In this work, we study the long time behaviors, including asymptotic contractivity and dissipativity, of the solutions to several numerical methods for fractional ordinary differential equations (F-ODEs). The existing...
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We initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise for the isoparametric bilinear finite volume element scheme by employing the energy-embe...
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We initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise for the isoparametric bilinear finite volume element scheme by employing the energy-embedded method on some non-uniform grids. Furthermore, we prove that the approximate derivatives are convergent of order two. Numerical examples confirm theoretical results.
Using first-principles calculations, we investigate the evolution of electronic and magnetic properties of zigzag silicene nanoribbon (ZSiNR) along with the concentration of edge adsorbed hydrogen adatoms. Our study s...
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Using first-principles calculations, we investigate the evolution of electronic and magnetic properties of zigzag silicene nanoribbon (ZSiNR) along with the concentration of edge adsorbed hydrogen adatoms. Our study shows that the significant covalent bonding helps to stabilize the configurations of hydrogen adsorbed ZSiNRs. The ferro-metallic electronic property of ZSiNR originated from the σ-π mixing effect is suppressed by mono-hydrogenation at the adsorption sites due to the sp 2 bonding. However, bi-hydrogenation at the adsorbed sites will lead to the typical sp 3 bonding, which dominates the electronic property with the increasing of hydrogen adatoms. Under the coexisting situation with mono-hydrogenation and bi-hydrogenation, we find that both the number of adsorption sites and the bonding type of sp 2 or sp 3 have impact on the electronic property of ZSiNR. It is found that symmetry adsorption at the edges changes the stable magnetic state of ZSiNR from ferromagnetic to antiferromagnetic. In contrast, unsymmetrical adsorption along the two edges of ZSiNR keeps its ferromagnetic property.
The paper aims to establish a fully discrete finite element (FE) scheme and provide cost-effective solutions for one-dimensional time-space Caputo-Riesz fractional diffusion equations on a bounded domain Ω. Firstly, ...
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In this study we construct a time-space finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equations on a bounded domain Ω. Firstly...
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In this paper, we study the Hermite cubic spline collocation method with two parame- ters for solving a initial value problem （IVP） of nonlinear fractional differential equations with two Caputo derivatives. The con...
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In this paper, we study the Hermite cubic spline collocation method with two parame- ters for solving a initial value problem （IVP） of nonlinear fractional differential equations with two Caputo derivatives. The convergence and nonlinear stability of the method are established. Some illustrative examples are provided to verify our theoretical results. The numerical results also indicate that the convergence order is min{4 - α, 4 - β}, where 0 〈β〈 αa 〈 1 are two parameters associated with the fractional differential equations.
SUMMARY:A number of alignment-free methods have been proposed for phylogeny reconstruction over the past two decades. But there are some long-standing challenges in these methods, including requirement of huge compute...
SUMMARY:A number of alignment-free methods have been proposed for phylogeny reconstruction over the past two decades. But there are some long-standing challenges in these methods, including requirement of huge computer memory and CPU time, and existence of duplicate computations. In this article, we address these challenges with the idea of compressed vector, fingerprint and scalable memory management. With these ideas we developed the DLTree algorithm for efficient implementation of the dynamical language model and whole genome-based phylogenetic analysis. The DLTree algorithm was compared with other alignment-free tools, demonstrating that it is more efficient and accurate for phylogeny reconstruction.
AVAIlabILITY AND IMPLEMENTATION:The DLTree algorithm is freely available at http://***.
CONTACT:yuzuguo@*** or yangjy@***.
SUPPLEMENTARY INFORMATION:Supplementary data are available at Bioinformatics online.
A balancing domain decomposition by constraints (BDDC) algorithm with adaptive primal constraints in variational form is introduced and analyzed for high-order mortar discretization of two-dimensional elliptic problem...
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Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality o...
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Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality of weighted complex networks are still to be undertaken. In this paper, inspired by the concepts of Koch networks and Koch island, we propose a new family of weighted Koch networks, and investigate their multifractal behavior and topological properties. We find some key topological properties of the new networks: their vertex cumulative strength has a power-law distribution; there is a power-law relationship between their topological degree and weight strength; the networks have a high weighted clustering coefficient of 0.41004 (which is independent of the scaling factor c ) in the limit of large generation t ; the second smallest eigenvalue μ 2 and the maximum eigenvalue μ n are approximated by quartic polynomials of the scaling factor c for the general Laplacian operator, while μ 2 is approximately a quartic polynomial of c and μ n = 1.5 for the normalized Laplacian operator. Then, we find that weighted koch networks are both fractal and multifractal, their fractal dimension is influenced by the scaling factor c . We also apply these analyses to six real-world networks, and find that the multifractality in three of them are strong.
Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these prope...
Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.
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