On the counting function of the lattice profile of periodic sequences

The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period.     

基于椭圆型方程的扭叶片造型方法的研究

本文以偏微分方程造型为基础,提出了一种基于椭圆型方程的扭叶片三维型面直接设计方法,详细推导了叶型曲面函数,给出了型面方程的求解及其前后缘修正。该方法具有设计叶型曲面自然光顺,设计参数少且各参数具有明显的几何意义,叶型曲面调整方便,利于采用非数值优化算法对其进行气动优化等优点。文中给出了设计实例,并通过数值实验分析了所设计叶片型面的流动特性。分析结果表明设计叶片具有良好的气动性能,同时也证明了本文提出的基于椭圆型方程的扭叶片三维型面设计方法的可靠性和实用性。     

A Dominated Theorem on 5L(2, R) and Its Application

In this paper, we give the following dominated theorem: Let φ(g) ∈ L1(G//K),φε(t)=ε> 0, and the least radical decreasing dominatedfunction φ(t) = sup |φ(y)| ∈L1(G//K). If shtφ(t) is monotonically decreasingon (0, ∞), then for any f∈L1loc(G//K) , the following inequality holds:sup |φε * f(x)| ≤ Cmf(x),where mf(x) is the Hardy-Littlewood maximal function of f, and C = ||φ||1.An application of this dominated theorem is also given.     

Spin polarization effect for Tc2 molecule

Density functional method (DFT) (B3p86) of Gaussian98 has been used to optimize the structure of the Tc_2 molecule. The result shows that the ground state for Tc_2 molecule is an 11-multiple state and its electronic configuration is {}^{11}Σ_g^-, which shows the spin polarization effect of Tc_2 molecule of a transition metal element for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions of higher energy states. So, that the ground state for Tc_2 molecule is an 11-multiple state is indicative of the spin polarization effect of Tc_2 molecule of a transition metal element: that is, there exist 10 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Tc_2 molecule is minimized. It can be concluded that the effect of parallel spin of the Tc_2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell--Sorbie potential functions with the parameters for the ground state {}^{11}Σ_g^- and other states of Tc_2 molecule are derived. Dissociation energy D_e for the ground state of T_{c2} molecule is 2.266eV, equilibrium bond length R_e is 0.2841nm, vibration frequency ω_e is 178.52cm^{-1}. Its force constants f_2, f_3, and f_4 are 0.9200aJ·nm^{-2}, --3.5700aJ·nm^{-3}, 11.2748aJ·nm^{-4} respectively. The other spectroscopic data for the ground state of Tc_2 molecule ω_eχ_e, B_e, α_e are 0.5523cm^{-1}, 0.0426cm^{-1}, 1.6331×10^{-4}cm^{-1} respectively.     

On Brennan's Conjecture for a Special Class of Functions

In this paper, we prove Brennan's conjecture for conformal mappings f of the disk {z : | z| < 1} assuming that the Taylor coefficients of the function log(zf′(z)/f(z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle |z| = r of the squared modulus of the function zf′(z)/f(z).     

试探方程法及其在非线性发展方程中的应用

提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式，再利用三阶多项式的完 全判别系统求解，由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解 关键词： 试探方程法 非线性发展方程 孤波解 Jacobi椭圆函数 周期解     

Finding finer functions for partially characterized proteins by protein-protein interaction networks

Based on high-throughput data, numerous algorithms have been designed to find functions of novel proteins. However, the effectiveness of such algorithms is currently limited by some fundamental factors, including (1) the low a-priori probability of novel proteins participating in a detailed function; (2) the huge false data present in high-throughput datasets; (3) the incomplete data coverage of functional classes; (4) the abundant but heterogeneous negative samples for training the algorithms; and (5) the lack of detailed functional knowledge for training algorithms. Here, for partially characterized proteins, we suggest an approach to finding their finer functions based on protein interaction sub-networks or gene expression patterns, defined in function-specific subspaces. The proposed approach can lessen the above-mentioned problems by properly defining the prediction range and functionally filtering the noisy data, and thus can efficiently find proteins’ novel functions. For thousands of yeast and human proteins partially characterized, it is able to reliably find their finer functions (e.g., the translational functions) with more than 90% precision. The predicted finer functions are highly valuable both for guiding the follow-up wet-lab validation and for providing the necessary data for training algorithms to learn other proteins.     

Besov-Morrey spaces: Function space theory and applications to non-linear PDE

This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.

     

第三部门青年组织的社会功能研究

第三部门在公共领域所扮演的特殊角色引起了公众与学术界的广泛关注。采用个案研究的方法,借鉴西方女童子军个案来探讨第三部门青年组织的现实意义和特点,主要从教育功能和社会文明营造两个方面研究了第三部门青年组织的社会功能,并进一步探讨了中国和西方国家第三部门青年组织在社会功能发挥上的差异以及西方第三部门青年组织给国内第三部门青年组织发展带来的启示。     

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.