On the boomerang uniformity of a class of permutation quadrinomials over finite fields

Let ${\mathbb{F}}_{2^n}$ be a finite field with $2^n$ elements and $f_{\underset{\_}{c}}(x)=c_0{x}^{2^m(2^k+1)}+c_1{x}^{2^{m+k}+1}+c_2{x}^{2^m+2^k}+c_3{x}^{2^k+1}\in {\mathbb{F}}_{2^n}[x]$, where n, m and k are positive integers with $n=2m$ and $\gcd ?(m,k)=e$. In this paper, motivated by a recent work of Li, Xiong and Zeng (Li et al. (2021) [12]), we further study the boomerang uniformity of $f_{\underset{\_}{c}}(x)$ by using similar ideas and carrying out particular techniques in solving equations over finite fields. As a consequence, we generalize Li, Xiong and Zeng's result from the case of m being odd and $e=1$ to that of both $m/e$ and $k/e$ being odd.     

Translating Surfaces of the Non-parametric Mean Curvature Flow in Lorentz Manifold M2 × R*

In this paper, for the Lorentz manifold M² × R with M² a 2-dimensional complete surface with nonnegative Gaussian curvature, the authors investigate its spacelike graphs over compact, strictly convex domains in M² , which are evolving by the nonparametric mean curvature flow with prescribed contact angle boundary condition, and show that solutions converge to ones moving only by translation.     

Giant magnetocurrent in triple-barrier ferromagnetic resonant-tunneling diode with different magnetization configurations

The authors theoretically investigate a triple-barrier ferromagnetic resonant-tunneling diode composing nonmagnetic couple wells and three GaMnN magnetic barriers, in which two kinds of antiparallel configurations are formed by changing the relative orientation of magnetization in the barriers. Based on a two-band model, the achievement of large magnetocurrents in the resonant bias regime is proposed under an optimal magnetization configuration. The magnetocurrents in both antiparallel configurations of triple-barrier system are much higher than that in double-barrier structure.     

可参数化曲面上特征值比较的数值计算原理

对于一个给定的完备可参数化曲面,我们给出了其上特征值比较时进行数值计算所遵循的基本原理.     

Ricci curvature,radial curvature and large volume growth

In this paper, we study complete noncompact Riemannian manifolds with Ricci curvature bounded from below. When the Ricci curvature is nonnegative, we show that this kind of manifolds are diffeomorphic to a Euclidean space, by assuming an upper bound on the radial curvature and a volume growth condition of their geodesic balls. When the Ricci curvature only has a lower bound, we also prove that such a manifold is diffeomorphic to a Euclidean space if the radial curvature is bounded from below. Moreover, by assuming different conditions and applying different methods, we shall prove more results on Riemannian manifolds with large volume growth.     

Weight distributions and weight hierarchies of two classes of binary linear codes

Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of a linear code has many applications such as on the type II wire-tap channel, dealing with t-resilient functions and trellis or branch complexity of linear codes and so on. In this paper, we present a formula for computing the weight hierarchies of linear codes constructed by the generalized method of defining sets. Then, we construct two classes of binary linear codes with a few weights and determine their weight distributions and weight hierarchies completely. Some codes of them can be used in secret sharing schemes.     

The Surface Area Preserving Mean Curvature Flow in Quasi-Fuchsian Manifolds

In this paper, we consider the surface area preserving mean curvature flow in quasi-Fuchsian 3-manifolds. We show that the flow exists for all times and converges exponentially to a smooth surface of constant mean curvature with the same surface area as the initial surface.     

On the nucleation of a Zener crack from a wedge disclination dipole in the presence of a circular inhomogeneity

The nucleation of a Mode-I Zener crack from a wedge disclination dipole in the presence of a circular inhomogeneity is investigated. It is assumed that the disclination dipole and the nucleated Zener crack are along the radial direction of the inhomogeneity. Two cases are studied herein, i.e., the positive or negative wedge disclination of the dipole locates nearer to the inhomogeneity respectively. In order to investigate how various factors such as the elastic mismatch between the inhomogeneity and the matrix influence the nucleation of the Zener crack, the Stress Intensity Factor (SIF) at the sharp tip of the Zener crack is determined for different sets of geometric and material parameters with the distributed dislocation technique. The formulated singular integral equations are then solved numerically. Our results indicate that a nearby ‘hard’ inhomogeneity (having a higher shear modulus than the matrix) is beneficial to the crack nucleation for the first case (the positive disclination locates nearer to the inhomogeneity) while it retards the crack nucleation for the second case (the negative disclination locates nearer to the inhomogeneity). A nearby ‘soft’ inhomogeneity is helpful to the crack nucleation for the second case while it has inverse effects on the crack nucleation for the first case. This phenomenon can be explained with the concept of material force. The characteristics of the crack nucleation and the effects of the disclination strength, the distance between the inhomogeneity and the dipole, the disclination dipole arm length and inhomogeneity size on the crack nucleation are also systematically studied. The obtained results are helpful to characterize and enhance the strength of precipitate alloys and particle reinforced composites.