Integral representation of the sub-elliptic heat kernel on the complex anti-de Sitter fibration

We derive an integral representation for the subelliptic heat kernel of the complex anti-de Sitter fibration. Our proof is different from the one used in Wang (Potential Anal 45:635–653, 2016) since it appeals to the commutativity of the D’Alembertian and of the Laplacian acting on the vertical variable rather than the analytic continuation of the heat semigroup of the real hyperbolic space. Our approach also sheds the light on the connection between the sub-Laplacian of the above fibration and the so-called generalized Maass Laplacian, and on the role played by the odd dimensional real hyperbolic space.     

Free Jacobi Process

In this paper, we define and study two parameters dependent free processes (λ,θ) called free Jacobi, obtained as the limit of its matrix counterpart when the size of the matrix goes to infinity. The main result we derive is a free SDE analogous to that satisfied in the matrix setting, derived under injectivity assumptions. Once we did, we examine a particular case for which the spectral measure is explicit and does not depend on time (stationary). This allows us to determine easily the parameters range ensuring our injectivity requirements so that our result applies. Then, we show that under an additional condition of invertibility at time t=0, this range extends to the general setting. To proceed, we set a recurrence formula for the moments of the process via free stochastic calculus.     

Vapor pressure measurements in the range 10 Pa to 1 Pa of four pentaerythritol esters: Density and vapor–liquid equilibria modeling of ester lubricants

Vapor pressures of four pure pentaerythritol esters, PE, pentaerythritol tetrapentanoate, pentaerythritol tetraheptanoate, pentaerythritol tetranonanoate and pentaerythritol tetra 2-ethylhexanoate were measured between 334 and 476 K in a recently developed gas saturation apparatus. The experimental vapor pressure values for the four polyolesters range from 5.6 × 10⁻⁵ Pa to 0.94 Pa. These data together with density values were used to determined SAFT and PC-SAFT characteristic parameters. The linearity of molecular parameters for both models with the molecular weight permits to interpolate and extrapolate these parameters for pentaerythritol ester with linear chains. For pentaerythritol esters with ethyl-alkanoic chains, the parameters of SAFT and PC-SAFT have been estimated assuming that the slope of these straight lines is the same for PEs with linear chains that for PE with branched chains. This procedure was used to predict density of commercial POEs, estimating the molecular weight when it is not available from the viscosity at 313.15 K. PC-SAFT gives better performances than SAFT to predict density data for these four compounds at high pressures and for other PEs at atmospheric pressure. Furthermore, characteristic parameters for Soave-Redlich-Kwong and Peng Robinson EoSs were also estimated from the experimental vapor pressures and literature density values.     

Generalized Bessel functions of dihedral-type: expression as a series of confluent Horn functions and Laplace-type integral representation

The Ramanujan Journal - In the first part of this paper, we express the generalized Bessel function associated with dihedral systems and a constant multiplicity function as an infinite series of...     

Remarkable Enhancement of Enantioselectivity in the Asymmetric Conjugate Addition of Dimethylzinc to (Z)‐Nitroalkenes with a Catalytic [(MeCN)4Cu]PF6–Hoveyda Ligand Complex

An enantioselective copper‐catalyzed asymmetric conjugate addition of Me₂Zn to (Z)‐nitroalkenes led to the formation of all‐carbon quaternary stereogenic centers with high stereoselectivity. The key features of the new method are the unprecedented use of [(MeCN)₄Cu]PF₆ in conjunction with the Hoveyda ligand L1 and the use of (Z)‐nitroalkene substrates so that undesired nitroalkene isomerization is minimized and enantioselectivity is enhanced dramatically. We also describe a novel, practical, and highly (Z)‐selective nitroalkene synthesis.     

Reduction of tertiary phosphine oxides with DIBAL-H

The reduction of tertiary phosphine oxides (TPOs) and sulfides with diisobutylaluminum hydride (DIBAL-H) has been studied in detail. An extensive solvent screen has revealed that hindered aliphatic ethers, such as MTBE, are optimum for this reaction at ambient temperature. Many TPOs undergo considerable reduction at ambient temperature and then stall due to inhibition. 31P and 13C NMR studies using isotopically labeled substrates as well as competition studies have revealed that the source of this inhibition is tetraisobutyldialuminoxane (TIBAO), which builds up as the reaction proceeds. TIBAO selectively coordinates the TPO starting material, preventing further reduction. Several strategies have been found to circumvent this inhibition and obtain full conversion with this extremely inexpensive reducing agent for the first time. Practical reduction protocols for these critical targets have been developed.     

Tandem Pd(II)-catalyzed vinyl ether exchange-Claisen rearrangement as a facile approach to gamma,delta-unsaturated aldehydes

A sequential allyl vinyl ether formation-Claisen rearrangement process catalyzed by a palladium(II)-phenanthroline complex is reported. The effects of allylic alcohol structure, type of vinylating agent, and palladium catalysts are discussed. This method provides a convenient approach to gamma,delta-unsaturated aldehydes under mild conditions that avoid the use of toxic Hg(II) catalysts. The new methodology has been successfully demonstrated on the kilogram scale.     

Palladium catalyzed alkoxy- and aminocarbonylation of vinyl tosylates

The palladium catalyzed alkoxycarbonylation and aminocarbonylation of vinyl tosylates are described. A variety of ketone and aldehyde derived vinyl tosylates may be carbonylated in the presence of primary, secondary, and tertiary alcohols, or primary and secondary amines, to provide the corresponding esters and amides in good yields. The alkoxycarbonylation was applied to a short synthesis of isoguvacine.     

Chelation controlled reductive amination of cyclic ketones to trans-4-methoxycyclohexylamines: 9-BBN reduction mediated with FeCl3

A novel trans-diastereoselective reductive amination of 4-substituted cyclohexanones is described using 9-BBN as reducing agent in the presence of FeCl₃. The method permits efficient synthesis of structurally diverse 4-trans-alkoxycyclohexylamines.     

Wellposedness of second order backward SDEs

We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order extension is connected to fully nonlinear PDEs, as suggested in Cheridito et?al. (Commun. Pure Appl. Math. 60(7):1081–1110, 2007). In particular, we provide a fully nonlinear extension of the Feynman–Kac formula. Unlike (Cheridito et?al. in Commun. Pure Appl. Math. 60(7):1081–1110, 2007), the alternative formulation of this paper insists that the equation must hold under a non-dominated family of mutually singular probability measures. The key argument is a stochastic representation, suggested by the optimal control interpretation, and analyzed in the accompanying paper (Soner et?al. in Dual Formulation of Second Order Target Problems. arXiv:1003.6050, 2009).