超紧集的刻划与层次结构

本文给出了ＬＦ集的超紧性的网式、滤子式等几种刻划，剖析了超紧集的层次结构，得出了在导出分明拓扑满足Ｔ２分离性的前提下子集的超紧性与其任一α－截集的紧性等价等一系列结果。     

壁面加热湍流耗散率标度指数测量的实验研究

对中等雷诺数下壁面常温和壁面加热的平板湍流边界层中速度和温度粗粒化的耗散率结构函数标度指数进行了实验测量.用热线风速仪测量了风洞中壁面常温和加热的平板湍流边界层中不同法向位置的流向速度分量和温度的时间序列信号,研究了由于湍流边界层近壁区域相干结构的存在而导致的非各向同性、非均匀性对湍流耗散率结构函数标度指数的影响,研究发现,中等雷诺数下壁面加热的边界条件和剪切湍流的平均速度梯度对速度和温度耗散率结构函数的标度指数没有影响,均匀各向同性湍流的耗散率结构函数标度指数的层次结构模型对壁面加热平板湍流边界层的速度和温度耗散率结构函数的标度指数也是适用的.     

A novel hierarchy of differential integral equations and their generalized bi-Hamiltonian structures

With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 x 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy.     

A New Liouville Integrable Hamiltonian System

With the help of a Lie algebra, an isospectral Lax pair is introduced for which a new Liouville integrable hierarchy of evolution equations is generated. Its Hamiltonian structure is also worked out by use of the quadratic-form identity.     

A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.     

一种有效的簇集主干点P2P网络结构模型

P2P计算近年来已经日趋普遍。它提供很多吸引人的特性。比如自主性、负载平衡、有效性、容错冗余和匿名。但它同样面临一些严峻的挑战。在本论文中，提出一种有效的簇集主干点层级P2P结构模型（ECGP）。该模型提供了一种半结构化的层次结构（类似混合P2P系统），克服了现存的非结构化P2P系统中存在的扩展性不好和效率不高的问题。     

大数假说与物质层次结构

 1937年,诺贝尔奖获得者,英国物理学家狄拉克在《自然》杂志的139卷323页上发表了《大数假说及其后果》的论文,提出了著名的“大数假说”。宇宙中存在着两个数量级相等的神秘大数,一个大数是氢原子中静电力和万有引力之比:e²/Gmpme=2.3×10³⁹,e是电子或质子的电量,G是万有引力常量,me、mp分别是电子和质子的质量。另一个大数是根据大爆炸宇宙模型,以原子单位来量度的宇宙年龄t=7×10³⁹s,这两个貌似毫不相干的大数,分别来自一个小世界和一个大世界,却有着相同的数量级。狄拉克不认为这仅仅是一种巧合,他说:“这样两个大数如此接近,在自然界一定有某种基本的原因,我们目前不知道这个原因.     

Sequence Hiberarchy Evolution Measurement Method and its Application

A novel method based on discrete wavelet transform （DWT） and cross-covariance for revealing the evolution of species at different spatial resolutions is presented. The trypsin proteins of different species are chosen as an example to describe the evolution relationship according to the evolution vectors by using this method. The results indicated that this method is a promising approach to reveal species evolution at different spatial resolutions.     

A Few Expanding Integrable Models,Hamiltonian Structures and Constrained Flows

Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup (BK) hierarchy and the dispersive long wave (DLW) hierarchy as well as the TB hierarchy are obtained. From the reductions of the coupling integrable couplings, the corresponding coupled integrable couplings of the BK equation, the DLW equation, and the TB equation are obtained, respectively. Especially, thecoupling integrable coupling of the TB equation reduces to a few integrable couplings of the well-known mKdV equation. The Hamiltonian structures of the coupling integrable couplings of the three kinds of soliton hierarchies are worked out, respectively, by employing the variational identity. Finally, we decompose the BK hierarchy of evolution equations into x-constrained flows and t_n-constrained flows whose adjoint representations and the Lax pairs are given.     

Super Jaulent-Miodek hierarchy and its super Hamiltonian structure,conservation laws and its self-consistent sources

A super Jaulent-Miodek hierarchy and its super Hamiltonian structures are constructed by means of a kind of Lie super algebras and super trace identity. Moreover, the self-consistent sources of the super Jaulent-Miodek hierarchy is presented based on the theory of self-consistent sources. Further- more, the infinite conservation laws of the super Jaulent-Miodek hierarchy are also obtained. It is worth noting that as even variables are boson variables, odd variables are fermi variables in the spectral problem, the commutator is different from the ordinary one.