"广义芝诺悖论"的再探讨

在第25卷第5期的《大学物理》上,一篇文章对"广义芝诺悖论"进行了探讨,但他们分析的并不是"悖论"中的匀速率的理想运动,而且还存在推导错误.本文通过对"广义芝诺悖论"物理情境的分析,抽象建立起VPV模型,并由此得出:从运动学角度考虑,"广义芝诺悖论"正过程的初态和末态是"多对一"的关系,"广义芝诺悖论"并不为悖论.     

低汉明重量序列的分布

数n的汉明重量是指n的二进制字符串表达式中数字1的个数,用Ham(n)来表示.低汉明重量序列在密码系统和编码理论中有非常广泛的应用.本文建立了低汉明重量数的序列表达式,并且利用指数和的上界以及Erd?s-Turán不等式证明低汉明重量序列的均匀分布性质,从而确保密码算法的随机性和运算效率.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.     

Magnetization switching modes in nanopillar spin valve under the external field

The current-induced magnetic switching is studied in Co/Cu/Co nanopillar with an in-plane magnetization traversed under the perpendicular-to-plane external field.Magnetization switching is found to take place when the current density exceeds a threshold.By analyzing precessional trajectories,evolutions of domain walls and magnetization switching times under the perpendicular magnetic field,there are two different magnetization switching modes:nucleation and domain wall motion reversal;uniform magnetization ...     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.     

Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms

Explicit and partly sharp estimates are given of integrals over the square of Bessel functions with an integrable weight which can be singular at the origin. They are uniform with respect to the order of the Bessel functions and provide explicit bounds for some smoothing estimates as well as for the L² restrictions of Fourier transforms onto spheres in which are independent of the radius of the sphere. For more special weights these restrictions are shown to be Hölder continuous with a Hölder constant having this independence as well. To illustrate the use of these results a uniform resolvent estimate of the free Dirac operator with mass in dimensions is derived.     

A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.     

Carbon nanospheres with well‐controlled nano‐morphologies as support for palladium‐catalyzed Suzuki coupling reaction

Uniform carbon nanospheres (UCS) with well‐controlled nano‐morphologies were fabricated by hydrothermal carbonization of sucrose in the presence of kayexalate. Highly dispersed and ultrafine palladium nanoparticles were supported on the UCS through a facile co‐reduction process with NaBH₄ as reducing agent. The obtained Pd@UCS exhibited efficient catalytic activity for the Suzuki coupling reaction. Moreover, the as‐prepared catalyst could be recycled and reused at least five times without significant loss of its catalytic activity.     

Optimal uniform approximation on angles by entire functions

The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Δ. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions ? subject to approximation are holomorphic in a larger angle containing Δ and there is no restriction on the growth of ? at infinity. In [8], the problem was investigated for a wider class of functions ? continuously complex differentiable on Δ, with sharper estimates on the growth of approximating entire functions, linked with the growth of ? on Δ and the differential properties of ? on the boundary of Δ. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10].