A generalisation of de la Vallée-Poussin procedure to multivariate approximations

Advances in Computational Mathematics - Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data....     

Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red

Methodology and Computing in Applied Probability - In this paper, we study a generalized version of the expected time in the red and the expected area in red introduced in Loisel (2005). We derive...     

Accounting for local capillary effects in two-phase flows with relaxed surface tension formulation in enriched finite elements

This paper introduces a numerical method able to deal with a general bi-fluid model integrating capillary actions. The method relies first on the precise computation of the surface tension force. Considering a mathematical transformation of the surface tension virtual work, the regularity required for the solution on the evolving curved interface is weakened, and the mechanical equilibrium of the triple line can be enforced as a natural condition. Consequently, contact angles of the liquid over the solid phase result naturally from this equilibrium. Second, for an exhaustive representation of capillary actions, pressure jumps across the interface must be accounted for. A pressure enrichment strategy is used to properly compute the discontinuities in both pressure and gradient fields. The resulting method is shown to predict nicely static contact angles for some test cases, and is evaluated on complex 3D cases.     

Highly Phosphorescent Crystals of Square‐Planar Platinum Complexes with Chiral Organometallic Linkers: Homochiral versus Heterochiral Arrangements,Induced Circular Dichroism,and TD‐DFT Calculations

A novel class of chiral luminescent square‐planar platinum complexes with a π‐bonded chiral thioquinonoid ligand is described. Remarkably the presence of this chiral organometallic ligand controls the aggregation of this square planar luminophor and imposes a homo‐ or hetero‐chiral arrangement at the supramolecular level, displaying non‐covalent Pt–Pt and π–π interactions. Interestingly these complexes are highly luminescent in the crystalline state and their photophysical properties can be traced to their aggregation in the solid state. A TD‐DFT calculation is obtained to rationalize this unique behavior.     

Detrimental Ni(0) transfer in Kumada catalyst transfer polycondensation of benzo[2,1‐b:3,4‐b']dithiophene

This article deals with the Kumada Catalyst Transfer Polycondensation (KCTP) of 4,7‐dioctylbenzo[2,1‐b:3,4‐b']dithiophene ( BDP‐Oct ) using Ni(II) catalyst or In/cat combination. A combination of MALDI MS, GPC, and ³¹P NMR spectroscopy is used to reveal the failure of the KCTP of this particular monomer. Intermolecular transfer reactions to monomer appeared to prevent the formation of polymer. This result is remarkable, since isomeric benzo[1,2‐b:4,5‐b']dithiophene polymerizes in a controlled way. The presence of a “non‐aromatic double bond” in annulated monomers is discussed. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1706–1712     

Heavy-Atom Tunneling in Semibullvalenes: How Driving Force,Substituents, and Environment Influence the Tunneling Rates

The Cope rearrangement of selectively deuterated isotopomers of 1,5-dimethylsemibullvalene 2 a and 3,7-dicyano-1,5-dimethylsemibullvalene 2 b were studied in cryogenic matrices. In both semibullvalenes the Cope rearrangement is governed by heavy-atom tunneling. The driving force for the rearrangements is the small difference in the zero-point vibrational energies of the isotopomers. To evaluate the effect of the driving force on the tunneling probability in 2 a and 2 b , two different pairs of isotopomers were studied for each of the semibullvalenes. The reaction rates for the rearrangement of 2 b in cryogenic matrices were found to be smaller than the ones of 2 a under similar conditions, whereas differences in the driving force do not influence the rates. Small curvature tunneling (SCT) calculations suggest that the reduced tunneling rate of 2 b compared to that of 2 a results from a change in the shape of the potential energy barrier. The tunneling probability of the semibullvalenes strongly depends on the matrix environment; however, for 2 a in a qualitatively different way than for 2 b .