Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems

Numerical Algorithms - In this paper, basing on the subgradient extragradient method and inertial method with line-search process, we introduce two new algorithms for finding a common element of...     

Two weight commutators in the Dirichlet and Neumann Laplacian settings

In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian ${\mathrm{\Delta }}_{N_{+}}$ on the upper half space ${\mathbb{R}}_{+}^n$ and the reflection Neumann Laplacian ${\mathrm{\Delta }}_N$ on ${\mathbb{R}}^n$ with respect to the weights associated to ${\mathrm{\Delta }}_{N_{+}}$ and ${\mathrm{\Delta }}_N$ respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to ${\mathrm{\Delta }}_N$ is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on ${\mathbb{R}}^n$ and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt $A^p$ weights with $p\in (1,2]$ while the previously known related results cover only $p\in (1,\frac{n+1}{n}]$. We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian ${\mathrm{\Delta }}_{D_{+}}$ on ${\mathbb{R}}_{+}^n$.     

Synthesis of fused indolines by interrupted Fischer indolization in a microfluidic reactor

This study describes our development of a microfluidic reaction scheme for the synthesis of fused indoline ring systems found in several bioactive compounds. We have utilized a continuous-flow microfluidic reactor for the reaction of hydrazines with latent aldehydes through the interrupted Fischer indolization reaction to form fused indoline and azaindoline products. We have identified optimal conditions and evaluated the scope of this microfluidic reaction using various hydrazine and latent aldehyde surrogates. This green chemistry approach can be of general utility to rapidly produce indoline scaffolds and intermediates in a continuous manner.     

An Improved Model for Polyether Production from 1,3‐Propanediol

A dynamic mathematical model is developed for production of Cerenol polyether from 1,3‐propanediol in a batch reactor system. The model accounts for polycondensation reactions and side reactions in the liquid phase and for mass transfer of volatile species to the vapor. Parameters are estimated using measured liquid‐phase concentrations of monomer, oligomers, water, and end groups as well as the mass and composition of condensate collected from the overhead condenser system. The proposed model uses novel probability factors to keep the model equations relatively simple while accounting for the complex influence of superacid catalyst on reaction rates. The model is a significant advance over previous Cerenol models because it better accounts for mass‐transfer rates and for the dynamic behavior of the condenser. In addition, the proposed model accounts for the inhibitory influence of water on polycondensation kinetics due to hydration of hydroxyl ends. The model equations and parameter estimates provide a substantial improvement in fit to the data, especially for long reaction times and high catalyst levels, resulting in a 97% reduction in the value of the weighted least squared objective function compared to equations and parameters from a previous model.     

Chemical Constituents of the Leaves of Artocarpus integer

Chemistry of Natural Compounds -     

One‐Step Pyro‐Synthesis of a Nanostructured Mn3O4/C Electrode with Long Cycle Stability for Rechargeable Lithium‐Ion Batteries

A nanostructured Mn₃O₄/C electrode was prepared by a one‐step polyol‐assisted pyro‐synthesis without any post‐heat treatments. The as‐prepared Mn₃O₄/C revealed nanostructured morphology comprised of secondary aggregates formed from carbon‐coated primary particles of average diameters ranging between 20 and 40 nm, as evidenced from the electron microscopy studies. The N₂ adsorption studies reveal a hierarchical porous feature in the nanostructured electrode. The nanostructured morphology appears to be related to the present rapid combustion strategy. The nanostructured porous Mn₃O₄/C electrode demonstrated impressive electrode properties with reversible capacities of 666 mAh g^?1 at a current density of 33 mA g^?1, good capacity retentions (1141 mAh g^?1 with 100 % Coulombic efficiencies at the 100^th cycle), and rate capabilities (307 and 202 mAh g^?1 at 528 and 1056 mA g^?1, respectively) when tested as an anode for lithium‐ion battery applications.     

Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd.