Sunlight-Active BiOI Photocatalyst as an Efficient Adsorbent for the Removal of Organic Dyes and Antibiotics from Aqueous Solutions

A bismuth oxyiodide (BiOI) photocatalyst with excellent sunlight-driven performance was synthesized by a solvothermal route without the addition of surfactants or capping agents. The prepared photocatalyst exhibited a tetragonal phase with an energy band gap of 2.15 eV. The efficiency of the photocatalyst was elucidated by monitoring the photodegradation of organic dyes and antibiotics. The BiOI photocatalyst provided a 95% removal of norfloxacin (NOR) antibiotics under visible light illumination. Interestingly, the complete removal of Rhodamine B (RhB) dye was achieved after 80 min of natural sunlight irradiation. The photodegradation reaction followed the first-order reaction. Both photo-generated holes and electrons play vital roles in the photodegradation of the pollutant. The BiOI photocatalyst remains stable and still shows a high efficiency even after the fifth run. This confirms the great cycling ability and high structural stability of the photocatalyst. The prepared BiOI catalyst, with a high surface area of 118 m² g⁻¹, can act as an excellent adsorbent as well. The synergistic effect based on both adsorption and photocatalysis is a key factor in achieving a very high removal efficiency. The photoactivity under sunlight is higher than that observed under visible light, supporting the practical use of the BiOI photocatalyst for the removal of organic pollutants in wastewater through the utilization of abundant solar energy.     

Complete reducibility of gyrogroup representations

Abstract

In this article, we show that any finite gyrogroup can be represented on a space of complex-valued functions. In particular, we prove that any linear representation of a finite gyrogroup on a finite-dimensional complex inner product space is unitary and hence is completely reducible using strong connections between linear actions of groups and gyrogroups. Also, we provide an example of a unitary representation of an arbitrary finite gyrogroup, which resembles the group-theoretic left regular representation.     

Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk

Möbius addition is defined on the complex open unit disk by

$$\begin{aligned} a\oplus _M b = \dfrac{a+b}{1+\bar{a}b} \end{aligned}$$

and Möbius’s exponential equation takes the form \(L(a\oplus _M b) = L(a)L(b)\), where L is a complex-valued function defined on the complex unit disk. In the present article, we indicate how Möbius’s exponential equation is connected to Cauchy’s exponential equation. Möbius’s exponential equation arises when one determines the irreducible linear representations of the unit disk equipped with Möbius addition, considered as a nonassociative group-like structure. This suggests studying Schur’s lemma in a more general setting.