关键词： Phase equilibria  

摘要： A robust but rigorous flash algorithm allows for simulating multicomponent two-phase equilibria in supercritical asymmetric solutions that contain very large and very small components, such as polymers and supercritical solvents or monomers. The approach is to solve simultaneously all the equilibrium and material balance equations using a Newton iterative procedure in the framework of block algebra. The SAFT equation of state is used to estimate the required thermodynamic properties. This approach is illustrated with an example of single-stage fractionation of polyethylene with supercritical ethylene and 1-hexene. The calculated solvent capacities and selectivities are related to ethylene concentration, pressure, and temperature.

摘要： We present an algorithm for computing Gr?bner and free canonical Schreier bases for finitely generated one-sided ideals in free group algebras. That is, given a set of n elements of a free group algebra, we construct a canonical Schreier basis of free generators as well as a Gr?bner basis for the right ideal generated by the original set. In contrast to Buchberger's algorithm in polynomial rings, at any stage the current number of polynomials does not exceed 2n and their maximal degree is bounded by d + 2, where d is the maximal degree of the original polynomials. A corollary is that the generalised membership problem for free group algebras is solvable. As a special case we obtain an algorithm similar to the Nielsen-Hall algorithm for constructing free bases for subgroups of free groups. A generalisation of the notion of a Gr?bner basis is given by the definition of algebras satisfying constructive division algorithms.

关键词： ITERATIVE IMAGE RECONSTRUCTION   ITERATIVE FILTERED BACKPROJECTION   ATTENUATION CORRECTION  

摘要： In this paper, a unified framework of iterative algebraic reconstruction for emission computed tomography (ECT) and its application to positron emission tomography (PET) is presented. The unified framework is based on an algebraic image restoration model and contains conventional iterative algebraic reconstruction algorithms: ART, SIRT, Landweber iteration (LWB), the generalized Landweber iteration (GLWB), the steepest descent method (STP), as well as iterative filtered backprojection (IFBP) reconstruction algorithms: Chang's method, Walters' method, and a modified iterative MAP. The framework provides an effective tool to systematically study conventional iterative algebraic algorithms and IFBP algorithms. Based on this framework, conventional iterative algebraic algorithms and IFBP algorithms are generalized. It is shown from the algebraic point of view that IFBP algorithms are not only excellent methods for correction of attenuation (either uniform or nonuniform) but are also good general iterative reconstruction algorithms (they can be applied to either attenuated or attenuation-free projections and converge very fast). The convergence behavior of iterative algebraic algorithms is discussed and insight is drawn into the fast convergence proper-ty of IFBP algorithms. A simulated PET system is used to evaluate IFBP algorithms and LWB in comparison with the maximum likelihood estimation via expectation maximization algorithm (MLE-EM) and the filtered backprojection (FBP) algorithm. The simulation results indicate that for both attenuation-free projection and attenuated projection cases IFBP algorithms have a significant computational advantage over LWB and MLE-EM, and have performance advantages over FBP in terms of contrast recovery and/or noise-to-signal ratios (NSRs) in regions of interest.

关键词： COMPUTATIONAL GEOMETRY   COMPUTER GRAPHICS   ALGEBRAIC CURVE   GENERAL SWEEP   BRUSH STROKE DESIGN   RESULTANT   CURVE TRACING   PLANE SWEEP ALGORITHM  

摘要： We present an algebraic algorithm to generate the exact general sweep boundary of a 2D curved object which changes its shape dynamically while moving along a parametric curve trajectory.

摘要： Three models of different degrees of rigor are developed for diffusion and reaction in porous catalyst pellets for the industrially important multicomponents' system with a multiple reversible reaction for the steam reforming of natural gas. The more rigorous model is based on the Stefan-Maxwell equation for multicomponents' diffusion, while the other less rigorous models are based on the simplified Fick's law. The resulting nonlinear two-point boundary value differential equations are solved using an efficient algorithm based on the global orthogonal collocation technique. A simple transformation is used, which shifts the collocation points towards the region close to the surface, where the profiles are steepest, without the need to use spline collocation. The algorithm is augmented with a technique to obtain suitable initial guesses that guarantees the convergence of the solution of the large system of nonlinear algebraic equations resulting from the application of the orthogonal collocation technique. The algorithm works very efficiently under industrial conditions characterized by high temperature, strong diffusional limitations and, therefore, very steep concentration profiles.

摘要： In this article I describe an algorithm for computing finite dimensional graded algebras, and I describe an implementation of the algorithm. As an application of the algorithm, I investigate associative algebras satisfying the identity x⁴ = 0. I show that if A is an associative algebra over a field of characteristic zero, and if a⁴ = 0 for all a ? A, then A¹⁰ = {0}.

关键词： 开式电网   数学模型   计算机应用  

摘要： 本文提出了以节点数字编号与相关矩阵为基础的开式供电网络的简单直接算法,确立了数学模型及程序实现方法,评价了其优缺点并给出了计算实例。图3,参5。

关键词： Algorithms  

摘要： Algorithms related to normalization of autonomous Hamiltonian systems are considered. These include expansion of a Hamiltonian in Taylor series, linear normalization and, finally, nonlinear normalization. Algorithms most appropriate for use in computer algebra systems from the standpoint of economy of computer memory are suggested. They are employed in a program package written in REDUCE.

关键词： ALGORITHMS   VARIATIONAL METHODS   ALGEBRA   QUANTUM MECHANICS   CHEMICAL REACTIONS   SCATTERING   EQUATIONS   POTENTIAL ENERGY   COUPLING  

摘要： Variational basis-set formulations of the quantum mechanical reactive scattering problem lead to large, dense sets of equations. In previous work, we showed that the generalized minimal residual (GMRes) algorithm is sometimes competitive in terms of computer time with direct methods for these dense matrices, even when complex-valued boundary conditions are used, leading to non-Hermitian matrices. This paper presents a preconditioning scheme to accelerate convergence and improve performance. We block the potential energy coupling into a series of distortion blocks, and we employ the outgoing wave variational principle with nonorthogonal basis functions, including both dynamically adapted Green's functions for the distortion blocks and also square integrable functions. The coefficient matrix of the resulting linear system couples the blocks. We have found that preconditioners formed from diagonal blocks of the coefficient matrix corresponding to the distortion blocks and vibrational blocks are effective at accelerating the iterative method in every test case, by factors of 2.9-20, with an average speedup of a factor of 6.5. The storage requirements and computational efficiency of the new scheme compare favorably to those for preconditioners based on banded matrices of variable bandwidth. The new preconditioners yield converged transition probabilities in less computer time than a direct solver even in cases which do not converge in a reasonable amount of time without preconditioning, and the average speedup compared to the direct solution is a factor of 7.6.

关键词： 系统可靠性   数学模型   算法  

摘要： 讨论了“n 中取k 好”表决系统和“n 中取相邻k 好(坏)”系统这两种可靠性模型的算法,给出了计算复杂性最小的算法。