Some improved inclusion methods for polynomial roots with Weierstrass' corrections

AbstractOne decade ago, the third order method without derivatives for the simultaneous inclusion of simple zeros of a polynomial was proposed in [1]. Following Nourein's idea [2], some modifications of this method with the increased convergence are proposed. The acceleration of convergence is attained by using Weierstrass' corrections without additional calculations, which provides a high computational efficiency of the modified methods. It is proved that their R-orders of convergence are asymptotically greater than 3.5. The presented interval methods are realized in circular complex arithmetic

Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general

Holographic Resonant Laser Printing of metasurfaces using plasmonic template

Laser printing with a spatial light modulator (SLM) has several advantages over conventional raster-writing and dot-matrix display (DMD) writing: multiple pixel exposure, high power endurance and existing software for computer generated holograms (CGH). We present a technique for the design and manufacturing of plasmonic metasurfaces based on ultrafast laser printing with an SLM. As a proof of principle, we have used this technique to laser print a plasmonic metalens as well as high resolution plasmonic color decorations. The high throughput holographic resonant laser printing (HRLP) approach enables on-demand mass-production of customized metasurfaces.Comment: Supplementary information is available upon request to author

Interruption of Weakly Cooled Arcs in Air and Airplus

Switching of low current arcs in free burning or weakly cooled conditions is mainly determined by the thermal properties of the gas. Products with such switching conditions are widely found in secondary distribution medium voltage (MV) gas insulated switchgears (GIS). In this study, we compare the current interruption capability of synthetic air and AirPlusTM, i.e. a mixture of synthetic air with C5F10O fluoroketone (C5-FK). We focus on thermal interruption performance of the gases. AirPlus mixture corresponds to -25 °C condensation temperature of C5-FK. An arc is drawn between the contacts and cooled by blowing cold gas from a tank. Blowing pressure required for current interruption is compared. Within the measurement accuracy, the current interruption performance of both gases is similar. Chemical analysis of the AirPlus mixture after 69 shots was performed using Gas Chromatography Mass Spectroscopy (GCMS) and it shows very little decrease in the concentration of C5-FK

Intestinal obstruction caused by a Meckel’s diverticulum adherent to an infected urachal cyst

Urachal remnant diseases are rare and frequently misdiagnosed, as the clinical presentation is similar to more common causes of intra-abdominal and pelvic disease. We report the rare case of a 1½-year-old boy with small-bowel obstruction caused by an adhesion band between a Meckel’s diverticulum and an infected urachal cyst. The condition was initially misdiagnosed and treated as a periappendiceal abscess on the basis of clinical examination and ultrasonography findings. In addition to the case report, we present an overview of urachal diseases