High-order adaptive method for computing two-dimensional invariant manifolds of three-dimensional maps

An efficient and accurate numerical method is presented for computing invariant manifolds of maps which arise in the study of dynamical systems. A quasi-interpolation method due to Hering-Bertram et al. is used to decrease the number of points needed to compute a portion of the manifold. Bézier triangular patches are used in this construction, together with adaptivity conditions based on properties of these patches. Several numerical tests are performed, which show the method to compare favorably with previous approaches.     

Low cost method for location service in the WCDMA system

A new and low cost method for a location service (LCS) in the Wideband Code Division Multiple Access (WCDMA) system is outlined. This method, which is called TDOA+RTT, enables calculation of the geographical position of a mobile station (MS) without knowledge of relative time differences (RTDs) between base stations (BSs). The TDOA+RTT method is based on the measurement of round trip times (RTTs) between the MS and the serving BS, and the solution of a nonlinear system of equations with six variables. The elimination of the RTD parameters significantly simplifies the localisation process in 3G (3rd Generation) real-life cellular networks. The paper concentrates on solving the nonlinear system of equations with six variables. In this context, a new algorithm for solving nonlinear equations is proposed.     

On functional equations stemming from actuarial mathematics

We determine extensions of some implicitly defined functionals stemming from actuarial mathematics.     

Stereoselective preparation of chiral compounds in Mannich-type reactions of a bicyclic imine and phenols or indole

Mannich-type reactions of a chiral bicyclic imine and various nucleophiles yield the corresponding adducts with good to high diastereoselectivity. The influence of the reaction conditions on the yield and stereochemical outcome is investigated. The configuration of the products is established by ¹H NMR spectroscopy, and the major isomers of two adducts are characterized by X-ray crystallography.     

An asymptotic-preserving method for highly anisotropic elliptic equations based on a Micro–Macro decomposition

The concern of the present work is the introduction of a very efficient asymptotic preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter 0 < ε ? 1, the applicability (on cartesian grids) to cases of non-uniform and non-aligned anisotropy fields b and the simple extension to the case of a non-constant anisotropy intensity 1/ε. The mathematical approach and the numerical scheme are different from those presented in the previous work [P. Degond, F. Deluzet, A. Lozinski, J. Narski, C. Negulescu, Duality-based asymptotic-preserving method for highly anisotropic diffusion equations, Communications in Mathematical Sciences 10 (1) (2012) 1–31] and its considerable advantages are pointed out.     

Shapley-Based Estimation of Company Value—Concept,Algorithms and Parameters

The aim of the article is to propose a new method of valuation of a company, considering its ownership relations with other companies. For this purpose, the concept of the Shapley value from cooperative game theory is used as the basis for assessing such dependent companies. The paper presents proposals for Shapley value calculation algorithms for our model. We expand our model by discussing personal relations in addition to ownership relations and point out how intuitionistic fuzzy sets may be helpful in this context. As a result, we propose two new expanded models. In the first probabilistic model, we apply Pearson’s correlation coefficient, in the second, we use a correlation coefficient between intuitionistic fuzzy sets to determine the personal relationships. Finally, we present and interpret results for a real-world economic network with 17 companies.