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 ${\mathbb{R}}_{+}^n$.     

Chemical Constituents of the Leaves of Artocarpus integer

Chemistry of Natural Compounds -     

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.     

Multi‐Species Multi‐Channel (MSMC): An Ab Initio‐based Parallel Thermodynamic and Kinetic Code for Complex Chemical Systems

Multi‐Species Multi‐Channel (MSMC) is an ab initio parallel program to calculate thermodynamic quantities (e.g., , , , and , time‐dependent species profiles, and rate coefficients as functions of temperature and pressure for complex chemical reaction systems, which consist of multiple stable species and multiple reaction channels interconnecting them. Thermodynamic properties of the species involved are calculated using statistical mechanics with molecular information from electronic structure calculations. Temperature‐ and pressure‐dependent behaviors are rigorously characterized within the eigenpair master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) framework. Corrections, e.g., for hindered internal rotation and tunneling treatment, are included. With the implementation of an ultra‐high precision package and rigorous matrix setup, MSMC is able to correctly mimic real behaviors of different types of chemical systems. Different eigenpair‐based approaches to extract phenomenological/macroscopic rate coefficients are implemented for different applications. Moreover, a friendly and platform‐independent graphical‐user‐interface (GUI) is provided to facilitate the use of MSMC and the pre‐/postcalculation data visualization/analysis on the fly. The program can be freely downloaded at https://sites.google.com/site/msmccode/ .     

Channel effect in isomeric ratio of 137m,gCe produced in different nuclear reactions

This work presents the experimental study of the isomeric ratio of ^137mCe–^137gCe produced in ¹³⁸Ce(γ, n) ^137m,gCe photonuclear reaction, in neutron capture reaction ¹³⁶Ce(n, γ) ^137m,gCe and in the two simultaneous reactions ¹³⁸Ce(γ, n) ^137m,gCe and ¹³⁶Ce(n, γ) ^137m,gCe in the mixed photon—neutron field by the activation method. The investigated samples were irradiated at the bremsstrahlung photon flux, in the epithermal and thermal-epithermal neutron beam and in the mixed photon-neutron field constructed at the electron accelerator Microtron MT-25 of the Flerov Laboratory of Nuclear Reaction, Joint Institute for Nuclear Research, Dubna, Russia. The results were analyzed, discussed and compared with those of other authors to examine the role of the channel effect in nuclear reaction and provide the nuclear data for theoretical model interpretation of nuclear reactions.

     

Copper ferrite superparamagnetic nanoparticles as a heterogeneous catalyst for directed phenol/formamide coupling

The copper ferrite-catalyzed, directed coupling of ortho-arylated phenols and dialkylformamides in the presence of a peroxide oxidant is described. Acyclic and cyclic amides were compatible with the reaction conditions. The copper ferrite catalyst is heterogeneous since substantial leaching was not detected and re-use of the catalyst for 9 consecutive reactions proceeded without a significant decrease in yield. To the best of our knowledge, this transformation has not been previously performed under heterogeneous catalysis conditions.     

Electrochemical Characterization of the Interaction of Multiwalled Carbon Nanotubes with Doxorubicin

It has been suggested that multiwalled carbon nanotubes (MWCNTs) interacting with pharmaceutics may be introduced into the body as nanocarriers. To deliver the anticancer drugs, covalent or noncovalent functionalization of MWCNTs is required. In this study, the influence of oxidation on MWCNTs in the interaction with chemotherapeutic drug, doxorubicin, was characterized. The binding of doxorubicin with MWCNTs decreased rapidly with the increasing oxidation period with sulfuric acid. However, with nitric acid, the interaction increased initially and slowly decreased with time. The best results were obtained for sulfuric and nitric acid following 1 and 3?h of oxidation, respectively. The results show that sulfuric acid provided more favorable interaction for MWCNTs with doxorubicin than nitric acid.     

Carleson measures,BMO spaces and balayages associated to Schrdinger operators

Let L be a Schrdinger operator of the form L =-? + V acting on L~2(R~n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R~n) denote the BMO space associated to the Schrdinger operator L on R~n. In this article, we show that for every f ∈ BMO_L(R~n) with compact support, then there exist g ∈ L~∞(R~n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R~n), where S_(μ,P)=∫(R_+~(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-~(t(L)~(1/2))}t0 on L~2(R~n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R~n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators.