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In this paper, we propose a decentralized parallel computation model for global optimization using interval analysis. The model is adaptive to any number of processors and the workload is automatically and evenly distributed among all processors by alternative message passing. The problems received by each processor are processed based on their local dominance properties, which avoids unnecessary interval evaluations. Further, the problem is treated as a whole at the beginning of computation so that no initial decomposition scheme is required. Numerical experiments indicate that the model works well and is stable with different number of parallel processors, distributes the load evenly among the processors, and provides an impressive speedup, especially when the problem is time-consuming to solve. [ABSTRACT FROM AUTHOR]

A new evolving network based on the scale-free network of Barabási and Albert (BA) is studied, and the accelerated attachment of new edges is considered in its evolving process. The accelerated attachment is different from the previous accelerated growth of edges and has two particular meanings in this paper. One is that a new vertex with the edges is inserted into the network with acceleration at each time step; the other is that, with a given probability, some additional edges are linked with the vertices in proportion to the number of their obtained edges in the latest evolving periods. The new model describes the cases of those complex networks with a few exceptional vertices. The attachment mechanism of the new adding edges for these vertices does not follow the preferential attachment rule. Comparing with the linear edge growth model, the characteristics of the accelerated growth model are studied theoretically and numerically. We show that the degree distributions of these models have a power law decay and the exponents are larger than that of the BA model. We point out that the characteristics of the exceptional vertices and the aging vertices in an aging network are not identical. The reasons for neglecting this attachment in most of evolving networks are also summarized. [ABSTRACT FROM AUTHOR]

Families of matrices smoothly depending on a vector of parameters are considered. Arnold [Russian Math. Surveys, 26 (1971), pp. 29–43] and Galin [Uspekhi Mat. Nauk, 27 (1972),pp. 241–242] have found and listed normal forms of families of complex and real matrices (miniversal deformations), to which any family of matrices can be transformed in the vicinity of a point in the parameter space by a change of basis, smoothly dependent on a vector of parameters, and by a smooth change of parameters. In this paper a constructive method of determining functions describing a change of basis and a change of parameters, transforming an arbitrary family to the miniversal deformation, is suggested. Derivatives of these functions with respect to parameters are determined from a recurrent procedure using derivatives of the functions of lower orders and derivatives of the family of matrices. Then the functions are found as Taylor series. Examples are given. The suggested method allows using efficiently miniversal deformations for investigation of different properties of matrix families. This is shown in the paper where tangent cones (linear approximations) to the stability domain at the singular boundary points are found. [ABSTRACT FROM AUTHOR]

We develop a family of new interior penalty discontinuous Galerkin methods for the Keller-Segel chemotaxis model. This model is described by a system of two nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction-diffusion equation for the chemoattractant concentration. It has been recently shown that the convective part of this system is of a mixed hyperbolic-elliptic-type, which may cause severe instabilities when the studied system is solved by straightforward numerical methods. Therefore, the first step in the derivation of our new methods is made by introducing the new variable for the gradient of the chemoattractant concentration and by reformulating the original Keller-Segel model in the form of a convection-diffusionreaction system with a hyperbolic convective part. We then design interior penalty discontinuous Galerkin methods for the rewritten Keller-Segel system. Our methods employ the central-upwind numerical fluxes, originally developed in the context of finite-volume methods for hyperbolic systems of conservation laws. In this paper, we consider Cartesian grids and prove error estimates for the proposed high-order discontinuous Galerkin methods. Our proof is valid for pre-blow-up times since we assume boundedness of the exact solution. We also show that the blow-up time of the exact solution is bounded from above by the blow-up time of our numerical solution. In the numerical tests presented below, we demonstrate that the obtained numerical solutions have no negative values and are oscillation-free, even though no slope-limiting technique has been implemented. [ABSTRACT FROM AUTHOR]

Judy and Motta developed a customizable electrodeposition process for fabrication of very small metal structures on a substrate. In this process, layers of metal of various shapes are placed on the substrate, then the substrate is inserted in an electroplating solution. Some of the metal layers have power applied to them, while the rest of the metal layers are not connected to the power initially. Metal ions in the plating solution start depositing on the powered layers and a surface grows from the powered layers. As the surface grows, it will touch metal layers that were initially unpowered, causing them to become powered and to start growing with the rest of the surface. The metal layers on the substrate are known as seed layer patterns, and different seed layer patterns can produce different shapes. This paper presents a mathematical model, a forward simulation method, and an inverse problem solution for the growth of a surface from a seed layer pattern. The model describes the surface evolution as uniform growth in the direction normal to the surface. This growth is simulated in two and three dimensions using the level set method. The inverse problem is to design a seed layer pattern that produces a desired surface shape. Some surface shapes are not attainable by any seed layer pattern. For smooth attainable shapes, we present a computational method that solves this inverse problem. [ABSTRACT FROM AUTHOR]

Unique parametrizations of models are very important for parameter interpretation and consistency of estimators. In this paper we analyze the identifiability of a general class of finite mixtures of multinomial logits with varying and fixed effects, which includes the popular multinomial logit and conditional logit models. The application of the general identifiability conditions is demonstrated on several important special cases and relations to previously established results are discussed. The main results are illustrated with a simulation study using artificial data and a marketing dataset of brand choices. [ABSTRACT FROM AUTHOR]

In this paper, we study the solution of a certain non-smooth eigenvalue problem, using operator-splitting methods to solve an equivalent, constrained minimization problem. We present the Marchuk-Yanenko and Peaceman-Rachford schemes for solving the problem and compare their performance numerically on some model problems. The Peaceman-Rachford scheme turns out to be superior to the Marchuk-Yanenko scheme in terms of accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

A material model based on fiber–fiber Coulomb and viscous friction for connective tissue was introduced in references Mijailovic (1991) and Mijailovic et al. (1993). A numerical procedure was developed in reference Mijailovic (1991) by considering sliding of fibers as a contact problem between bodies, and results were verified by experiments. Another numerical approach, much more stable and efficient, for stress calculation in case of Coulomb friction only, was proposed in reference Kojic et al. (1998). This paper represents an extension of the numerical algorithm of reference Kojic et al. (1998) to include viscous friction between fibers. The complex history of sliding is traced by dividing the current sliding length between fibers on a number of segments. The computational procedure is simple, numerically reliable and provides stress calculation for arbitrary cyclic loading of connective tissue material in tension, shear, and tension and shear simultaneously. Typical hysteresis loops can be reproduced by using the proposed numerical algorithm. The model is implemented into a finite element program PAK (Kojic et al., 1996), with a possibility of solving real problems of connective tissue. Solved examples illustrate the main features of the fiber–fiber kinetics model and of the developed numerical procedure. [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]

Let WN = WN(z1,z2,…,zn) be a rectangular Vandermonde matrix of order n×N, N ≥ n, with distinct nodes zj in the unit disk and zjk-1 as its (j,k) entry. Matrices of this type often arise in frequency estimation and system identification problems. In this paper, the conditioning of WN is analyzed and bounds for the spectral condition numberk2(WN) are derived. The bounds depend on n, N, and the separation of the nodes. By analyzing the behavior of the bounds as functions of N, we conclude that these matrices may become well conditioned, provided the nodes are close to the unit circle but not extremely close to each other and provided the number of columns of WN is large enough. The asymptotic behavior of both the conditioning itself and the bounds is analyzed and the theoretical results arising from this analysis verified by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper we consider real or complex skew-Hamiltonian/Hamiltonian pencils λS - H, i.e., pencils where S is a skew-Hamiltonian and H is a Hamiltonian matrix. These pencils occur, for example, in the theory of continuous time, linear quadratic optimal control problems. We reduce these pencils to canonical and Schur-type forms under structure-preserving transformations, i.e., J-congruence-transformations (λS-H) → -JP*J(λS-H)P, where P is nonsingular or unitary. [ABSTRACT FROM AUTHOR]

In this paper we present three theorems which give insight into the regularizing properties of MINRES. While our theory does not completely characterize the regularizing behavior of the algorithm, it provides a partial explanation of the observed behavior of the method. Unlike traditional attempts to explain the regularizing properties of Krylov subspace methods, our approach focuses on convergence properties of the residual rather than on convergence analysis of the harmonic Ritz values. The import of our analysis is illustrated by two examples. In particular, our theoretical and numerical results support the following important observation: in some circumstances the dimension of the optimal Krylov subspace can be much smaller than the number of the components of the truncated spectral solution that must be computed to attain comparable accuracy. [ABSTRACT FROM AUTHOR]

The basic difference between what may be called curve fitting and what is here called mathematical modeling is that curve fitting is an ad hoc procedure while modeling focuses on the structure of relationships between variables, If one explains observations by curve fitting there is no reason to think that much more than a convenient summarization of data has occurred. Centroids or Gini coefficients for sets of data do not generally explain but summaries. However, coefficients and curves introduced to summaries data often do not remain as uninterpreted summary measures. Introductory material indicated that the paper was to deal with models that are both realistic enough to be of value in research and simple enough for parameters to be estimated. The authors believe that the models presented meet the realism criteria and believe little would be gained by debate on this in the paper. This indicates a need to examine the models to see what kinds of data are critical in distinguishing between the models and seeing that the considerations which could be said to be involved in designing a critical experiment are built into analysis or built into data collection so that there is discrimination between models where this is considered to be necessary or desirable.

This paper develops a new lower bound for single facility location problems with lp distances. We prove that the method produces superior results to other known procedures. The new bound is also computationally efficient. Numerical results are given for a range of examples with varying numbers of existing facilities and p values. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, properties of symmetric neighborhood assignments are discussed. We show that in some results of Balogh and Gruenhage, the family of spherical neighborhoods in a metric space can be generalized to a symmetric open neighborhood assignments in any topology space. By a simple example, we answer a question raised by Hung negatively. We also discuss two questions raised by Nagata about metrization and symmetric neighborhood assignments. By giving new characterizations of strongly paracompact metrizable spaces and orthocompact Moore spaces respectively, we show that answer of the first question is negative, while the second question is undecidable under ZFC. [Copyright &y& Elsevier]

We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this paper is to systematically study the qualitative properties of the solutions of the discrete nonlinear delay survival red blood cells model where , and are positive periodic sequences of period . First, by using the continuation theorem in coincidence degree theory, we prove that the equation has a positive periodic solution with strictly positive components. Second, we prove that the solutions are permanent and establish some sufficient conditions for oscillation of the positive solutions about . Finally, we give an estimation of the lower and upper bounds of the oscillatory solution and establish some sufficient conditions for global attractivity of . From applications point of view permanence guarantees the long term survival of mature cells, oscillation implies the prevalence of the mature cells around the periodic solution and the convergence implies the absence of any dynamical diseases in the population. Our results in the special case when the coefficients are positive constants involve and improve the oscillation and global attractivity results on the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the nonautonomous Lotka–Volterra system with dispersion. Under the assumption that the intrinsic growth rates of the species may be negative, we show that certain average conditions imply the uniform persistence of all species. Some known result is improved. [Copyright &y& Elsevier]

Objectives: This paper describes the development of a model-based approach to estimating both open-loop and causal time-varying coherence functions (TVCF). Theoretical derivations of the coherence bounds using the proposed approach are also provided.Methods: A time-varying vector autoregressive (VAR) model was used to estimate both open-loop and causal TVCF. The time-varying optimal parameter search method was employed to identify the time-varying model coefficients as well as the model order of the VAR model.Results: Simulation results revealed interesting observations, and they were corroborated using experimental renal blood pressure and flow data. Specifically, experimental data showed that in certain cases, the calculation of the open-loop TVCF might provide incorrect interpretation of the results when the system under investigation was a closed-loop system, which is consistent with theoretical derivations.Conclusions: The use of the closed-loop TVCF not only provides quantitative assessment of the coupling between the two signals, but it also provides valuable insights into the composition of the physical structure of the system. [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]

In this paper we examine how causality inference and forecasting within a bivariate VAR, consisting of y(t) and x(t), are affected by the omission of a third variable, w(t), which causes (a) none, (b) one, and (c) both variables in the bivariate system. We also derive conditions under which causality inference and forecasting are invariant to the selection of a bivariate or a trivariate model. The most general condition for the invariance of both causality and forecasting to model selection is shown to require the omitted variable not to cause any of the variables in the bivariate system, although it allows the omitted variable to be caused by the other two. We also show that the conditions for one-way causality inference to be invariant to model selection are not sufficient to ensure that forecasting will also be invariant to the model selected. Finally, we present a numerical illustration of the potential losses, in terms of the variance of the forecast, as a function of the forecast horizon and for alternative parameter values-they can be rather large, as the omission of a variable can make the incomplete model unstable. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of optimizing a function over a finite or countably infinite set of alternatives, in situations where this objective function cannot be evaluated exactly, but has to be estimated or measured. A special focus is on situations where simulation is used to evaluate the objective function. We present two versions of a new iterative method for solving such discrete stochastic optimization problems. In each iteration of the proposed method, a neighbor of the "current" alternative is selected, and estimates of the objective function evaluated at the current and neighboring alternatives are compared. The alternative that has a better observed function value becomes the next current alternative. We show how one version of the proposed method can be used to solve discrete optimization problems where the objective function is evaluated using transient or steady-state simulation, and we show how the other version can be applied to solve a special class of discrete stochastic optimization problems and present some numerical results. A major strength of the proposed method is that it spends most of the computational effort at local minimizers of the objective function. In fact, we show that for both versions of the proposed method, the alternative that has been visited most often in the first m iterations converges almost surely to a local optimizer of the objective function as m goes to infinity. [ABSTRACT FROM AUTHOR]

Background: Expressing anthropometric parameters (height, weight, BMI) as z-score is a key principle in the clinical assessment of children and adolescents. The Centre for Disease Control and Prevention (CDC) growth charts and the CDC-LMS method for z-score calculation are widely used to assess growth and nutritional status, though they can be imprecise in some percentiles. Objective: To improve the accuracy of z-score calculation by revising the statistical method using the original data used to develop current z-score calculators. Design: A Gaussian Process Regressions (GPR) was designed and internally validated. Z-scores for weight-for-age (WFA), height-for-age (HFA) and BMI-for-age (BMIFA) were compared with WHO and CDC-LMS methods in 1) standard z-score cut-off points, 2) simulated population of 3000 children and 3) real observations 212 children aged 2 to 18 yo. Results: GPR yielded more accurate calculation of z-scores for standard cut-off points (p<<0.001) with respect to CDC-LMS and WHO approaches. WFA, HFA and BMIFA z-score calculations based on the 3 different methods using simulated and real patients, showed a large variation irrespective of gender and age. Z-scores around 0 +/- 1 showed larger variation than the values above and below +/- 2. Conclusion: The revised z-score calculation method was more accurate than CDC-LMS and WHO methods for standard cut-off points. On simulated and real data, GPR based calculation provides more accurate z-score determinations, and thus, a better classification of patients below and above cut-off points. Statisticians and clinicians should consider the potential benefits of updating their calculation method for an accurate z-score determination. [ABSTRACT FROM AUTHOR]

This paper presents the results of a study on the resonant frequencies of a system of idle rollers and web spans. A simple linear model that describes the behavior of tension in a web span is considered. It is shown experimentally on a web platform that the simple model is capable of predicting resonant frequencies in an idler system consisting of idle rollers and spans between two driven rollers. This model is used to investigate the behavior of the minimum resonant frequency as a function of the number of idle rollers and span lengths. Analytical solutions for computing the minimum resonant frequency for the one-idler system (one idle roller and two spans) and the two-idler system (two idle rollers and three spans) are given. Discussions on how to maximize the minimum resonant frequency for two-, three-, and four-idler systems based on numerical analysis are also given. An analytical approximation of the minimum resonant frequency for equal span lengths and any number of idle rollers is derived. This approximation is a lower bound on the minimum resonant frequency and tends to converge to it, with the increase in the number of idle rollers. This is useful in getting a quick and reliable estimate of the minimum resonant frequency in festoons/accumulators which contain many idle rollers and web spans of equal lengths. The results of this study are expected to be useful to the web machine designer and developers of web tension control systems. [ABSTRACT FROM AUTHOR]

The article discusses the development of a mathematical model for the angular motion of large space structures (LSS) with gyroscopic drive for elastic oscillations' active compensation. It accounts the tones of elastic oscillations of the structure. It notes that the first mathematical models for LSS are created with the capability to control precision and orientation stabilization. It shows the forms of the measurement mathematical models for LSS angular coordinates. It also notes the application of estimates of parameters and coordinates in the formation of a controlling signal.

We show that under a suitable transversality condition, the intersection of two rational subtori in an algebraic torus (ℂ*)n is a finite group which can be determined using the torsion part of some associated lattice. We also give applications to the study of characteristic varieties of smooth complex algebraic varieties. As an example we discuss A. Suciu's line arrangement, the so-called deleted B3-arrangement. [ABSTRACT FROM AUTHOR]

A mixed spectral method is proposed and analyzed for the Stokes problem in a semi-infinite channel. The method is based on a generalized Galerkin approximation with Laguerre functions in the x direction and Legendre polynomials in the y direction. The well-posedness of this method is established by deriving a lower bound on the inf-sup constant. Numerical results indicate that the derived lower bound is sharp. Rigorous error analysis is also carried out. [ABSTRACT FROM AUTHOR]

A BDDC (balancing domain decomposition by constraints) method is developed for elliptic equations, with discontinuous coefficients, discretized by mortar finite element methods for geometrically nonconforming partitions in both two and three space dimensions. The coarse component of the preconditioner is defined in terms of one mortar constraint for each edge/face, which is the intersection of the boundaries of a pair of subdomains. A condition number bound of the form C maxi{(1 + log(Hi/hi))2} is established under certain assumptions on the geometrically nonconforming subdomain partition in the three-dimensional case. Here Hi and hi are the subdomain diameters and the mesh sizes, respectively. In the geometrically conforming case and the geometrically nonconforming cases in two dimensions, no assumptions on the subdomain partition are required. This BDDC preconditioner is also shown to be closely related to the Neumann-Dirichlet version of the FETI-DP algorithm. The results are illustrated by numerical experiments which confirm the theoretical results. [ABSTRACT FROM AUTHOR]

A Weighted multipoint interpolated discrete fourier transform (WMIpDFT) method for high accuracy frequency estimation of a multi-frequency signal component is presented. This method uses the maximum sidelobe decay windows. The relationships to estimate the frequency when an H-term maximum sidelobe decay window (H≥2) is used for (2J+1)-point interpolation (1≤J≤H+1) are given. The effectiveness of the method proposed was analysed by means of computer simulations for a multi-frequency signal without noise as well as with quantisation noise. [ABSTRACT FROM AUTHOR]

This article discusses a splitting extrapolation method for solving second-order parabolic equations with curved boundaries by using domain decomposition and d-quadratic isoparametric finite elements. This method possesses superconvergence, a high order of accuracy and a high degree of parallelism. First, we prove the multi-variable asymptotic expansion of fully discrete d-quadratic isoparametric finite element errors. Based on the expansion, we generate splitting extrapolation formulas. These formulas generate a numerical solution on a globally fine grid with higher accuracy by solving only a set of smaller discrete subproblems on different coarser grids. Therefore, a large-scale multidimensional problem with a curved boundary is turned into a set of smaller discrete subproblems on a polyhedron. Because these subproblems are independent of each other and have similar scales, our algorithm possesses a high degree of parallelism. In addition, this method is effective for solving discontinuous problems if we regard the interfaces of the problems as the interfaces of the initial domain decomposition. Our numerical results also show that the algorithm is effective for solving nonlinear parabolic equations. [ABSTRACT FROM AUTHOR]

Although Runge-Kutta and partitioned Runge-Kutta methods are known to formally satisfy discrete multisymplectic conservation laws when applied to multi-Hamiltonian PDEs, they do not always lead to well-defined numerical methods. We consider the case study of the nonlinear Schrödinger equation in detail, for which the previously known multisymplectic integrators are fully implicit and based on the (second order) box scheme, and construct well-defined, explicit integrators, of various orders, with local discrete multisymplectic conservation laws, based on partitioned Runge-Kutta methods. We also show that two popular explicit splitting methods are multisymplectic. [ABSTRACT FROM AUTHOR]

We propose a time-splitting spectral method for the generalized Gross-Pitaevskii equations, which describe the dynamics of spinor F=1 Bose-Einstein condensates at a very low temperature. The new numerical method is explicit, unconditionally stable, and of spectral accuracy in space. Moreover, it conserves the position densities at the discretized level. We apply the method for studying both the dynamic generation of vortices and vortex lattice dynamics for the spinor F=1 Bose-Einstein condensates held in an Ioffe-Pritchard magnetic field. [ABSTRACT FROM AUTHOR]

A mixed optimal model approximation is presented to obtain reduced-order models for truly fast descriptor systems. By a projection from truly fast descriptor systems to discrete-time systems, a mixed optimal model approximation for truly fast descriptor systems is transformed to a mixed optimal model approximation of the corresponding discrete-time systems. The structure of the fast descriptor systems is preserved in the model approximation procedure. The expression of the error and its gradient are given explicitly in terms of the solutions of certain Lyapunov equations. A numerical example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The modiclus, a relative of the prenucleolus, assigns a singleton to any cooperative TU game. We show that the modiclus selects a member of the core for any exact orthogonal game and for any assignment game that has a stable core. Moreover, by means of an example we show that there is an exact TU game with a stable core that does not contain the modiclus. [ABSTRACT FROM AUTHOR]

The binary space partition (BSP) technique is a simple and efficient method to adaptively partition an initial given domain to match the geometry of a given input function. As such, the BSP technique has been widely used by practitioners, but up until now no rigorous mathematical justification for it has been offered. Here we attempt to put the technique on sound mathematical foundations, and we offer an enhancement of the BSP algorithm in the spirit of what we are going to call geometric wavelets. This new approach to sparse geometric representation is based on recent developments in the theory of multivariate nonlinear piecewise polynomial approximation. We provide numerical examples of n-term geometric wavelet approximations of known test images and compare them with dyadic wavelet approximation. We also discuss applications to image denoising and compression. [ABSTRACT FROM AUTHOR]

A spatial modal logic (SML) is introduced as an extension of the modal logic S4 with the addition of certain spatial operators. A sound and complete Kripke semantics with a natural space (or location) interpretation is obtained for SML. The finite model property with respect to the semantics for SML and the cut-elimination theorem for a modified subsystem of SML are also presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Deformation behavior of soft-matrix two-phase alloys has been computed using a continuum mechanics model based on an Isostrain condition, while the stress is distributed by the rule of mixtures. A genetic algorithm (GA) was used to optimize the mechanical modeling parameters such as the resistance and the formability of each phase. The stress–strain curves have been calculated as a function of volume fraction and mechanical properties of phases. The calculated and experimental stress–strain curves are compared and good agreement is found. The resistances increases with the rise of the hard phase volume fraction; this is more important with the presence of the hard phase than with the soft one. A linear law of variation of the phase resistance allows to interpolate and extrapolate the model, a good agreement is found with the evolution of the mechanical behavior. [ABSTRACT FROM AUTHOR]

We present a semi-analytical approach for three-dimensional elastostatic normal contact problems with friction. The numerical approach to iteration on contact area and stick zone size is supported by an underlying analytical solution relating normal and tangential surface tractions to surface displacements in three coordinate directions. The governing equations are fully coupled. The analytical surface displacement solutions for a basic loading element have been derived elsewhere (Li and Berger 2001), and the total surface displacements are constructed as a superposition of deflections due to overlapping pyramid load segments. This approach requires no interpolation scheme for the field variables, which distinguishes it from other numerical techniques such as the FEM, BEM, and meshless methods. A background grid is defined only on the contact surfaces, and iteration approaches are used to determine a convergent configuration for contact domain and stick zone size. The approach is exercised on several normal contact problems, with and without friction, and the results compare favorably to existing analytical and numerical solutions. [ABSTRACT FROM AUTHOR]

The formulation of a nonlinear composite shell element is presented for the solution of stability problems of composite plates and shells. The formulation of the geometrical stiffness presented here is exactly defined on the midsurface and is efficient for analyzing stability problems of thin and thick laminated plates and shells by incorporating bending moment and transverse shear resultant forces. The composite element is free of both membrane and shear locking behaviour by using the assumed natural strain method such that the element performs very well as thin shells. The transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The proposed formulation is computationally efficient and the test results showed good agreement. In addition the effect of the viscoelastic material is investigated on the postbuckling behaviour of laminated composite shells. [ABSTRACT FROM AUTHOR]

Estimation of the frequency and spatial dependent boundary traction vector from measured vibration responses in a vibrating structure is addressed. This problem, also referred to as the inverse problem, may in some circumstances be ill-conditioned. Here a technique to overcome the ill-conditioning is proposed. A subset of a set of available eigenmodes is chosen such that the problem becomes well-conditioned enough. It is shown that the ill-conditioning originates from the fact that not all eigenmodes are orthogonal over the surface where the traction vector is sought. Consequently, by choosing a set of eigenmodes orthogonal over the surface of interest, the problem becomes well-conditioned. The calculated traction vector is shown to converge to the true one in the sense of a L2-norm on the boundary of the body. The proposed technique is verified, using numerical simulation of measured responses, with good agreement. [ABSTRACT FROM AUTHOR]

A method for finding the best approximation of a matrix A by a full rank Hankel matrix is given. The initial problem of best approximation of one matrix by another is transformed to a problem involving best approximation of a given vector by a second vector whose elements are constrained so that its inverse image is a Hankel matrix. The map from a matrix to a vector is the invertible map between a subspace represented as the row space of the matrix A and the Grassman vector representing that subspace. The relation between the principle angles associated with a pair of subspaces and the angle between the Grassman vectors associated with the subspaces is established. [ABSTRACT FROM AUTHOR]