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ON DISCRETE LIMITS OF SEQUENCES OF piecewise linear functionS

REAL ANALYSIS EXCHANGE 2007年第1期33卷 107-110页

作者： Grande, Zbigniew Kazimierz Wielki Univ Inst Math Plac Weyssenhoffa 11 PL-85072 Bydgoszcz Poland

In this article we characterize the discrete limits of sequences of piece-wise linear functions. A function f : [0, 1] -> R is the discrete limit of a sequence of piecewise linear functions iff there are closed set... 详细信息

关键词： discrete convergence sequence of functions piecewise linear function

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A novel linear recurrent neural network for multivariable system identification

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2006年第3期28卷 229-242页

作者： Fei, Minrui Zhang, Jian Hu, Huosheng Yang, Taicheng Shanghai Univ Sch Mechatron Engn & Automat Shanghai 200072 Peoples R China Univ Essex Dept Comp Sci Colchester CO4 3SQ Essex England Univ Sussex Dept Engn Brighton BN1 9QT E Sussex England

This paper proposes a novel linear recurrent neural network for multivariable system identification, namely a linerec neural network (LNN). Based on this network, the transfer function matrix model of a multivariable system can be identified directly according to its input and output data. In this way, LNNs differ from existing neural networks. An LNN is constructed based on the identification of prior knowledge in a system, and its weights have definite physical meaning. An LNN is equivalent to a linear equation set, and its training algorithm is based on Widrow- Hoff learning rules. In this paper, the theoretical foundation, structural algorithm and learning rules of LNNs are proposed and studied. To guarantee learning convergence, network training stability is analysed using discrete Lyapunov stability theory. Finally, simulation results show the feasibility of LNNs for multivariable system identification.

关键词： discrete Lyapunov function linear recurrent neural network multivariable system identification piecewise linear function

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Generation of multi-scroll delayed chaotic oscillator

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ELECTRONICS LETTERS 2006年第25期42卷 1439-1441页

作者： Wang, L. Yang, X. Chongqing Univ Coll Comp Sci Chongqing 400044 Peoples R China SW Univ Sch Elect & Informat Engn Chongqing 400715 Peoples R China

A novel delayed chaotic oscillator capable of generating multi-scroll chaos is investigated. The nonlinear activation function can be represented as a piecewise linear function, and its circuitry implementation requires only a few operational amplifiers. The typical waveforms and phase portraits of the attractor are presented to illustrate mono- two- or four-scroll chaotic oscillations.

关键词： nonlinear activation function delayed chaotic oscillator oscillators chaotic oscillations phase portraits chaos generators attractor piecewise linear function Chaotic behaviour in circuits circuitry implementation waveforms Oscillators operational amplifiers multi-scroll delayed chaotic oscillator piecewise linear techniques

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A branch-and-cut algorithm without binary variables for nonconvex piecewise linear optimization

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OPERATIONS RESEARCH 2006年第5期54卷 847-858页

作者： Keha, Ahmet B. de Farias, Ismael R., Jr. Nemhauser, George L. Arizona State Univ Dept Ind Engn Tempe AZ 85287 USA SUNY Buffalo Dept Ind Engn Buffalo NY 14260 USA Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

We give a branch-and-cut algorithm for solving linear programs (LPs) with continuous separable piecewise-linear cost functions (PLFs). Models for PLFs use continuous variables in special-ordered sets of type 2 (SOS2). Traditionally, SOS2 constraints are enforced by introducing auxiliary binary variables and other linear constraints on them. Alternatively, we can enforce SOS2 constraints by branching on them, thus dispensing with auxiliary binary variables. We explore this approach further by studying the inequality description of the convex hull of the feasible set of LPs with PLFs in the space of the continuous variables, and using the new cuts in a branch-and-cut scheme without auxiliary binary variables. We give two families of valid inequalities. The first family is obtained by lifting the convexity constraints. The second family consists of lifted cover inequalities. Finally, we report computational results that demonstrate the effectiveness of our cuts, and that branch-and-cut without auxiliary binary variables is significantly more practical than the traditional mixed-integer programming approach.

关键词： piecewise linear function special-ordered set branch-and-cut

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Gray level image enhancement using piecewise linear functions

Gray level image enhancement using piecewise linear function...

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7th International Symposium on Signals, Circuits and Systems (ISSCS 2005)

作者： Patrascu, V Politehn Univ Bucharest LAPI Bucharest Romania

ISBN: (纸本)0780390296

This paper presents a method for enhancing the gray level images. This method takes part from the category of point transforms and it is based on interpolation functions. The latter have a graphic represented by piecewise linear functions. The interpolation nodes of these functions are calculated taking into account the statistics of gray levels belonging to the image.

关键词： image enhancement interpolation function piecewise linear function

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On the mixed integer signomial programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2005年第2期170卷 1436-1451页

作者： Chang, CT Changhua Univ Educ Dept Informat Management Changhua 50058 Taiwan

This paper proposes an approximate method to solve the mixed integer signomial programming problem, for which the objective function and the constraints may contain product terms with exponents and decision variables, which Could be continuous or integral. A linear programming relaxation is derived for the problem based on piecewise linearization techniques, which first convert a signomial term into the sum of absolute terms;these absolute terms are then linearized by linearization strategies. In addition, a novel approach is included for solving integer and undefined problems in the logarithmic piecewise technique, which leads to more usefulness of the proposed method. The proposed method could reach a solution as close as possible to the global optimum. (c) 2005 Elsevier Inc. All rights reserved.

关键词： piecewise linear function signomial programming linearization technique

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Hierarchical TS fuzzy system and its universal approximation

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INFORMATION SCIENCES 2005年第3-4期169卷 279-303页

作者： Liu, PY Li, HX Natl Univ Def Technol Dept Math Changsha 410073 Peoples R China Beijing Normal Univ Dept Math Beijing 100875 Peoples R China

An efficient tool to deal with the 'rule explosion' problem is the hierarchical system by which a fuzzy system can be decomposed into a number of hierarchically connected low-dimensional systems. In this paper a generalized hierarchical Tagaki-Sugeno (TS) system is built. It is shown that the input-output (I/O) relationship of this generalized hierarchical system can be represented as one of a standard TS fuzzy system. And the system approximation capability is analyzed by taking piecewise linear functions as a bridge. By constructive method it is proven that the hierarchical fuzzy systems (HFS's) can be universal approximators. For the given approximation accuracy, an estimation formula about the number of the rules needed in the HFS is established. Finally some simulation examples confirm that the HFS's with smaller size rule base can approximate the given functions with high accuracy. The results obtained here provide us with the theoretical basis for various applications of HFS's. (C) 2004 Elsevier Inc. All rights reserved.

关键词： TS fuzzy system hierarchical system universal approximator piecewise linear function

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Dynamical study of a second-order DPCM transmission system modeled by a piecewise-linear function

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2002年第11期49卷 1592-1609页

作者： Taralova, I Fournier-Prunaret, D Ecole Cent Nantes CNRS UMR 6597 IRCCyN F-44321 Nantes 3 France INSA DGEI LESIA SYD F-31077 Toulouse 4 France

This paper analyzes the behavior of a second-order differential pulse code modulation (DPCM) transmission system when the nonlinear characteristic of the quantizer is taken into consideration. In this way, qualitatively new properties of the DPCM system have been unraveled, which cannot be observed and explained if the nonlinearity of the quantizer is neglected. For the purpose of this study, a piecewise-linear nondifferentiable quantizer characteristic is considered. The resulting model of the DPCM is of the form of iteration equations (i.e., map), where the inverse iterate is not unique (i.e., noninvertible map). Therefore, the mathematical theory of noninvertible maps is particularly suitable for this analysis, together with the more classic tools of nonlinear dynamics. This study allowed us, in addition, to show, from a theoretical point of view, some new properties of nondifferentiable maps, in comparison with differentiable ones. After a short review of noninvertible maps, the presented methods and tools for noninvertible maps are applied to the DPCM system. An original algorithm for calculation of bifurcation curves for the DPCM map is proposed. Via the studies in the parameter and phase plane, different nonlinear phenomena such as the overlapping of bifurcation curves causing multistability, chaotic behavior, or multiple basins with fractal boundary are pointed out. All observed phenomena show a very complex dynamical behavior even in the constant input signal case, discussed here.

关键词： differential pulse code modulation (DPCM) piecewise linear function

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linear semi-openness and the Lyusternik theorem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第1期157卷 16-27页

作者： Pühl, H Schirotzek, W Tech Univ Dresden Fachrichtung Math Inst Anal D-01062 Dresden Germany

A class of set-valued mappings called linearly semi-open mappings is introduced which properly contains the class of linearly open set-valued mappings. A stability result for linearly semi-open mappings is established. The main result is a Lyusternik type theorem. Sufficient conditions for linear semi-openness of processes are derived. To verify these conditions, the openness bounds of certain processes are computed. A representation of the openness bound of a locally Lipschitz function in a Clarke non-critical point is given. It is shown that continuous piecewise linear functions on R-n are linearly semi-open under certain algebraic conditions. (C) 2003 Elsevier B.V. All rights reserved.

关键词： set-valued mapping linear semi-openness linear openness metric regularity Lyusternik theorem contingent cone piecewise linear function openness bound

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A cost analysis of the transmission backbone

A cost analysis of the transmission backbone

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11th International Telecommunications Network Strategy and Planning Symposium

作者： Naldi, M Pelusi, P Univ Roma Tor Vergata I-00173 Rome Italy

ISBN: (纸本)3800728400

The application of the principle of cost orientation to the tariffs of leased lines makes the cost analysis of services based on the transmission backbone relevant both for the incumbent operator and for the alternative ones. In this paper a simple procedure, based on the Fully Accounted Costs criterion, is proposed for deriving the annual cost of the transport of a 2 Mbit/s stream and for analyzing its relation to the distance between the stream endpoints. The procedure is applied to the network of a national alternative operator. The cost-distance relationship appears to be well modelled by a piecewise linear function, showing a near invariance of costs for the longer distances (over 700 km).

关键词： costing optical fibre networks synchronous digital hierarchy piecewise linear techniques cost analysis transmission backbone fully accounted costs criterion piecewise linear function optical networks

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