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41.
A growing interest exists currently in the analysis of time series by the complex network theory. Here we present a simple and quick way for mapping time series to complex networks. Using a simple rule allows us to transform time series into a textual sequence then we divide it into words with fixed size. Distinct words are nodes of the network, and we have complete control on the network scale by adjusting the word size. Two nodes are linked if their associated words co-occur in sequence. We show that the network topological measures quantify the persistence and the long range correlations in fractional Brownian processes. For a particular word size we assume some relations between the topological measures and the Hurst exponent which characterised the persistence in fractional Brownian processes. 相似文献
42.
We consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold M isometrically immersed into another Riemannian manifold . We first assume the pull back Weitzenböck operator of bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results. Second, when the pull back Weitzenböck operator of bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of M and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then M is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates are optimal when is the space form. 相似文献
43.
《Optimization》2012,61(4):677-687
In this paper we give a necessary and sufficient condition for the pseudoconvexity of a function f which is the ratio of a quadratic function over an affine function. The obtained results allow to suggest a simple algorithm to test the pseudoconvexity of f and also to characterize the pseudoconvexity of the sum of a linear and a linear fractional function. 相似文献
44.
Mohammad Khorrami Ahmad Shariati Amir Aghamohammadi Amir H. Fatollahi 《Physics letters. A》2012,376(5):687-691
It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time. 相似文献
45.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(9):2935-2941
Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations. 相似文献
46.
In this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results. 相似文献
47.
Mohamed Ben Chrouda 《复变函数与椭圆型方程》2018,63(10):1378-1395
We investigate the existence and nonexistence of positive entire large solutions of a class of semilinear equations involving the fractional Laplacian. Sharp lower and upper bounds of the minimal solution, if it exists, are also given. 相似文献
48.
Siegfried Cools Bram Reps Wim Vanroose 《Numerical Linear Algebra with Applications》2014,21(4):513-533
In this paper, we construct and analyze a level‐dependent coarse grid correction scheme for indefinite Helmholtz problems. This adapted multigrid (MG) method is capable of solving the Helmholtz equation on the finest grid using a series of MG cycles with a grid‐dependent complex shift, leading to a stable correction scheme on all levels. It is rigorously shown that the adaptation of the complex shift throughout the MG cycle maintains the functionality of the two‐grid correction scheme, as no smooth modes are amplified in or added to the error. In addition, a sufficiently smoothing relaxation scheme should be applied to ensure damping of the oscillatory error components. Numerical experiments on various benchmark problems show the method to be competitive with or even outperform the current state‐of‐the‐art MG‐preconditioned Krylov methods, for example, complex shifted Laplacian preconditioned flexible GMRES. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
49.
《随机分析与应用》2013,31(5):1209-1233
Abstract In the paper we compute the explicit form of the fractional chaos decomposition of the solution of a fractional stochastic bilinear equation with the drift in the fractional chaos of order one and initial condition in a finite fractional chaos. The large deviations principle is also obtained for the one-dimensional distributions of the solution of the equation perturbed by a small noise. 相似文献
50.
The Laplacian spectrum of a graph consists of the eigenvalues (together with multiplicities) of the Laplacian matrix. In this article we determine, among the graphs consisting of disjoint unions of paths and cycles, those ones which are determined by the Laplacian spectrum. For the graphs, which are not determined by the Laplacian spectrum, we give the corresponding cospectral non-isomorphic graphs. 相似文献