In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced that converges to the solution under suitable conditions. In the nonlinear case, the terms of the seq...
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In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced that converges to the solution under suitable conditions. In the nonlinear case, the terms of the sequence become complicated after a few iterations, and thus computing a highly accurate solution is difficult or even impossible. In this study, we propose a new approach for one-dimensional initial value problems, which is based on approximating each term of the sequence by a piecewise linear function. Moreover, we prove the convergence of the method. Three illustrative examples are given to demonstrate the superior performance of the proposed method compared with the classical variational iteration method. (C) 2015 Elsevier Inc. All rights reserved.
We consider linear generalized Nash games and introduce the so-called cone condition, which characterizes the smoothness of a gap function that arises from a reformulation of the generalized Nash equilibrium problem a...
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We consider linear generalized Nash games and introduce the so-called cone condition, which characterizes the smoothness of a gap function that arises from a reformulation of the generalized Nash equilibrium problem as a piecewiselinear optimization problem based on the Nikaido-Isoda function. Other regularity conditions such as the linear independence constraint qualification or the strict Mangasarian-Fromovitz condition are only sufficient for smoothness, but have the advantage that they can be verified more easily than the cone condition. Therefore, we present special cases, where these conditions are not only sufficient, but also necessary for smoothness of the gap function. Our main tool in the analysis is a global extension of the gap function that allows us to overcome the common difficulty that its domain may not cover the whole space.
The paper deals with positively homogeneous functions defined on a finite-dimensional space. Our attention is mainly focused on those subspaces of positively homogeneous functions that are important in nonsmooth analy...
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The paper deals with positively homogeneous functions defined on a finite-dimensional space. Our attention is mainly focused on those subspaces of positively homogeneous functions that are important in nonsmooth analysis and optimization: the subspace of continuous positively homogeneous functions, of Lipschitz continuous positively homogeneous functions, of difference sublinearfunctions, and of piecewise linear functions. We reproduce some known results and present a number of new ones, in particular, those that concern Lipschitz continuous positively homogeneous functions.
The problem of approximating the complex-valued function modulus using a minimax criterion is of interest in many technical applications, such as standard process controlling systems with limiting the transient oscill...
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ISBN:
(纸本)9781509013227
The problem of approximating the complex-valued function modulus using a minimax criterion is of interest in many technical applications, such as standard process controlling systems with limiting the transient oscillations, low-side-lobe antenna arrays, or multiplexing devices having a deep channel isolation. The paper introduces approximate formulas to compute the absolute value of a complex number based on piecewiselinear inequalities, thanks to which the approximation problem may be reduced to the minimax linear programming problem allowing the use of standard application packages. Computational experiments, the results of which are discussed, have proven the efficiency of the proposed computing algorithm combining high speed and good approximation accuracy.
This paper focuses utilization of I/Q-modulation technique for radio channel orthogonal frequency division multiplexing. Particularly, quasi harmonic piece-wise linearfunctions (QLF) are introduced to construct ortho...
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ISBN:
(纸本)9786176078067
This paper focuses utilization of I/Q-modulation technique for radio channel orthogonal frequency division multiplexing. Particularly, quasi harmonic piece-wise linearfunctions (QLF) are introduced to construct orthogonal functional basis due to solely phase modulation of radio channel carrier. In contrast to conventional OFDM coding, the QLF basis confines peak to-average power ratio and provides elastic channel performance adaptation.
We consider isosceles orthogonality and Birkhoff orthogonality, which are the most used notions of generalized orthogonality. In 2006, Ji and Wu introduced a geometric constant D(X) to give a quantitative characteriza...
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We consider isosceles orthogonality and Birkhoff orthogonality, which are the most used notions of generalized orthogonality. In 2006, Ji and Wu introduced a geometric constant D(X) to give a quantitative characterization of the difference between these two orthogonality types. From their results, we have that D(X)=D(X∗) holds for any symmetric Minkowski plane. On the other hand, for the James constant J(X), Saito, Sato and Tanaka recently showed that if the norm of a two-dimensional space X is absolute and symmetric then J(X)=J(X∗) holds. In this paper, we consider the constant D(X,λ) such that D(X)=infλ∈RD(X,λ) and obtain that in the same situation D(X,λ)=D(X∗,λ) holds for any λ∈(0,1).
This paper presents a new chaotic Hopfield network with a piecewiselinear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectru...
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This paper presents a new chaotic Hopfield network with a piecewiselinear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.
This paper proposes a dense stereo-based robust vertical road profile estimation method. The vertical road profile is modeled by a cubic B-spline curve, which is known to be accurate and flexible but difficult to esti...
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This paper proposes a dense stereo-based robust vertical road profile estimation method. The vertical road profile is modeled by a cubic B-spline curve, which is known to be accurate and flexible but difficult to estimate under a large proportion of outliers. To robustly estimate a cubic B-spline curve, the proposed method utilizes a two-step strategy that initially estimates a piecewise linear function and then obtains a cubic B-spline curve based on the initial estimation result. A Hough transform and dynamic programming are utilized for estimating a piecewise linear function to achieve robustness against outliers and guarantee optimal parameters. In the experiment, a performance evaluation and comparison were conducted using three publicly available databases. The result shows that the proposed method outperforms three previous methods in all databases. In particular, its performance is superior to the others in the cases of a large proportion of outliers and road surfaces distant from the ego-vehicle.
Working jointly in the equivalent categories of MV-algebras and lattice-ordered abelian groups with strong order unit (for short, unital l-groups), we prove that isomorphism is a sufficient condition for a separating ...
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Working jointly in the equivalent categories of MV-algebras and lattice-ordered abelian groups with strong order unit (for short, unital l-groups), we prove that isomorphism is a sufficient condition for a separating subalgebra A of a finitely presented algebra F to coincide with F. The separation and isomorphism conditions do not individually imply A= F. Various related problems, like the separation property of A, or A congruent to F (for A a separating subalgebra of F), are shown to be (Turing-) decidable. We use tools from algebraic topology, category theory, polyhedral geometry and computational algebraic logic.
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