Modulating opto-electronic and magnetic responses of Mo- and Zn-adsorbed LiNbO3 (1 1 1) surface for advanced energy harvesting applications: A comprehensive study

This study aimed to comprehensively investigate the optoelectronic and magnetic properties of Mo, Zn/LiNbO₃ (1 1 1) material. The primary objectives were to understand the potential for manipulating the material's magnetism and to elucidate the origin of spin-polarized states and magnetic moments, particularly with respect to the unpaired d orbitals of Nb, Mo, and Zn atoms. To achieve these objectives, we employed the Pardew–Burke–Ernzerhof (PBE) method within the Generalized Gradient Approximation (GGA + U) framework. This computational approach allowed us to examine the optoelectronic and magnetic characteristics of the material in detail. Our research yielded several key findings that enhance our understanding of Mo, Zn/LiNbO₃ (1 1 1) material. We observed a modest improvement in the material's absorption capacity within the visible spectrum, accompanied by a discernible red-shift. Notably, our study involved the calculation of the dielectric function and refractive constant of the material, revealing a strong correlation between absorption trends and the dielectric constant. Furthermore, our investigation uncovered that Mo, Zn/LiNbO₃ (1 1 1) exhibits distinct conduction and valence bands, with p and d orbitals predominantly contributing to each, respectively. The energy gap of the material falls within a range of 0.30–1.04 eV. A particularly significant finding was the narrower band gap of Mo, Zn/LiNbO₃ (1 1 1) material, which can be attributed to the superposition of Mo-d and Zn-p orbit energy levels with O-p orbit energy levels, ultimately forming a covalent bond. Importantly, our research demonstrated the material's heightened optical absorption within the visible spectrum, suggesting its suitability for various photonic and optoelectronic applications. Additionally, we calculated a wide range of optical characteristics, including the dielectric function, absorption coefficient, energy loss, reflectivity, refractive index, extinction coefficient, and optical conductivity, providing a comprehensive assessment of the material's optical properties.     

Electronic and optical properties of quaternary selenides for optoelectronic applications: Insights from DFT+U-computations

The optical properties, electronic charge density, electronic structure of the new layered selenides materials, BaGdCuSe₃, CsUCuSe₃, CsZrCuSe₃, and CsGdZnSe₃ compounds have been calculated by using the full potential and linear augmented plane wave (FP-LAPW) methods as applied in the WIEN2k package, which is based on the density functional theory. The ALnMSe3 compound's structure of these was (A = Cs, Ba; Ln = Zr, Gd, U; M = Cu, Zn) is composed of (n = 1, 2) layers, which might be separated by A atoms. It is to be observed that there is strong hybridization between the s, p, and d states of Zr, Gd, and Cu atoms. Around the gadolinium atom, the charge density contours are completely circular, but the Gadolinium “Gd” atom shows an ionic nature. To calculate the refractive index, we used Kramer's Kronig correlations with the imaginary part dielectric function. The decrease in the refractive index is due to the lack of probability for direct excitation of the electrons, resulting in a loss of energy. The value of the static refractive index for all reference compounds is about 1.75–2.25, which is indication that the material used in optoelectronic devices.     

Uniqueness of uniform norm and C*-norm in L p (G, ω)

Let G be a locally compact abelian group with a fixed Haar measure and ω be a weight on G. For 1 < p < ∞, we study uniqueness of uniform and C*-norm properties of the invariant weighted algebra L ^p (G, ω).     

Solving stochastic chemical kinetics by Metropolis-Hastings sampling

This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred chemically reacting systems as a desired distribution. A new numerical solvers based on exponential form of exact and approximate solutions of CME (Chemical Master Equation) is employed for obtaining target and proposal distributions in Metropolis-Hastings algorithm to accelerate the accuracy of the tau-leap method. Samples generated by this technique have the same distribution as SSA and the histogram of samples show it''s convergence to SSA     

Some fixed point theorems in convex metric spaces

The concept of a convex metric space was introduced by Takahashi [10]. He observed that it is possible to generalize fixed point theorems in Banach spaces. Subsequently, Machado [8], Itoh [5], Naimpally, Singh and Whitfield [9] and Beg and Azam [2], among others have studied fixed point theorems in convex metric spaces. This paper is a continuation of these investigations.     

Some properties of almostS-continuous functions

Noiri et al. in [16] introduced and investigated the notion of almosts-continuous functions. The object of this paper is to investigate some more properties of this type of functions.     

Certain strict topologies on the space of regular Borel measures on locally compact groups

Let G   denote a locally compact Hausdorff group and M(G)$M(G)$ be the space of all bounded complex-valued regular Borel measures on G  . In this paper, we define two strict topologies on M(G)$M(G)$ and study various properties of these topologies such as metrizability, barrelledness and completeness. We also determine the dual space of M(G)$M(G)$ and consider various continuity properties for the convolution product on M(G)$M(G)$ under these topologies.     

A presentation for reduced extended affine weyl groups

In 1985 K. Saito [Sal] introduced the concept of an extended affine Weyl group (EAWG), the Weyl group of an extended affine root system (EARS). In [A2, Section 5J, we gave a presentation called “a presentation by conjugation” for the class of EAWGs of index zero, a subclass of EAWGs. In this paper we will give a presentation wh.ich we call a “generalized present.ation by conjugation” for the class of reduced EAWGs. If the extended affine Weyl group is of index zero this presentation reduces to “a presentation by conjugation”. Our main result states that when the nullity of the EARS is 2, these two presentations coincide that is, EAWGs of nullity 2 have “a presentation by conjugation”. In [ST] another presentation for EAWGs of nullity 2 is given.