The reduced basis method for the electric field integral equation

We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field integral equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first step consists of a computationally intense assembling of the reduced basis, that needs to be effected only once. In the second step, we compute output functionals of the solution, such as the Radar Cross Section (RCS), independently of the dimension of the discretization space, for many different parameter values in a many-query context at very little cost. Parameters include the wavenumber, the angle of the incident plane wave and its polarization.     

Three-dimensional pore evolution of nanoporous metal particles for energy storage

A well characterized and predictable aging pattern is necessary for practical energy storage applications of nanoporous particles that facilitate rapid transport of ions or redox species. Here we use STEM tomography with segmentation to show that surface diffusion and grain boundary diffusion are responsible for pore evolution at intermediate and higher temperatures, respectively. This unprecedented three dimensional understanding of pore behavior as a function of temperature suggests routes for optimizing pore stability in future energy storage materials.     

A differential equation for approximate wall distance

A partial differential equation to compute the distance from a surface is derived and solved numerically. The benefit of such a formulation especially in combination with turbulence models is shown. The details of the formulation as well as several examples demonstrating the influence of its parameters are presented. The proposed formulation has computational advantages and can be favourably incorporated into one‐ and two‐equation turbulence models like e.g. the Spalart–Allmaras, the Secundov or Menter's SST model. Copyright © 2002 John Wiley & Sons, Ltd.     

Regularity of the Solution to Nonlinear Anisotropic Elliptic Equations with Variable Exponents and Irregular Data

In this paper, we prove the existence and regularity of weak solutions for a class of nonlinear anisotropic elliptic equations with \(p_i(x)\) growth conditions and \(L^m\) data, with m being small. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Our results are generalizations of the corresponding results in the constant exponent case and some results given in Bendahmane et al. (Commun Pure Appl Anal 12:1201–1220, 2013).     

The Decay of 140La to Levels in 140Ce

The decay of ¹⁴⁰La to levels in ¹⁴⁰Ce has been studied in detail using a GMX-Ge and Hp-Ge coincidence spectrometer. Singles gamma-ray spectra as well as gamma-gamma coincidence were carried out to determine some γ-transitions and to insure others. Energies and relative intensities of 36 γ-transitions in the range from 26 to 3319 keV have been measured. The doubted γ-lines 936.7, 1087.9, 1303.5, 1404.2, 1415.3 and 2533.4 keV were confirmed, while other ones at 798.3, 902.0, 907.0, 1521.8 and 2494.0 keV were not observed. The two γ-lines at 1924 and 2082 keV which were a source of large discrepancies in the previous studies are confirmed in the present work to be sum peaks. Special care was paid in identifying the weak γ-transitions 936.7, 1087.9, 1415.3 and 2533.4 keV.

Es wurde der Zerfall von ¹⁴⁰La in Energienivcaus des ^l40Ce unter Verwendung eines GMX-Ge und Hp-Ge-Koinzidenzspeklrometers untersucht. Es werden einzclne Gammaspektren r und Gamma-Gamma-Koinzidenzen aufgenommen, um einige Gamma-Übergänge zu bestimmen und andere abzusichern. Die Energien und die relativen Intcnsitäten von 36 Gamma-Übergangen im Bereich von 26 … 3319 keV wurden vermessen. Die unsicheren Gamma-Linien 936,7, 1087,9, 1303,5, 1404,2, 1415,3 und 2533,4 keV wurden bestätigt, während die Linien 798,3, 902,0, 907,0, 1521,8 und 2494,0 keV nicht beobachtet werden konnten. Die zwei Gamma-Linien bei 1924 und 2082 keV, die eine Quclle groβer Unstimmigkeiten in früheren Untersuchungen gewesen sind, konnten als Summenpeaks bestätigt werden. Besondere Beachtung wurde der Zuordnung der schwachen Gamma-Übergange bei 936,7, 1087,9, 1415,3 und 2533,4 keV geschenkt.     

Integer valued polynomials on lower triangular integer matrices

Let $D$ be an integral domain with quotient field $K$ . In this paper we study the algebra of polynomials in $K[x]$ which map the set of lower triangular $n\times n$ matrices with coefficients in $D$ into itself and show that it coincides with the algebra of polynomials whose divided differences of order $k$ map $D^{k+1}$ into $D$ for every $k< n$ . Using this result we describe the polynomial closure of this set of matrices when $D$ is the ring of integers in a global field.     

Post‐oxidizing effects on surface characteristics of salt bath nitrocarburized AISI 02 tool steel type

The effect of post‐oxidizing treatment on the characteristics of modified surface layers produced by salt bath nitrocarburizing on the industrial American Iron and Steel Institute (AISI) 02 tool steel types is investigated. Nitrocarburizing treatment is performed for 6 h and 8 h at 570 °C and post‐oxidizing treatment for 30, 60 and 90 min at 520 °C, using argon–steam mixture. Formed layers are characterized by their basic properties such as thickness layer, depth, surface hardness and wear resistance. Detailed estimation of the modified metal surface quality, in terms of chemical composition, formed phases, microstructures and diffusion mechanisms are performed by metallographic techniques, EDX, X‐ray diffraction, scanning electron microscopy (SEM) and glow discharge optical electron spectroscopy (GDOES). The corrosion resistance was investigated in 0.4 M H₂SO₄ solutions, using steady‐state electrochemical polarization methods. The obtained results revealed the existence of a superficial oxide layer which consists of magnetite (Fe₃O₄) and hematite (Fe₂O₃) and the presence of an ε‐phase associated with a small amount of γ′‐phase. Important improvements in wear, microhardness and corrosion resistance occur after these treatments and it is specifically concluded that the sole application of a nitrocarburizing treatment does not significantly ameliorate the corrosion resistance of the as‐received steel. In fact, post‐oxidation treatment contributes to increase corrosion resistance by forming a dense magnetite layer and at the same time, it partially covers the compound layer pores. Copyright © 2009 John Wiley & Sons, Ltd.     

Surface characteristics analysis of nitrocarburized (Tenifer) and carbonitrided industrial steel AISI 02 types

Generally, tool steels for cold work are obtained by rolling and forging processes. They are treated to have a structure conferring to the material a high toughness limit in terms of wear resistance and endurance. The objective of this study is the thermochemical heat treatment of industrial steel blades made of AISI 02 types, intended for polymer crushing. The effects of nitrocarburizing (Tenifer) and gaseous carbonitriding processes on surface characteristics are considered. These surface treatments increase the usefulness of properties, that is, fatigue strength, wear and corrosion resistance of this microalloyed steel. The influence of treatment duration and the thickness of the layers on surface properties are investigated. The analysis and characterization are carried out using physical analysis [optical microscopy, scanning electron microscopy, X‐ray diffraction and glow discharge optical emission spectroscopy (GDOES) techniques] and mechanical measurements (microhardness, weight loss and residual stresses) of treated material. The results are intended to contribute in defining and optimizing the adequate choice of treatments for this type of steel in industrial conditions. Copyright © 2008 John Wiley & Sons, Ltd.     

An Eco‐friendly Synthesis and Biological Screening of Fused Heterocyclic Compounds Containing a Thiophene Moiety via Gewald Reaction

5‐Amino‐3‐phenyl‐1‐(2,4,6‐trichlorophenyl)‐1H‐thieno[3,2‐c]pyrazole‐6‐carbonitrile ( 2 ) was designed and synthesized by one‐pot multicomponent reaction. Compound 2 was reacted with different reagents to obtain new condensed moieties with our thienopyrazole skeleton. The compounds were prepared by using environmentally benign techniques as microwave irradiation, ultrasonic irradiation, and ball‐milling. The structure of the prepared compounds was elucidated through spectroscopic methods. The new compounds were evaluated for their in vitro antibacterial and antifungal potentialities.     

Three Dimensional Network Polymeric Structure of (4,4′-bipyridinium)[CdBr<Subscript>4</Subscript>]<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>: Supramolecular Motifs and Crystal Supramolecularity

Abstract A single crystal structure determination of the complex (4,4′-bipyridinium)[CdBr₄] _n , [henceforth (I)], has been carried out. It crystallizes in the monoclinic space group C2/c, with the following cell parameters: a = 16.119(3) ?, b = 13.206(3) ?, c = 7.2601(15) ?, β = 115.62°, V = 1393.5(6) ?³, with Z = 4 formula units. The polymeric anion forms an infinite zig-zag chain of edge-sharing octahedra along c, with a distorted octahedral stereochemistry around Cd. There are N–H···Br [Br2···N1 of 3.386(13) ? and Br1···N1 of 3.363(13) ?] and C–H···Br [Br2···C5 of 3.552(16) ?] hydrogen bonding interactions, tying the CdBr chains to the cations to form 2D-network. The resulting 2D-networks are further linked by aryl···aryl (π···π) interactions within the cationic chains leading to a 3D-network. Index Abstract Three dimensional network polymeric structure of (4,4′-bipyridinium)[CdBr₄] _n : Supramolecular motifs and crystal supramolecularity. Rawhi Al-Far and Basem F. Ali The polymeric anion consists of a zig–zag chain of distorted edge shared octahedra run along c axis. The protonated cation bridges the anion chains through N–H···Br and C–H···Br into a supramolecular array.