Density-difference maps in quantum chemistry

Electron density-difference maps, used to study the changes that occur when a molecule changes its state or when the nuclei of a molecule change their relative positions, are generally useful only if the atomic densities cancel when one molecular density distribution is subtracted from the other. When, as in the case of the nonrigid internal rotation in ethane, such a cancellation of atomic densities is not possible the method of simple subtraction is no longer appropriate. It is shown that useful density-difference maps can nevertheless be obtained, when the changes in geometric parameters are small, by the calculation of two generalized density-difference functions: a point difference function which allows a comparison of the densities at corresponding points in the two systems, and a volume difference function to compare the amounts of charge in corresponding regions. The method is illustrated by consideration of a change in bond length of the nitrogen molecule and by the nonrigid internal rotation in ethane.Presented at the XIVth Quantum Theory Conference in Canterbury, England, September 1981.     

Sensitivity analysis in multiobjective optimization

Sensitivity analysis in multiobjective optimization is dealt with in this paper. Given a family of parametrized multiobjective optimization problems, the perturbation map is defined as the set-valued map which associates to each parameter value the set of minimal points of the perturbed feasible set in the objective space with respect to a fixed ordering convex cone. The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps. Particularly, it is shown that the sensitivity is closely related to the Lagrange multipliers in multiobjective programming.This research was made while the author stayed at the International Institute for Applied Systems Analysis, Laxenburg, Austria.The author would like to thank an anonymous referee for his helpful suggestions; particularly, he pointed out that Proposition 2.2 and Theorem 2.1 are valid also in infinite-dimensional spaces.     

The Loewner differential equation and slit mappings

We show that the Loewner equation generates slits if the driving term is Hölder continuous with exponent 1/2 and small norm and that this is best possible.

     

Convergence theorems for fixed points of uniformly continuous generalized Φ-hemi-contractive mappings

Let E be a real normed linear space, K be a nonempty subset of E and be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., , and there exist x^∗∈F(T) and a strictly increasing function , Φ(0)=0 such that for all x∈K, there exists j(x−x^∗)∈J(x−x^∗) such that

〈Tx−x^∗,j(x−x^∗)〉?‖x−x^∗‖2−Φ(‖x−x^∗‖).     

W-空间上自映射族的唯一公共不动点

 首先引进一个新的空间,然后在该空间上讨论了具有反交换的映射族的唯一公共不动点的存在问题.所得结论推广和改进了一些相应结果.     

地质AutoCAD图件转换成MAPGIS图件的可行性研究

针对作为国土资源部门在资料汇交时要求提交利用MAPGIS软件编制的图件,虽然该软件的功能强大,但在图件的编辑上远不如AutoCAD软件方便快捷;同时,目前还有大量以AutoCAD格式存储的地质图件,需重新绘制成MAPGIS图件,浪费了大量的人力物力等问题。开展了将地质AutoCAD图件转换成MAPGIS图件的研究工作,研究发现地质AutoCAD图件不仅能够转换成MAPGIS图件,并且能够加快绘图速度,提高工作效率,具有较好实用价值。     

Dynamic maps in phase-conjugated optical resonators

In this article the dynamical behavior of a beam within a ring-phase-conjugated resonator is modeled using two-dimensional iterative maps. In particular and as an example it is explicitly shown how the difference equations of the Duffing map can be used to describe the dynamic behavior of what we call Duffing beams i.e. beams that behave according to the Duffing map. The matrix of a Duffing map generating device is found in terms of the Duffing parameters, the state variables and the resonator parameters. To our knowledge this is the first time that the mathematical characteristics of an optical device in an optical cavity are stated so that a Duffing map is obtained as the dynamics for the ray beams.     

An algorithm for the determination of graphs associated to fold maps between closed surfaces

The aim of this paper is to introduce a computational tool that checks theoretical conditions in order to determine whether a weighted graph, as a topological invariant of stable maps, can be associated to stable maps without cusps (ie, fold maps) from closed surfaces to the projective plan.