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.
This paper considers the initial value problem of general nonlinear stochastic fractional integro-differential equations with weakly singular kernels. Our effort is devoted to establishing some fine estimates to inclu...
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The aim of this paper is to develop a refined error estimate of L1.finite element scheme for a reaction-subdiffusion equation with constant delay τ and uniform time mesh. Under the non-uniform multi-singularity assum...
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In this paper, applying majorization inequalities, new upper and lower bounds for summation of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation are presented. Correspondin...
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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 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 random walk is one of the most basic dynamic properties of complex networks,which has gradually become a research hotspot in recent years due to its many applications in actual *** important characteristic of the ...
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The random walk is one of the most basic dynamic properties of complex networks,which has gradually become a research hotspot in recent years due to its many applications in actual *** important characteristic of the random walk is the mean time to absorption,which plays an extremely important role in the study of topology,dynamics and practical application of complex *** the mean time to absorption on the regular iterative self-similar network models is an important way to explore the influence of self-similarity on the properties of random walks on the *** existing literatures have proved that even local self-similar structures can greatly affect the properties of random walks on the global network,but they have failed to prove whether these effects are related to the scale of these self-similar *** this article,we construct and study a class of Horizontal Par-titioned Sierpinski Gasket network model based on the classic Sierpinski gasket net-work,which is composed of local self-similar structures,and the scale of these structures will be controlled by the partition coefficient ***,the analytical expressions and approximate expressions of the mean time to absorption on the network model are obtained,which prove that the size of the self-similar structure in the network will directly restrict the influence of the self-similar structure on the properties of random walks on the ***,we also analyzed the mean time to absorption of different absorption nodes on the network tofind the location of the node with the highest absorption efficiency.
The numerical stability of nonlinear equations has been a long-standing concern and there is no standard framework for analyzing long-term qualitative behavior. In the recent breakthrough work [XX23], a rigorous numer...
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The numerical stability of nonlinear equations has been a long-standing concern and there is no standard framework for analyzing long-term qualitative behavior. In the recent breakthrough work [XX23], a rigorous numerical analysis was conducted on the numerical solution of a scalar ODE containing a cubic polynomial derived from the Allen-Cahn equation. It was found that only the implicit Euler method converge to the correct steady state for any given initial value u0 under the unique solvability and energy stability. But all the other commonly used second-order numerical schemes exhibit sensitivity to initial conditions and may converge to an incorrect equilibrium state as tn → ∞. This indicates that energy stability may not be decisive for the long-term qualitative correctness of numerical solutions. We found that using another fundamental property of the solution, namely monotonicity instead of energy stability, is sufficient to ensure that many common numerical schemes converge to the correct equilibrium state. This leads us to introduce the critical step size constant h∗ = h∗(u0, ϵ) that ensures the monotonicity and unique solvability of the numerical solutions, where the scaling parameter ϵ ∈ (0, 1.. For a given numerical method, if the initial value u0 is given, no matter how large it is, we prove that h∗ > 0. As long as the actual simulation step 0 ∗, the numerical solution preserves monotonicity and converges to the correct equilibrium state. On the other hand, we prove that the implicit Euler scheme h∗ = h∗(ϵ), which is independent of u0 and only depends on ϵ. Hence regardless of the initial value taken, the simulation can be guaranteed to be correct when h ∗. But for various other numerical methods, no mater how small the step size h is in advance, there will always be initial values that cause simulation errors. In fact, for these numerical methods, we prove that infu0∈R h∗(u0, ϵ) = 0. Various numerical experiments are used to confirm the theoretical anal
Metasurfaces are a type of metamaterial that have two-dimensional structures. In comparison to traditional metamaterials, metasurfaces have several advantages such as being lightweight, easily controllable, and simple...
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