不动点集为RP（1）×CP（N）的带有对合的流形

令 (M,T)是一个在光滑闭流形上的光滑对合 ,它的不动点集为 F ,本文确定了 F=RP(1 )× CP(N )的对合的协边分类     

Two-Phase Image Segmentation by Nonconvex Nonsmooth Models with Convergent Alternating Minimization Algorithms

Two-phase image segmentation is a fundamental task to partition an image into foreground and background. In this paper, two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation. They extend the convex regularization on the characteristic function on the image domain to the nonconvex case, which are able to better obtain piecewise constant regions with neat boundaries. By analyzing the proposed non-Lipschitz model, we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm. This leads to two alternating strongly convex subproblems which can be easily solved. Similarly, we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case. Using the Kurdyka-Łojasiewicz property of the objective function, we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem. Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.     

刚体撞块撞击弹性长杆的二次撞击分析

本文采用应力波特征线方法详细分析了刚体撞击固支的弹性长杆的撞击过程，指出当撞块质量和长杆质量的比值满足一定条件时，在第一次撞击过程结束后会发生第二次撞击。     

岩石结构面的表面形态特征研究

本文用理论分析和数值模拟方法对具有不同粗糙度和起伏度的岩石结构面的形态特征作了定量研究, 着重研究了结构面表面形态参数与基本形态特征参数的关系, 并研究了它们的采样效应。得到了一系列在建立表面形态参数与物理量相互关系时对合理选用表面形态参数有重要意义的结果, 并可为选取合理的采样间隔和最小采样长度提供依据。     

脲和盐酸胍诱导的卵清溶菌酶分子去折叠过程中各稳定构象态的分布和过渡

以内源荧光光谱和荧光相图法研究了脲和盐酸胍诱导的卵清溶菌酶分子的去折叠过程,结果表明,当变性液中脲和盐酸胍的浓度分别约为4.0和3.0 mol/L时,卵清溶菌酶分子的去折叠过程均存在一个折叠中间态,这两个去折叠过程均符合"三态模型".在卵清溶菌酶分子"三态"去折叠过程的基础上,通过变性剂分子和卵清溶菌酶分子之间的缔合一...     

Function-valued Padé-type approximant via E-algorithm and its applications in solving integral equations

The function-valued Padé-type approximant (FPTA) was defined in the inner product space [8]. In this work, we choose the coefficients in the Neumann power series to make the inner product with both sides a function-valued system of equations to yield a scalar system. Then we express an FPTA in the determinant form. To avoid the direct computation of the determinants, we present the E-algorithm for FPTA based on the vector-valued E-algorithm given by Brezinski [4]. The method of FPTA via E-algorithm (FPTAVEA) not only includes all previous methods but overcomes their essential difficulties. The numerical experiment for a typical integral equation [1] illustrates that the method of FPTAVEA is simpler and more effective for obtaining the characteristic values and the characteristic functions than all previous methods. In addition, this method is also applicable to other Fredholm integral equations of the second kind without explicit characteristic values and characteristic functions. A corresponding example [12] is given and the numerical result is the same as that in [12].     

粗信息矩阵的数量特征

利用已给出粗信息矩阵及粗集的有关理论,提出并研究了粗信息矩阵的两个数量特征--粗牲度短阵及粗精度矩阵,给出了一系列性质及定理.     

Hopf cyclic cohomology and transverse characteristic classes

We refine the cyclic cohomological apparatus for computing the Hopf cyclic cohomology of the Hopf algebras associated to infinite primitive Cartan–Lie pseudogroups, and for the transfer of their characteristic classes to foliations. The main novel feature is the precise identification as a Hopf cyclic complex of the image of the canonical homomorphism from the Gelfand–Fuks complex to the Bott complex for equivariant cohomology. This provides a convenient new model for the Hopf cyclic cohomology of the geometric Hopf algebras, which allows for an efficient transport of the Hopf cyclic classes via characteristic homomorphisms. We illustrate the latter aspect by indicating how to realize the universal Hopf cyclic Chern classes in terms of explicit cocycles in the cyclic cohomology of étale foliation groupoids.     

A new result on irreducible NFSRs with respect to cascade connection

Nonlinear feedback shift registers (NFSRs) are widely used in stream cipher design as building blocks. The cascade connection of NFSRs, known as an important architecture, has been adopted in Grain family of stream ciphers. In this paper, a new sufficient condition under which an NFSR cannot be decomposed into the cascade connection of two smaller NFSRs is presented, which is easy to be verified from the algebraic normal form (ANF) of the characteristic function. In fact, our results are also applicable to nonsingular Boolean functions, which actually improve a previous research of Rhodes [6] where the characteristic functions of NFSRs cannot be contained.     

基于优选NIR光谱波数的绿豆产地无损检测方法

产地是影响农作物生产的重要环境因素,产地溯源对于食品安全具有重要意义。针对传统农产品产地检测一般采用化学分析法,其操作繁琐且存在破坏性和耗时较长等不足的问题,以北方寒地绿豆为研究对象,分别在白城、杜蒙、泰来等优质绿豆主产区,获取绿豆的籽粒和粉末两种状态的近红外光谱数据（NIR）,利用优选NIR光谱特征波数,建立了绿豆产地无损检测的新方法。首先在吸光度值较强的10 105.37~4 078.655 cm-1波数范围内,采用多元散射校正法（MSC）,对不同产地的绿豆原始光谱数据进行预处理,以消除光谱干扰信息。应用竞争性自适应重加权采样算法（CARS）,优选不同产地绿豆籽粒和粉末状态的光谱特征波数,以减少光谱曲线的特征向量维度。最后利用前馈神经网络（BP）自适应推理机制,建立了绿豆产地与其光谱特征波数之间非线性映射模型,并将网络输出的编码向量解析至产地名称,作为绿豆产地检测的输出结果。研究结果表明：（1）原始光谱经过多元散射校正预处理后,绿豆粉末光谱曲线的误差从12.87降到3.20,绿豆籽粒光谱曲线的误差从153.04降到27.73,提供有效可靠的光谱数据。（2）通过竞争性自适应重加权采样算法,提取绿豆光谱曲线的重要特征波数,从籽粒和粉末状态原始2 114个波数中,分别优化为61个和107个特征波数,波段总数目减少了94.94%以上,并将其作为绿豆产地识别的特征指标。（3）创新性提出了MSC-CARS-BP绿豆产地检测模型,以优选出的光谱特征波数为定量依据,分别对绿豆籽粒和粉末进行产地检测,预测集准确率为92.59%和98.63%,相关系数均达到0.99以上。该方法能够利用近红外光谱处理技术,实现绿豆产地无损检测的目标,为农产品产地自动快速溯源提供了技术支持和参考。