Abstract
This article presents an analysis of conventional single-phase cascaded H-bridge multilevel inverters composed of two and three cells. The dc-link can be a dc source or a floating capacitor. Two methods are given to regulate the floating capacitor voltage. In this way, according to the capacitor voltage balancing method used, operating regions and power distribution on the floating capacitor are presented for different dc-link voltage ratios and several ranges of modulation index and load power factor. A mathematical analysis is done in order to demonstrate the influence of the modulation index and load power factor over the power distribution. Finally, simulation and experimental results are provided to validate the theoretical considerations.

Abstract
The fourth author name was missed in the original publication. The correct list of authors should read as "Hugo Fernandes, Paulo Costa, Vitor Filipe, Hugo Paredes, Joao Barroso". It has been corrected in this erratum. The original article has been updated.

Abstract
This work models the propagation of an optical pulse in a four-level atomic system in the electromagnetically induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a continuous-wave control laser beam and an assisting incoherent pump field, it is shown how these media can provide an excellent framework to experimentally explore pulse dynamics in the presence of non-conservative terms, either gain or loss. Furthermore, we explore the existence of stable dissipative soliton solutions, testing the analytical results with computational simulations of both the effective (1+1)-dimensional model and the full Maxwell-Bloch system of equations.

Abstract
First order off-axis fiber Bragg gratings (FBGs) were fabricated in a standard single mode fiber (SMF-28e) through femtosecond laser direct writing. A minimum offset distance between the grating and core center of 2.5 mu m was found to create a multimode section, which supports two separate fiber modes (LP0,1 and LP1,1), each split into two degenerate polarization modes. The resulting structure breaks the cylindrical symmetry of the fiber, introducing birefringence (approximate to 10(-4)) resulting in a polarization dependent Bragg wavelength for each mode. Based on the modal and birefringence behavior, three off-axis FBGs were fabricated with 3.0, 4.5 and 6.0 mu m offsets from the core center, and then characterized in strain, temperature, and curvature. The tested off-axis FBGs exhibited a similar strain sensitivity of similar to 1.14 pm/mu epsilon and a temperature sensitivity of similar to 12 pm/C. The curvature and orientation angle were simultaneously monitored by analyzing the intensity fluctuation and the wavelength shift of the LP1,1 Bragg resonance. A maximum curvature sensitivity of 0.53 dB/m(-1) was obtained for the off-axis FBG with a 3.0 mu m offset.

Abstract
Geocoding is the process of converting an address or a place name into geographic coordinates. This conversion process has become a fundamental subject in many scientific domains and real world applications, from health and crime analysis to route optimization. In this paper, we present a conversion process of over 4.5 million entities, mostly Portuguese Economic Operators, through their addresses or names. We also describe how this information can be useful to detect and remove duplicate information in databases. The results demonstrate the power, flexibility and accuracy of many of today’s online geocoding services. © 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract