基于正交多项式的称重仪表非线性校正算法

针对称重仪表检测电路中输入与输出值之间存在非线性关系的特性,在比较了几种非线性校正方法的基础上,给出了一种易于微处理器实现的正交多项式的非线性校正方法,求取称重仪表检测电路的非线性特征,实现了称重仪表的非线性校正。同时讨论了该算法的原理、校正参数的空间复杂度和算法的时间复杂度,从而论证了此算法在简单微处理器上的可用性,并以3阶多项式为例介绍了该算法的实验效果。实践表明,该算法简单实用,效果较好。     

Convergence of iteration systems

Summary An iteration system is a set of assignment statements whose computation proceeds in steps: at each step, an arbitrary subset of the statements is executed in parallel. The set of statements thus executed may differ at each step; however, it is required that each statement is executed infinitely often along the computation. The convergence of such systems (to a fixed point) is typically verified by showing that the value of a given variant function is decreased by each step that causes a state change. Such a proof requires an exponential number of cases (in the number of assignment statements) to be considered. In this paper, we present alternative methods for verifying the convergence of iteration systems. In most of these methods, upto a linear number of cases need to be considered. Anish Arora is currently completing his Ph.D. degree at the University of Texas at Austin, and has been working in the Software Technology Program at MCC since December 1988. Anish received a B.Tech. degree in Computer Science and Engineering from the Indian Institute of Technology, New Dehli in 1986, and an M.S. degree in Computer Sciences from the University of Texas at Austin in 1988. His research interests inclde fault-tolerance, distributed computing, program correctness, and semantics of concurrency. Paul Attie is currently completing his Ph.D. degree of the University of Texas at Austin, and has been a member of technical staff in the Software Technology Program of the MCC since January 1990. Paul received a B.A. degree in Engineering Science from Oxford University in 1981, and an M.Sc. degree from the University of London in 1982. His research interests include distributed computing, temporal logic, and algebraic process theory. Michael Evangelist received his Ph.D. in 1978 from Northwestern, where he did research in formal language theory, graph theory, logic, and computational complexity theory. He taught computer science at Colgate University and, in 1982, became a member of technical staff at Bell Labs and did research in software engineering. Three years later, he joined the Software Technology Program at MCC, where he spent five years working on theoretical and practical issues in the design of distributed systems. Evangelist now heads the Software Engineering Laboratory in the Chicago research center of Andersen Consulting. Mohamed G. Gouda currently works on and teaches the stabilization of computing systems at the University of Texas at Austin. He designs cute communication protocols as a hobby, and proves them correct for fun.     

A modified newton method in parallel circular iteration of single-step and double-step

In this paper, two theorems for the convergence of a modified Newton method in parallel circular iteration are given. The convergent condition of single-step method's circular iteration is relaxed compared with the classical theorem in the same field, while the one of the first proposed double-step method of the five-order is obtained accurately as well.     

Convergence theorems by a new iteration process for a finite family of nonself asymptotically nonexpansive mappings with errors in Banach spaces

In this paper, we study a new iteration process for a finite family of nonself asymptotically nonexpansive mappings with errors in Banach spaces. We prove some weak and strong convergence theorems for this new iteration process. The results of this paper improve and extend the corresponding results of Chidume et al. (2003) [10], Osilike and Aniagbosor (2000) [3], Schu (1991) [4], Takahashi and Kim (1998) [9], Tian et al. (2007) [18], Wang (2006) [11], Yang (2007) [17] and others.     

时间复杂性和空间复杂性研究

计算复杂性是衡量问题求解的难易程度的。研究问题的计算复杂性,可以明确该问题是否存在有效的求解算法。介绍并分析了计算理论的一些基本概念,论述了时间复杂性（包括P、NP、NP-hard、NP-complete和EXPTIME）和空间复杂性（包括PSPACE、NPSPACE、PSPACE-hard和PSAPCE-complete）中的各个主要分类。最后分析了各个复杂性类之间的关系。     

Convergence — The pathway to integration

The convergence of computer and telecommunications technologies into an integrated system solution is now widely accepted as an achievable objective. However, the evolutionary passage towards this goal has been somewhat prolonged and tortuous, and there is still some way to go.

The article reviews that passage, discusses the meanings and implications of the terms ‘convergence’ and ‘integration’, and identifies a number of useful cost-effective techniques which can currently be used to achieve some of the benefits of integration now, in advance of the UK System X architecture.

Fully integrated public systems are unlikely to achieve substantial penetration in the UK until System X architecture is widely introduced into the UK network. Until this happens the full benefits of the convergence of telecommunications and computers will not be realized.

Computer information is already in digital form, so that little change is envisaged in routing this via System X. Speech is analogue however, and it is here that a number of changes are necessary. The article therefore concentrates on this aspect, leaving scope for a further contribution which could focus on nonvoice information.     

Weak and strong stabilisation of bilinear systems in a Banach space

In this paper, we study the feedback stabilisation of homogeneous bilinear systems on a Banach state-space. Sufficient conditions for weak and strong stabilisation are given. A decay rate of the stabilised state is explicitly estimated. Applications to heat and transport equations are provided.     

Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces

We prove the existence of a solution of the mixed equilibrium problem (MEP) by using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solutions set of a mixed equilibrium problem and the fixed points set of a countable family of nonexpansive mappings in the frameworks of Banach spaces. By using a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solutions set of MEP and common fixed points set of nonexpansive mappings. Moreover, some applications concerning the equilibrium and the convex minimization problems are obtained.     

Asymptotic equilibrium of ordinary differential systems in a Banach space

The asymptotic equilibrium of differential systems in Euclidean spaces has been considered by several authors. These papers deal with a majorant function,g(t, u), which is either non-decreasing or non-increasing inu for eacht. In extending these results to differential systems in a Banach space additional conditions must be placed on the system. In this paper the Kuratowski measure of non-compactness is used to give conditions yielding asymptotic equilibrium of the system in a Banach space.     

On local convergence of a Newton-type method in Banach space

In this study we are concerned with the local convergence of a Newton-type method introduced by us [I.K. Argyros and D. Chen, On the midpoint iterative method for solving nonlinear equations in Banach spaces, Appl. Math. Lett. 5 (1992), pp. 7–9.] for approximating a solution of a nonlinear equation in a Banach space setting. This method has also been studied by Homeier [H.H.H. Homeier, A modified Newton method for rootfinding with cubic convergence, J. Comput. Appl. Math. 157 (2003), pp. 227–230.] and Özban [A.Y. Özban, Some new variants of Newton's method, Appl. Math. Lett. 17 (2004), pp. 677–682.] in real or complex space. The benefits of using this method over other methods using the same information have been explained in [I.K. Argyros, Computational theory of iterative methods, in Studies in Computational Mathematics, Vol. 15, C.K. Chui and L. Wuytack, eds., Elsevier Science Inc., New York, USA, 2007.; I.K. Argyros and D. Chen, On the midpoint iterative method for solving nonlinear equations in Banach spaces, Appl. Math. Lett. 5 (1992), pp. 7–9.; H.H.H. Homeier, A modified Newton method for rootfinding with cubic convergence, J. Comput. Appl. Math. 157 (2003), pp. 227–230.; A.Y. Özban, Some new variants of Newton's method, Appl. Math. Lett. 17 (2004), pp. 677–682.]. Here, we give the convergence radii for this method under a type of weak Lipschitz conditions proven to be fruitful by Wang in the case of Newton's method [X. Wang, Convergence of Newton's method and inverse function in Banach space, Math. Comput. 68 (1999), pp. 169–186 and X. Wang, Convergence of Newton's method and uniqueness of the solution of equations in Banach space, IMA J. Numer. Anal. 20 (2000), pp. 123–134.]. Numerical examples are also provided.     

Convergence and stability analysis of a novel iteration method for fractional biological population equation

We put into action new analytical technique for solving nonlinear fractional partial differential equations arising in biological population dynamics system. We present in details the stability, the convergence, and the uniqueness analysis by constructing a suitable Hilbert space. Some exact analytical solutions are given, and a quantity of properties gives you an idea about signs of biologically practical reliance on the parameter values. The regularity of this course of action and the diminution in computations confer a wider applicability. In all examples, in the limit of infinitely, many terms of the series solution yield the exact solution.     

A geometric property of control systems with states in a Banach space

In this paper we are concerned with admissible trajectories x(·) of infinite-dimensional linear systems, defined on an interval [0, t₁] and such that x(0)−x(t₁) is small. We show that these trajectories satisfy certain geometric properties.     

The space complexity of unbounded timestamps

The timestamp problem captures a fundamental aspect of asynchronous distributed computing. It allows processes to label events throughout the system with timestamps that provide information about the real-time ordering of those events. We consider the space complexity of wait-free implementations of timestamps from shared read-write registers in a system of n processes. We prove an lower bound on the number of registers required. If the timestamps are elements of a nowhere dense set, for example the integers, we prove a stronger, and tight, lower bound of n. However, if timestamps are not from a nowhere dense set, this bound can be beaten: we give an implementation that uses n − 1 (single-writer) registers. We also consider the special case of anonymous implementations, where processes are programmed identically and do not have unique identifiers. In contrast to the general case, we prove anonymous timestamp implementations require n registers. We also give an implementation to prove that this lower bound is tight. This is the first anonymous timestamp implementation that uses a finite number of registers.     

Worst-case space and time complexity of recursive procedures

The purpose of this paper is to show that recursive procedures can be used for implementing real-time applications without harm, if a few conditions are met. These conditions ensure that upper bounds for space and time requirements can be derived at compile time. Moreover they are simple enough such that many important recursive algorithms can be implemented, for example Mergesort or recursive tree-traversal algorithms.In addition, our approach allows for concentrating on essential properties of the parameter space during space and time analysis. This is done by morphisms that transfer important properties from the original parameter space to simpler ones, which results in simpler formulas of space and time estimates.Supported by the Austrian Science Foundation (FWF) under grant P10188-MAT.A preliminary version of this paper has been presented at the 7th Euromicro Workshop on Real-Time Systems (Blieberger and Lieger, 1995).     

Convergence of the variational iteration method for solving multi-delay differential equations

This paper employs the variational iteration method (VIM) to obtain analytical solutions of multi-delay differential equations. Some convergence results are given, and an effective technique for choosing a reasonable initial solution is designed in the solving process; an example is given to elucidate it.     

Public online pool—a method for managing online direct access space

This paper describes a software system, implemented at the Weizmann Institute of Science Computer Center, for managing online direct access space in a heavy batch/time sharing environment. Appropriate background discussion of the problem is presented in general, yet practical, terms. We describe the ‘ideal’ solution along with its shortcomings as we see them, followed by the solution as implemented at our installation and successfully operating for 5 years. Finally, we point out the effect this system had on our installation and show where future efforts could be rewarding. The work this paper describes won the 1975 prize of the Information Processing Association of Israel.