Thermodynamic Limit for Directed Polymers and Stationary Solutions of the Burgers Equation

The first goal of this paper is to prove multiple asymptotic results for a time-discrete and space-continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the infinite-volume limit for every fixed asymptotic slope, concentration inequalities for free energy implying a bound on its fluctuation exponent, and straightness estimates implying a bound on the transversal fluctuation exponent. The culmination of this program is almost sure existence and uniqueness of polymer measures on one-sided infinite paths with given endpoint and slope, and interpretation of these infinite-volume Gibbs measures as thermodynamic limits. Moreover, we prove that marginals of polymer measures with the same slope and different endpoints are asymptotic to each other. The second goal of the paper is to develop ergodic theory of the Burgers equation with positive viscosity and random kick forcing on the real line without any compactness assumptions. Namely, we prove a one force–one solution principle, using the infinite-volume polymer measures to construct a family of stationary global solutions for this system, and proving that each of those solutions is a one-point pullback attractor on the initial conditions with the same spatial average. This provides a natural extension of the same program realized for the inviscid Burgers equation with the help of action minimizers that can be viewed as zero temperature limits of polymer measures. © 2018 Wiley Periodicals, Inc.     

Controlled ring‐opening homo‐ and copolymerization of ɛ‐caprolactone and d,l‐lactide by iminophenolate aluminum complexes: An efficient approach toward well‐defined macromonomers

The aluminum complexes containing two iminophenolate ligands of the type (p‐XC₆H₄NCHC₆H₄O‐o)₂AlR' (R′=Me ( 3, 4 ) or R′=O(CH₂)₄OCH=CH₂ ( 5, 6 ), X=H ( 3, 5 ), F( 4, 6 )) were synthesized and characterized by ¹H, ¹³C NMR spectroscopy, and X‐ray crystallography. The reaction of AlMe₃ with two equivalents of substituted iminophenols gave five‐coordinated {ONR}₂AlMe ( 3, 4 ) complexes. Subsequent reaction of these methyl complexes with unsaturated alcohol, HO(CH₂)₄OCH=CH₂, resulted in target compounds 5 and 6 in a good yield. It was shown that the complexes ( 3 ‐ 6 ) are monomeric in solution (NMR) and in solid state (X‐ray analysis). The catalytic activity of the complexes 5 and 6 towards ring‐opening polymerization (ROP) of ?‐caprolactone and d,l ‐lactide was assessed. Complex 5 showed higher activity as compared with 6 , while both of these catalysts induced controlled homo‐ and copolymerization to afford the macromonomers with high content of vinyl ether end groups (F_n > 80%) in a broad range of molecular weights (M_n = 4000–30,000 g mol^?1) with relatively narrow MWD (M_w/M_n = 1.1–1.5). © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1237–1250     

Rate constants of the reactions of O(3P) atoms with Br2 and NO2 over the temperature range 220-950 K

The kinetics of the reactions of Br₂ and NO₂ with ground state oxygen atoms have been studied over a wide temperature range, T = 220-950 K, using a low-pressure flow tube reactor coupled with a quadrupole mass spectrometer: O + NO₂ → NO + O₂ (1) and O + Br₂ → Br + BrO (2). The rate constant of reaction (1) was determined under pseudo–first-order conditions, either monitoring the kinetics of O-atom or NO₂ consumption in excess of NO₂ or of the oxygen atoms, respectively: k₁ = (6.1 ± 0.4) × 10⁻¹² exp((155 ± 18)/T) cm³ molecule⁻¹ s⁻¹ (where the uncertainties represent precision at the 2σ level, the estimated total uncertainty on k₁ being 15% at all temperatures). The temperature dependence of k₁, found to be in excellent agreement with multiple previous low-temperature data, was extended to 950 K. The rate constant of reaction (2) determined under pseudo–first-order conditions, monitoring the kinetics of Br₂ consumption in excess of O-atoms, showed upward curvature at low and high temperatures of the study and was fitted with the following three-parameter expression: k₂ = 9.85 × 10⁻¹⁶ T^1.41 exp(543/T) cm³ molecule⁻¹ s⁻¹ at T = (220-950) K, which is recommended from the present study with an independent of temperature conservative uncertainty of 15% on k₂.     

Generation of 1-aryl-3-methoxycarbonylnitrilimines and their reaction with halogen-containing unsaturated compounds

Thermal decomposition of 1-(4-methoxyphenyl)- and 1-(4-fluorophenyl)hepta(methoxycarbonyl)-3a,7a-dihydroindazoles at 135 °C in the presence of allyl or propargyl halides leads to the elimination of hexamethyl benzenehexacarboxylate and the formation of the corresponding pyrazolines or pyrazoles as the products of 1,3-dipolar cycloaddition of 1-aryl-3-methoxycarbonylnitrilimines to the multiple bonds of the substrates used. In the case of vinyl halides, the products of the target reactions are either obtained in low yields or nonexistent, with a side conversions taking place instead. Thus, for example, in the case of 1,1-dichloro-4-methylpenta-1,3-diene, besides hexamethyl benzenehexacarboxylate, 3,5,5-trichloro-2-methylpent-4-en-2-ol and arylchlorohydrazones MeO₂CC(Cl)=N-NHAr were unexpectedly isolated as the main products, as well.     

New nanomolar negative modulators of AMPA receptors

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Spectroscopy of Hafnium Monohalides

The modern intracavity laser method has been applied to study electronic spectra of the hafnium monohalides molecules. Results of new investigation of HfF and HfBr molecules are presented: the bands at 589.3, 590.6, and 593.1 nm observed in intracavity laser spectra of HfF₄ have been assigned to the bands of HfF or ionized HfF; new molecular constants of the HfBr molecule have been obtained. Spectroscopic studies of HfCl and Hfl molecules are discussed, and the most reliable molecular constants of HfCl, HfBr, and Hfl molecules are recommended.     

Reduction Principle and Asymptotic Phase for Center Manifolds of Parabolic Systems with Nonlinear Boundary Conditions

We prove the reduction principle and study other attractivity properties of the center and center-unstable manifolds in the vicinity of a steady-state solution for quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on bounded or exterior domains.     

Synthesis and Structure of the Heterocyclic Phosphorus Containing Derivatives of [60] Fullerene

Abstract

Data on the structure of cycloadducts of organophosphorus dipolar reagents and fullerenes arc absent, to our knowledge. We died the reactions and the shucturc of cycloadducts of phosphorylated azidcs and nitrile oxide with [60]fullcrcnc. The cycloaddition of diphcnylphosphinic llzide to fullcrme has bcm determined to lead to the 1 -[(N-diphenylphosphoryl)amino]-2-hydroxy[6O]hllcrme (l), the mixhuc of phosphorylated aziridinofullcrcne (2) and derivative of fullerne (3) with one aziridine fragment and one aminohydmxy-fragment, or to product (4), depending on the conditions of don .     

Heterocyclization of electrophilic alkenes with tetranitromethane revisited: regiochemistry and the mechanism of nitroisoxazole formation

Revised regiochemistry for the heterocyclization of electrophilic alkenes with tetranitromethane (TNM) in the presence of triethylamine, providing rapid access to nitroisoxazoles, is reported. The formation of 5-nitroisoxazoles previously incorrectly assigned as 3-nitro regioisomers, has now been established unambiguously by X-ray crystallography. Empirical computations with ACD/CNMR Predictor, based both on hierarchical ordering of spherical environments (HOSE) and an algorithm of artificial neural networks (ANN), and also Density Functional Theory computations of the ¹³C NMR chemical shifts for the 3- versus 5-nitroisoxazoles are shown to consistently match the spectra of the experimentally observed 5-regioisomers.