We investigate optimal control problems for a class of non-stationary hybrid systems with autonomous location transitions. Using the Lagrange approach and the technique of the reduced gradient, we derive necessary opt...
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We investigate optimal control problems for a class of non-stationary hybrid systems with autonomous location transitions. Using the Lagrange approach and the technique of the reduced gradient, we derive necessary optimality conditions for the considered class of problems. These optimality conditions are closely related to a variant of the Hybrid Maximum Principle and can be used for constructive optimization algorithms.
Visual accuracy, low computational cost, and numerical stability are foremost goals in computer animation. An important ingredient in achieving these goals is the conservation of fundamental motion invariants. For exa...
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(纸本)9781450378338
Visual accuracy, low computational cost, and numerical stability are foremost goals in computer animation. An important ingredient in achieving these goals is the conservation of fundamental motion invariants. For example, rigid or deformable body simulation have benefited greatly from conservation of linear and angular momenta. In the case of fluids, however, none of the current techniques focuses on conserving invariants, and consequently, they often introduce a visually disturbing numerical diffusion of vorticity. Visually just as important is the resolution of complex simulation domains. Doing so with regular (even if adaptive) grid techniques can be computationally *** this chapter, we propose a novel technique for the simulation of fluid flows. It is designed to respect the defining differential properties, i.e., the conservation of circulation along arbitrary loops as they are transported by the flow. Consequently, our method offers several new and desirable properties: (1) arbitrary simplicial meshes (triangles in 2D, tetrahedra in 3D) can be used to define the fluid domain; (2) the computations are efficient due to discrete operators with small support; (3) the method is stable for arbitrarily large time steps; and (4) it preserves a discrete circulation avoiding numerical diffusion of vorticity. The underlying ideas are easy to incorporate in current approaches to fluid simulation and should thus prove valuable in many applications.
A new unified theory underlying the theoretical design of linear computational algorithms in the context of time dependent first-order systems is presented. Providing for the first time new perspectives and fresh idea...
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A new unified theory underlying the theoretical design of linear computational algorithms in the context of time dependent first-order systems is presented. Providing for the first time new perspectives and fresh ideas, and unlike various formulations existing in the literature, the present unified theory involves the following considerations: (i) it leads to new avenues for designing new computational algorithms to foster the notion of algorithms by design and recovering existing algorithms in the literature, (ii) describes a theory for the evolution of time operators via a unified mathematical framework, and (iii) places into context and explains/contrasts future new developments including existing designs and the various relationships among the different classes of algorithms in the literature such as linear multi-step methods, sub-stepping methods, Runge-Kutta type methods, higher-order time accurate methods, etc. Subsequently, it provides design criteria and guidelines for contrasting and evaluating time dependent computational algorithms. The linear computational algorithms in the context of first-order systems are classified as distinctly pertaining to Type 1, Type 2, and Type 3 classifications of time discretized operators. Such a distinct classification, provides for the first time, new avenues for designing new computational algorithms not existing in the literature and recovering existing algorithms of arbitrary order of time accuracy including an overall assessment of their stability and other algorithmic attributes. Consequently, it enables the evaluation and provides the relationships of computational algorithms for time dependent problems via a standardized measure based on computational effort and memory usage in terms of the resulting number of equation systems and the corresponding number of system solves. A generalized stability and accuracy limitation barrier theorem underlies the generic designs of computational algorithms with arbitrary order o
A procedure to accelerate the convergence of quasi-Monte Carlo approximations is described and investigated. The procedure applies a weighted least-squares smoothing method to improve the approximations that were obta...
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A procedure to accelerate the convergence of quasi-Monte Carlo approximations is described and investigated. The procedure applies a weighted least-squares smoothing method to improve the approximations that were obtained using low-discrepancy sequences. The acceleration procedure is tested computationally on several numerical integration problems including two problems of interest in mathematical finance. The results indicate that when Halton low-discrepancy points are used in the quasi-Monte Carlo method, the accelerated sequence often converges a factor of five or more faster than the original quasi-Monte Carlo approximations. (C) 2002 Elsevier Inc. All rights reserved.
It has been shown that for any nonsingular matrix M, there exists a finite set of ‘unmixing’ matrices S such that at least one member Si ϵ S will exhibit the property that MSi will be stable, i.e. MSi will be a Hurw...
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It has been shown that for any nonsingular matrix M, there exists a finite set of ‘unmixing’ matrices S such that at least one member Si ϵ S will exhibit the property that MSi will be stable, i.e. MSi will be a Hurwitz Matrix. The purpose of this note is to construct such a set for the cases n = 2, 3 and for the specific case of companion matrices of arbitrary dimension. A direct application of such ‘unmixing’ matrices is in the construction of adaptive-type controllers using switching controllers.
A computational method to identify residues important in creating a protein promoting vibration (PPV) in enzymes was previously developed and applied to horse liver alcohol dehydrogenase (HLADH), resulting in the iden...
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A computational method to identify residues important in creating a protein promoting vibration (PPV) in enzymes was previously developed and applied to horse liver alcohol dehydrogenase (HLADH), resulting in the identification of eight important residues. From these residues, we define a sequence motif, the PPV generating sequence, and find it to be unique and general to a larger group of alcohol dehydrogenases from diverse sources, demonstrating that nature has selected for the PPV generating sequence.
An innovative, geometrically appealing, derivation of the differential motion of an end-effector and the corresponding Jacobian matrix is presented. The use of the differential. T form of the skew-symmetric matrix W =...
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An innovative, geometrically appealing, derivation of the differential motion of an end-effector and the corresponding Jacobian matrix is presented. The use of the differential. T form of the skew-symmetric matrix W = (A)over dot A(T) and the corresponding differential rotation is central to the development, A being the usual rotation matrix. This allows a novel side-by-side presentation of the vector and matrix form of differential rigid motion based on the forward kinematics of the manipulator. The corresponding treatment of the homogeneous motion includes a detailed discussion of the derivative and differential of homogeneous rigid motion and a clarification of some notational ambiguities and errors in previous treatments of this topic. It is also shown that the results are equivalent to what may be termed classical results, The analytical treatment is followed by a detailed presentation of computational and symbolic methods for the derivation and evaluation of the Jacobian matrix, including the use of recently developed methods of automatic differentiation. The AdeptOne Robot is used as an illustrative example with complete agreement of the theoretical and computational results. (C) 2000 Elsevier Science Ltd. All rights reserved.
Acceptance sampling plans are used to assess the quality of an ongoing production process, in addition to the lot acceptance. In this paper, we consider sampling inspection plans for monitoring the Markov-dependent pr...
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Acceptance sampling plans are used to assess the quality of an ongoing production process, in addition to the lot acceptance. In this paper, we consider sampling inspection plans for monitoring the Markov-dependent production process. We construct sequential plans that satisfy the usual probability requirements at acceptable quality level and rejectable quality level and. in addition, possess the minimum average sample number under semicurtailed inspection. As these plans result in large sample sizes, especially when the serial correlation is high, we suggest new plans called "systematic sampling plans." The minimum average sample number systematic plans that satisfy the probability requirements are constructed. Our algorithm uses some simple recurrence relations to compute the required acceptance probabilities. The optimal systematic plans require much smaller sample sizes and acceptance numbers, compared to the sequential plans. However, they need larger production runs to make a decision. Tables for choosing appropriate sequential and systematic plans are provided. The problem of selecting the best systematic sampling plan is also addressed. The operating characteristic curves of some of the sequential and the systematic plans are compared, and are observed to be almost identical. (C) 2001 John Wiley & Sons, Inc.
Protein engineering by inserting stretches of random DNA sequences into target genes in combination with adequate screening or selection methods is a versatile technique to elucidate and improve protein functions. Est...
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Protein engineering by inserting stretches of random DNA sequences into target genes in combination with adequate screening or selection methods is a versatile technique to elucidate and improve protein functions. Established compounds for generating semi-random DNA sequences are spiked oligonucleotides which are synthesised by interspersing wild type (wt) nucleotides of the target sequence with certain amounts of other nucleotides. Directed spiking strategies reduce the complexity of a library to a manageable format compared with completely random libraries. computational algorithms render feasible the calculation of appropriate nucleotide mixtures to encode specified amino acid subpopulations. The crucial element in the ranking of spiked codons generated during an iterative algorithm is the scoring function. In this report three scoring functions are analysed: the sum-of-square-differences function s, a modified cubic function c,and a scoring function m derived from maximum likelihood considerations. The impact of these scoring functions on calculated amino acid distributions is demonstrated by an example of mutagenising a domain surrounding the active site serine of subtilisin-like proteases. At default weight settings of one for each amino acid, the new scoring function m is superior to functions s and c in finding matches to a given amino acid population.
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