noll. [ABSTRACT FROM AUTHOR]

Discrete and continuous refinement equations have been widely studied in the literature for the last few years, due to their applications to the areas of wavelet analysis and geometric modeling. However, there is no "universal" theorem that deals with the problem about the existence of compactly supported distributional solutions for both discrete and continuous refinement equations simultaneously. In this paper, we provide a uniform treatment for both equations. In particular, a complete characterization of the existence of distributional solutions of nonhomogeneous discrete and continuous refinement equations is given, which covers all cases of interest. [ABSTRACT FROM AUTHOR]

In this paper we discuss the power of a pivoting transformation introduced by Castillo, Cobo, Jubete, and Pruneda [Orthogonal Sets and Polar Methods in Linear Algebra: Ap- plications to Matrix Calculations, Systems of Equations and Inequalities, and Linear Programming, John Wiley, New York, 1999] and its multiple applications. The meaning of each sequential tableau appearing during the pivoting process is interpreted. It is shown that each tableau of the process corresponds to the inverse of a row modified matrix and contains the generators of the linear sub- space orthogonal to a set of vectors and its complement. This transformation, which is based on the orthogonality concept, allows us to solve many problems of linear algebra, such as calculating the inverse and the determinant of a matrix, updating the inverse or the determinant of a matrix after changing a row (column), determining the rank of a matrix, determining whether or not a set of vectors is linearly independent, obtaining the intersection of two linear subspaces, solving systems of linear equations, etc. When the process is applied to inverting a matrix and calculating its determi- nant, not only is the inverse of the final matrix obtained, but also the inverses and the determinants of all its block main diagonal matrices, all without extra computations. [ABSTRACT FROM AUTHOR]

In this paper we consider domain decomposition methods for solving the radial basis function interpolation equations. There are three interwoven threads to the paper. The first thread provides good ways of setting up and solving small- to medium-sized radial basis function interpolation problems. These may occur as subproblems in a domain decomposition solution of a larger interpolation problem. The usual formulation of such a problem can suffer from an unfortunate scale dependence not intrinsic in the problem itself. This scale dependence occurs, for instance, when fitting polyharmonic splines in even dimensions. We present and analyze an alternative formulation, available for all strictly conditionally positive definite basic functions, which does not suffer from this drawback, at least for the very important example previously mentioned. This formulation changes the problem into one involving a strictly positive definite symmetric system, which can be easily and efficiently solved by Cholesky factorization. The second section considers a natural domain decomposition method for the interpolation equations and views it as an instance of von Neumann's alternating projection algorithm. Here the underlying Hilbert space is the reproducing kernel Hilbert space induced by the strictly conditionally positive definite basic function. We show that the domain decomposition method presented converges linearly under very weak nondegeneracy conditions on the possibly overlapping subdomains. The last section presents some algorithmic details and numerical results of a domain decomposition interpolatory code for polyharmonic splines in 2 and 3 dimensions. This code has solved problems with 5 million centers and can fit splines with 10,000 centers in approximately 7 seconds on very modest hardware. [ABSTRACT FROM AUTHOR]

The Schwarz alternating method can be used to solve linear elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approx- imated by an infinite sequence of functions which result from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers four Schwarz alternating methods for the N-dimensional, steady, viscous, incompressible Navier­Stokes equations, N ≤ 4. It is shown that the Schwarz sequences converge to the true solution provided that the Reynolds number is sufficiently small. [ABSTRACT FROM AUTHOR]

In this paper we apply the generalized Taylor­Galerkin finite element model to simulate bore wave propagation in a domain of two dimensions. For stability and accuracy reasons, we generalize the model through the introduction of four free parameters. One set of parameters is rig- orously determined to obtain the high-order finite element solution. The other set of free parameters is determined from the underlying discrete maximum principle to obtain the monotonic solutions. The resulting two models are used in combination through the flux correct transport technique of Zalesak, thereby constructing a finite element model which has the ability to capture hydraulic dis- continuities. In addition, this paper highlights the implementation of two Krylov subspace iterative solvers, namely, the bi-conjugate gradient stabilized (Bi-CGSTAB) and the generalized minimum residual (GMRES) methods. For the sake of comparison, the multifrontal direct solver is also con- sidered. The performance characteristics of the investigated solvers are assessed using results of a standard test widely used as a benchmark in hydraulic modeling. Based on numerical results, it is shown that the present finite element method can render the technique suitable for solving shallow water equations with sharply varying solution profiles. Also, the GMRES solver is shown to have a much better convergence rate than the Bi-CGSTAB solver, thereby saving much computing time compared to the multifrontal solver. [ABSTRACT FROM AUTHOR]

In this paper we address an initial-boundary-value problem for a generalized Fisher equation. In particular, we use the method of matched asymptotic expansions to develop a rational approach for determining the propagation speed for the large-t (time) travelling wave structures which evolve in the initial-boundary-value problem. This approach resolves apparent paradoxes which arise in the much used linearized approximation (in the cases R(u) ≤ U and R(u) ≤ u, where R(u) is the associated reaction function) and is readily adaptable to systems of Fisher-Kolmogorov type and to problems in higher spatial dimensions. [ABSTRACT FROM AUTHOR]

The paper contains a proposition of a model of adsorption in porous and granular materials. It is assumed that the mass source resulting from adsorption consists of two contributions: changes described by the Langmuir relation for bare sites and changes of the internal surface due to relaxation of porosity. The model is illustrated by a simple numerical example of a homogeneous adsorption process. [ABSTRACT FROM AUTHOR]

We consider meshless collocation methods for the numerical solution of transport processes described by hyperbolic conservation laws. The future goal is the construction of a robust and reliable meshfree discretization method for the equations of gas dynamics in complex geometries. In this paper we start with the simplest scalar model problems and analyze basic problems occurring in the grid-free approach. A topological condition on clouds of points is derived and several possible versions of a generalized Lax-Friedrichs scheme are discussed with respect to their numerical dissipation. A moving least-squares approach is followed to construct a positive discretization for solutions with shocks which is thoroughly analyzed and applied to test problems. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study properties of sequences that are recursively defined by a linear equation and their applications to the truncated moment problem in connection with the problem of subnormal completion of the truncated weighted shifts. Special cases are considered and some classical results due to Stampfli, Curto and Fialkow are recovered using elementary techniques. [ABSTRACT FROM PUBLISHER]

Steady laminar boundary layer flow and heat transfer of a micropolar fluid over a heated isothermal horizontal plate moving in a flowing stream has been studied in this paper. The cases corresponding to the isothermal horizontal plate moving in the same (parallel) or in the opposite (reverse) direction to the free stream are considered. Similarity and nonsimilarity equations of six special systems are reduced readily from universal formulation. The governing momentum, angular momentum, and energy equations have been solved numerically. The effects of buoyancy and relative velocity on the flow and temperature fields including surface friction and heat transfer rate are presented for a plate moving in parallel or reversely to the free stream. It is observed that micropolar fluids display drag reduction when compared to Newtonian fluids. [ABSTRACT FROM AUTHOR]

In this paper, the strongly Cohen-Macaulay ideals of second analytic deviation one are characterized in terms of the depth properties of the powers of the ideal in the ‘standard range’. This provides an explanation of the behaviour of certain ideals that have appeared in the literature. 2000 Mathematics Subject Classification 13H10 (primary), 13C40, 13D02, 13D25 (secondary). [ABSTRACT FROM PUBLISHER]

In this paper, we obtain elementary abelian coverings of the regular hypermaps of genus 2 corresponding to the orientation-preserving automorphism groups SL2(3), the special linear group of order 24. and Qs, the quaternion group of order 8. We also determine the reflexibility of these coverings. [ABSTRACT FROM AUTHOR]

In an earlier paper on a malignant cell invasion model (Marchant et al., SIAM J. Appl. Math, 60, 2000) we introduced a novel form of discontinuous travelling wave solution. These solutions could be studied easily by combining behaviour within a phase plane with the Rankine–Hugoniot shock conditions, which describe properties (such as the ratio of the jump discontinuities to the speed of propagation) that solutions may possess. These results were new for several reasons. The shock conditions relate to hyperbolic equations (which the model is) but were applied in a travelling wave ordinary differential equation phase plane using techniques that usually apply to parabolic reaction–diffusion systems. In addition the solutions possess singular behaviour near several points in the phase plane but in spite of this there exists a robust and stable family of physically interesting solutions. [ABSTRACT FROM PUBLISHER]

In a recent paper [4], Li et al . gave a generalized successive overrelaxation (GSOR) method for the least squares problems. In this paper, the connection between the GSOR method and the preconditioned conjugate gradient (PCG) method for the normal equations is investigated. It is shown that the PCG method is at least as fast as the GSOR method. Numerical examples demonstrates that the PCG method is much faster than the GSOR method. [ABSTRACT FROM AUTHOR]

In a parametric model the maximum likelihood estimator of a parameter of interest ψ may be viewed as the solution to the equation l′p(ψ) = 0, where lp denotes the profile loglikelihood function. It is well known that the estimating function l′p(ψ) is not unbiased and that this bias can, in some cases, lead to poor estimates of ψ. An alternative approach is to use the modified profile likelihood function, or an approximation to the modified profile likelihood function, which yields an estimating function that is approximately unbiased. In many cases, the maximum likelihood estimating functions are unbiased under more general assumptions than those used to construct the likelihood function, for example under first‐ or second‐moment conditions. Although the likelihood function itself may provide valid estimates under moment conditions alone, the modified profile likelihood requires a full parametric model. In this paper, modifications to l′p(ψ) are presented that yield an approximately unbiased estimating function under more general conditions. [ABSTRACT FROM PUBLISHER]

In this paper our propose is to find a common term which is included in the assumptions of theorems proving existence of zeros, implicit functions, fixed points or coincidence points. This new point of view allows us to weaken the assumptions which guarantee the solvability of nonlinear equations and to recommend a possible unified treatment of several classes of operators which appear in the theory of nonlinear equations. [ABSTRACT FROM AUTHOR]

In this paper, the traffic performance of dynamic channel assignment (DCA) in cellular mobile system with hand-off is investigated. A traffic model for cellular system incorporating hand-off is established first. Under the framework of the model, a hand-off priority scheme is developed to reduce the forced termination of calls in progress. This paper analyses and derives the traffic performance bound for DCA strategies with hand-off by extending the maximum packing (MP) scheme to include the hand-off procedure. For practical implementation, a distributed DCA algorithm (DDCA) is also proposed. A non-priority scheme and the proposed priority scheme can be combined with either MP or DDCA. It is shown that the simulation results of DDCA scheme are comparable with the analytical bounds given by MP for both the non-prioritized case and prioritized case. A reasonable trade-off between the new call blocking probability and forced termination probability can be achieved by using the proposed prioritized scheme in DCA. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]