New strong convergence theorem of the inertial projection and contraction method for variational inequality problems

Numerical Algorithms - In this paper, we introduce a new algorithm which combines the inertial projection and contraction method and the viscosity method for solving monotone variational inequality...     

Proximal point algorithms for solving convex minimization problem and common fixed points problem of asymptotically quasi-nonexpansive mappings in CAT(0) spaces with convergence analysis

In this paper, we introduce the modified proximal point algorithm for common fixed points of asymptotically quasi-nonexpansive mappings in CAT(0) spaces and also prove some convergence theorems of the proposed algorithm to a common fixed point of asymptotically quasi-nonexpansive mappings and a minimizer of a convex function. The main results in this paper improve and generalize the corresponding results given by some authors. Moreover, we then give numerical examples to illustrate and show efficiency of the proposed algorithm for supporting our main results.     

Random fixed point theorems for Hardy-Rogers self-random operators with applications to random integral equations

In this paper, we prove some random fixed point theorems for Hardy–Rogers self-random operators in separable Banach spaces and, as some applications, we show the existence of a solution for random nonlinear integral equations in Banach spaces. Some stochastic versions of deterministic fixed point theorems for Hardy–Rogers self mappings and stochastic integral equations are obtained.     

Algorithms for solutions of extended general mixed variational inequalities and fixed points

In this paper, we introduce and study a new class of extended general nonlinear mixed variational inequalities and a new class of extended general resolvent equations and establish the equivalence between the extended general nonlinear mixed variational inequalities and implicit fixed point problems as well as the extended general resolvent equations. Then by using this equivalent formulation, we discuss the existence and uniqueness of solution of the problem of extended general nonlinear mixed variational inequalities. Applying the aforesaid equivalent alternative formulation and a nearly uniformly Lipschitzian mapping S, we construct some new resolvent iterative algorithms for finding an element of set of the fixed points of nearly uniformly Lipschitzian mapping S which is the unique solution of the problem of extended general nonlinear mixed variational inequalities. We study convergence analysis of the suggested iterative schemes under some suitable conditions. We also suggest and analyze a class of extended general resolvent dynamical systems associated with the extended general nonlinear mixed variational inequalities and show that the trajectory of the solution of the extended general resolvent dynamical system converges globally exponentially to the unique solution of the extended general nonlinear mixed variational inequalities. The results presented in this paper extend and improve some known results in the literature.     

Non-Archimedean stability of a quadratic functional equation

Recently the Hyers–Ulam stability of the quadratic functional equation $ f(kx+y)+f(kx+\sigma (y))- 2k^2 f(x)-2f(y)=0 $ where $\sigma $ is an involution of the normed space $E$ and $k$ is a fixed positive integer greater that 1, has been proved in the earlier work. In this paper, using fixed point and direct methods, we prove the Hyers–Ulam stability of the above functional equation in non-Archimedean normed spaces.     

Visualizing Microglia with a Fluorescence Turn‐On Ugt1a7c Substrate

Microglia, the brain‐resident macrophage, are involved in brain development and contribute to the progression of neural disorders. Despite the importance of microglia, imaging of live microglia at a cellular resolution has been limited to transgenic mice. Efforts have therefore been dedicated to developing new methods for microglia detection and imaging. Using a thorough structure–activity relationships study, we developed CDr20, a high‐performance fluorogenic chemical probe that enables the visualization of microglia both in vitro and in vivo. Using a genome‐scale CRISPR‐Cas9 knockout screen, the UDP‐glucuronosyltransferase Ugt1a7c was identified as the target of CDr20. The glucuronidation of CDr20 by Ugt1a7c in microglia produces fluorescence.     

Luminescence of poly(N-vinylcarbazole) in the solution and solid state

Fluorescence spectra of poly(N-vinylcarbazole) have been studied as a function of various environments and temperature. Fluorescence spectra have been excited with UV light from 200 W Xenon lamp or with second-harmonics of a pulsed ruby laser. Polymer films and powders show exclusively excimer fluorescence at room temperature. At high intensities of excitation the observed fluorescence spectra have a weak quasiperiodic structure.     

Systems of generalized nonlinear variational inequalities and its projection methods

Based on relaxed cocoercive monotonicity, a new generalized class of nonlinear variational inequality problems is presented. Our results improve and extend the recent ones announced by [H. Y. Huang, M. A. Noor, An explicit projection method for a system of nonlinear variational inequalities with different (γ,r)$(\gamma ,r)$-cocoercive mappings, Appl. Math. Comput. 190 (2007) 356–361; S. S. Chang, H. W. Joseph Lee, C. K. Chan, Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329–334; R. U. Verma, Generalized system for relaxed cocoercive variational inequalities and its projection methods, J. Optim. Theory Appl. 121 (2004) 203–210; M. A. Noor, General variational inequalities, Appl. Math. Lett. 1 (1988) 119–121] and many others.     

Statistical mechanics of molecular adsorption: effects of adsorbate interaction on isotherms

We investigate a simple, exactly solvable model for interacting adsorbates. From the model study, we find that (1-theta)(-1) as a function of density of molecules in bulk media can have a positive curvature only in the presence of attractive interaction between adsorbed molecules. We propose a novel experimental observable, chi. Positive chi is the sufficient condition for the presence of attractive interactions between adsorbate molecules.     

Nonlinear optical characteristics of monolayer MoSe2

In this study, we utilized picosecond pulses from an Nd:YAG laser to investigate the nonlinear optical characteristics of monolayer MoSe₂. Two‐step growth involving the selenization of pulsed‐laser‐deposited MoO₃ film was employed to yield the MoSe₂ monolayer on a SiO₂/Si substrate. Raman scattering, photoluminescence (PL) spectroscopy, and atomic force microscopy verified the high optical quality of the monolayer. The second‐order susceptibility χ⁽²⁾ was calculated to be ～50 pm V^?1 at the second harmonic wavelength ～810 nm, which is near the optical gap of the monolayer. Interestingly, our wavelength‐dependent second harmonic scan can identify the bound excitonic states including negatively charged excitons much more efficiently, compared with the PL method at room temperature. Additionally, the MoSe₂ monolayer exhibits a strong laser‐induced damage threshold ～16 GW cm^?2 under picosecond‐pulse excitation_. Our findings suggest that monolayer MoSe₂ can be considered as a promising candidate for high‐power, thin‐film‐based nonlinear optical devices and applications.