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Linear operators with off‐diagonal decay appear in many areas of mathematics including harmonic and numerical analysis, and their stability is one of the basic assumptions. In this paper, we consider a family of localized integral operators in the Beurling algebra with kernels having mild singularity near the diagonal and certain Hölder continuity property, and prove that their weighted stabilities for different exponents and Muckenhoupt weights are equivalent to each other on a space of homogeneous type with Ahlfors regular measure. [ABSTRACT FROM AUTHOR]

Time‐dependent reliability analysis of structures by the use of an outcrossing approach normally requires the so‐called outcrossing rate to be estimated. A variety of methods has been recorded in the literature to evaluate this rate both for continues and discrete processes. Despite the availability of these methods, still more general and at the same time less sophisticated approaches are desired. In this paper, attempt is made to use the basic idea of "parallel system reliability formulation" to calculate the outcrossing rate for circumstances where the processes are continuous. These calculations are carried out by directional simulation. It is shown that this approach is simple to implement and may be used for the cases where the problem involves nonstationary processes and also for the cases where several limit state functions may have to be considered. [ABSTRACT FROM AUTHOR]

In this paper we study local existence, uniqueness, and continuous dependence of an abstract integrodifferential equation. We also present a result on unique continuation and a blow-up alternative for mild solutions of the integrodifferential equation. Finally, we apply our results to an interesting strongly damped plate equation with memory. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new Lyapunov-type inequalities for a class of even-order linear differential equations, the results are new and generalize and improve some early results in this field. [ABSTRACT FROM AUTHOR]

This paper discusses the eigenvalue problem for the real symmetric matrix, especially the determination of the largest eigenvalue. The largest eigenvalue is the maximum extremum of the objective function called the Rayleigh quotient and can be determined by the steepest descent method. It is known, however, that the steepest descent method suffers from slow convergence because it converges linearly. Especially, when the largest and the nest largest eigenvalues have very close values, the convergence is particularly slow. This paper analyzes this situation and shows that the convergence can be accelerated by combining the steepest descent method with a technique called shaking. Finally, it is demonstrated by a numerical example that the convergence is accelerated drastically by the proposed technique. [ABSTRACT FROM AUTHOR]

This paper considers the complex coefficient transfer function with transmission zeros on the imaginary axis and presents a method to realize such a transfer function by a reactance network including imaginary resistors with double resistor termination. Using the obtained network and the reference network for the complex-wave digital filter, the complex digital filter with transmission zeros on the imaginary axis can easily be extended, which is important in practice. In this paper, Brune's method modified by Belevitch as well as Fujisawa's method extended by Morimoto et. al. are improved and the realizability condition is relaxed. Then, several construction examples are shown an the features of construction methods are compared and discussed. [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]

The paper presents a new method for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient linear heat conduction equation is first integrated with respect to time over subsequent intervals. Then the resulting set of elliptic equations is discretized in space according to a finite-element procedure. The method is unconditionally stable. At the end of the paper, the effectiveness of the proposed method is assessed through some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, a modified characteristics finite element method for the time dependent Navier-Stokes/Darcy problem with the Beavers-Joseph-Saffman interface condition is presented. In this method, the Navier-Stokes/Darcy equation is decoupled into two equations, one is the Navier-Stokes equation, the other is the Darcy equation, and the Navier-Stokes equation is solved by the modified characteristics finite element method. The theory analysis shows that this method has a good convergence property. In order to show the effect of our method, some numerical results was presented. The numerical results show that this method is highly efficient. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We show that if the sum of the resistances of an electrical network N is finite, then there is a unique electrical current in N, provided that we do not allow, in a sense made precise in the paper, any flow to escape to infinity. [ABSTRACT FROM PUBLISHER]

The paper investigates the inclusion intervals of matrix singular values. By employing the digraph of a matrix, some new inclusion intervals of matrix singular values are presented. These intervals are based mainly on the use of positive scale vectors and their intersections. Theoretic analysis and numerical examples show that these results improve and generalize some known results of Li et al. (Numer. Linear Algebra Appl. 2007; 14(2):115–128) and Kolotilina (J. Math. Sci. 2006; 137(3):4794–4800). Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The scaled total least-squares (STLS) method unifies the ordinary least-squares (OLS), the total least-squares (TLS), and the data least-squares (DLS) methods. In this paper we perform a backward perturbation analysis of the STLS problem. This also unifies the backward perturbation analyses of the OLS, TLS and DLS problems. We derive an expression for an extended minimal backward error of the STLS problem. This is an asymptotically tight lower bound on the true minimal backward error. If the given approximate solution is close enough to the true STLS solution (as is the goal in practice), then the extended minimal backward error is in fact the minimal backward error. Since the extended minimal backward error is expensive to compute directly, we present a lower bound on it as well as an asymptotic estimate for it, both of which can be computed or estimated more efficiently. Our numerical examples suggest that the lower bound gives good order of magnitude approximations, while the asymptotic estimate is an excellent estimate. We show how to use our results to easily obtain the corresponding results for the OLS and DLS problems in the literature. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The γ index is a tool that compares a dose distribution with a reference distribution by combining dose-difference and distance-to-agreement criteria. It has been widely used for ten years despite its high computational cost. This cost is due to both a search process for each reference point and the necessity to remove overestimations caused by the discrete nature of dose grids. The method proposed in this paper is much faster since it avoids both these problems. It consists in computing the δ envelope formed by the γ ellipsoids around the points of the reference distribution. This δ envelope provides dose-difference tolerances that are then used to create new indices, called the δ indices, that provide useful information to interpret the deviations. Applied to both 1D and 2D test cases and compared to the γ index, the δ indices proved to be very accurate and intuitive. Their computational efficiency was evaluated on a 3D case: the δ envelope can be computed in 8 s on a 250×250×50 grid. Moreover it can be precomputed if the reference dose is known in advance. Then the δ indices are obtained in less than 2 s. [ABSTRACT FROM AUTHOR]

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are TIMSS items (a linear inequality and an equation involving square roots). The other problem involves square roots. We found that the majority of student pairs used symbol manipulation when solving the problems, and while many students seemed to prefer symbolic over graphical and tabular representations in their first attempt at solving the problems, we found that it was common for student pairs to use more than one strategy throughout the course of their solving. Students `use of graphing calculators to solve the problems is discussed. [ABSTRACT FROM AUTHOR]

The method proposed by J.C. Houbolt in 1950 is one of the pioneering methods of time integration. Nevertheless, especially due to its multi-step fashion and not having a well-defined starting procedure, the method has not met considerable acceptance. The conversion of the Houbolt method to a one-step method is reported in the literature. However, the resulting method still lacks an appropriate starting procedure for all practical cases. In this paper, a parameter-less unified starting procedure is proposed for time integration with the Houbolt method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Algebraic multigrid (AMG) is a powerful linear solver with attractive parallel properties. A parallel AMG method depends on efficient, parallel implementations of the coarse-grid selection algorithms and the restriction and prolongation operator construction algorithms. In the effort to effectively and quickly select the coarse grid, a number of parallel coarsening algorithms have been developed. This paper examines the behaviour of these algorithms in depth by studying the results of several numerical experiments. In addition, new parallel coarse-grid selection algorithms are introduced and tested. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the radial integration method is applied to transform domain integrals into boundary integrals in a boundary element formulation for anisotropic plate bending problems. The inertial term is approximated with the use of radial basis functions, as in the dual reciprocity boundary element method. The transformation of domain integrals into boundary integrals is based on pure mathematical treatments. Numerical results are presented to verify the validity of this method for static and dynamic problems and a comparison with the dual reciprocity boundary element method is carried out. Although the proposed method is more time-consuming, it presents some advantages over the dual reciprocity boundary element method as accuracy and the absence of particular solutions in the formulation. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm combining the numerical execution in time of implicit and explicit methods of solution is presented in this paper. The algorithm swaps between both methods as required for the analysis. The whole mesh is solved for an unique method at once, i.e. there are no partitions of the mesh for separate implicit or explicit treatment of the solution. The combination is in-time, in such a manner that if the implicit method starts diverging the explicit one is initiated by appropriate conditions of transition. The formulation is presented first and its implementation is validated by the analysis of a key numerical example. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

It is known that there is a close relation between Prikry forcing and the iteration of ultrapowers: If U is a normal ultrafilter on a measurable cardinal κ and 〈Mn, jm,n | m ≤ n ≤ ω〉 is the iteration of ultrapowers of V by U, then the sequence of critical points 〈j0,n(κ) | n ∈ ω〉 is a Prikry generic sequence over Mω. In this paper we generalize this for normal precipitous filters. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A Markov property associates a set of conditional independencies to a graph. Two alternative Markov properties are available for chain graphs (CGs), the Lauritzen–Wermuth–Frydenberg (LWF) and the Andersson–Madigan– Perlman (AMP) Markov properties, which are different in general but coincide for the subclass ofCGs with no flags. Markov equivalence induces a partition of the class of CGs into equivalence classes and every equivalence class contains a, possibly empty, subclass of CGs with no flags itself containing a, possibly empty, subclass of directed acyclic graphs (DAGs). LWF-Markov equivalence classes of CGs can be naturally characterized by means of the so-calledlargest CGs, whereas a graphical characterization of equivalence classes of DAGs is provided by theessential graphs. In this paper, we show the existence of largest CGs with no flags that provide a natural characterization of equivalence classes of CGs of this kind, with respect to both the LWF- and the AMP-Markov properties. We propose a procedure for the construction of the largest CGs, the largest CGs with no flags and the essential graphs, thereby providing a unified approach to the problem. As by-products we obtain a characterization of graphs that are largest CGs with no flags and an alternative characterization of graphs which are largest CGs. Furthermore, a known characterization of the essential graphs is shown to be a special case of our more general framework. The three graphical characterizations have a common structure: they use two versions of a locally verifiable graphical rule. Moreover, in case of DAGs, an immediate comparison of three characterizing graphs is possible. [ABSTRACT FROM AUTHOR]

We consider strategies to construct optimal order two- and multilevel hierarchical preconditioners for linear systems as arising from the finite element discretization of self-adjoint second order elliptic problems using non-conforming Crouzeix–Raviart linear elements. In this paper we utilize the hierarchical decompositions, derived in a previous work by the same authors (Numerical Linear Algebra with Applications 2004; 11:309–326) and provide a further analysis of these decompositions in order to assure robustness with respect to anisotropy. Finally, we show how to construct both multiplicative and additive versions of the algebraic multilevel iteration preconditioners and show robustness and optimal order convergence estimates. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we propose a wavelet Taylor–Galerkin method for the numerical solution of time-dependent advection–diffusion problems. The discretization in time is performed before the spatial discretization by introducing second- and third-order accurate generalization of the standard time stepping schemes with the help of Taylor series expansions in time step. Numerical schemes taking advantage of the wavelet bases capabilities to compress both functions and operators are presented. Numerical examples demonstrate the efficiency of our approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There exists a set U in the plane, such that elements of U correspond to minimal stable solutions of a two-parameter elliptic system. For points on the boundary ϒ of U, there exist weak solutions to the elliptic system. The paper studies the properties of the curve ϒ. 2000 Mathematics Subject Classification 35J55, 35B05, 35K50, 35K55. [ABSTRACT FROM PUBLISHER]

The Yee-method is a simple and elegant way of solving the time-dependent Maxwell's equations. On the other hand, this method has some inherent drawbacks too. The main one is that its stability requires a very strict upper bound for the possible time-steps. This is why, during the last decade, the main goal was to construct such methods that are unconditionally stable. This means that the time-step can be chosen based only on accuracy instead of stability considerations. In this paper we give a uniform treatment of methods that use the same spatial staggered grid approximation as the classical Yee-method. Three other numerical methods are discussed: the Namiki–Zheng–Chen–Zhang alternating direction implicit method (NZCZ), the Kole–Figge-de Raedt method (KFR) and a Krylov-space method. All methods are discussed with non-homogeneous material parameters. We show how the existing finite difference numerical methods are based on the approximation of a matrix exponential. With this formulation we prove the unconditional stability of the NZCZ method without any computer algebraic tool. Moreover, we accelerate the Krylov-space method with a skew-symmetric formulation of the semi-discretized equations. Our main goal is to compare the methods from the point of view of the computational speed. This question is investigated in ID numerical tests. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we discuss some linear algebra issues concerning the implementation of blended implicit methods (J. Comput. Appl. Math. 2000; 116:41–62, Appl. Numer. Math. 2002; 42:29–45, J. Comput. Appl. Math. 2004; 164–165:145–158, In Recent Trends in Numerical Analysis, Trigiante D (ed.), Nova Science Publication Inc.: New York, 2001; 81–105) for the numerical solution of ODEs. In particular, we describe the strategies, used in the numerical code BiM (J. Comput. Appl. Math. 2004; 164–165:145–158), for deciding whether re-evaluating the Jacobian and/or the factorization involved in the non-linear splitting for solving the discrete problem. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, some identities in laws involving ladder processes for random walks and Lvy processes are extended and unified. [ABSTRACT FROM AUTHOR]

This paper describes and compares several effective methods for the numerical solution of one-dimensional Stefan problems. It is not intended to be an exhaustive review but is restricted to a range of problems and geometries including melting in the half-plane, outward cylindrical solidification and outward spherical solidification. From the limited comparison of numerical results obtained, some helpful comments can be made which may prove valuable in the future use of these methods. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper contains a final identification theorem for the ‘generic’ $K^*$-groups of finite Morley rank. [ABSTRACT FROM AUTHOR]

There are two versions of the Proper Iteration Lemma. The stronger (but less well-known) version can be used to give simpler proofs of iteration theorems (e.g., [7, Lemma 24] versus [9, Theorem IX.4.7]). In this paper we give another demonstration of the fecundity of the stronger version by giving a short proof of Shelah's theorem on the preservation of the ωω-bounding property. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this paper we define the polyadic Pavelka algebras as algebraic structures for Rational Pavelka predicate calculus (RPL∀). We prove two representation theorems which are the algebraic counterpart of the completness theorem for RPL∀. [ABSTRACT FROM AUTHOR]

In [4] the authors studied the residue field of a model M of IΔ0 + Ω1 for the principal ideal generated by a prime p. One of the main results is that M/ has a unique extension of each finite degree. In this paper we are interested in understanding the structure of any quotient field of M, i.e. we will study the quotient M/I for I a maximal ideal of M. We prove that any quotient field of M satisfies the property of having a unique extension of each finite degree. We will use some of Cherlin's ideas from [3], where he studies the ideal theory of non standard algebraic integers. [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]

This paper suggests a new method, called AINV-A, for constructing sparse approximate inverse preconditioners for positive-definite matrices, which can be regarded as a modification of the AINV method proposed by Benzi and Túma. Numerical results on SPD test matrices coming from different applications demonstrate the robustness of the AINV-A method and its superiority to the original AINV approach. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Some methods for synthesizing a protocol specification from a given service specification have been proposed using various computational models. However, the existing methods cannot treat service specifications including both complex control flows and system variables. In this paper, we propose a method for synthesizing a protocol specification automatically from a pair consisting of a service specification and a resource allocation. In our method, service specifications are described in an extended model of Petri nets, which can treat system variables. We have developed a pair consisting of a synthesis system and an execution system, and applied them to CSCW (Computer Supported Cooperative Work). © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(8): 18–26, 1998 [ABSTRACT FROM AUTHOR]

This paper continues the theoretical and numerical study of the so-called factorized sparse approximate inverse (FSAI) preconditionings of symmetric positive-definite matrices and considers two new approaches to improving them. The first one is based on the a posteriori sparsification of an already constructed FSAI preconditioner, whereas the second one amounts to applying another FSAI preconditioning to an already preconditioned matrix. Numerical results for sample FE problems from structural mechanics are presented. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper discusses error spectrum shaping for 2D state-space digital filters. In order to reduce cost by reducing the total number of parameters, a method of analytic design is proposed in which the error feedback coefficient is specified by a diagonal matrix. The proposed algorithm has the feature that the optimal error feedback coefficient can be designed analytically in closed form by minimizing a quadratic form. The validity of the proposed algorithm is demonstrated with a numerical example. The noise reduction effect where the subdecimal part of the optimal coefficient is rounded by the power of 2 is also demonstrated. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 79–90, 1998 [ABSTRACT FROM AUTHOR]

This paper proposes a method of realizing arbitrary complex coefficient transfer functions with complex double resistively terminated lossless filters as the reference network for complex wave digital filters (CWDFs). For this purpose, the Darlington synthesis method, which is known for realizing arbitrary real coefficient transfer functions, is expanded into the complex domain. Furthermore, a new construction method for a digital adapter without a delay-free loop is presented. Finally, a complex coefficient transfer function using some realization method is constructed and the validity of the proposed method is confirmed. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(2): 12–23, 1997 [ABSTRACT FROM AUTHOR]

This paper proposes the optimal design for the separable-denominator two-dimensional digital filter, using the genetic algorithm (GA). The design proposed is for the specification in the frequency domain. The simple GA, which is the most basic among GA, is used in the proposed optimal design. The parameters of the transfer function of the separable-denominator two-dimensional digital filter are encoded into bit sequences, and then GA is applied to design the filter. By the use of the separable-denominator transfer function, the stability of the filter is completely guaranteed. The approximation error of the proposed method is compared to that of the conventional method through design examples. The convergence of GA is discussed. It is shown that the proposed optimal design can easily cope with the modification of the design specification of the two-dimensional digital filter. It is shown also that the filter can be designer using the maximum error or the absolute error sum as the error evaluation function in addition to the mean-square error. [ABSTRACT FROM AUTHOR]

This paper considers the design of transmitter and receiver FIR digital filters with partial response of class II and V for data transmission, The filters are required to band-limit the transmitting and receiving signal, while maintaining the overall impulse response with zero intersymbol interference (ISI). Two cases are considered: 1) the case where the transmitter itself has the zero ISI impulse response; and 2) the case where the transmitter and receiver filters are matched. In the former, the length of the filter is set to be equal to the number of samples between two zero-cross points, which are at a certain symmetrical distance from the center of the ideal impulse response. Then a linear-phase transfer function is derived with an equiripple approximation to the ideal amplitude frequency response. In the approxiamtion, the weight in the stopband is set as less than 1, and ISI of less than 1 percent is obtained. In the design of the matched filter pair, the overall order is set in the same way as in the former. Applying the Herrman-Schuessler design method for the minimum phase-shift filter in the frequency domain, the transfer function is derived. To realize ISI of less than 1 percent, it suffices to set the weight in the stopband less than 5 times in the passband. Although an effort was made to decrease ISI by successive approximation with the mirror zeros as the parameters, only a slight improvement was obtained. In either case, class V requires approximately a twice higher order than class II to realize the same attenuation and ISI. [ABSTRACT FROM AUTHOR]

The paper presents a combined fine-coarse mesh TLM method. This technique reduces the memory storage and the computational time when modelling complex structures. In the combined fine-coarse mesh model, the region of interest is covered with a set of transmission-line fine meshes. The remaining part is covered with regular (or irregular) coarse meshes. The fine-mesh nodes are connected through busbars to the adjacent coarse-mesh nodes. The combined fine-coarse mesh TLM technique is applied to some diffusion problems. Significant savings in computational time and memory storage are obtained without loss of accuracy. [ABSTRACT FROM AUTHOR]

The boundary residual method is a powerful technique for solving EM boundary-value problems. This technique produces matrices difficult to solve using many of the standard numerical techniques. This paper discusses lesser-known numerical aspects of this method, and it shows efficient and well-conditioned methods to solve both the homogeneous' and non-homogeneous boundary residual problem. [ABSTRACT FROM AUTHOR]

Utilizing systematically differential geometry the paper describes a method which substantially improves results obtained by Yuan et al. (1994), though the same technique is used in both articles. An 8-node isoparametric element with curved boundaries is analysed as an object of differential geometry. Inverse transformations between normal (geodesic) co-ordinates and natural (isoparametric) co-ordinates are derived in terms of a Taylor series which is convergent and does not need many terms to give an excellent approximation of the element shape with four curved sides. The concept of local normal co-ordinates results in the definition of distortion measures of a plane element. It is shown, by exploring the theory of geodesic curves, that the distortion parameters of a chord quadrilateral, spanned on the corner nodes of the 8-node element with curved boundaries, are the basic distortion measures for this 8-node element. Thus, significant reduction of the number of these parameters, from 12 to 4, from previous works is obtained. For the purpose of the finite element method, which is very sensitive to a shape of quadrilateral elements, only basic deviation measures from a regular form of a plane element are of interest. The distortion measures due to curvatures of sides seem to be of secondary significance in the analysis if straight sides of the chord quadrilateral and curved boundaries are isomorphic. The mathematical analysis used is quite general and relies strongly on differential geometry. The results are independent of co-ordinate systems. The meaning of element distortion measures is suggested. This analysis can be extended to curved surfaces in R3. © 1998 John Wiley & Sons, Ltd. [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 the paper a mathematical formulation for embedding reinforcements in 3D brick concrete elements is presented. The computational aspects and the implementation process of the model have been discussed. The proposed algorithm may be implemented in 3D finite element programs for stress analysis of reinforced concrete structures. [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]

The paper presents a formulation and analysis of three and four step least squares algorithms for first order IVPs. The three step algorithm is derived using cubic Lagrangian interpolation, and is found to be third order accurate but only conditionally stable. Fourth order Lagrangian interpolation is used to obtain a four step least squares scheme which is Ao-stable but inconsistent. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of convection discretization by extension and application of numerical schemes used in compressible flows: SONIC-A, SONIC-B. UNO2, MUSCL and MINMOD to predict steady incompressible recirculating convection dominated flows. A new scheme, SONIC-Q, is proposed together with a third-order non-oscillatory practice for pressure interpolation in non-staggered grids. Finite-volume calculations of the Navier-Stokes equations of a standard 2D driven square cavity standard test case and the laminar flow over a fence using primitive variables and non-staggered grid systems have shown that the schemes are alternatives to the conventional ones used in general algorithms for incompressible re circulating flows. In general these composite high-order schemes have proved to be good candidates to overcome the problems of false-diffusion and unboundedness encountered in non-composite high-order upwind schemes used in incompressible flows. [ABSTRACT FROM AUTHOR]

In the paper a computation code based on the finite-element method for temperature evolutions in composite elements with internal cavities is presented. It is suitable for the analysis of various thermal problems encountered in mechanical and civil engineering such as fire risk assessment. It is based on a plane isoparametric triangular element with six nodes allowing the modeling of curved boundaries. In order to analyze composite steel-concrete elements and to take into account the non-linearities coming from the temperature-dependent material properties and from the boundary conditions, an implicit integration scheme is used. Another advantage of the program is the possibility of describing internal cavities with convection and radiation exchanges. In order to show the capacity of the program two examples are presented. Comparisons have been made with experimental and other numerical results, exhibiting very good agreement. [ABSTRACT FROM AUTHOR]

In this paper a new method has been presented to determine the optimum number of knots for cubic splines. The knot-finding process is based on the numerical integration of the input curve. The number and the location of the knots is determined automatically. The method has been applied to a test case and the performance has been compared with two other existing methods. It is shown that fewer knots are retained for the portions of the curve having small curvature whereas a larger number of knots is retained for highly curved portions. The computer time required by our method depends only upon the number of points in the input curve and does not depend upon the shape of the curve or the desired accuracy. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to answer some questions posed by Doob [2] in 1965 concerning the boundary cluster sets of harmonic and superharmonic functions on the half-space D given by D = Rn−1 × (0, + ∞), where n ≥ 2. Let f: D → [−∞, +∞] and let Z ∈ δD. Following Doob, we write BZ (respectively CZ) for the non-tangential (respectively minimal fine) cluster set of f at Z. Thus l ∈ BZ if and only if there is a sequence (Xm) of points in D which approaches Z non-tangentially and satisfies f(Xm) → l. Also, l ∈ CZ if and only if there is a subset E of D which is not minimally thin at Z with respect to D, and which satisfies f(X) → l as X → Z along E. (We refer to the book by Doob [3, 1.XII] for an account of the minimal fine topology. In particular, the latter equivalence may be found in [3, 1.XII.16].) If f is superharmonic on D, then (see [2, §6]) both sets BZ and CZ are subintervals of [−∞, +∞]. Let λ denote (n − 1)-dimensional measure on δD. The following results are due to Doob [2, Theorem 6.1 and p. 123]. 1991 Mathematics Subject Classification 31B25. [ABSTRACT FROM AUTHOR]