Mathematical modelling and theoretical analysis of nonholonomic kinematic systems with a class of rheonomous affine constraints

In this paper, we deal with kinematic control systems subject to a class of rheonomous affine constraints. We first define A-rheonomous affine constraints and explain a geometric representation method for them. Next, we derive a necessary and sufficient condition for complete nonholonomicity of the A-rheonomous affine constraints. Then, a mathematical model of nonholonomic kinematic systems with A-rheonomous affine constraints (NKSARAC), which is included in the class of nonlinear affine control systems, is introduced. Theoretical analysis on linearly-approximated systems and accessibility for the NKSARAC is also shown. Finally, we apply the results to some physical examples in order to confirm the effectiveness of them.     

Baxterization of Solutions to Reflection Equation with Hecke R-matrix

Let R be a Hecke solution to the Yang–Baxter equation and K be a reflection equation matrix with coefficients in an associative algebra . Let R(x) be the baxterization of R and suppose that K satisfies a polynomial equation with coefficients in the center of . We construct solutions to the reflection equation with spectral parameter relative to R(x), in the form of polynomials in K.     

伪仿射对偶框架

对于给定冗余的仿射框架X（Ф）={Ф1,…,ФL）,存在对偶Y（ψ）={ψ1,…,ψL）,这个对偶可能不是仿射框架,因为它不满足Bessel条件．这样的对偶我们称为伪仿射对偶,并给出伪仿射对偶框架的一种构造公式．     

Affine transformations of the direct product of nonprojective Euclidean affinely connected spaces

In this paper we obtain exact bounds for dimensions of the Lie algebras of infinitesimal affine transformations of the direct product of two nonprojective Euclidean affinely connected spaces without torsion.     

F_(16)上线性化的正形置换多项式的形式与计数

利用置换多项式理论的有关结果,给出了有限域F16上线性化的正形置换多项式的具体表示形式及计数,其中得出其个数为1604.     

Half-space type theorems in warped product spaces with one-dimensional factor

This work states some half-space type theorems in a warped product space of the form I ×_ρ M, where is an open interval and M is either a compact n-manifold, or a complete simply connected surface with constant curvature c ≤ 0. Such theorems generalize the classical half-space theorem for minimal surfaces in R ³, obtained by Hoffmann and Meeks (Invent Math 101:373–377, 1990), and recent results for surfaces contained in a slab of R ×_ρ M, obtained by Dajczer and Alías (Comment Math Helvetici 81:653–663, 2006).      

有界约束非线性优化问题的仿射共轭梯度路径法

本文提出仿射内点离散共轭梯度路径法解有界约束的非线性优化问题,通过构造预条件离散的共轭梯度路径解二次模型获得预选迭代方向,结合内点回代线搜索获得下一步的迭代,在合理的假设条件下,证明了算法的整体收敛性与局部超线性收敛速率,最后,数值结果表明了算法的有效性.     

等离子体浸没离子注入非导电聚合物的适应性及栅网诱导效应的研究

本文建立了绝缘材料等离子体浸没离子注入过程的动力学Particle-in-cell(PIC)模型, 将二次电子发射系数直接与离子注入即时能量建立关联, 研究了非导电聚合物厚度、介电常数和二次电子发射系数对表面偏压电位的影响规律以及栅网诱导效应. 研究结果表明: 非导电聚合物较厚时, 表面自偏压难以实现全方位离子注入, 栅网诱导可以间接为非导电聚合物提供偏压, 并抑制二次电子发射, 为厚大非导电聚合物表面等离子体浸没离子注入提供了有效途径.     

Shapley-Folkman-Starr 定理的推广

本文引进了一个新的概念: R^d 中非空紧子集的两个向量的p 和, 当p = 1 时, p 和就是通常的向量加. 然后给出了p 和的一些属性. 进一步建立了p- 型Shapley-Folkman-Starr 定理.     

多模自适应电子稳像算法研究

电子稳像算法的主要目的是解决摄像机随机运动导致的图像序列的帧间抖动问题。根据摄像机成像模型,推导了摄像机平移振动和旋转运动对图像运动的影响,阐明了电子稳像算法中各种图像运动模型的物理成因,指出了模型之间的内在联系。提出了一种多模自适应电子稳像算法,根据摄像机工作时图像序列抖动的剧烈程度,自适应地选择适当的图像运动模型和相应的运动估计方法。实验结果表明,该算法在各种情况下都能实现对图像序列的高精度稳定,有效地提高了电子稳像算法的适用性。