Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations

In this paper,we investigate the non-autonomous Hamilton-Jacobi equation ■ where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary.We obtain the viscosity solution denoted by T_(t_0)~tφ(x) and show T_(t_0)~tφ(x) converges uniformly to a time-periodic viscosity solution u~*(x,t) of ?_tu+H(t,x,?_xu,u)=0.     

DFT mechanistic study of the H2‐assisted chain transfer copolymerization of propylene and p‐methylstyrene catalyzed by zirconocene complex

DFT computations have been performed to investigate the mechanism of H₂‐assisted chain transfer strategy to functionalize polypropylene via Zr‐catalyzed copolymerization of propylene and p‐methylstyrene (pMS). The study unveils the following: (i) propylene prefers 1,2‐insertion over 2,1‐insertion both kinetically and thermodynamically, explaining the observed 1,2‐insertion regioselectivity for propylene insertion. (ii) The 2,1‐inserion of pMS is kinetically less favorable but thermodynamically more favorable than 1,2‐insertion. The observation of 2,1‐insertion pMS at the end of polymer chain is due to thermodynamic control and that the barrier difference between the two insertion modes become smaller as the chain length becomes longer. (iii) The pMS insertion results in much higher barriers for subsequent either propylene or pMS insertion, which causes deactivation of the catalytic system. (iv) Small H₂ can react with the deactivated [Zr]?pMS?PP_n facilely, which displace functionalized pMS?PP_n chain and regenerate [Zr]? H active catalyst to continue copolymerization. The effects of counterions are also discussed. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 576–585     

Compensation for the Influence of Fluctuations in the Distance to the Object During Noncontact Probing in Spectral Domain Optical Coherence Tomography

Radiophysics and Quantum Electronics - We propose and experimentally test a numerical method for correction of the influence of fluctuations in the distance to objects during noncontact probing in...     

Boiling Water Reactor with a Combined Moderator for Utilization of Reactor Grade Plutonium

Physics of Atomic Nuclei - The article presents the concept of a channel-type reactor with a combined cooled moderator. The moderator consists of ceramic beryllium oxide and a liquid...     

Divergent Synthesis of Oxa-Cyclic Nitrones through Gold(I)-Catalyzed 1,3-Azaprotio Transfer of Propargylic α-Ketocarboxylate Oximes: Experimental and DFT Studies

1,3-Azaprotio transfer of propargylic α-ketocarboxylate oximes, a new type of alkynyl oximes featuring an ester tether, has been explored by taking advantage of gold catalysis. The incorporation of an oxygen atom to the chain of alkynyl oximes led to the formation of two different oxa-cyclic nitrones. It was found that internal alkynyl oximes with an E-configuration deliver five-membered nitrones, whereas terminal alkynyl oximes with an E-configuration afford six-membered nitrones. DFT calculations on four possible pathways supported a stepwise formation of C−N and C−H bonds, in which a 1,3-acyloxy-migration competes with the 1,3-azaprotio-transfer, especially in the case of internal alkynyl oximes. The relative nucleophilic properties of oxygen in the carbonyl group and the nitrogen in the oxime, the electronic effects of alkynes, and the influence of the ring system have been investigated computationally.     

Scanning a Silicon Photomultiplier with a Laser Beam

Physics of Particles and Nuclei Letters - The Silicon Photomultiplier (SiPM) is a novel semiconducting photodetector which can detect single photons. It consists of many microcells (pixels)...     

Global dynamics of a flexible asymmetrical rotor

Nonlinear Dynamics - Global dynamics of a flexible asymmetrical rotor resting on vibrating supports is investigated. Hamilton’s principle is used to derive the partial differential governing...     

Rational Development of Remote C−H Functionalization of Biphenyl: Experimental and Computational Studies

A simple and efficient nitrile-directed meta-C−H olefination, acetoxylation, and iodination of biaryl compounds is reported. Compared to the previous approach of installing a complex U-shaped template to achieve a molecular U-turn and assemble the large-sized cyclophane transition state for the remote C−H activation, a synthetically useful phenyl nitrile functional group could also direct remote meta-C−H activation. This reaction provides a useful method for the modification of biaryl compounds because the nitrile group can be readily converted to amines, acids, amides, or other heterocycles. Notably, the remote meta-selectivity of biphenylnitriles could not be expected from previous results with a macrocyclophane nitrile template. DFT computational studies show that a ligand-containing Pd–Ag heterodimeric transition state (TS) favors the desired remote meta-selectivity. Control experiments demonstrate the directing effect of the nitrile group and exclude the possibility of non-directed meta-C−H activation. Substituted 2-pyridone ligands were found to be key in assisting the cleavage of the meta-C−H bond in the concerted metalation–deprotonation (CMD) process.     

Effect of increasing pressure on the structure and temperature-induced changes in magnetic properties of heterospin complexes

Russian Chemical Bulletin - The study is concerned with structural rearrangements in the crystals of heterospin complexes Cu(hfac)2 with nitroxide radicals LR (hfac is hexafluoroacetylacetonate, LR...