Search

Many planning problems for robots are of considerable interest. In this paper, we consider the discrete minimum constraint removal motion planning problem that can be used for a motion planning formulation with explanations for failure. We consider an efficient approach to solve the problem. In particular, we consider an explicit reduction from the decision version of the problem to the satisfiability problem. We present the results of computational experiments for different satisfiability algorithms. [ABSTRACT FROM AUTHOR]

The conjugate gradient (CG) and Davidon, Fletcher and Powell (DFP) method are both well known solvers for solving unconstrained optimization problems. In this paper, we proposed a new hybrid DFP-CG method and compared with the ordinary DFP method in terms of number of iteration and CPU times. Numerical results show that the new algorithm is more efficient compared to the ordinary DFP method and proven to posses both sufficient descent and global convergence properties. [ABSTRACT FROM AUTHOR]

The paper introduces a bio-inspired approach to solve the route allocation problem (RAP) in the transportation networks. The approach extends a well-known meta-heuristics algorithm with the real life constraints that are dealt with in the scheduling process (i.e. the uniform distribution of routes diversity for vehicles, the average distance travelled in a month, the driver’s rest between subsequent trips etc.). The paper is focusing on the engineering aspects of employing bio-inspired algorithms (which proved to have near-optimal results for toy-like problems) to a real-life application domain. The approach proved to be capable of preserving the software components (agents) to the complexity and dynamics of the situation when the RAP requires incremental extensions of constraints to reflect the traffic conditions in the transportation network. [ABSTRACT FROM AUTHOR]

In this paper the dynamic performances of the Perturb and Observe and Incremental Conductance algorithms, which are commonly used to track the maximum power point of photovoltaic power plants, are analyzed according to the procedure provided in the European Standard EN 50530. The analysis was performed by simulation in MATLAB/SIMULINK for a grid-connected photovoltaic system. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce the algorithm of context recognition in the functional programming language TIL-Script, which is a necessary condition for the implementation of the TIL-Script inference machine. The TIL-Script language is an operationally isomorphic syntactic variant of Tichý's Transparent Intensional Logic (TIL). From the formal point of view, TIL is a hyperintensional, partial, typed λ-calculus with procedural semantics. Hyperintensional, because TIL λ-terms denote procedures (defined as TIL constructions) producing set-theoretic functions rather than the functions themselves; partial, because TIL is a logic of partial functions; and typed, because all the entities of TIL ontology, including constructions, receive a type within a ramified hierarchy of types. These features make it possible to distinguish three levels of abstraction at which TIL constructions operate. At the highest hyperintensional level the object to operate on is a construction (though a higher-order construction is needed to present this lower-order construction as an object of predication). At the middle intensional level the object to operate on is the function presented, or constructed, by a construction, while at the lowest extensional level the object to operate on is the value (if any) of the presented function. Thus a necessary condition for the development of an inference machine for the TIL-Script language is recognizing a context in which a construction occurs, namely extensional, intensional and hyperintensional context, in order to determine the type of an argument at which a given inference rule can be properly applied. As a result, our logic does not flout logical rules of extensional logic, which makes it possible to develop a hyperintensional inference machine for the TIL-Script language. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new global optimization algorithm for non-smooth unconstrained optimization problems. We construct a new global optimization (GO) method based on the function new smoothing technique. We give some numerical examples in order to demonstrate the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a derivative-free nonmonotone hybrid tabu search to compute a solution of overdetermined systems of inequalities and equalities through the global optimization of an appropriate merit function. The proposed algorithm combines global and local searches aiming to reduce computational effort. Preliminary numerical results show the effectiveness of the combined heuristic. [ABSTRACT FROM AUTHOR]

In this paper we present an algorithm to construct self-dual codes over Zpm. To show the powerful of our algorithm, we obtained several new self-dual MDS, near-MDS, MDR, near-MDR codes over Zpm partly by using generator matrices presented by Lee and Lee (2008) as inputs. [ABSTRACT FROM AUTHOR]

The purpose of the present paper was to report the recent results, obtained in development of digital pulse processing mathematics for prompt fission neutron (PFN) investigation using twin ionization chamber (TIC) along with fast neutron time-of-flight detector (ND). Due to well known ambiguities in literature (see refs. [4, 6, 9 and 11]), concerning a pulse induction on TIC electrodes by FF ionization, we first presented detailed mathematical analysis of fission fragment (FF) signal formation on TIC anode. The analysis was done using Ramo-Shockley theorem, which gives relation between charged particle motion between TIC electrodes and so called weighting potential. Weighting potential was calculated by direct numerical solution of Laplace equation (neglecting space charge) for the TIC geometry and ionization, caused by FF. Formulae for grid inefficiency (GI) correction and digital pulse processing algorithms for PFN time-of-flight measurements and pulse shape analysis are presented and discussed. [ABSTRACT FROM AUTHOR]

A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented. [ABSTRACT FROM AUTHOR]

Let T be the recurrence equation in N associated to a given algorithm. If we denote by f the complexity function which is the solution of such a recurrence equation, then f constitutes a total mapping defined recursively that is, at the same time, the limit of a sequence (fn)n of partial mappings also defined recursively. In this paper we present a model to compute the complexity represented by f by means of the values that take a certain relativized norm on the sequence (fn)n and its initial segments. This is done with the help of a suitable space of semi-Lipschitz functions which is constructed here. [ABSTRACT FROM AUTHOR]

Constitutive models for the crystal plasticity have the common objective which relates the behavior of microscopic single crystals in the crystallographic texture to the macroscopic continuum response. This paper presents the texture analysis of polycrystalline materials using the rate-dependent single crystal plasticity to develop a multi-scale description of the mechanism at the grain and aggregate levels. The texture analysis requires a numerical algorithm for integrating the constitutive equations. The implicit deformation gradient approach is employed to update the stresses and texture orientations as an integration algorithm. It considers elastic or plastic deformation gradient as the primary unknown variables and constructs the residual of the elastic and plastic velocity gradients as the governing equations. This algorithm is shown to be an efficient and robust algorithm in rather large time steps. The texture analysis of the asymmetric rolling process is also presented to show investigation of the effect of texture evolution based on the finite element analysis as a numerical example. The analysis result for texture evolution is investigated by comparing the pole figure before and after the asymmetric rolling process. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper is a presentation of how to implement quantum algorithms (namely, Shor’s algorithm ) on a classical computer by using the well-known Mathematica package. It will give us a lucid connection between mathematical formulation of quantum mechanics and computational methods. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Problems of swarm robotics are extensively studied in contemporary robotics. In this paper, we consider the problem of robot swarms control with only global signals. We propose an efficient approach to solve the problem. In particular, we consider an explicit reduction from the decision version of the problem to the satisfiability problem. For different satisfiability algorithms, we present the results of computational experiments. [ABSTRACT FROM AUTHOR]

This paper presents a gradient-related algorithm for solving large scale, spatially explicit, welfare models with transportation. It introduces the theory, describes the different components of the algorithm, and reports on experience gained in applying it. [ABSTRACT FROM AUTHOR]

We investigate in this paper the recovery of the local volatility surface in a parametric framework similar to that of Coleman, Li and Verma [1]. The quality of a surface is assessed through a functional which is optimized; the specificity of the approach is to separate the optimization on the parametric space (performed with any suitable optimization algorithm) from the computation of the functional where we use an adjoint formulation similar to that of the optimal control; the procedure can thus incorporate information from any derivative contract compatible with the adjoint approach. The procedure was implemented and was shown to perform satisfactory on real-world data. [ABSTRACT FROM AUTHOR]

This short paper is concerned with a new algorithm for collision and distance calculation between CSG octrees, a generalization of an octree model created from a Constructive Solid Geometry (CSG) object. The data structure uses interval arithmetic and allows us to extend the tests for classifying points in space as inside, on the boundary, or outside a CSG object to entire sections of the space at once. Tree nodes with additional information about relevant parts of the CSG object are introduced in order to reduce the depth of the required subdivision. The new data structure reduces the input complexity and enables us to reconstruct the CSG object. We present an efficient algorithm for computing the distance between CSG objects encoded by the new data structure. The distance algorithm is based on a distance algorithm for classical octrees but, additionally, it utilizes an elaborated sort sequence and differentiated handling of pairs of octree nodes to enhance its efficiency. Experimental results indicate that, in comparison to common octrees, the new representation has advantages in the field of proximity query. [ABSTRACT FROM AUTHOR]

An algorithm for the construction of hash function based on optical time averaging techniques is proposed in this paper. Algebraic structures of grayscale color functions and time average operators are constructed. Properties of time average operators and effects of digital image representation are explored. The fact that the inverse problem of identification of the original grayscale color function from its time averaged image is an ill-posed problem helps to construct an efficient algorithm for the construction of a new class of one-way collision free hash functions. The algorithm can be generalized to 2D or even 3D problem. [ABSTRACT FROM AUTHOR]

Recently the author has presented a non-standard algorithm of second-order for numerically solving initial-value problems [1]. This algorithm performs well for different kinds of problems such as singular or singularly perturbed problems. Now, in this paper an improved method of third order is proposed for solving autonomous problems of special type. To test the efficiency of the new method a well-known numerical example is provided. [ABSTRACT FROM AUTHOR]

Methodology and aggregated algorithm of problem-oriented systems engineering are under consideration in the paper. The algorithm was implemented in bundled software, developed in DELPHI programming support environment. Results, obtained with the help of developed bundled software, are presented. [ABSTRACT FROM AUTHOR]

The integrable discrete hungry Toda (dhToda) equation has already been applied to design an eigenvalue algorithm which computes eigenvalues of totally nonnegative (TN) matrices with lower Hessenberg form. In this paper, an eigenvalue algorithm for computing eigenvalues of TN matrices with upper Hessenberg form is derived based on a variant of the dhToda equation. [ABSTRACT FROM AUTHOR]

This paper presents the results of differential attack on Mini-AES algorithm. The differential trails are constructed using all combinations of propagation ratio without repetition. To give practical results, we implement the key extraction for differential characteristics which have the highest and lowest probability as a comparison. Based on total propagation ratio and complexity resulted, Mini-AES algorithms are vulnerable to differential attack. The best differential characteristic is the differential characteristic using a single active s-box with the propagation ratio of 8 / 16. [ABSTRACT FROM AUTHOR]

2-dimensional finite cellular automata defined by local rule based on hexagonal cell structure are studied. Rule matrix of the hexagonal finite cellular automaton is obtained. The rank of rule matrices related to hexagonal finite cellular automata via an algorithm is computed. By using the matrix algebra it is shown that the hexagonal finite cellular automata are reversible, if the number of columns is even and the hexagonal finite cellular automata are not reversible, if the number of the columns is odd. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic perturbed nonlinear diffusion equation is studied under a stochastic nonlinear nonhomogeneity. The Pickard approximation method is used to introduce a reference first order approximate solution. Under different correction levels, the WHEP technique is used to obtain approximate solutions. Using Mathematica-5, the solution algorithm is operated and several comparisons among correction levels together with error curves have been demonstrated. The method of solution is illustrated through case studies and figures. [ABSTRACT FROM AUTHOR]

Vehicle Routing and Flexible Job Shop Scheduling Problems (VRP and FJSSP) are two common hard combinatorial optimization problems that show many similarities in their conceptual level [2, 4]. It was proved for both problems that solving techniques like exact methods fail to provide good quality solutions in a reasonable amount of time when dealing with large scale instances [1, 5, 14]. In order to overcome this weakness, we decide in the favour of meta heuristics and we focalize on evolutionary algorithms that have been successfully used in scheduling problems [1, 5, 9]. In this paper we investigate the common properties of the VRP and the FJSSP in order to provide a new controlled evolutionary approach for the CVRP optimization inspired by the FJSSP evolutionary optimization algorithms introduced in [10]. [ABSTRACT FROM AUTHOR]

In the past few years, fractional calculus appeared to be a useful tool for the modeling and control of dynamic systems. Although, some methods of the control theory have been developed for the commensurate case, the difficulties of the non commensurate called generalized fractional systems still remain unsolved. In this paper, a method is presented for obtaining the state space model of a generalized fractional system starting from its transfer function. The method remains valid for the particular cases of commensurate and integer systems. An application to some examples illustrates the algorithm. [ABSTRACT FROM AUTHOR]

The main limiting factor of the model checker integrated in the concurrency verification environment FOCOVE [1, 2], which use the maximality based labeled transition system (noted MLTS) as a true concurrency model[3, 4], is currently the amount of available physical memory. Many techniques have been developed to reduce the size of a state space. An interesting technique among them is the alpha equivalence reduction. Distributed memory execution environment offers yet another choice. The main contribution of the paper is to show that the parallel state space construction algorithm proposed in [5], which is based on interleaving semantics using LTS as semantic model, may be adapted easily to the distributed implementation of the alpha equivalence reduction for the maximality based labeled transition systems. [ABSTRACT FROM AUTHOR]

The rolling of rods with slitting of the strip calls for the use of special mathematical models that would allow for the separating of metal. A theoretical analysis of the effect of the gap of slitting rollers on the process of band slitting during the rolling of 20 mm and 16 mm-diameter ribbed rods rolled according to the two-strand technology was carried out within this study. For the numerical modeling of strip slitting the Forge3® computer program was applied. The strip slitting in the simulation is implemented by the algorithm of removing elements in which the critical value of the normalized Cockroft - Latham criterion has been exceeded. To determine the value of the criterion the inverse method was applied. Distance between a point, where crack begins, and point of contact metal with the slitting rollers was the parameter for analysis. Power and rolling torque during slit rolling were presented. Distribution and change of the stress in strand while slitting were presented. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Solving global optimization problems plays a key role in most branches of natural sciences whilst dealing with everyday problems. With the help of optimization algorithms and the exponentially fast growth of the capabilities of the underlying hardware, the scale of feasible optimization tasks is reaching new levels. We help this goal with revisiting GLOBAL, a stochastic optimization method aiming to solve non-linear constrained optimization problems by the penalty function approach. It is a versatile tool for a broad range of problems, proven to be competitive in multiple comparisons. With the similarly rapid evolution of programming habits and tools, time naturally passed by GLOBAL’s latest implementation so that it became a drawback. Now, we present GlobalJ, a fully modularized Java framework refurbishing and extending the potential of this algorithm. [ABSTRACT FROM AUTHOR]

In the article, an application of evolutionary topology optimization procedure to searching alternative quasi-optimal solutions is presented. In the work, the constant criterion surface algorithm of evolutionary topology optimization is used. The algorithm is equipped with the procedure of restarting the search after reaching the subsequent quasi-optimal solution. This procedure uses a simulated annealing mechanism that is suitable for finding an optimal solution but also provides a set of alternative solutions. As shown in the test example, this method enables effective search within the solution space and finding a high number of alternative design layouts. [ABSTRACT FROM AUTHOR]

We propose a new method for solving univariate global optimization problems by combining a lower bound function given in (αBB) method [1] [For more details (Algorithms,Methods) one see [1]], with the improved lower bound function of the method developed in [2]. The new lower bound function is better than the two lower bound functions by its construction. The complementarity of the two lower bound functions allows us to derive the convex/concave test and the pruning step which accelerate the convergence of the proposed method. Illustrative examples are treated efficiently. [ABSTRACT FROM AUTHOR]

The simultaneous diagonalization problem of various size matrices is considered. We propose an algorithm for the problem that always finds a solution if one exists. The algorithm uses an algorithm for the simultaneous diagonalization of square matrices as a subroutine. [ABSTRACT FROM AUTHOR]

This study introduces a new algorithm for finding derivation of associative dialgebras. The algorithm applied to compute the derivations of low dimensional associative dialgebras. Some simple properties of derivation in terms of left multiplication operators also are provided. [ABSTRACT FROM AUTHOR]

In this work we report recent achievements in design of twin back-to-back ionization chamber (TIC) for fission fragment (FF) mass and kinetic energy spectroscopy. Correlated FF kinetic energies, their masses and the angle of the fission axes in 3D Cartesian coordinates can be determined from analysis of the heights and shapes of the pulses induced by the fission fragments on the anodes of TIC. Anodes of TIC were designed as consisting of isolated strips each having independent electronic circuitry and special multi-channel pulse processing apparatus. Mathematical algorithms were provided along with formulae derived for fission axis angles determination. It was shown how the point of fission fragments origin on the target plane may be determined using the same measured data. The last feature made the TIC a rather powerful tool for prompt fission neutron (PFN) emission investigation in event by event analysis of individual fission reactions from non point fissile source. Position sensitive neutron induced fission detector for neutron imaging applications with both thermal and low energy neutrons was found as another possible implementation of the designed TIC. [ABSTRACT FROM AUTHOR]

An efficient algorithm has been proposed for the solution of inverse boundary-value problem. Parameters of the right-hand side of biharmonic equation are identified by using available information about the solution of the direct problem. [ABSTRACT FROM AUTHOR]

MOQA is a high-level data structuring language, designed to allow for modular static timing analysis [1, 2, 3]. In essence,MOQA allows the programmer to determine the average running time of a broad class of programmes directly from the code in a (semi-)automated way. The modularity property brings a strong advantage for the programmer. The capacity to combine parts of code, where the average-time is simply the sum of the times of the parts, is a very helpful advantage in static analysis, something which is not available in current languages. Modularity also improves precision of average-case analysis, supporting the determination of accurate estimates on the average number of basic operations ofMOQA programs. The mathematical theory underpinning this approach is that of random structures and their preservation. Applying any MOQA operation to all elements of a random structure results in an output isomorphic to one or more random structures, which is the key to systematic timing. Here we introduce the approach in a self contained way and provide a MOQA version of the well-known algorithm of Min-Max heapify, constructed with the MOQA product operation. We demonstrate the 'randomness preservation' property of the algorithm and illustrate the applicability of our method by deriving the exact average time of the algorithm. [ABSTRACT FROM AUTHOR]

The following new q-integral inequalities are presented ... [ABSTRACT FROM AUTHOR]

We present first insights into the relation between two popular yet apparently dissimilar approaches to denoising of one dimensional signals, based on (i) total variation (TV) minimization and (ii) ideas from topological persistence. While a close relation between (i) and (ii) might phenomenologically not be unexpected, our work appears to be the first to make this connection precise for one dimensional signals. We provide a link between (i) and (ii) that builds on the equivalence between TV-L2 regularization and taut strings and leads to a novel and efficient denoising algorithm that is contrast preserving and operates in O(nlogn) time, where n is the size of the input. [ABSTRACT FROM AUTHOR]

The QuadCover algorithm is a well received and flexible algorithm for surface parameterization. For demonstrating QuadCover, we originally used principal curvature lines to guide the parameterization. The current work focuses on fine-tuning the vector fields used in QuadCover to yield state-of-the-art surface parameterizations. We propose new techniques for generating smooth frame fields in non-descriptive regions, branch point movement and frame field scaling with regard to optimal parameterization results. [ABSTRACT FROM AUTHOR]

In this note, we describe the Gel’fand-Tsetlin procedure for the construction of an orthogonal basis in spaces of Hermitean monogenic polynomials of a fixed bidegree. The algorithm is based on the Cauchy-Kovalevskaya extension theorem and the Fischer decomposition in Hermitean Clifford analysis. [ABSTRACT FROM AUTHOR]

Why do they matter? Applications abound, even to the extent that fast N-body methods merit a place in the core of numerical analysis. Why are they fast? The basis for all fast N-body solvers is (i) a separable approximation for a pairwise interaction kernel and (ii) exploitation of the associativity (and distributivity) of linear transformations. What are the various N-body methods? Kernel splitting and hierarchical clustering are the two fundamental paradigms. Which is the best N-body method? For molecular biophysics and structural biology, multilevel summation is suggested. [ABSTRACT FROM AUTHOR]

Due to both mathematical tractability and efficiency on computational resources, it is very common to find in the realm of numerical modeling in hydro-engineering that regular linearization techniques have been applied to nonlinear partial differential equations properly obtained in environmental flow studies. Sometimes this simplification is also made along with omission of nonlinear terms involved in such equations which in turn diminishes the performance of any implemented approach. This is the case for example, for contaminant transport modeling in streams. Nowadays, a traditional and one of the most common used water quality model such as QUAL2k, preserves its original algorithm, which omits nonlinear terms through linearization techniques, in spite of the continuous algorithmic development and computer power enhancement. For that reason, the main objective of this research was to generate a flexible tool for non-linear water quality modeling. The solution implemented here was based on two genetic algorithms, used in a nested way in order to find two different types of solutions sets: the first set is composed by the concentrations of the physical-chemical variables used in the modeling approach (16 variables), which satisfies the non-linear equation system. The second set, is the typical solution of the inverse problem, the parameters and constants values for the model when it is applied to a particular stream. From a total of sixteen (16) variables, thirteen (13) was modeled by using non-linear coupled equation systems and three (3) was modeled in an independent way. The model used here had a requirement of fifty (50) parameters. The nested genetic algorithm used for the numerical solution of a non-linear equation system proved to serve as a flexible tool to handle with the intrinsic non-linearity that emerges from the interactions occurring between multiple variables involved in water quality studies. However because there is a strong data limitation in local assessment studies, further work is necessary to develop a strong validation scheme for this modeling approach. [ABSTRACT FROM AUTHOR]

A fully coupled meshfree algorithm is proposed for numerical analysis of Biot’s formulation. Spatial discretisation of the governing equations is accomplished using radial point interpolation method. Temporal discretization is achieved based on a novel three-point approximation technique with variable time step, which has second order accuracy and avoids oscillatory response observed in the conventional methods of time discretization. Application of the model is demonstrated using two numerical examples with analytical solution. It is shown that the model proposed is efficient in simulating the coupled flow deformation behavior in fluid saturated porous media with good accuracy and stability irrespective of the magnitude of the time step adopted. [ABSTRACT FROM AUTHOR]

This symmetric key algorithm and its implementation convert manually entered password into mathematical expression, which is further used to generate an infinitely non-repetitive sequence of presumably random characters. These random series of characters are used to encrypt the data. This encrypted data stream is in turn swapped by dividing the data, block by block and the size of the blocks keep changing from the beginning of the data to the end of the data. The swapping commences from the beginning of the encryption and proceeds. The size of the block for swapping is narrow compared to the full length of the data and entirely depends on the one of the earlier characters which has already got swapped away from its initial position. All the characters will be mapped uniquely to mathematical expressions of a set of parameters in a pool of 256 expressions. These expressions corresponding to all characters in a password are added together to obtain a resultant expression. The above mentioned expressions corresponding to each character are further modified in advance (before summing up together) by including a ‘position index’. This is inevitable to take care of the repetition of characters within a password and also in the case of a permutated password. In the case of permutated passwords, the random characters generated should be different in each case. In another words, each character and its position in the password have its own unique identity. Two pools of mathematical expressions are employed, coupled with different initiations to the parameters, to get a couple of pseudorandom character series, one’s value being fed to the other. These are XORed together giving rise to a random series passing the popularly available randomness tests done by Nernst and Die hard. The initiating vector will be using, possibly the system time, and annexed with the original password to get the modified password. The system is similar to the conventional IV manipulation. The swapping will obviate substitution attack and the initiating vector method will prevent the possibility of reuse of key. [ABSTRACT FROM AUTHOR]

We present an analysis of A0-stability of BDF methods and proof that zero-stable BDF methods are A0-stable using the Schur-Cohn criterion. With this result we have that zero-stable BDF methods are stiffly-stable. [ABSTRACT FROM AUTHOR]

Construction of two haplotypes from a set of Single Nucleotide Polymorphism (SNP) fragments is called haplotype reconstruction problem. One of the most popular computational model for this problem is Minimum Error Correction (MEC). Since MEC is an NP-hard problem, here we propose a novel heuristic algorithm based on clustering analysis in data mining for haplotype reconstruction problem. Based on hamming distance and similarity between two fragments, our iterative algorithm produces two clusters of fragments; then, in each iteration, the algorithm assigns a fragment to one of the clusters. Our results suggest that the algorithm has less reconstruction error rate in comparison with other algorithms. [ABSTRACT FROM AUTHOR]

For some function classes it is known that using copies of a scaled down lattice rule can reduce the worst-case error for numerical integration of functions from this class. In a slight generalization we show that it is possible to construct these so-called “copy rules” by the fast component-by-component algorithm and review the conditions on when these rules would be preferable over normal lattice rules. We then present a generalization of copy rules to polynomial lattice rules and show similar results for the polynomial case as exist for the standard case of scalar lattice rules. [ABSTRACT FROM AUTHOR]

Given a large set of scattered points on a sphere and their associated real values, we analyze sequential and parallel algorithms for the construction of a function defined on the sphere satisfying the interpolation conditions. The algorithms we implemented are based on a local interpolation method using spherical radial basis functions and the Inverse Distance Weighted method. Several numerical results show accuracy and efficiency of the algorithms. [ABSTRACT FROM AUTHOR]

A solution to mesh distortion and subsequent breakdown in solution procedure in the finite element analysis of multi-stand rolling is presented in this work. Simple cubic spline fits are applied on the deformed outer surface of the rolled material to smoothen the geometry due to distortion from the deformation in the previous stands. A mesh re-zoning algorithm found in the literature is applied while retaining the original number of elements in the new mesh. The appropriate boundary conditions are applied efficiently with the use of a linear interpolation. The approach is illustrated for the multi-stand rolling of a nickel-base super alloy bar of circular cross-section. An in-house finite element program for steady state rolling, based on ALE technique was employed for the current work. The results show that the mesh re-zoning algorithm eliminates the numerical issues associated with the mesh distortion. The predicted results for the final shape are also found to be in good agreement with the experimental data. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]