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Abstract  In this paper we present an efficient numerical algorithm for solving linear and nonlinear boundary value problems with two-point boundary conditions of tenth-order. The differential transform method is applied to construct the numerical solutions. The proposed algorithm avoids the complexity provided by other numerical approaches. Several illustrative examples are given to demonstrate the effectiveness of the present algorithm. [ABSTRACT FROM AUTHOR]

Abstract??Several sets of reductions rules are known for preprocessing a graph when computing its treewidth. In this paper we give reduction rules for a weighted variant of treewidth, motivated by the analysis of algorithms for probabilistic networks. We present two general reduction rules that are safe for weighted treewidth. They generalise many of the existing reduction rules for treewidth. Experimental results show that these reduction rules can significantly reduce the problem size for several instances of real-life probabilistic networks. [ABSTRACT FROM AUTHOR]

This paper presents asymmetric agglomerative hierarchical clustering algorithms in an extensive view point. First, we develop a new updating formula for these algorithms, proposing a general framework to incorporate many algorithms. Next we propose measures to evaluate the fit of asymmetric clustering results to data. Then we demonstrate numerical examples with real data, using the new updating formula and the indices of fit. Discussing empirical findings, through the demonstrative examples, we show new insights into the asymmetric clustering. [ABSTRACT FROM AUTHOR]

This paper proposes a line search technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee the descent condition at each iteration of the Polak-Ribière-Polyak conjugate gradient algorithm. It is proved that this line search algorithm preserves the usual convergence properties of any descent algorithm. In particular, it is shown that the Zoutendijk condition holds under mild assumptions. It is also proved that the resulting conjugate gradient algorithm is convergent under a strong convexity assumption. For the nonconvex case, a globally convergent modification is proposed. Numerical tests are presented. [ABSTRACT FROM AUTHOR]

Abstract  This paper is devoted to multiresolution schemes that use a stencil selection procedure in order to obtain adaptation to the presence of edges in the images. Since non adapted schemes, based on a centered stencil, are less affected by the presence of texture, we propose the introduction of some weight that leads to a more frequent use of the centered stencil in regions without edges. In these regions the different stencils have similar weights and therefore the selection becomes an ill-posed problem with high risk of instabilities. In particular, numerical artifacts appear in the decompressed images. Our attention is centered in ENO schemes, but similar ideas can be developed for other multiresolution schemes. A nonlinear multiresolution scheme corresponding to a nonlinear interpolatory technique is analyzed. It is based on a modification of classical ENO schemes. As the original ENO stencil selection, our algorithm chooses the stencil within a region of smoothness of the interpolated function if the jump discontinuity is sufficiently big. The scheme is tested, allowing to compare its performances with other linear and nonlinear schemes. The algorithm gives results that are at least competitive in all the analyzed cases. The problems of the original ENO interpolation with the texture of real images seem solved in our numerical experiments. Our modified ENO multiresolution will lead to a reconstructed image free of numerical artifacts or blurred regions, obtaining similar results than WENO schemes. Similar ideas can be used in multiresolution schemes based in other stencil selection algorithms. [ABSTRACT FROM AUTHOR]

We report an examination algorithm of stability of molecular aggregates based on the estimation of rigidity of intermolecular contacts in a crystal structure. The algorithm includes the intermolecular interaction energy calculation (in the atom-atom potential approximation) of a pair of molecules selected in the crystal structure. Further, the energy is minimized using a least-squares technique by varying the position and orientation of one of the molecules. The contact rigidity is quantitatively assessed by the minimized rms difference between the positions of the atoms in the original and optimized structures (Zorkii’s criterion). Every rigid contact revealed in the structure determines finite or infinite stable agglomerates. The paper presents the results of testing the computer program based on this algorithm with a number of real crystal structures previously determined by single crystal X-ray diffraction, and also the examples of the most common stable molecular agglomerates found with the aid of the program. [ABSTRACT FROM AUTHOR]

The construction of the iteration procedure for synthesizing the law of control of observation over the processes, appeared one after another according to random flux regularities, is considered. The general approach to solution of the problem and the approximate algorithm for synthesizing the law of observations control are given for the case of a simple Poissonian flux. The example is presented in the paper. [ABSTRACT FROM AUTHOR]

In this paper we present a level set-based algorithm for the solution of incompressible two-phase flow problems. The technique is applied to the numerical simulation of impact of two surge fronts resulting from the collapse of liquid columns. The incompressible Navier-Stokes equations are solved using a projection method based on forward Euler time-stepping. The Hamilton-Jacobi type equation for the transport of level set function is carried out by a high resolution fifth-order accurate WENO scheme. For efficient implementation of the WENO scheme we have proposed grid staggering for the level set function. The solution of the pressure Poisson equation is obtained using an efficient preconditioned conjugate gradient method. It is shown that the present formulation works very well for large density and viscosity ratios. For the purpose of validation, we have simulated small-amplitude free sloshing of liquid in a container and the well-known two-dimensional broken-dam problem of Martin and Moyce. Simulations of impact of surge fronts have been carried out and the results are discussed. [ABSTRACT FROM AUTHOR]

This paper considers constrained and unconstrained parametric global optimization problems in a real Hilbert space. We assume that the gradient of the cost functional is Lipschitz continuous but not smooth. A suitable choice of parameters implies the linear or superlinear (supergeometric) convergence of the iterative method. From the numerical experiments, we conclude that our algorithm is faster than other existing algorithms for continuous but nonsmooth problems, when applied to unconstrained global optimization problems. However, because we solve 2n + 1 subproblems for a large number n of independent variables, our algorithm is somewhat slower than other algorithms, when applied to constrained global optimization. [ABSTRACT FROM AUTHOR]

A new method, to parallel the dominating computing work of structural dynamic response analysis, is presented in this paper. Then, based on “ShenWei I” supercomputer, MSC.NASTRAN and PATRAN, a parallel and integrated system is implemented. The system tightly couples advantages of the FEA code and high performance of the supercomputer. The system can improve the structural scale and velocity of dynamic response analysis greatly. Finally two examples are presented to demonstrate the validity and efficiency of the system. [ABSTRACT FROM AUTHOR]

There are many applications related to singly linearly constrained quadratic programs subjected to upper and lower bounds. In this paper, a new algorithm based on secant approximation is provided for the case in which the Hessian matrix is diagonal and positive definite. To deal with the general case where the Hessian is not diagonal, a new efficient projected gradient algorithm is proposed. The basic features of the projected gradient algorithm are: 1) a new formula is used for the stepsize; 2) a recently-established adaptive non-monotone line search is incorporated; and 3) the optimal stepsize is determined by quadratic interpolation if the non-monotone line search criterion fails to be satisfied. Numerical experiments on large-scale random test problems and some medium-scale quadratic programs arising in the training of Support Vector Machines demonstrate the usefulness of these algorithms. [ABSTRACT FROM AUTHOR]

This paper considers the regularized learning algorithm associated with the least-square loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and on the capacity of the reproducing kernel Hilbert space measured by covering numbers. When the kernel is C∞ and the regression function lies in the corresponding reproducing kernel Hilbert space, the rate is mζ with ζ arbitrarily close to 1, regardless of the variance of the bounded probability distribution. [ABSTRACT FROM AUTHOR]

In this paper, we reinvestigate the trust-region method by reformulating its subproblem: the trust-region radius is guided by gradient information at the current iteration and is self-adaptively adjusted. A trust-region algorithm based on the proposed subproblem is proved to be globally convergent. Moreover, the superlinear convergence of the new algorithm is shown without the condition that the Hessian of the objective function at the solution be positive definite. Preliminary numerical results indicate that the performance of the new method is notable. [ABSTRACT FROM AUTHOR]

This paper presents a novel solution to the illuminant estimation problem: the problem of how, given an image of a scene taken under an unknown illuminant, we can recover an estimate of that light. The work is founded on previous gamut mapping solutions to the problem which solve for a scene illuminant by determining the set of diagonal mappings which take image data captured under an unknown light to a gamut of reference colours taken under a known light. Unfortunately, a diagonal model is not always a valid model of illumination change and so previous approaches sometimes return a null solution. In addition, previous methods are difficult to implement. We address these problems by recasting the problem as one of illuminant classification: we define a priori a set of plausible lights thus ensuring that a scene illuminant estimate will always be found. A plausible light is represented by the gamut of colours observable under it and the illuminant in an image is classified by determining the plausible light whose gamut is most consistent with the image data. We show that this step (the main computational burden of the algorithm) can be performed simply and efficiently by means of a non-negative least-squares optimisation. We report results on a large set of real images which show that it provides excellent illuminant estimation, outperforming previous algorithms. [ABSTRACT FROM AUTHOR]

Within the framework of the finite element method, this paper presents new algorithms implementing implicit stress integration and consistent tangent matrix calculations for an elasto-plastic model with rotational hardening. The sub-stepping technique is used for both the numerical integration of the constitutive relations and determination of the consistent tangent matrix in order to overcome the convergence difficulty arising from the complexity of the elasto-plastic model with rotational hardening. The integration of the constitutive relations and the computation of the consistent tangent matrix are incorporated into a unique procedure. Numerical tests are carried out and discussed to demonstrate the global accuracy and stability of the presented algorithms. [ABSTRACT FROM AUTHOR]

The flat histogram Monte Carlo algorithms have been successfully used in many problems in scientific computing.However, there is no a rigorous theory for the convergence of the algorithms. In this paper, a modified flat histogram algorithm is presented and its convergence is studied. The convergence of the multicanonical algorithm and the Wang-Landau algorithm is argued based on their relations to the modified algorithm. The numerical results show the superiority of the modified algorithm to the multicanonical and Wang-Landau algorithms. [ABSTRACT FROM AUTHOR]

This paper deals with monotone finite difference iterative algorithms for solving nonlinear singularly perturbed reaction-diffusion problems of elliptic and parabolic types. Monotone domain decomposition algorithms based on a Schwarz alternating method and on box-domain decomposition are constructed. These monotone algorithms solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear discrete problems. The rate of convergence of the monotone domain decomposition algorithms are estimated. Numerical experiments are presented. [ABSTRACT FROM AUTHOR]

In this paper a new predictor-corrector noninterior method for LCP is presented, in which the predictor step is generated by the Levenberg-Marquadt method, which is new in the predictor-corrector type methods, and the corrector step is generated as in [3]. The method has the following merits: (i) any cluster point of the iteration sequence is a solution of the P0 LCP; (ii) if the generalized Jacobian is nonsingular at a solution point, then the whole sequence converges to the (unique) solution of the P0 LCP superlinearly; (iii) for the P0 LCP, if an accumulation point of the iteration sequence satisfies the strict complementary condition, then the whole sequence converges to this accumulation point superlinearly. Preliminary numerical experiments are reported to show the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

In this study, we investigate a method to detect damage in a laminated composite structure by analyzing its dynamic response to impact loads. The combined finite element method (FEM) with seven degrees of freedom (DOF) and the advanced microgenetic algorithm described in this paper may allow us not only to detect the damaged elements but also to find their locations and the extent of damage. A high order shear deformation theory (HSDT) is used to predict the structural behavior and to detect damage of laminated composite plates. The effects of noise associated with the uncertainty of measurements due to the complex nature of composites are considered for [0/90] s and [±45] s layup sequences. The results indicate that the new method is computationally efficient in characterizing damage for complex structures such as laminated composites. [ABSTRACT FROM AUTHOR]

Very recently we have proposed to use a complex Ginzburg-Landau equation for high contrast inpainting, to restore higher dimensional (volumetric) data (which has applications in frame interpolation), improving sparsely sampled data and to fill in fragmentary surfaces. In this paper we review digital inpainting algorithms and compare their performance with a Ginzburg-Landau inpainting model. For the solution of the Ginzburg-Landau equation we compare the performance of several numerical algorithms. A stability and convergence analysis is given and the consequences for applications to digital inpainting are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with the real-time NURBS interpolation method in which the interpolation error between the ideal curve and the interpolated curve is compensated within the machine basic length unit (BLU). Parametric curve interpolation methods are based on the Taylor series expansion of curve parameters and an approximation. This approach enables effective feed command generation following the target curve. However, the interpolation error caused by the curve segmentation cannot be controlled. In this research, a two-stage interpolation method that compensates for interpolation errors within machine BLU is proposed. The interpolation result was filtered by an acceleration/jerk limitation equation. Through this two-stage interpolation, both the interpolation error condition and the motion dynamics can be satisfied. Using computer simulations in which interpolation results are revaluated by a numerical iteration method, it is shown that the two-stage interpolation algorithm can interpolate target curves precisely with geometric and dynamic contentment. The proposed algorithm was implemented in the CNC simulator system and an experimental run was conducted to identify the real-time adaptation. [ABSTRACT FROM AUTHOR]

The Kantorovich Theorem is a fundamental tool in nonlinear analysis which has been extensively used in classical numerical analysis. In this paper we show that it can also be used in analyzing interior point methods. We obtain optimal bounds for Newton’s method when relied upon in a path following algorithm for linear complementarity problems.Given a pointzthat approximates a pointz(t) on the central path with complementarity gapt, a parameter?? (0,1) is determined for which the pointzsatisfies the hypothesis of the affine invariant form of the Kantorovich Theorem, with regards to the equation definingz((1-?)t). The resulting iterative algorithm produces a point with complementarity gap less thanein at mostNewton steps, or simplified Newton steps, wheree0 is the complementarity gap of the starting point andnis the dimension of the problem. Thus we recover the best complexity results known to date and, in addition, we obtain the best bounds for Newton’s method in this context. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm to identify the occurrence of impact (contact) among structures. Structures are modeled here by finite elements and the resulting formulation is employed to solve two-dimensional frame impact problems by the Lagrange Multiplier technique. The proposed algorithm is based on potential theory, largely employed in various fields of physics. The potential theory is used together with integral equations making possible to compare relative positions among nodes of different structures involved in a collision process. The present technique may be used to model the contact prevision among two or three-dimensional structures or between structures and rigid obstacles. In order to show the applicability of the proposed technique, numerical answers for 2D problems are compared with both analytical solutions and numerical results given by other authors. [ABSTRACT FROM AUTHOR]

This paper presents a nonlinear implicit transient formulation for parallel contact analysis. A new ‘lumping’ algorithm based on the penalty method is developed to enforce contact constraints. This algorithm has the effect of incorporating contact generated connectivity and eliminating ill conditioning in the system stiffness matrix caused by the use of a large penalty parameter. Communication schemes are also developed to facilitate contact searching and enforcement in a parallel environment. Numerical analyses were conducted to verify the accuracy of the proposed algorithm. In addition, several contact simulations are also performed to study the performance of this new algorithm under different circumstances. Efficiency plots are also presented for one of the simulations to evaluate the performance of this parallel implicit contact formulation. [ABSTRACT FROM AUTHOR]

A central component of the analysis of panel clustering techniques for the approximation of integral operators is the so-called η admissibility condition "min{diam(τ), diam(σ)} ≤ 2ηdist(τ σ)" that ensures that the kernel function is proximated only on those parts of the domain that are far from the singularity. Typical techniques based on a Taylor expansion of the kernel function require a subdomain to be "far enough" from the singularity such that the parameter η has to be smaller than a given constant depending on properties of the kernel function. In this paper, we demonstrate that any η is sufficient if interpolation instead of Taylor expansion is used for the kernel approximation, which paves the way for grey-box panel clustering algorithms. [ABSTRACT FROM AUTHOR]

In this paper we develop techniques for computing elementwise conservative approximations of the flux on element boundaries for the continuous Galerkin method. The technique is based on computing a correction of the average normal flux on an edge or face. The correction is a jump in a piecewise constant or linear function. We derive a basic algorithm which is based on solving a global system of equations and a parallel algorithm based on solving local problems on stars. The methods work on meshes with different element types and hanging nodes. We prove existence, uniqueness, and optimal order error estimates. Lastly, we illustrate our results by a few numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a real-time control algorithm based on Taylor’s expansion for implementing variable feed rate non-uniform rational B-spline (NURBS) curve interpolators using a digital signal processor for precision CNC machining. To efficiently compute the NURBS curve and its derivatives in real-time, an effective method is proposed. The variable feed rate NURBS curve interpolator can be used to realise the ACC/DEC before feed rate interpolation in which the ACC/DEC (acceleration/deceleration) planning on the feed rate command executes before the interpolation takes place, so that the path command errors caused by conventional ACC/DEC planning using the post feed rate interpolation can be effectively eliminated. To demonstrate the performance of the proposed algorithm, an X-Y table driven by two servomotors is controlled to track command paths represented by multiple blocks of NURBS curves. Experimental results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we focus on the problem of identifying the index sets P(x):={i|x[sub i]>0}, N(x):={i|F[sub i](x)>0} and C(x):={i|x[sub i]=F[sub i](x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution. [ABSTRACT FROM AUTHOR]

Let G be a finite group. Let p(G) denote the minimal degree of a faithful permutation representation of G and let q(G) and c(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers, respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. The purpose of this paper is to calculate p(G), q(G), c(G) and r(G) for the group SP(4,q). [ABSTRACT FROM AUTHOR]

This paper presents a numerical study onfree-surface flow in curved open channel. An improved SIMPLEC algorithm with velocity-pressure-free-surface coupled correction is developed and validated. Such algorithm differs from the traditional SIMPLEC algorithm and includes three correction equations which are named as the velocity correction equation, the free-surface correction equation derived from the continuity equation with the kinematic boundary conditions on the free-surface and the bottom bed, and the pressure correction equation taking the same formulation as the traditional SIMPLEC algorithm does. In this study, the improved method is used to solve the incompressible, three-dimensional, Reynolds-averaged Navier–Stokes equation set combined with the standard k–ℇ model and/or the low Reynolds number k–ℇ model for free-surface viscous flow in curved open channels. The power law scheme (POW) is used to discretize the convection terms in these equations with a finite-volume method. The practical cases studied are free-surface flow through the 180° curved open channel with different hydraulic discharge rates. The comparisons between computations and experiments reveal that the model is capable of predicting the detailed velocity field, including changes in secondary motion, the distribution of bed shear, and the variations of flow depth in both the transverse and the longitudinal directions. In summary, the improved SIMPLEC algorithm is feasible and effective for numerical study of free-surface viscous flows in curved open channels. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of one-dimensional and multidimensional traveling wave solutions for general chemotaxis or so-called Keller-Segel models without reproduction of the chemotactic species. We present a constructive approach to give modelers a choice of chemotactic sensitivity functionals, production, and degradation terms for the chemical signal at hand. The main aim is to understand the type of functionals and the interplay between them that are needed for the traveling wave and pulse patterns to occur. [ABSTRACT FROM AUTHOR]

In this paper we study the number Mm;n of ways to place nonattacking pawns on an m x n chessboard. We find an upper bound for Mm;n and consider a lower bound for Mm;n by reducing this problem to that of tiling an (m+1)x(n+1) board with square tiles of size 1x1 and 2x2. Also, we use the transfer-matrix method to implement an algorithm that allows us to get an explicit formula for Mm;n for given m. Moreover, we show that the double limit υ := limm;n→ ∞ (Mm;n) 1/mn exists and 2.25915263 ≤ n ≤ 2.26055675. Also, the true value of n is around 2.2591535382327... [ABSTRACT FROM AUTHOR]

This paper describes a numerical procedure for solving two-dimensional elastostatics problems with multiple circular holes and elastic inclusions in a finite domain with a circular boundary. The inclusions may have arbitrary elastic properties, different from those of the matrix, and the holes may be traction free or loaded with uniform normal pressure. The loading can be applied on all or part of the finite external boundary. Complex potentials are expressed in the form of integrals of the tractions and displacements on the boundaries. The unknown boundary tractions and displacements are approximated by truncated complex Fourier series. A linear algebraic system is obtained by using Taylor series expansion without boundary discretization. The matrix of the linear system has diagonal submatrices on its diagonal, which allows the system to be effectively solved by using a block Gauss-Seidel iterative algorithm. [ABSTRACT FROM AUTHOR]

In the present paper a natural extension of the Cholesky factorization, adapted to the peculiar matrix-structure of the solving system of Symmetric Galerkin Boundary Element Methods is presented. The implementation is described in some detail and preliminary timing figures are given, showing that the proposed approach is considerably faster than the Bunch-Kaufman factorization for non-definite matrices. Thread-based parallelism is exploited to show the scalability of the algorithm on moderately parallel shared memory multiprocessors. [ABSTRACT FROM AUTHOR]

Discrete element methods are emerging as useful numerical analysis tools for engineers concerned with granular materials such as soil, food grains, or pharmaceutical powders. Obviously, the first step in a discrete element simulation is the generation of the geometry of the system of interest. The system geometry is defined by the boundary conditions as well as the shape characteristics (including size) and initial coordinates of the particles in the system. While a variety of specimen generation methods for particulate materials have been developed, there is no uniform agreement on the optimum specimen generation approach. This paper proposes a new triangulation based approach that can easily be implemented in two or three dimensions. The concept of this approach (in two dimensions) is to triangulate a system of points within the domain of interest, creating a mesh of triangles. Then the particles are inserted as the incircles of these triangles. Extension to three dimensions using a mesh of tetrahedra and inserting the inspheres is relatively trivial. The major advantages of this approach include the relative simplicity of the algorithm and the small computational cost associated with the preparation of an initial particle assembly. The sensitivity of the characteristics of the particulate material that is generated to the topology of the triangular mesh used is explored. The approach is compared with other currently used methods in both two and three dimensions. These comparisons indicate that while this approach can successfully generate relatively dense two-dimensional particle assemblies, the three- dimensional implementation is less effective at generating dense systems than other available approaches. [ABSTRACT FROM AUTHOR]

For the problem of minimizing the sum of Euclidean norms (MSN), most existing quadratically convergent algorithms require a strict complementarity assumption. However, this assumption is not satisfied for a number of MSN problems. In this paper, we present a globally and quadratically convergent algorithm for the MSN problem. In particular, the quadratic convergence result is obtained without assuming strict complementarity. Examples without strictly complementary solutions are given to show that our algorithm can indeed achieve quadratic convergence. Preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

Macroscopic simulations of non-convex minimisation problems with enforced microstructures encounter oscillations on finest length scales-too fine to be fully resolved. The numerical analysis must rely on an essentially equivalent relaxed mathematical model. The paper addresses a prototype example, the scalar 2-well minimisation problem and its convexification and introduces a benchmark problem with a known (generalised)solution. For this benchmark, the stress error is studied empirically to asses the performance of adaptive finite element methods for the relaxed and the original minimisation problem. Despite the theoretical reliability-efficiency gap for the relaxed problem, numerical evidence supports that adaptive mesh-refining algorithms generate efficient triangulations and improve the experimental convergence rates optimally. Moreover, the averaging error estimators perform surprisingly accurate. [ABSTRACT FROM AUTHOR]

In this paper, we study the potential of adaptive sparse grids for multivariate numerical quadrature in the moderate or high dimensional case, i.e. for a number of dimensions beyond three and up to several hundreds. There, conventional methods typically suffer from the curse of dimension or are unsatisfactory with respect to accuracy. Our sparse grid approach, based upon a direct higher order discretization on the sparse grid, overcomes this dilemma to some extent, and introduces additional flexibility with respect to both the order of the 1 D quadrature rule applied (in the sense of Smolyak's tensor product decomposition) and the placement of grid points. The presented algorithm is applied to some test problems and compared with other existing methods. [ABSTRACT FROM AUTHOR]

This paper presents the procedure of a computational scheme leading to approximate general solution of the axi-symmetric, 2-degrees of freedom dynamical systems. Also the results of application of this scheme in two such systems of the non-linear double oscillator with third and fifth order potentials in position variables. Their approximate general solution is constructed by computing a dense set of families of periodic solutions and their presentation is made through plots of initial conditions. The accuracy of the approximate general solution is defined by two error parameters, one giving a measure of the accuracy of the integration and calculation of periodic solutions procedure, and the second the density in the initial conditions space of the periodic solutions calculated. Due to the need to compute families of periodic solutions of large periods the numerical integrations were carried out using the eighth order, variable step, R-K algorithm, which secured for almost all results presented here conservation of the energy constant between 10-9 and 10-12 for single runs of any and all solutions. The accuracy of the approximate general solution is controlled by increasing the number of family curves and also by `zooming' into parts of the space of initial conditions. All families of periodic solutions were checked for their stability. The computation of such families within areas of `deterministic chaos' did not encounter any difficulty other than poorer precision. Furthermore, on the basis of the stability study of the computed families, the boundaries of areas of `order' and `chaos' were approximately defined. On the basis of these results it is concluded that investigations in the Poincaré sections have to disclose 3 distinct types of areas of `order' and 2 distinct types of areas of `chaos'. Verification of the `order'/`chaos' boundary calculation was made by working out several Poincaré surfaces of sections. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of piston-driven heat transfer and fluid flow in a plane channel containing a sudden expansion. The numerical method employed is based on a control-volume-based finite element method for incompressible flow with a staggered and moving grid and SIMPLER algorithm for pressure-velocity coupling. The numerical results show a good agreement with the experimental data reported in the literature. Results concerning time and space evolution of the thermal and flow fields are presented for different values of the expansion ratio, the initial clearance volume, and the piston velocity. [ABSTRACT FROM AUTHOR]

This paper describes the first algorithm for computing the inverse chirp z-transform (ICZT) in O(n log n) time. This matches the computational complexity of the chirp z-transform (CZT) algorithm that was discovered 50 years ago. Despite multiple previous attempts, an efficient ICZT algorithm remained elusive until now. Because the ICZT can be viewed as a generalization of the inverse fast Fourier transform (IFFT) off the unit circle in the complex plane, it has numerous practical applications in a wide variety of disciplines. This generalization enables exponentially growing or exponentially decaying frequency components, which cannot be done with the IFFT. The ICZT algorithm was derived using the properties of structured matrices and its numerical accuracy was evaluated using automated tests. A modification of the CZT algorithm, which improves its numerical stability for a subset of the parameter space, is also described and evaluated. [ABSTRACT FROM AUTHOR]

In this paper, we consider an efficient numerical algorithm for solving the two-dimensional fractional cable equation. The stability and convergency of the numerical scheme are rigorously proved by the Fourier analysis. Then we find that the convergence order is O(τ2+hx4+hy4). Finally, numerical experiments are carried out to verify the accuracy and effectiveness of the new scheme. [ABSTRACT FROM AUTHOR]

Network-based similarity measures have found wide applications in recommendation algorithms and made significant contributions for uncovering users’ potential interests. However, existing measures are generally biased in terms of popularity, that the popular objects tend to have more common neighbours with others and thus are considered more similar to others. Such popularity bias of similarity quantification will result in the biased recommendations, with either poor accuracy or poor diversity. Based on the bipartite network modelling of the user-object interactions, this paper firstly calculates the expected number of common neighbours of two objects with given popularities in random networks. A Balanced Common Neighbour similarity index is accordingly developed by removing the random-driven common neighbours, estimated as the expected number, from the total number. Recommendation experiments in three data sets show that balancing the popularity bias in a certain degree can significantly improve the recommendations’ accuracy and diversity simultaneously. [ABSTRACT FROM AUTHOR]