On the enumeration of finite Abelian and solvable groups

Let a(n) be the number of nonisomorphic abelian groups of order n. We obtain a short interval result for the local density of a(n). More generally, we get short interval version of results of Ivi? on the local density of prime independent multiplicative functions. Also we prove a short interval version of the theorem of Erdös and Szekeres on the summatory function of a(n) and the theorem of Greenberg and Newman on the enumeration of a certain type of finite solvable groups.     

Locating a nearest matrix with an eigenvalue of prespecified algebraic multiplicity

The Wilkinson distance of a matrix A is the two-norm of the smallest perturbation E so that A + E has a multiple eigenvalue. Malyshev derived a singular value optimization characterization for the Wilkinson distance. In this work we generalize the definition of the Wilkinson distance as the two-norm of the smallest perturbation so that the perturbed matrix has an eigenvalue of prespecified algebraic multiplicity. We provide a singular value characterization for this generalized Wilkinson distance. Then we outline a numerical technique to solve the derived singular value optimization problems. In particular the numerical technique is applicable to Malyshev’s formula to compute the Wilkinson distance as well as to retrieve a nearest matrix with a multiple eigenvalue.     

Probabilistic nonlinear analysis of CFR dams by MCS using Response Surface Method

This paper presents the probabilistic analysis of concrete-faced rockfill (CFR) dams according to the Monte Carlo Simulation (MCS) results which are obtained through the Response Surface Method (RSM). ANSYS finite element program is used to get displacement and principal stress components. First of all, some parametric studies are performed according to the simple and representative finite element model of dam body to obtain the optimum approximate model. Secondly, a sensitivity analysis is performed to get the most effective parameters on dam response. Then, RSM is used to obtain the approximate function through the selected parameters. After the performed analyses, star experimental design with quadratic function without mixed terms according to the k = 1 is determined as the most appropriate model. Finally, dam-foundation-reservoir interaction finite element model is constituted and probabilistic analyses are performed with MCS using the selected parameters, sampling method, function and arbitrary factor under gravity load for empty and full reservoir conditions. Geometrically and materially nonlinearity are considered in the analysis of dam-foundation-reservoir interaction system. Reservoir water is modeled by fluid finite elements based on the Lagrangian approach. Structural connections are modeled as welded contact and friction contact based on Coulomb’s friction law. Probabilistic displacements and stresses are presented and compared with deterministic results.     

Dye‐sensitized solar cells based on zinc(II) phthalocyanines bearing 3‐pyridin‐3‐ylpropoxy anchoring groups

In this study, nonperipherally tetra‐substituted ( 2 ), peripherally tetra‐substituted ( 3 ), and peripherally octa‐substituted ( 4 ) zinc(II) phthalocyanines were synthesized as sensitizers for dye‐sensitized solar cells (DSSCs) in which 3‐pyridin‐3‐ylpropoxy substituent acts as anchoring unit to bind TiO₂ surface. The optical results indicated that there is an interaction between the dyes and the TiO₂ surface. The photovoltaic performances of the DSSCs based on these dyes were found to depend on both the position and number of the substituents. Despite the more red‐shifted absorption, the DSSC based on 2 showed the conversion efficiency of 0.68%, which is lower than 1.36% and 0.92% for 3 and 4 , respectively, under one sun (AM 1.5G). The vertical orientation of the dye on TiO₂ surface could be the main reason for the higher photovoltaic performance of complex 3 , which is beneficial for not only injecting the electrons into the conduction band of TiO₂ but also reducing the charge recombination. Overall, these results demonstrate that the peripherally tetra‐substituted 3‐pyridin‐3‐ylpropoxy zinc(II) phthalocyanine complex ( 3 ) as a sensitizer can more efficiently utilize the photons in the red/near‐infrared region with respect to the other complexes studied.     

The Paul wavelet algorithm: an alternative approach to calculate the refractive index dispersion of a dielectric film from transmittance spectrum

A new application of the Paul wavelet algorithm was presented to determine the refractive index dispersion of a dielectric film from transmittance spectrum in the visible and near infrared region. The developed algorithm was tested by simulated data and experimentally applied to a sample of mica. The obtained refractive index dispersion determined by the Paul wavelet algorithm was compared with the refractive index values determined by the envelope and fringe counting methods, and also with the established result. It was shown that the degree of the Paul wavelet has a major effect on the outcome of a refractive index determination. The noise immunity of the presented method was shown by the simulation study.     

Oxidative Fluorination of Cu/ZnO Methanol Catalysts

The influence of a mild difluorine treatment on Cu/ZnO precatalysts for methanol synthesis was investigated. It led to the incorporation of 1.2…1.3±0.1 wt % fluoride into the material. Fluorination considerably increased the amount of ZnO_x related defect sites on the catalysts and significantly increased the space‐time yields. Although the apparent activation energy E_A,app for methanol formation from CO₂ and H₂ was almost unchanged, the E_A,app for the reverse water‐gas shift (rWGS) reaction increased considerably. Overall, fluorination led to a significant gain in methanol selectivity and productivity. Apparently, also the quantity of active sites increased.     

First-principles investigation of the structural,dynamical, electronic,and elastic properties of WGe2 and W5Ge3

ABSTRACT

We have investigated the structural, dynamical, elastic, and electronic properties of WGe₂ and W₅Ge₃ compounds in different phases. We have considered the C11_b (tetragonal, space group I4/mmm) and C23 (orthorhombic, space group Pnma) strukturbericht phases for WGe₂ compound and D8₁ (tetragonal, space group I4/mcm), D8_m (tetragonal space group I4/mcm) strukturbericht phases for W₅Ge₃ compound. The structural parameters, formation enthalpies, phonon dispersion curves, elastic constants, mechanical modulus, anisotropic factors, thermal conductivities, and electronic structures have been investigated using generalised gradient approximation within in the plane wave pseudopotential density functional theory. The calculated lattice constants are in a good agreement with the experimental data. The considered phases for WGe₂ and W₅Ge₃ compounds have a metallic character. The results indicated that all phases for compounds are both mechanically stable and dynamically stable except for W₅Ge₃-D8₁. The anisotropy in some mechanical modulus has been investigated using several elastic anisotropy indexes and directional dependence of compressibility, Young’s moduli, shear moduli, and Poisson’s ratio.