On Hanner type inequalities with a weight for Banach spaces

We shall present several Hanner type inequalities with a weight constant and characterize 2-uniformly smooth and 2-uniformly convex Banach spaces with these inequalities. p-Uniformly smooth and q-uniformly convex Banach spaces will be also characterized with another Hanner type inequalities with a weight in the other side term. The best value of the weight in these inequalities will be determined for Lp spaces. Also we shall present a duality theorem between these inequalities in a generalized form.     

一种考虑多尺度噪声的平滑去噪方法

针对在实际采集三维点数据模型中遇到多种尺度噪声的问题,提出了一种基于噪声分类组合滤波平滑去噪的方法。首先根据点模型中噪声的位置、密度和无用性等特点,将其分为伪噪声、大尺度噪声和小尺度噪声三类;分别使用直通滤波、半径滤波和统计滤波,以及移动最小二乘重采样(MLS)去除;同时考虑到点云冗余,将体素化网格滤波与移动最小二乘重采样相结合,实现重采样点模型的优化。实验结果表明:能够很好的解决地面三维激光扫描仪采集的点数据模型中存在多种尺度噪声的问题。从模型视觉效果上的漏洞修复、特征保持和光顺效果,以及实际变形度上看,方法优于直接使用MLS重采样和Laplace平滑去噪。     

Reconstruction of a Piecewise Smooth Absorption Coefficient by an Acousto-Optic Process

The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the case where the optical absorption distribution is supposed to be a perturbation of a piecewise constant function. Analyzing the acousto-optic measurements, we prove that the optical absorption coefficient satisfies, in the sense of distributions, a new equation. For doing so, we introduce a weak Helmholtz decomposition and interpret in a weak sense the cross-correlation measurements using the spherical Radon transform. We next show how to find an initial guess for the unknown coefficient. Finally, in order to construct the true coefficient we provide a Landweber type iteration and prove that the resulting sequence converges to the solution of the system constituted by the optical diffusion equation and the new equation mentioned above. Our results in this paper generalize the acousto-optic process proposed in [5 Ammari , H. , Bossy , E. , Garnier , J. , Seppecher , L. ( 2012 ). Acousto-electromagnetic tomography . SIAM J. Appl. Math. 72 : 1592 – 1617 .[Crossref], [Web of Science ®] , [Google Scholar]] for piecewise smooth optical absorption distributions.     

Explicit piecewise smooth solutions of Landau-Lifshitz equation with discontinuous external field

In this paper, we shall construct some explicit piecewise smooth （global continuous） solutions as well as blow up solutions to the multidimensional Landau-Lifshitz equation, subject to the external magnetic fields being both discontinuous and unbounded. When the external magnetic field is continuous, some explicit exact smooth solutions and blow up solution are also constructed. We also establish some necessary and sufficient conditions to ensure that the solution of multidimensional Landau-Lifshitz equation with external magnetic field converges to the solution of equation without external magnetic field when the external magnetic field tends to zero.     

Spatiotemporal dynamics of Ca2+ signaling and its physiological roles

Changes in the intracellular Ca²⁺ concentration regulate numerous cell functions and display diverse spatiotemporal dynamics, which underlie the versatility of Ca²⁺ in cell signaling. In many cell types, an increase in the intracellular Ca²⁺ concentration starts locally, propagates within the cell (Ca²⁺ wave) and makes oscillatory changes (Ca²⁺ oscillation). Studies of the intracellular Ca²⁺ release mechanism from the endoplasmic reticulum (ER) showed that the Ca²⁺ release mechanism has inherent regenerative properties, which is essential for the generation of Ca²⁺ waves and oscillations. Ca²⁺ may shuttle between the ER and mitochondria, and this appears to be important for pacemaking of Ca²⁺ oscillations. Importantly, Ca²⁺ oscillations are an efficient mechanism in regulating cell functions, having effects supra-proportional to the sum of duration of Ca²⁺ increase. Furthermore, Ca²⁺ signaling mechanism studies have led to the development of a method for specific inhibition of Ca²⁺ signaling, which has been used to identify hitherto unrecognized functions of Ca²⁺ signals.     

上下料机器人关节速度规划

新兴的高新技术产业和智能化产业推动了上下料机器人的快速发展,但是其运动的平稳性限制着进一步的推广与应用.设计了一种4R上下料机器人.首先建立梯形、7段S曲线加减速控制算法,通过分析这两种算法对机器人运动平稳性的影响,提出了一种新型的S形加减速控制算法.利用ADAMS对三种算法进行仿真分析,结果表明新型的S形加减速控制算法在提高4R上下料机器人的运动平稳性方面更具优势并为4R上下料机器人后续的运动控制分析和优化奠定了基础.     

实一致光滑Banach空间中m增生映射零点的带误差项的迭代格式

令E为实一致光滑Banach空间,A：D（A）=E→2^E为m增生映射,z∈E为任意元,x1∈E为任意初始向量,0∈R（A）。序列{xn}∪→D（A）定义为xn＋1=xn-λn（un＋θn（xn-z＋en））,其中un∈Axn,A↓n≥1,这里{λn}和{θn}为满足一定条件的非负实数列,得到了xn→x^＊∈A^-1 0。本质上将Chidume和Zegeye于2002年提出的关于m增生映射零点的精确迭代格式推广为带误差项的形式。     

New bifurcations of basin boundaries involving Wada and a smooth Wada basin boundary

This paper demonstrates and analyses double heteroclinic tangency in a three-well potential model, which can produce three new types of bifurcations of basin boundaries including from smooth to Wada basin boundaries, from fractal to Wada basin boundaries in which no changes of accessible periodic orbits happen, and from Wada to Wada basin boundaries. In a model of mechanical oscillator, it shows that a Wada basin boundary can be smooth.     

Numerical treatment of two‐parameter singularly perturbed parabolic convection diffusion problems with non‐smooth data

In the present work, we consider a parabolic convection‐diffusion‐reaction problem where the diffusion and convection terms are multiplied by two small parameters, respectively. In addition, we assume that the convection coefficient and the source term of the partial differential equation have a jump discontinuity. The presence of perturbation parameters leads to the boundary and interior layers phenomena whose appropriate numerical approximation is the main goal of this paper. We have developed a uniform numerical method, which converges almost linearly in space and time on a piecewise uniform space adaptive Shishkin‐type mesh and uniform mesh in time. Error tables based on several examples show the convergence of the numerical solutions. In addition, several numerical simulations are presented to show the effectiveness of resolving layer behavior and their locations.     

一类迭代泛函方程光滑解的存在性

文章利用Faàdi Bruno公式及Schauder不动点定理,证明一类迭代泛函方程的光滑解的存在性和唯一性;在此基础上,进一步给出光滑解关于给定常数的连续依赖性定理;最后给出一个例子以说明本文的主要定理.