Convergence of a finite volume scheme for nonlinear degenerate parabolic equations

Summary. One approximates the entropy weak solution u of a nonlinear parabolic degenerate equation by a piecewise constant function using a discretization in space and time and a finite volume scheme. The convergence of to u is shown as the size of the space and time steps tend to zero. In a first step, estimates on are used to prove the convergence, up to a subsequence, of to a measure valued entropy solution (called here an entropy process solution). A result of uniqueness of the entropy process solution is proved, yielding the strong convergence of to{\it u}. Some on a model equation are shown. Received September 27, 2000 / Published online October 17, 2001     

The sublimation enthalpy of dimethyl oxalate

The sublimation enthalpy of dimethyl oxalate has been measured by calorimetric and head space analysis. These results along with vaporization enthalpy measured by correlation gas chromatography and fusion enthalpy measurements are compared to results predicted by two estimation techniques. A previous experimental measurement was found to be in error. A mean value of (75.2±0.5) kJ/mol was obtained which results in a corrected molar value of (–681.5±0.8) kJ/mol for the enthalpy of formation of gaseous dimethyl oxalate, _f H _m ^o (g, 298.15 K). This new value of _f H _m ^o (g, 298.15 K) for dimethyl oxalate, in combination with other enthalpies of formation, suggests that the ground state of oxalates are destabilized relative to -diketones by approximately 25 kJ/mol.     

Thermodynamique de substances azotees. IX. Etude thermochimique de la benzamide. Comparaison des grandeurs energetiques liees a la structure de quelques amides et thioamides

The enthalpy of sublimation of benzamide was obtained by calorimetry in the range 323<T (K)<350. From values of ΔH_sub(T)=f(T), it was possible to determine ΔH⁰_sub (298.15 K)=101.7±1.0 kJ mole^?1. Using previous data on ΔH⁰_f (c, 298.15 K) obtained by combustion calorimetry, the value of ΔH⁰_f (g, 298.15 K)=?100.9±1.2 kJ mole^?1 was calculated. With the use of energetical values concerning thioacetamide, thiobenzamide and thiourea, on the one hand, and acetamide, benzamide and urea, on the other, a comparative study was made.     

High-Order Composite Likelihood Inference for Max-Stable Distributions and Processes

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of points is a very challenging problem and current approaches typically rely on less expensive composite likelihoods constructed from small subsets of data. In this work, we explore the limits of modern state-of-the-art computational facilities to perform full likelihood inference and to efficiently evaluate high-order composite likelihoods. With extensive simulations, we assess the loss of information of composite likelihood estimators with respect to a full likelihood approach for some widely used multivariate or spatial extreme models, we discuss how to choose composite likelihood truncation to improve the efficiency, and we also provide recommendations for practitioners. This article has supplementary material online.     

Codimension One Threshold Manifold for the Critical gKdV Equation

We construct the “threshold manifold” near the soliton for the mass critical gKdV equation, completing results obtained in Martel et al. (Acta Math 212:59–140, 2014, J Math Eur Soc 2015). In a neighborhood of the soliton, this C¹ manifold of codimension one separates solutions blowing up in finite time and solutions in the “exit regime”. On the manifold, solutions are global in time and converge locally to a soliton. In particular, the soliton behavior is strongly unstable by blowup.     

Reversible Isomerization Between Silacyclopropyl Cation and Cyclic (Alkyl)(Amino)Silylene

A phosphine-stabilized silacyclopropyl cation 2 has been synthesized and fully characterized. Of particular interest, 2 reversibly isomerizes into the corresponding seven-membered cyclic (alkyl)(amino)silylene 3 at room temperature via a formal migratory ethylene insertion into the Si−P bond. Although silylene 3 has not been spectroscopically detected, its transient formation has been evidenced by the isolation of the corresponding disilene dimer 5 as well as by trapping reactions.     

Electrochemically-driven conformational shift in mono- and di-copper constrained macrotricyclic cyclen receptors

An electrochemical study of mono- and di-copper constrained cyclen macrotricycles is presented. Electrochemical data in DMF solution indicate that the reduction of dinuclear complexes occurs in two steps in the -0.4 to -0.8 V vs.AgCl/Ag potential range yielding CuII CuI and CuI CuI species further reduced to Cu metal at highly negative potentials. Mononuclear complexes are reduced in two steps to CuI and Cu metal. Electrochemical data suggest that reduction of both mononuclear and dinuclear complexes approach a square scheme involving electrochemically-driven conformational shifts for metal ions. The presence of endo- and exo-forms of the complexes are revealed by changes in the electrochemical response of the complexes in the presence of tetraethylammonium chloride, 1-azabicyclo[2.2.2]octane and diazabicyclo[2.2.2]octane competing ligands.     

Synthesis of eight- and star-shaped poly(epsilon-caprolactone)s and their amphiphilic derivatives

Spirocyclic tin dialkoxides are unique initiators for the ring-expansion polymerization of lactones leading to complex, but well-defined macromolecular architectures. In a first example, epsilon-caprolactone (epsilon CL) was polymerized, followed by the resumption of polymerization of a mixture of epsilon CL and epsilon CL alpha-substituted by a chloride (alpha Cl epsilon CL), so leading to "living" eight-shaped chains. Upon hydrolysis of the alkoxides, a four-arm star-shaped copolyester was formed, whose each arm was grafted by conversion of the chloride units into azides, followed by the Huisgen's [3+2] cycloaddition of alkyne end-capped poly(ethylene oxide) (PEO) onto the azide substituents. The complexity of this novel amphiphilic architecture was increased further by substituting the four-arm interconnecting PCL by an eight-shaped PCL. In a preliminary step, epsilon CL was polymerized followed by a few units of epsilon CL alpha-substituted by an acrylate. The intramolecular photo-crosslinking of the acrylates adjacent to the tin dialkoxides was effective in stabilizing the eight-shaped polyester while preserving the chain growth sites. This quite unusual tetrafunctional macroinitiator was used to copolymerize epsilon CL and alpha Cl epsilon CL, followed by hydrolysis of the alkoxides, conversion of the chloride units into azides and grafting of the four arms by PEO (see above). This architecture reported for the very first time is nothing but a symmetrical four-tail eight-shaped copolyester macromolecule.