A note on Hamilton sequences for extremal Beltrami coefficients

F. P. Gardiner gave a sufficient condition for a sequence to be a Hamilton sequence for an extremal Beltrami coefficient. In this note, we shall consider the converse problem, proving that the condition is not necessary.

     

-actions whose fixed data has a section

Given a collection of real vector bundles over a closed manifold , suppose that, for some is of the form , where is the trivial one-dimensional bundle. In this paper we prove that if is the fixed data of a -action, then the same is true for the Whitney sum obtained from by replacing by . This stability property is well-known for involutions. Together with techniques previously developed, this result is used to describe, up to bordism, all possible -actions fixing the disjoint union of an even projective space and a point.     

Exact Distribution of the Distances between Any Occurrences of a Set of Words

The distribution of the distance between two (or more) successive occurrences of a specific word in a random sequence of letters is known under different models. In this paper, a more general problem is studied: the distribution of the distance between two (or more) successive occurrences of any word of a given set under a Markov model for the sequence. The generating function and a recurrence for obtaining the probabilities are given. These results are applied to study the distribution of the "CHI" motif in the genome sequence of Haemophilus influenzae.     

-sequences

A sequence of positive integers is called a -sequence if every integer has at most representations with all in and . A -sequence is also called a -sequence or Sidon sequence. The main result is the following

Theorem. Let be a -sequence and for an integer . Then there is a -sequence of size , where .

Corollary. Let . The interval then contains a -sequence of size , when .

     

The -theory of toric manifolds

Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an -dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the -theory of all toric manifolds and certain singular toric varieties.

     

Nuclear magnetic resonance in inhomogeneous magnetic fields

The response of the spin system has been investigated by numerical simulations in the case of a nuclear magnetic resonance (NMR) experiment performed in inhomogeneous static and radiofrequency fields. The particular case of the NMR-MOUSE was considered. The static field and the component of the radiofrequency field perpendicular to the static field were evaluated as well as the spatial distribution of the maximum NMR signal detected by the surface coil. The NMR response to various pulse sequences was evaluated numerically for the case of an ensemble of isolated spins (1/2). The behavior of the echo train in Carr-Purcell-like pulse sequences used for measurements of transverse relaxation and self-diffusion was simulated and compared with the experiment. The echo train is shown to behave qualitatively differently depending on the particular phase schemes used in these pulse sequences. Different echo trains are obtained, because of the different superposition of Hahn and stimulated echoes forming mixed echoes as a result of the spatial distribution of pulse flip angles. The superposition of Hahn and stimulated echoes originating from different spatial regions leads to distortions of the mixed echoes in intensity, shape, and phase. The volume selection produced by Carr-Purcell-like pulse sequences is also investigated for the NMR-MOUSE. The developed numerical simulation procedure is useful for understanding a variety of experiments performed with the NMR-MOUSE and for improving its performance. Copyright 2000 Academic Press.     

一种基于正负差图像的运动目标检测新方法

运动目标检测领域中现有的差图像法是利用绝对值差图像检测差图像上运动目标区域，用现有方法检测时易受噪声干扰，而且当摄像机有自运动时需要进行背景运动补偿。因此，提出一种新算法，即首先分别计算正差图像与负差图像，然后利用运动目标区域在正差图像与负差图像中的幅值、形状以及运动等信息的对称性对其进行检测，最后给出针对飞机尾焰序列图像进行检测的结果。实验结果表明：该方法可提高运动目标检测的可靠性与效率。     

光学波段菲波纳契序列一维光子晶体纳米膜传输特性研究

为了研究光学波段菲波纳契序列一维光子晶体纳米膜的传输特性,应用传输矩阵方法数值模拟各种情况下的透射率即传输函数随频率的变化.数值结果表明在正入射时,菲波纳契序列一维光子晶体中的禁带宽度、中心位置、数目都与构成序列的项数、组元物理厚度、组成序列组元初始次序、组元折射率差值都对传输特性有较大影响,在可见光区组元折射率差值越大越易形成较宽禁带,进一步研究广义菲波纳契序列一维光子晶体纳米膜的传输特性,发现比典型情况更易在可见光区形成禁带.     

二次域Q（√7）的单位给出的三角数及相关的不定方程问题

研究了二次域Q（√7）中单位Vn＋Un√7）=（8＋3√7）n所给出的两个递归数列{Vn},{Un}中的三角数问题,找到了{Vn},{Un}中的所有的三角数.作为应用,给出了与其相关的两个不定方程的整数解.     

A new graphical coding of DNA sequence and its similarity calculation

The DNA primary sequence is translated into “structure graph” based on classification of its four bases. Then the invariants, such as topological indices, are extracted from those graphic representations of DNA primary sequences, and used to calculate the similarities among the eleven species. From these similarities/dissimilarities the homologies can be revealed that they are in agreement with evolutionary relation satisfactorily.