Control of an Adaptive Refinement Technique of Generalized Cell Mapping by System Dynamics

Generalized cell mapping is an efficient and powerful numerical tool for the prediction of the long-term behavior and global analysis of nonlinear dynamic systems. The only drawback of this method is the enormous computational effort it requires for high-dimensional systems. We overcome this problem by adaptively refining a very rough starting cell grid, where the adaptation is controlled by the long-term dynamics of the system. We illustrate the efficiency of our approach by examples.     

On fixed-points and singular values of transcendental meromorphic functions

In this paper we make a further discussion of a relationship between the number of fixed-points and distribution of singular values along the round annuli centered at the origin of a transcendental meromorphic function. To attain our purpose we first establish a fundamental inequality for the modulus of derivative of a holomorphic covering mapping whose image is an annulus by virtue of the hyperbolic metric. The inequality is of independent significance. We make a simple survey on some domain constants for ...     

关于三个非扩张映射收敛于其公共不动点的具误差的三重迭代法

在一致凸Banach空间中,研究了关于三个不同非扩张映射的具误差的三步迭代算法,并在一定条件下证明了此迭代序列收敛于其公共不动点的弱强收敛定理.     

Revealing doctors’ prescribing choice dimensions with multivariate tools: A perceptual mapping approach

This article explores the use of multivariate techniques to build perceptual maps that show the perceived competitive positions of a set of ethical drugs. The data were drawn from a commercial panel of 283 family doctors working for the UK National Health Service. Factor analysis was applied to identify the main dimensions used by doctors to perceive and evaluate antihypertensive brands. Perceptual maps showing the competitive positions of 14 antihypertensives were produced using the factor scores of the medicines. Multiple regression analysis enabled the relative importance of each perceptual dimension to be determined. The results reveal that doctors use a small number of perceptual dimensions to evaluate competitive antihypertensive drugs, namely: “medical support”, “long term efficacy”, and the “additional beneficial effects” provided by the brand. The implications for marketing managers in the ethical pharmaceutical industry are explained and ways in which the perceptual analysis can be used to guide strategic marketing decisions considered.     

Pre-, Post and Hybrid Dispersion Mapping Techniques for CSRZ Optical Networks with Nonlinearities

In this paper, different dispersion mapping techniques like pre-compensated, post-compensated or hybrid-compensation are compared in the presence of fiber nonlinearities in 10 and 40 Gbps carrier-suppressed return to zero (CSRZ) systems. It is observed that the hybrid-compensation is the best in dispersion mapping technique, which reduces the bit error rate (BER) produced due to the fiber nonlinearities to the more extent than that of pre- and post-compensations. By using the hybrid-compensation, the repeater length is increased almost up to double than that of pre- and post-compensations. It is also observed that with increase in the input bit rate and input power, the BER for hybrid is better as compared to other mapping techniques.     

Subdivision schemes for the fair discretization of the spherical motion group

We present two subdivision schemes for the fair discretization of the spherical motion group. The first one is based on the subdivision of the 600-cell according to the tetrahedral/octahedral subdivision scheme in [S. Schaefer, J. Hakenberg, J. Warren, Smooth subdivision of tetrahedral meshes, in: R. Scopigno, D. Zorin (Eds.), Eurographics Symposium on Geometry Processing, 2004, pp. 151–158]. The second presented subdivision scheme is based on the spherical kinematic mapping. In the first step we discretize an elliptic linear congruence by the icosahedral discretization of the unit sphere. Then the resulting lines of the elliptic three-space are discretized such that the difference in the maximal and minimal elliptic distance between neighboring grid points becomes minimal.     

广义L-KKM定理及其应用

引入广义L-KKM映射的概念,它包含R-KKM映射,G-KKM映射,H-KKM映射为其特例.在具有(H)性质的拓扑空间中证明了一些新的广义L-KKM型定理,并进一步获得了关于开覆盖的匹配定理.作为广义L-KKM型定理应用,证明了非空交定理.     

Numerical solutions of two non-linear simultaneous equations

In this article, we shall give practical and numerical representations of inverse mappings of two-dimensional mappings (of the solutions of two non-linear simultaneous equations) and show their numerical experiments by using computers. We derive a concrete formula from a very general idea for the representation of the inverse functions.     

Stochastic processes with independent increments for random mappings

Using additive functions defined on the combinatorial structure of all mappings of anN set into itself, we define paths in the space endowed with the Skorokhod topology. Taking a mapping with equal probability, we get a sequence of random processes. Necessary and sufficient conditions for the weak convergence of this sequence to a stochastic process with independent increments are established. It is shown that the class of such processes contains all possible limits, provided that, on the components of a mapping, the additive functions have values small in average. Partially supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 498–516, October–December, 1999. Translated by E. Manstavičius     

Scalarization of Tangential Regularity of Set-Valued Mappings

A set-valued mapping M from a topological vector space E into a normed vector space F is tangentially regular at a point in its graph g p h M if the Clarke tangent cone to g p h M at is equal to the Bouligand contingent cone to g p h M at . In this paper we characterize, in several cases, this tangential regularity as the directional regularity of the scalar function _M defined by _M (x, y) : = d(y, M(x)). The results allow us to express, in a useful formula, the subdifferential of _M in terms of the normal cone to the graph of M.