Application of Born series for modeling of Mie-resonant nanostructures

Born series formalism is a widely-used approach to solve a scattering problem in quantum mechanics and optics, including a problem of electromagnetic scattering on the ensembles of Mie-resonant nanoparticles. In the latter case, the Born series formalism can be used when the electromagnetic coupling between nanoparticles is weak. This can be violated near the multipole Mie-resonance of the nanoparticle. In this work, we analyze the applicability of the Born series approach for modeling the resonant optical response of Mie-nanoparticle ensembles and formulate quantitative criteria of Born series convergence and, subsequently, the applicability of this approach.

Unendliche Reihen im Mathematikunterricht

A radically new propaedeutic way of cognition to infinite series. Convergence is not a starting point but the result of a longer and detailed notional construction. In the beginning a series and its „sum” is considered as a symbolic alternative formula for an elementary problem of a certain type and its known solution respectively. Classification: B10, B15, B19; C30, C35, C39; I30, I35, I39. Keywords: Infinite series, propaedeutics to infinite series, Convergence, pursuit processes, psychological-genetic method.

Convergence Dynamics of Robbery Rates in Mexico

This work presents a time-series convergence (divergence) analysis for robbery rates in Mexico. Two distinctive features, in relation to previous studies, can be identified: first, the use of an autoregressive vector to better estimate the series dynamic compared with single-equation models, and second, the implementation of an escalation/de-escalation analysis is done using two variants of the same crime—high- and low-impact robberies. Our results suggest that modifications to the national security policy in Mexico have a direct—and rapid—effect on robbery crime trends. Moreover, the three phases of the dynamics between the rates coincide with the three major national security policies implemented in recent years: (a) 1997 to 2006, (b) 2007 to 2011, and (c) 2012 to 2018.

PERBANDINGAN DAN KARAKTERISTIK BEBERAPATES KONVERGENSI PADA DERET TAK HINGGA

The infinite series is an infinite sum of elements of a sequence of real numbers. A main thing related to the infinite series is to determine its convergence (convergent or divergent). Purpose this research were to analyze and determine a comparison and characteristics of each convergence test, such as: D'Alembert test, Raabe test, Gauss's test, Cauchy's Root Test, and Logarithm Test. A method used descriptive method by analyzing theories relevant to the problems discussed and based on literature study.The results showed that each convergence test had characteristics for its convergence test. The D'Alembert Ratio test is easier to use in a series that contains the formn! ,rn, and nn. Raabe test used if the ratio test obtained value limit comparison is, so the test does not give conclusion. Whereas logarithmic test is used in the infinite series that contains the logarithmic form. The Cauchy n-th root test, can be used to determine the absolute series convergence of the nth power