Global Exponential Stability of a Neural Network for Inverse Variational Inequalities

Journal of Optimization Theory and Applications - We investigate the convergence properties of a projected neural network for solving inverse variational inequalities. Under standard assumptions,...     

Visible‐Light‐Enabled Direct Decarboxylative N‐Alkylation

The development of efficient and selective C?N bond‐forming reactions from abundant feedstock chemicals remains a central theme in organic chemistry owing to the key roles of amines in synthesis, drug discovery, and materials science. Herein, we present a dual catalytic system for the N‐alkylation of diverse aromatic carbocyclic and heterocyclic amines directly with carboxylic acids, by‐passing their preactivation as redox‐active esters. The reaction, which is enabled by visible‐light‐driven, acridine‐catalyzed decarboxylation, provides access to N‐alkylated secondary and tertiary anilines and N‐heterocycles. Additional examples, including double alkylation, the installation of metabolically robust deuterated methyl groups, and tandem ring formation, further demonstrate the potential of the direct decarboxylative alkylation (DDA) reaction.     

Cycloisomerization of Olefins in Water

Preparative reactions that occur efficiently under dilute, buffered, aqueous conditions in the presence of biomolecules find application in ligation, peptide synthesis, and polynucleotide synthesis and sequencing. However, the identification of functional groups or reagents that are mutually reactive with one another, but unreactive with biopolymers and water, is challenging. Shown here are cobalt catalysts that react with alkenes under dilute, aqueous, buffered conditions and promote efficient cycloisomerization and formal Friedel–Crafts reactions. The constraining conditions of bioorthogonal chemistry are beneficial for reaction efficiency as superior conversion at low catalyst concentration is obtained and competent rates in dilute conditions are maintained. Efficiency at high dilution in the presence of buffer and nucleobases suggests that these reaction conditions may find broad application.     

Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators

This paper considers the nonparametric estimation of the densities of the latent variable and the error term in the standard measurement error model when two or more measurements are available. Using an identification result due to Kotlarski we propose a two-step nonparametric procedure for estimating both densities based on their empirical characteristic functions. We distinguish four cases according to whether the underlying characteristic functions are ordinary smooth or supersmooth. Using the loglog Law and von Mises differentials we show that our nonparametric density estimators are uniformly convergent. We also characterize the rate of uniform convergence in each of the four cases.     

Qualitative properties of strongly pseudomonotone variational inequalities

Qualitative properties of strongly pseudomonotone variational inequalities such as solution existence, stability and global error bound are studied in this paper.     

Nonlinear analysis on dynamic buckling of eccentrically stiffened functionally graded material toroidal shell segment surrounded by elastic foundations in thermal environment and under time-dependent torsional loads

The nonlinear analysis with an analytical approach on dynamic torsional buckling of stiffened functionally graded thin toroidal shell segments is investigated. The shell is reinforced by inside stiffeners and surrounded by elastic foundations in a thermal environment and under a time-dependent torsional load. The governing equations are derived based on the Donnell shell theory with the von K′arm′an geometrical nonlinearity,the Stein and McE lman assumption, the smeared stiffeners technique, and the Galerkin method. A deflection function with three terms is chosen. The thermal parameters of the uniform temperature rise and nonlinear temperature conduction law are found in an explicit form. A closed-form expression for determining the static critical torsional load is obtained. A critical dynamic torsional load is found by the fourth-order Runge-Kutta method and the Budiansky-Roth criterion. The effects of stiffeners, foundations, material,and dimensional parameters on dynamic responses of shells are considered.     

Self-focusing dynamics of polarization vortices in Kerr media

We investigate numerically and experimentally the spatial collapse dynamics and polarization stability of radially and azimuthally polarized vortex beams in pure Kerr medium. These beams are unstable to azimuthal modulation instabilities and break up into distinct collapsing filaments. The polarization of the filaments is primarily linear with weak circular components at the filaments' boundaries. This unique hybrid linear-circular polarization collapse pattern persists to advanced stages of collapse and appears to be a general feature of beams with spatially variant linear polarization.     

A Comprehensive Review on the Techniques for Extraction of Bioactive Compounds from Medicinal Cannabis

Cannabis is well-known for its numerous therapeutic activities, as demonstrated in pre-clinical and clinical studies primarily due to its bioactive compounds. The Cannabis industry is rapidly growing; therefore, product development and extraction methods have become crucial aspects of Cannabis research. The evaluation of the current extraction methods implemented in the Cannabis industry and scientific literature to produce consistent, reliable, and potent medicinal Cannabis extracts is prudent. Furthermore, these processes must be subjected to higher levels of scientific stringency, as Cannabis has been increasingly used for various ailments, and the Cannabis industry is receiving acceptance in different countries. We comprehensively analysed the current literature and drew a critical summary of the extraction methods implemented thus far to recover bioactive compounds from medicinal Cannabis. Moreover, this review outlines the major bioactive compounds in Cannabis, discusses critical factors affecting extraction yields, and proposes future considerations for the effective extraction of bioactive compounds from Cannabis. Overall, research on medicinal marijuana is limited, with most reports on the industrial hemp variety of Cannabis or pure isolates. We also propose the development of sustainable Cannabis extraction methods through the implementation of mathematical prediction models in future studies.     

Modified projection method for strongly pseudomonotone variational inequalities

A modified projection method for strongly pseudomonotone variational inequalities is considered. Strong convergence and error estimates for the sequences generated by this method are studied in two versions of the method: the stepsizes are chosen arbitrarily from a given fixed closed interval and the stepsizes form a non-summable decreasing sequence of positive real numbers. We also propose some interesting examples to analyze the obtained results.