一类二阶椭圆型微分方程振动性的判定

利用积分平均和完全平方技巧，给出了一类二阶椭圆型微分方程所有解在R^n的一个外区域Ω上均振动的新的充分条件。     

奇异非线性二阶三点边值问题正解的存在唯一性

本文研究了一类奇异非线性二阶三点边值问题，通过摄动技巧和比较原理获得了所论问题正解的存在唯一性。     

Condensations of projective sets onto compacta

For a coanalytic-complete or -complete subspace of a Polish space we prove that there exists a continuous bijection of onto the Hilbert cube . This extends results of Pytkeev. As an application of our main theorem we give an answer to some questions of Arkhangelskii and Christensen.

Under the assumption of Projective Determinacy we also give some generalizations of these results to higher projective classes.

     

多维正态分布均值在序约束下的假设检验

在序限制下的统计推断是统计分析中的一个重要领域，保序回归理论在这个领域中起着关键性的作用。多维保序回归是一维保序回归的推广，本文给出了k=2,p=2时多维保序回归的求解方法。令Xij,j=1,2…，n是来自总体为二维正态分布N（μi，Λ)的样本，这是μi是未知的，Λ是已知的，i=1,2。令μ=（μ1,μ2)，-={（μ1,μ2)|μ1,μ∈R^2,}-0={(μ1,μ2)|μ1≤μ2,μ1，μ2∈R^2}。μ1≤μ2表示μ2-μ1的每一个分量为非负。本文也讨论了假设检验问题H0:μ∈-0,H1:μ∈-0=---0(H0是零假设）。     

Skew Schubert polynomials

We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in Bruhat order of the symmetric group. These skew Schubert polynomials expand in the basis of Schubert polynomials with nonnegative integer coefficients that are precisely the structure constants of the cohomology of the complex flag variety with respect to its basis of Schubert classes. We rederive the construction of Bergeron and Sottile in a purely combinatorial way, relating it to the construction of Schubert polynomials in terms of rc-graphs.

     

On non-measurability of in its second dual

We show that with the weak topology is not an intersection of Borel sets in its Cech-Stone extension (and hence in any compactification). Assuming (CH), this implies that has no continuous injection onto a Borel set in a compact space, or onto a Lindelöf space. Under (CH), this answers a question of Arhangel'ski.

     

A fractional order hyperchaotic system derived from Liu system and its circuit realization

In this paper we propose a novel four-dimensional fractional order hyperchaotic system derived from Liu system. Electronics workbench (EWB) and Matlab simulations show the dynamical behavior of the proposed four-dimensional fractional order hyperchaotic system. Finally, after separately using EWB and Matlab, an electronic circuit is designed to realize the novel four-dimensional fractional order hyperchaotic system and the experimental circuit results are obtained which are identical to software simulations.     

亚铁磁Heusler合金Mn2CoGa和Mn2CoAl掺杂Cr,Fe和Co的局域铁磁结构

通过实验和计算的方法研究了Mn₂CoM_xGa_1-x 和Mn₂CoM_xAl_1-x (M=Cr, Fe, Co)掺杂系列合金样品. 研究发现, 在共价作用的影响下, Fe和Co原子占A位, 使被取代的MnA (-2.1 μ_B)变成MnD (3.2 μ_B), 在最近邻的强交换作用下亚铁磁基体中形成了MnB-CoC-MnD局域铁磁性结构, 使分子磁矩的增量最高可达6.18 μ_B. Fe, Co 掺杂后建立同样的局域铁磁结构, 居里温度的变化趋势却不同. 实验观察到Mn₂Co_1+xAl_1-x中掺杂容忍度高达x=0.64, 远高于在Mn₂CoGa中(x=0.36)的结果; 以及随着Al的减少, 合金由B2有序向A2混乱转变等现象, 为共价作用对合金结构稳定的影响提供了证据. 磁测量中发现Cr掺杂后磁矩增量高达3.65 μ_B以及居里温度快速上升的反常现象, 意味着对占位规则的违背.     

抑制高阶谐波误差的随机相移条纹分析算法

高阶谐波和随机相移误差是影响条纹分析精度的主要因素。为了同时解决这两个问题,提出了基于频域滤波的迭代相移算法。该算法采用巴特沃斯低通滤波器,从频域上滤除条纹的高阶谐波分量,再运用最小二乘迭代方法从三帧随机相移条纹图像中提取相位信息。数值模拟和实验结果表明,该算法可有效地抑制由高阶谐波和随机相移引入的波纹误差,误差PV值和RMS值分别为0.368 8 rad和0.025 3 rad,其精度高于传统的三步相移算法和Wang算法。该方法适合于高精度干涉测量和三维物体表面轮廓测量。     

Torsion Structure in Riemann-Cartan Manifold and Dislocation

The U(1) gauge structure of torsion and dislocation in three dimensional Riemann-Cartan manifold have been studied. The local topological structure of dislocation have been presented by so-called topological method in which the quantum number is by Hopf indices and Brouwer degree. Furthermore, the relationship between the dislocation lines and Wilson lines of the U(1) gauge theory is discussed by using the Chern-Simons theory.