SOME SUBGROUPS OF THE EXTENDED HECKE GROUPS (H)(λq)

The authors consider the extended Hecke groups H(λq) generated by T(z) =-1 / z, S(z) = -1/(z+λq) and R(z) = 1 / -z with λq = 2cos(π/q) for q ≥ 3 an integer. Inthis paper, the even subgroup He(λq), the second commutator subgroup H"(λq) and theprincipal congruence subgroups Hp(λq) of the extended Hecke groups H(λq) are studied.Also, relations between them are given.     

Bernstein series solution of linear second‐order partial differential equations with mixed conditions

The purpose of this study is to present a new collocation method for numerical solution of linear PDEs under the most general conditions. The method is given with a priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Also, one can specify the optimal truncation limit n, which gives better result in any norm ∥ ∥ . Finally, the effectiveness of the method is illustrated in some numerical experiments. Numerical results are consistent with the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Formal Analysis of Optical Systems

Optical systems are becoming increasingly important by resolving many bottlenecks in today’s communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical system models using traditional paper-and-pencil and computer simulation approaches sets limits especially in safety-critical applications. In order to overcome these limitations, we propose to employ higher-order-logic theorem proving as a complement to computational and numerical approaches to improve optical model analysis in a comprehensive framework. The proposed framework allows formal analysis of optical systems at four abstraction levels, i.e., ray, wave, electromagnetic, and quantum.     

Two-stage quadratic integer programs with stochastic right-hand sides

We consider two-stage quadratic integer programs with stochastic right-hand sides, and present an equivalent reformulation using value functions. We propose a two-phase solution approach. The first phase constructs value functions of quadratic integer programs in both stages. The second phase solves the reformulation using a global branch-and-bound algorithm or a level-set approach. We derive some basic properties of value functions of quadratic integer programs and utilize them in our algorithms. We show that our approach can solve instances whose extensive forms are hundreds of orders of magnitude larger than the largest quadratic integer programming instances solved in the literature.     

Associated Family of G-Structure Preserving Minimal Immersions in Semi-Riemannian Manifolds

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details minimal embeddings into product of space forms.     

High‐Density Polyethylene Micro‐ and Nanocomposites: Effect of Particle Shape,Size and Surface Treatment on Polymer Crystallinity and Gas Permeability

Summary: High‐density polyethylene (HDPE) micro‐ and nanocomposites with spherical and platelike inclusions were prepared and the effect of filler particles on polymer crystallinity and gas permeability was investigated. Platelike inclusions strongly reduce the polymer permeability coefficient, while spherical ones have no influence on it, irrespective of their size. The reduction in gas permeability depends on the average aspect ratio of the inclusions, which in turn depends on the exfoliation of the organo‐montmorillonites (OM) and consequently on its surface treatment.

A TEM micrograph of 3 vol.‐% 2C18 · M‐HDPE nanocomposite, showing partial exfoliation of the organo‐montmorillonite.     

Self-reported Side-effects of Ultraviolet-C Disinfection Devices

The COVID-19 pandemic increased sales of portable UV-C devices as a means of inactivating the SARS-CoV-2 virus. Research suggests that excessive UV-C exposure to the eyes and skin can lead to side-effects, primarily photokeratitis and erythema, but these findings are limited to case studies. This study explores self-reported side-effects of UV-C devices by collating five waves of UK consumer survey data from April 2020–December 2021 (N = 26 864). 30%–46% of owners report a side-effect after using a device claiming to emit UV-C. However, detailed analysis of Wave 4 data (N = 309) highlights inconsistencies between reported and plausible side-effect(s) associated with skin or eye exposure from UV-C devices. Alternative explanations are considered, namely that the reported side-effect(s) were psychosomatic or misattributed to direct exposure of UV-C radiation. Data regarding awareness of warnings about device side-effect(s) supports the misattribution explanation. For risk assessment purposes, limited reliable information about specific irritation or injury to the eye and skin was found from self-reporting surveys. To optimize future data collection, we recommend addressing recall errors by: reducing the period under investigation, supplementing responses with empirical measures, and incentivizing respondents to provide accurate information about the make and model of the UV-C device.     

Geometrical patterns of time variable Kadomtsev–Petviashvili (I) equation that models dynamics of waves in thin films with high surface tension

Lump solutions are a prominent option for numerous models of nonlinear evolution. The intention of this research is to explore the variable coefficients Kadomtsev–Petviashvili equation. We auspiciously provide multiple soliton and M-lump solutions to this equation. Additionally, the presented results are also supplied with collision phenomena. Owing of its essential role, we employ appropriate parameter values to emphasis the physical characteristics of the provided results using 3D and contour charts. The outcomes of this work convey the physical characteristics of lump and lump interactions that occur in many dynamical regimes.

     

Hydrogen storage in SiC,GeC, and SnC nanocones functionalized with nickel,Density Functional Theory—Study

Hydrogen is regarded as one of the most potential sustainable energy sources in the future. Applications include transportation. Still, the event of materials for its storage is difficult notably as a fuel in vehicular transport. Nanocones are a promising hydrogen storage material. Silicon, germanium, and tin carbide nanocones have recently been proposed as promising hydrogen storage materials. In the present study, we have investigated the hydrogen storage capacity of $\mathrm{SiC},\mathrm{GeC},$ and $\mathrm{SnC}$ nanocones functionalized with Ni. The functionalized Ni atom are found to be adsorbed on $\text{SiCNC},\text{GeCNC},$ and $\text{SnCNC}$ with an adsorption energy of −5.56, −6.70, and −4.25 eV. The functionalized $\text{SiCNC},\text{GeCNC}$, and $\text{SnCNC}$ bind up to seven, six and four molecules of hydrogen with the adsorption energy of (−0.34, −0.35, and −0.26 eV) and an average desorption temperature of around 434, 447, and 332 K (ideal for fuel cell applications). The SiC, GeC, and SnC nanocones systems exhibit a maximum gravimetric storage capacity of 12.51, 7.78, and 4.08 wt%. We suggested that Ni SiCNC and Ni GeCNC systems can act as potential H₂ storage device materials because of their higher H₂ uptake capacity as well as their stronger interaction with adsorbed hydrogen molecules than Ni SnCNC systems. The hydrogen storage reactions are characterized in terms of the charge transfer, the partial density of states, the frontier orbital band gaps, and isosurface plots. And electrophilicity are calculated for the functionalized and hydrogenated $\mathrm{SiC},\mathrm{GeC},$ and $\mathrm{SnC}$ nanocones.