The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics

This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.     

Self-oscillating gels based on novel catalyst for the Belousov–Zhabotinsky reaction

We report on the synthesis of new Ru(bpy)₂(phen) catalyst for the oscillatory Belousov–Zhabotinsky chemical reaction and on the preparation of novel Ru(bpy)₂(phen)-based self-oscillating gels. The synthesized gels exhibit high-amplitude autonomous mechanical oscillations when the Belousov–Zhabotinsky reaction proceeds inside these gels     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Defects related emission and nanosecond optical power limiting in CuS quantum dots

We report optical and nonlinear optical properties of CuS quantum dots and nanoparticles prepared through a nontoxic, green, one-pot synthesis method. The presence of surface states and defects in the quantum dots are evident from the luminescent behavior and enhanced nonlinear optical properties measured using the open aperture Z-scan, employing 5 ns laser pulses at 532 nm. The quantum dots exhibit large effective third order nonlinear optical coefficients with a relatively lower optical limiting threshold of 2.3 J cm⁻², and the optical nonlinearity arises largely from absorption saturation and excited state absorption. Results suggest that these materials are potential candidates for designing efficient optical limiters with applications in laser safety devices.     

Molecular design of ambipolar redox-active molecules II: closed-shell systems

This mini-review highlights key structural features that should be taken into account when creating ambipolar redox-active closed-shell metal-free molecules. This type of compound is strongly required for the fabrication of all-organic ‘poleless’ batteries and semiconductors. The suggested strategies aimed at stabilization of both oxidized (cationic) and reduced (anionic) redox-states are based on the comprehensive analysis of the most successful structures taken from the recent publications.     

Excited-State Dynamics of Non-Luminescent and Luminescent π-Radicals

Recently, the potential use of organic π-radicals and related spin systems has been expanded to modern technological applications. The unique excited-state dynamics of organic π-radicals can be useful to improve the stability of photochemically unstable organic compounds, make the polarization transfer applicable to information technology, and achieve effective up-conversion of interest for luminescence bioimaging, among others. Furthermore, highly luminescent stable π-radicals have been recently reported, which are especially interesting for application in organic light-emitting devices owing to their potential to provide an internal quantum efficiency of 100 %. Thus, the excited-state nature of stable π-radicals as well as the control of their excited-state spin dynamics are emerging topics both in terms of fundamental science and related technological applications. In this minireview, we focus on the excited-state dynamics of both photostable non(weakly)-luminescent and luminescent π-radicals, which are opposites of each other. In particular, we cover the following topics: 1) effective generation of high-spin photoexcited states and control of the excited-state dynamics by using non-luminescent π-radicals, 2) unique excited-state dynamics of luminescent π-radicals and radical excimers, and 3) applications utilizing excited-state dynamics of π-radicals.     

Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrödinger Equation

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.