An inequality connecting entropy distance,Fisher Information and large deviations

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.     

Semilinear wave models with friction and viscoelastic damping

In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.     

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     

Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.     

Triacetic acid lactone as a bioprivileged molecule in organic synthesis

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Synthesis and antimycobacterial activity of purine conjugates with (S)-lysine and (S)-ornithine

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Stability of O3 + N2, O3 + O2 and O3 + CO2 double hydrates: DFT study

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Extended Open-Chain Polyenides as Versatile Delocalized Anion Ligands for Metal Chain Clusters

Although small cyclic- and open-chain unsaturated hydrocarbon anions such as cyclopentadienide and open-chain pentadienide are used as the strongly electron-donating auxiliary ligands for metal complexes, more extended π-conjugated unsaturated hydrocarbon anions have rarely been used in coordination chemistry, despite their potential ability to serve as the multiply bridging π-ligands for metal clusters. This work reports isolation of metal chain clusters bearing the multi-dentate, open-chain extended unsaturated hydrocarbon anion ligands. The extended open-chain π-conjugated polyenyl ligands could effectively stabilize oxidized palladium chains, including an unprecedented [Pd₄]⁴⁺ chain.