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Non-Darcian effect on a variable-rate pumping test in a confined aquifer

HYDROGEOLOGY JOURNAL 2020年第8期28卷 2853-2863页

作者： Li, Yabing Zhou, Zhifang Zhuang, Chao Huang, Yong Wang, Jinguo Hohai Univ Sch Earth Sci & Engn 8 Fochengxi Rd Nanjing 211100 Jiangsu Peoples R China

Groundwater flow in an aquifer has frequently been found to be non-Darcian. In this study, a transient model of a variable-rate pumping test in a confined aquifer was established considering non-Darcian flow in the aquifer. A piecewise-linear function was adopted to reproduce the variability in pumping rate, and the classical Izbash equation was employed to describe the non-Darcian flow. The type-curve analysis suggested that a smaller quasi-conductivity will result in an earlier deviation and a smaller extent of the decreasing features in the drawdown under the condition of a linearly decreasing pumping rate compared to that under the condition of a constant pumping rate. The sensitivity analysis indicated that the variability in pumping rates under non-Darcian flow can increase the sensitivity of drawdown to the radius of the well casing at inflection times of the discrete linear stages, and drawdown closer to the pumping well is more sensitive to the change in the well casing. A type-curve method was proposed and employed to interpret the pumping test data, which were collected at a field site located in Wuxi city, Jiangsu Province, China. The parameter estimates indicate a high possibility of the occurrence of prelinear flow in the aquifer of interest.

关键词： Groundwater flow Non-Darcian flow Variable-rate pumping tests piecewise-linear function Hydraulic properties

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Self-sustained oscillation in a memristor circuit

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NONlinear DYNAMICS 2019年第2期96卷 1267-1281页

作者： Liao, Xingran Mu, Nankun Sichuan Univ Sch Math Chengdu 610065 Sichuan Peoples R China Southwest Univ Chongqing Key Lab Nonlinear Circuits & Intelligen Coll Elect & Informat Engn Chongqing 400715 Peoples R China

In this paper, we consider dynamical behavior of a comparatively simple self-oscillating circuit only with an inductor, a capacitor and a memristor, but this circuit can produce a self-sustained oscillation. By applying the point transformation method and the multiple-scale method, we carefully analyze dynamics of this circuit and find there exists a periodic solution. In our study, the two cases for the flux-charge relation of a memristor, i.e., continuous piecewise-linear function and discontinuous function, are considered. By using the above two approaches, we analytically obtain the approximated period and amplitude of the periodic solution. Some numerical examples also verify the correctness of theoretical analysis.

关键词： Memristor piecewise-linear function Discontinuous function Oscillation The point transformation method The multiple-scale method

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Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 2019年第14期29卷

作者： Kuate, P. D. Kamdem Lai, Qiang Fotsin, Hilaire Univ Dschang Dept Phys Lab Condensed Matter Elect & Signal Proc POB 067 Dschang Cameroon East China Jiaotong Univ Sch Elect & Automat Engn Nanchang 330013 Jiangxi Peoples R China

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott's work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincare map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

关键词： Chaotic system Lorenz system Sprott system electronic implementation piecewise-linear function nonhyperbolic equilibrium

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Analysis of cloudiness by intensity segmentation and clustering

Analysis of cloudiness by intensity segmentation and cluster...

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44th WILGA Symposium on Photonics Applications and Web Engineering

作者： Melnyk, Roman A. Kalychak, Yuriy I. Tushnytskyy, Ruslan B. Sawicki, Daniel Yeraliyeva, Bakhyt Lviv Polytech Natl Univ Lvov Ukraine Lublin Univ Technol Lublin Poland Taraz State Univ Taraz Kazakhstan

ISBN: (纸本)9781510630666

Algorithm of Ramer-Douglas-Peucker for piecewise approximation was used for image multilevel segmentation. The cumulative histogram was chosen as a function for approximation. The developed algorithm was applied to the satellite map images to divide clouds of different intensity. The map images of clouds with different intensity were clustered to obtaine cloudiness values and classification.

关键词： approximation clustering cloudiness cumulative histogram piecewise-linear function threshold

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Computing the Distance between piecewise-linear Bivariate functions

Computing the Distance between Piecewise-Linear Bivariate Fu...

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23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

作者： Moroz, Guillaume Aronov, Boris INRIA Nancy Grand Est 615 Rue Jardin Bot F-54600 Villers Les Nancy France NYU Dept Comp Sci & Engn Tandon Sch Engn 2 MetroTech Ctr Brooklyn NY 11201 USA

ISBN: (纸本)9781611972108

We consider the problem of computing the distance between two piecewise-linear bivariate functions f and g defined over a common domain M, induced by the L-2 norm-that is, parallel to f -g parallel to 2 = root integral M(f - g)(2). If f is defined by linear interpolation over a triangulation of M with n triangles and g is defined over another such triangulation, the obvious naive algorithm requires Theta(n(2)) arithmetic operations to compute this distance. We show that it is possible to compute it in O(n log(4) n log log n) arithmetic operations by reducing the problem to multipoint evaluation of a certain type of polynomials. We also present several generalizations and an application to terrain matching.

关键词： piecewise-linear function polyhedral terrain multipoint evaluation

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Computing the Distance between piecewise-linear Bivariate functions

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ACM TRANSACTIONS ON ALGORITHMS 2016年第1期12卷 3-3页

作者： Moroz, Guillaume Aronov, Boris INRIA Nancy Grand Est 615 Rue Jardin Bot F-54600 Villers Les Nancy France NYU Dept Comp Sci & Engn Tandon Sch Engn 2 MetroTech Ctr Brooklyn NY 11201 USA

关键词： piecewise-linear function polyhedral terrain multipoint evaluation

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Action of the complex Monge-Ampere operator on piecewise-linear functions and exponential tropical varieties

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IZVESTIYA MATHEMATICS 2014年第5期78卷 902-921页

作者： Kazarnovskii, B. Ya. RAS Inst Informat Transmiss Problems Kharkevich Inst Moscow Russia

We consider exponential tropical varieties, which appear as analogues of algebraic tropical varieties when we pass from algebraic varieties to varieties given by zero sets of systems of exponential sums. We describe a construction of exponential tropical varieties arising from the action of the complex Monge-Ampere operator on piecewise-linear functions and show that every such variety can be obtained in this way. As an application, we deduce a criterion for the vanishing of the value of the mixed Monge-Ampere operator. This is an analogue and generalization of the criterion for the vanishing of the mixed volume of convex bodies.

关键词： piecewise-linear function Monge-Ampere operator exponential tropical variety

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COMPUTING CORRELATION BETWEEN piecewise-linear functionS

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SIAM JOURNAL ON COMPUTING 2013年第5期42卷 1867-1887页

作者： Agarwal, Pankaj K. Aronov, Boris van Kreveld, Marc Loffler, Maarten Silveira, Rodrigo I. Duke Univ Dept Comp Sci Durham NC 27708 USA Polytech Inst New York Dept Comp Sci & Engn Brooklyn NY 11201 USA Univ Utrecht Dept Informat & Comp Sci Utrecht Netherlands Univ Politecn Cataluna Dept Matemat Aplicada 2 ES-08034 Barcelona Spain

We study the problem of computing correlation between two piecewise-linear bivariate functions defined over a common domain, where the surfaces they define in three dimensions-polyhedral terrains-can be transformed vertically by a linear transformation of the third coordinate (scaling and translation). We present a randomized algorithm that minimizes the maximum vertical distance between the graphs of the two functions, over all linear transformations of one of the terrains, in O(n(4/3) polylog n) expected time, where n is the total number of vertices in the graphs of the two functions. We also present approximation algorithms for minimizing the mean distance between the graphs of univariate and bivariate functions. For univariate functions we present a (1 + epsilon)-approximation algorithm that runs in O(n(1 + log(2)(1/epsilon))) expected time for any fixed epsilon > 0. The (1 + epsilon)-approximation algorithm for bivariate functions runs in O(n/epsilon) time, for any fixed epsilon > 0, provided the two functions are defined over the same triangulation of their domain.

关键词： piecewise-linear function polyhedral terrain similarity approximation algorithm correlation

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Prior distribution elicitation for generalized linear and piecewise-linear models

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JOURNAL OF APPLIED STATISTICS 2013年第1期40卷 59-75页

作者： Garthwaite, Paul H. Al-Awadhi, Shafeeqah A. Elfadaly, Fadlalla G. Jenkinson, David J. Open Univ Dept Math & Stat Milton Keynes MK7 6AA Bucks England Kuwait Univ Safat 13060 Kuwait Univ Birmingham Birmingham B15 2TT W Midlands England

An elicitation method is proposed for quantifying subjective opinion about the regression coefficients of a generalized linear model. Opinion between a continuous predictor variable and the dependent variable is modelled by a piecewise-linear function, giving a flexible model that can represent a wide variety of opinion. To quantify his or her opinions, the expert uses an interactive computer program, performing assessment tasks that involve drawing graphs and bar-charts to specify medians and other quantiles. Opinion about the regression coefficients is represented by a multivariate normal distribution whose parameters are determined from the assessments. It is practical to use the procedure with models containing a large number of parameters. This is illustrated through practical examples and the benefit from using prior knowledge is examined through cross-validation.

关键词： assessment tasks elicitation generalized linear model piecewise-linear function prior distribution subjective probability

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Identification of Wiener systems with nonlinearity being piecewise-linear function

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Science in China(Series F) 2008年第1期51卷 1-12页

作者： HUANG YiQing CHEN HanFu FANG HaiTao Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Graduate School of the Chinese Academy of Sciences Beijing 100039 China

Identification of the Wiener system with the nonlinear block being a piecewiselinear function is considered in the paper, generalizing the results given by H. E. Chen to the case of noisy observation. Recursive algorithms are given for estimating all unknown parameters contained in the system, and their strong consistency is proved. The estimation method is similar to that used by H. E. Chen for Hammerstein systems with the same nonlinearity. However, the assumption imposed by H. E. Chen on the availability of an upper bound for the nonsmooth points of the piecewise-linear function has been removed in this paper with the help of designing an additional algorithm for estimating the upper bound.

关键词： Wiener system recursive identification strong consistency piecewise-linear function stochastic approximation

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