Vektorfelder und Integralformeln für Strahlensysteme

In this paper we study some vectorfields arising in the theory of rectilinear congruences in the real Euclidean space E³. We also derive some integral formulae concerning the vectorfields above.     

On Surfaces of Finite Chen — Type

We investigate some relations concerning the first and the second Beltrami operators corresponding to the fundamental forms I, II, III of a surface in the Euclidean space E³ and we study surfaces which are of finite type in the sense of B.-Y. Chen with respect to the fundamental forms II and III.     

Eine Charakterisierung Der W-Flächen

Let ℱ: x=x(u¹, u²) be a C³-surface in the euclidean space E³, n the unit normal vector of ℱ and let . We consider the vector of ℝ⁶ and we denote with μ the rank of the matrix (a, a₁, a₂, a_{1, 1}, a_{1, 2}, a_{2, 2}). We then prove the Theorem: ℱ is a W-surface if and only if μ≦5. Further, μ is 4 resp. 3 if and only if the surface ℱ is part of a cylinder of revolution resp. part of a sphere or a plane.      

A time-domain nonlinear system identification method based on multiscale dynamic partitions

Based on a theoretical foundation for empirical mode decomposition, which dictates the correspondence between the analytical and empirical slow-flow analyses, we develop a time-domain nonlinear system identification (NSI) technique. This NSI method is based on multiscale dynamic partitions and direct analysis of measured time series, and makes no presumptions regarding the type and strength of the system nonlinearity. Hence, the method is expected to be applicable to broad classes of applications involving time-variant/time-invariant, linear/nonlinear, and smooth/non-smooth dynamical systems. The method leads to nonparametric reduced order models of simple form; i.e., in the form of coupled or uncoupled oscillators with time-varying or time-invariant coefficients forced by nonhomogeneous terms representing nonlinear modal interactions. Key to our method is a slow/fast partition of transient dynamics which leads to the identification of the basic fast frequencies of the dynamics, and the subsequent development of slow-flow models governing the essential dynamics of the system. We provide examples of application of the NSI method by analyzing strongly nonlinear modal interactions in two dynamical systems with essentially nonlinear attachments.     

NPK 2.0: Introducing tensor decompositions to the kinetic analysis of gas–solid reactions

A method for deriving kinetic models of gas–solid reactions for reactor and process design is presented. It is based on the nonparametric kinetics (NPK) method and resolves many of its shortcomings by applying tensor rank-1 approximation methods. With this method, it is possible to derive kinetic models based on the general kinetic equation from any combination of experiments without additional a priori assumptions. The most notable improvements over the original method are that it is computationally much simpler and that it is not limited to two variables. Two algorithms for computing the rank-1 approximation as well as a tailored initialization method are presented, and their performance is assessed. Formulae for the variance estimation of the solution values are derived to improve the accuracy of the model identification and to provide a tool for diagnosing the quality of the kinetic model. The methods effectiveness and performance are assessed by applying it to a simulated data set. A Matlab implementation is available as Supporting Information.     

Short communication on the discrete deffuant and alternative models in one dimension

The discrete Deffuant model and its alternatives is a family of stochastic spatial models for the dynamics of binary opinions on f issues. Another parameter is also incorporated that prevents interaction between two agents whenever their opinion profiles are at a Hamming distance greater than the confidence threshold θ. By numerical simulations, it was conjectured in (Adamopoulos and Scarlatos, Complexity 2012, 17, 43) that one‐dimensional models exhibit a phase transition at a critical value . We report on recent mathematical results on this problem that originates from the community of complex systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 437–439, 2016