An example in holomorphic fixed point theory

If is the open unit ball in the Cartesian product furnished with the -norm , where and , then a holomorphic self-mapping of has a fixed point if and only if for some

     

Retrieval Properties of Bidirectional Associative Memories

We study a two-layer neural network made of N and M(N) neurons, producing a two-way association search for a family of p(N) patterns, where each pattern is a pair of two independent sub-categories of information having respectively N and M(N) components. In terms of the ratio =lim _N M(N)/N, we study the retrieval capability of this network and show that there exists, at least, three regimes of association for which we determine the evolution of the threshold _c () of the storage capacity =lim _N p(N)/N.     

Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up

In this paper we prove uniqueness of positive solutions to logistic singular problems , , 1$">, 0$"> in , where the main feature is the fact that . More importantly, we provide exact asymptotic estimates describing, in the form of a two-term expansion, the blow-up rate for the solutions near . This expansion involves both the distance function and the mean curvature of .

     

On the use of Laplace's equation for global predictions of internuclear separation and dissociation energy

Properties of target species can be estimated by various means including interpolations in periodic charts. Interpolation is equivalent to numerical solution of the Laplace equation. A test of this equivalence, within some confidence level, for any N-atomic molecule surrounded by 4N nearest neighbors: the sum of the second differences of the data in all directions must be zero. Since very few molecules have 4N neighbors with known data, the test becomes: the sum of the averages of the second differences must be zero. The validity of these tests is explored. For radii of main-group atoms, and for internuclear separations of their diatomic combinations, the averages are different from zero and the sums of the averages are zero to within one if second-nearest neighbors are used. Dissociation potentials pass the tests but with larger scatter. Predictions for dissociation potentials, using iterative interpolation within boundaries on which there are known data, are reviewed.     

Dead-time free measurement of dipole-dipole interactions between electron spins

A four-pulse version of the pulse double electron-electron resonance (DEER) experiment is presented, which is designed for the determination of interradical distances on a nanoscopic length-scale. With the new pulse sequence electron-electron couplings can be studied without dead-time artifacts, so that even broad distributions of electron-electron distances can be characterized. A version of the experiment that uses a pulse train in the detection period exhibits improved signal-to-noise ratio. Tests on two nitroxide biradicals with known length indicate that the accessible range of distances extends from about 1.5 to 8 nm. The four-pulse DEER spectra of an ionic spin probe in an ionomer exhibit features due to probe molecules situated both on the same and on different ion clusters. The former feature provides information on the cluster size and is inaccessible with previous methods.     

对物体沿散斑片纵向移动二次曝光全息干涉条纹的诠释

从光学几何关系出发,推导了在平行光照明、物体沿散斑片纵向方向微小移动情况下的一种全息干涉条纹的解释方法.该方法可以根据任一瞬间的条纹间距测量物体的位移,并适用于实时全息监测的定量分析,对全息干涉计量术提供有效的条纹解释方法和物体位移的计算方法.     

轴角编码器测量中偏心带来的误差分析

介绍了应运多面体和自准直光管组合测量高准确度编码器角度的原理和方法，具体分析了多面体中心和编码器轴中心偏心时对测量角度产生的测量误差，并对自准直光管光轴和多面体中心、编码器轴中心两者偏心连线不重合时产生的测量误差进行了分析，同时对两中心偏心的方向进行了判定．实验证明，多面体中心与编码器轴中心不重合时对测量将产生按正弦或余弦规律变化的系统误差，同时自准直光管光轴和两者中心连线不重合对测量结果将不会产生影响．     

Ostrowski type inequalities on H-type groups

The main aim of this paper is to establish an Ostrowski type inequality on H-type groups using the L^∞ norm of the horizontal gradient. The work has been motivated by the work of Anastassiou and Goldstein in [G.A. Anastassiou, J.A. Goldstein, Higher order Ostrowski type inequalities over Euclidean domains, J. Math. Anal. Appl. 337 (2008) 962-968].     

What is the maximum stretching for C–C single bond?

The objective of this work is to determine the maximum stretch of the C–C bond before it misses the character of single bond, employing both the Atoms in Molecules (AIM) and Electron Localization Function (ELF) methods. It was concluded that C–C distances up to 2.0 Å could be considered single bonds.     

利用小车的上班族在拥有辐射环状交通网络的城市工作区内通勤时的平均移动距离

在一拥有辐射环状交通网络的城市工作区内，使用小车上下班的职员在通勤时的平均移动距离约为多少？本文基于一个较现实的模型对此进行了理论上的解析，所得结果，从城市规划的观点来看，具有一定的实际意义。