Thicknesses of 70 southern spiral galaxies

Using the method proposed by Peng (1988) and analyzing the spiral patterns, the thicknesses of 70 southern spiral galaxies whose images were taken from the Digitized Sky Survey at Xinglong Observational Station of Beijing Observatory were measured. The spiral arms of all these galaxies have been fitted on their images with some logarithmic spiral curves to get their optimum inclinations. Project supported by the Yational Natural Science Foundation of China, the National Climbing Project of China and the Doctoral Program Foundation of State Education Cummission.     

Scale heights of 84 northern spiral galaxies

Using the method proposed by Peng (1988) on the basis of density waves theory and the solution of three-dimensional Poisson’s equation for a logarithmic disturbance of density, and analyzing the spiral patterns, the scale heights of 84 northern spiral galaxies, whose images are taken from the Digitized Sky Survey¹⁾ at Xinglong Observational Station of Beijing Observatory, are measured. The spiral arms of all these galaxies have been fitted on their photographs with some logarithmic spiral curves for getting their correct inclinations.     

The formation of compact groups of galaxies

In the compact group of galaxies the galaxies can merge into a few massive ones in a very short time, so they must be formed very recently. On the other hand, according to the theory of structure formation, the denser system should form earlier. By analyzing the apparent paradox, we suggest that the merging process of CDM halo plays an important role in the formation of the compact groups of galaxies: it delays the formation of compact groups of galaxies, and makes the pups of galaxies much denser. Project partially supporter1 hy the Ministry of Science and Technology (of China).     

Counting algebraic numbers with large height II

We count algebraic numbers of fixed degree over a fixed algebraic number field. When the heights of the algebraic numbers are bounded above by a large parameter , we obtain asymptotic estimates for their cardinality as .

     

Super-large-scale structures in the distribution of infrared galaxies

Typical scales in the distribution of IRAS galaxies with the unnormalized pair count method. Samples are those provided by QDOT redshift survey and sorted out from the IRAS faint sources catalog. Analysis is concentrated on the structures at super-large scales. The results show that statistically significant typical scales do exist in the distribution of all these samples from both 2-dimensiortal and 3-dimensional analyses. These scales are consistent with those found from the analyses of galaxies and clusters of galaxies by Mo et al. and also consistent with those found from analysis of quasars by Deng et al. The analysis provides additional evidence for the existence of typical scales in the large-scale structure of the universe. The existence of typical scales challenges all the existing models on the formation of galaxies and structures. Project supported by the National Natural Science Foundation of China (Grant Nos. 19773014 and 19773010).     

自由剪切流大尺度结构的二次稳定性*

本文用二次稳定性理论研究自由剪切湍流中周期性基本流空间增长扰动的稳定性。数值结果表明三维亚谐扰动对横向波数有很强的选择性,二维亚谐波的空间增长率最大。与之相反,基本模式的三维扰动在很大的波数范围内存在不稳定性,证明β=0时存在“转移”不稳定性;当KH波的幅值A≥0.06时出现分叉现象。     

一类大系统目标规划问题分解算法中最优解之间的关系

将一类大系统目标规划问题分解为若干个子问题,研究了原问题的最优解和各个子问题最优解之间的关系,并讨论了原问题最优解的判别条件。     

Computing the canonical height on K3 surfaces

Let be a surface in given by the intersection of a (1,1)-form and a (2,2)-form. Then is a K3 surface with two noncommuting involutions and . In 1991 the second author constructed two height functions and which behave canonically with respect to and , and in 1993 together with the first author showed in general how to decompose such canonical heights into a sum of local heights . We discuss how the geometry of the surface is related to formulas for the local heights, and we give practical algorithms for computing the involutions , , the local heights , , and the canonical heights , .

     

The Remak height for units

We investigate the values of the Remak height, which is a weighted product of the conjugates of an algebraic number. We prove that the ratio of logarithms of the Remak height and of the Mahler measure for units αof degree d is everywhere dense in the maximal interval [d/2(d-1),1] allowed for this ratio. To do this, a “large” set of totally positive Pisot units is constructed. We also give a lower bound on the Remak height for non-cyclotomic algebraic numbers in terms of their degrees. In passing, we prove some results about some algebraic numbers which are a product of two conjugates of a reciprocal algebraic number. This revised version was published online in June 2006 with corrections to the Cover Date.     

A planar cubic Bézier spiral

A planar cubic Bézier curve segment that is a spiral, i.e., its curvature varies monotonically with arc-length, is discussed. Since this curve segment does not have cusps, loops, and inflection points (except for a single inflection point at its beginning), it is suitable for applications such as highway design, in which the clothoid has been traditionally used. Since it is polynomial, it can be conveniently incorporated in CAD systems that are based on B-splines, Bézier curves, or NURBS (nonuniform rational B-splines) and is thus suitable for general curve design applications in which fair curves are important.     

具有对称循环结构线性大系统的分散镇定特征

研究一类具有对称循环结构的连续和离散线性大系统的分散镇定特征,充分利用对称循环的特点,建立了判断这类系统可分散镇定的充分条件．在连续情形下,通过引进耦合结构模这一概念,揭示了这类系统分散镇定的重要特征,这就是当整个系统的耦合结构模给定之后,系统的分散镇定特性可以完全由各孤立子系统的结构所决定．这表明在这类系统的实际设计中,不管系统内中各子系统之间的耦合结构多么复杂,只要按一定的条件适当设计或修正各孤立子系统的结构参数,就能使所设计的大系统具有分散镇定特征,并提供了相应的分散镇定算法．对离散情形也进行了讨论,结果表明,连续系统与离散系统的分散镇定特征有着很大的差异．     

Smooth polynomial approximation of spiral arcs

Constructing fair curve segments using parametric polynomials is difficult due to the oscillatory nature of polynomials. Even NURBS curves can exhibit unsatisfactory curvature profiles. Curve segments with monotonic curvature profiles, for example spiral arcs, exist but are intrinsically non-polynomial in nature and thus difficult to integrate into existing CAD systems. A method of constructing an approximation to a generalised Cornu spiral (GCS) arc using non-rational quintic Bézier curves matching end points, end slopes and end curvatures is presented. By defining an objective function based on the relative error between the curvature profiles of the GCS and its Bézier approximation, a curve segment is constructed that has a monotonic curvature profile within a specified tolerance.     

客户知识管理—概念与量表开发

通过文献分析,将客户知识管理的定义划分为三类。从客户知识管理的概念和客户知识活动的特性入手,以文献研究和已有相关问卷、量表为基础,结合半结构化问卷和人员访谈所获得的资料,编制客户知识管理量表。研究结果表明,客户知识管理具有多维度结构,其量表的开发具有较好的可信度和可靠性,客户知识管理包括五个维度,即客户知识获取、客户知识整合、客户知识共享、客户知识使用和客户知识创新。本文对概念的界定以及量表的开发可以为企业进行客户知识管理提供参考和借鉴。     

The average norm of polynomials of fixed height

Let be any integer and let

be the set of all polynomials of height 1 and degree . Let

Here is the power of the norm on the boundary of the unit disc. So is the average of the power of the norm over

In this paper we give exact formulae for for various values of . We also give a variety of related results for different classes of polynomials including polynomials of fixed height H, polynomials with coefficients and reciprocal polynomials. The results are surprisingly precise. Typical of the results we get is the following.

Theorem 0.1. For , we have

and

     

The height of depth‐weighted random recursive trees

In this paper, we introduce a model of depth‐weighted random recursive trees, created by recursively joining a new leaf to an existing vertex . In this model, the probability of choosing depends on its depth in the tree. In particular, we assume that there is a function such that if has depth then its probability of being chosen is proportional to . We consider the expected value of the diameter of this model as determined by , and for various increasing we find expectations that range from polylogarithmic to linear.     

The galaxies of nonstandard enlargements of infinite and transfinite graphs

The galaxies of the nonstandard enlargements of connected, conventionally infinite graphs as well as of walk-connected transfinite graphs are defined, analyzed, and illustrated by some examples. It is then shown that any such enlargement either has exactly one galaxy, its principal one, or it has infinitely many galaxies. In the latter case, the galaxies are partially ordered by their “closeness” to the principal galaxy. If an enlargement has a galaxy Γ different from its principal galaxy, then it has a two-way infinite sequence of galaxies that contains Γ and is totally ordered according to that “closeness” property. There may be many such totally ordered sequences.Furthermore, a walk-connected graph G¹ of transfinite rank 1 consists in general of connected conventional graphs (graphs of rank 0, called 0-sections) that are walk-connected together at their infinite extremities. The enlargement of G¹ consists of the enlargement of G¹, as well as of the enlargements of its 0-sections. The latter enlargements are all contained within the principal galaxy of . Moreover, may have other galaxies of rank 1; these too are partially and totally ordered as before. These results extend to the enlargements of transfinite graphs of ranks greater than 1.     

a尺度多重正交小波包

本文给出了ａ尺度多重正交小波包的构造方法,它是通过对ａ尺度多重正交小波向量等长截取为ａ－１个子向量之后得到的,对同一多重正交小波而言,采用本方法可以构造多种不同的正交小波包,从而使多重正交小波包不仅具有传统的小波包的特点,而且在应用中具有较强的灵活性。     

On the height of random m-ary search trees

A random m-ary seach tree is constructed from a random permutation of 1,…, n. A law of large numbers is obtained for the height H_n of these trees by applying the theory of branching random walks. in particular, it is shown that H_n/log n→γ in probability as n→∞ where γ = γ(m) is a constant depending upon m only. Interestingly, as m→∞, γ(m) is asymptotic to 1/log m, the coefficient of log n in the asymptotic expression for the height of the complete m-ary search tree. This proves that for large m, random m-ary search trees behave virtually like complete m-ary trees.