Équations de Hamilton–Jacobi et inégalités entropiques généraliséesHamilton–Jacobi equations and inequalities for generalised entropies

We prove the equivalence between a general logarithmic Sobolev inequality and the hypercontractivity of a Hamilton–Jacobi equation. We also recover that this property imply a transportation inequality established by [5]. These results provide a natural generalization of the work performed in [3]. To cite this article: I. Gentil, F. Malrieu, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 437–440.     

Kinetics of hydrazine exchange in the pentacyanohydrazineferrate(II) ion

Summary Rate constants and activation parameters for the release of hydrazine (both neutral and protonated) coordinated to the Fe(CN) ₅ ^3– moiety are reported, together with the corresponding stability constants. The rates of formation of the complexes have been evaluated indirectly. The results confirm the general dissociative mechanism for pentacyano(ligand) ferrate(II) ions but some significant differences are found on comparing the data with those from several coordinated diamines. The acidity of complexed N₂H ₅ ⁺ is enhanced byca. two orders of magnitude with respect to free N₂H ₅ ⁺ , its rate of release being greater than that of N₂H₄ by a factor of 31. A solvation controlled model for the dissociation of [Fe(CN)₅L]^n– is shown to be operative in its general features, although specific charge effects are shown to influence the rate of both the dissociation and the formation reactions.     

Ultracontractive bounds on Hamilton-Jacobi solutions

Following the equivalence between logarithmic Sobolev inequality, hypercontractivity of the heat semigroup showed by Gross and hypercontractivity of Hamilton-Jacobi equations, we prove, like the Varopoulos theorem, the equivalence between Euclidean-type Sobolev inequality and an ultracontractive control of the Hamilton-Jacobi equations. We obtain also ultracontractive estimations under general Sobolev inequality which imply in the particular case of a probability measure, transportation inequalities.     

Oxygen reduction activity and methanol tolerance of carbon-supported PtV nanoparticles and the effects of heat treatment at low temperatures

Journal of Solid State Electrochemistry - This paper reports on oxygen reduction activity and methanol tolerance of PtV/C prepared by a polyol method and the effects of heat treatments in reducing...     

Neue Anwendungen von Reaktionen mit Natriumrhodizonat in der Tüpfelanalyse

Zusammenfassung In Lösungen von Calciumsalzen entsteht auf Zusatz von Natriumrhodizonat und Alkalihydroxyd ein braunvioletter Niederschlag, der wahrscheinlich von einem basischen Calciumrhodizonat herrühren dürfte. Ein auf dieser Tatsache beruhender Nachweis von Calcium besitzt in Form einer Tüpfelreaktion die Erfassungsgrenze von 1g Calcium.Im Gegensatz zu Barium-und Strontiumsulfat reagiert auch Calciumsulfat mit alkalischem Natriumrhodizonat.Durch die Rhodizonatreaktion ist Calcium in Aschen, Trockenrückständen, pharmazeutischen Produkten, sowie auch neben Barium und Strontium nachweisbar.Bariumsulfat ist durch Abrauchen mit Ammoniumchlorid leicht in Bariumchlorid überführbar, das mit Natriumrhodizonat nachweisbar ist (Nachweis von Lithoponen).Mit Hilfe von Rhodizonatreaktionen ist Cölestin von Baryt und Strontianit von Witherit zu unterscheiden.Es wird eine Vorprüfung auf Salze von wasserlöslichen organischen Stickstoffbasen und Alkalisalzen organischer Säuren beschrieben, die auf der Bildung von löslichen und mit Natriumrhodizonat nachweisbaren Calciumsalzen beruht.

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Summary The addition of sodium rhodizonate and alkali hydroxide to solutions of calcium salts yields a brown-violet precipitate, which possibly may be due to a basic calcium rhodizonate. A spot test for calcium based on this fact has the detection limit of 1g. In contrast to barium and strontium sulfate, calcium sulfate to reacts with alkaline sodium rhodizonate. This rhodizonate reaction will reveal calcium in ashes, evaporation residues, pharmaceutical products, and even in the presence of barium and strontium. Barium sulfate is readily converted to barium chloride by fuming with ammonium chloride and then can be detected by sodium rhodizonate (detection of lithopones). The rhodizonate reactions serve to distinguish celestine from barite and strontianite from witherite.A preliminary test is described to be applied to salts of water-soluble organic nitrogen bases and alkali salts of organic acids. It is based on the formation of soluble calcium salts that can then be detected by means of sodium rhodizonate.

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Résumé Dans les solutions de sels de calcium, il se forme par addition de rhodizonate de sodium et d'hydroxyde alcalin, un précipité violet-brun qui, vraisemblablement, est dû à un rhodizonate de calcium basique. Sur la base de cette recherche, on a mis au point une analyse à la touche avec une sensibilité limite de 1g de calcium. En contraste avec le sulfate de baryum et de calcium, le sulfate de calcium réagit aussi avec le rhodizonate de sodium alcalin. Par la réaction au rhodizonate, le calcium est décelable dans les cendres, les résidus secs, les produits pharmaceutiques, de mÊme qu'en présence de baryum et de strontium. Le sulfate de baryum est facilement transformable par évaporation à fumées avec le chlorure d'ammonium, en chlorure de baryum qui peut se déceler avec le rhodizonate de sodium (Recherche dans les lithopones). A l'aide des réactions au rhodizonate, on peut distinguer la célestine de la barytine et la strontianite de la withérite.On décrit un essai préliminaire sur les sels organiques solubles dans l'eau de bases azotées et les sels alcalins d'acides organiques qui repose sur la formation de sels de calcium solubles décelables par le rhodizonate de sodium.

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Herrn Universitätsprofessor Dr.L. Ebert zum 60. Geburtstag gewidmet.     

Spot test detection of inositol

Summary A specific test for inositol is based on the fact that the residue obtained by evaporating the sample once with concentrated nitric acid contains acidic keto compounds which yield a red product when evaporated with calcium chloride and ammonia and then heated to 180°.If an inositol solution containing silver nitrate is taken to dryness and then heated to 150°, metallic silver is deposited. This test for inositol cannot be employed if reducing sugars are also present.These two tests can be conducted within the technique of spot test analysis. The respective identification limits are: 2.5g and 0.05g.

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Zusammenfassung Ein spezifischer Nachweis von Inosit kann darauf begründet werden, daß nach einmaligem Abdampfen mit konz. Salpetersäure ein Rückstand von sauren Ketoverbindungen hinterbleibt, der nach Abdampfen mit Calciumchlorid und Ammoniak und Erhitzen auf 180° ein rotes Produkt bildet.Wird eine silbernitrathaltige Inositlösung zur Trockne verdampft und dann auf 150° erhitzt, so erfolgt Abscheidung von metallischem Silber. Diese Redoxreaktion kann bei Anwesenheit von reduzierenden Zuckern nicht zum Nachweis von Inosit verwendet werden.Die beiden hier beschriebenen Nachweise sind in der Technik der Tüpfelanalyse ausführbar und besitzen Erfassungsgrenzen von 2,5g bzw. 0,05g Inosit.

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Résumé On a mis au point un test spécifique de l'inositol fondé sur les observations suivantes: en évaporant une fois l'échantillon en présence d'acide nitrique concentré on obtient un résidu contenant des composés cétoniques acides qui, par évaporation en présence de chlorure de calcium et d'ammoniaque suivie d'un chauffage à 180°, donnent naissance à un produit rouge. Si l'on évapore jusqu'à siccité une solution d'inositol contenant du nitrate d'argent et si l'on chauffe ensuite à 150°, il se forme un dépôt d'argent métallique. Ce test de l'inositol ne peut être utilisé en présence de sucres réducteurs. Ces deux tests peuvent être effectués dans le cadre de la technique des essais à la touche; les quantités limites qu'ils permettent d'identifier sont respectivement de 2,5g et 0,05g.

     

Electrocatalytic O2 Reduction at a Bio‐inspired Mononuclear Copper Phenolato Complex Immobilized on a Carbon Nanotube Electrode

An original copper‐phenolate complex, mimicking the active center of galactose oxidase, featuring a pyrene group was synthesized. Supramolecular pi‐stacking allows its efficient and soft immobilization at the surface of a Multi‐Walled Carbon Nanotube (MWCNT) electrode. This MWCNT‐supported galactose oxidase model exhibits a 4 H⁺/4 e^? electrocatalytic activity towards oxygen reduction at a redox potential of 0.60 V vs. RHE at pH 5.     

Approximate convex hull of affine iterated function system attractors

In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.     

Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations

We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensures a spectral gap in Wasserstein distance. We give practical criteria for this inequality and compare it to classical ones. The key point is to quantify the contribution of the diffusion term to the rate of convergence, in any dimension, which to our knowledge is a novelty.     

Nonlinear diffusions, hypercontractivity and the optimal L-Euclidean logarithmic Sobolev inequality

The equation u_t=Δ_p(u^1/(p−1)) for p>1 is a nonlinear generalization of the heat equation which is also homogeneous, of degree 1. For large time asymptotics, its links with the optimal L^p-Euclidean logarithmic Sobolev inequality have recently been investigated. Here we focus on the existence and the uniqueness of the solutions to the Cauchy problem and on the regularization properties (hypercontractivity and ultracontractivity) of the equation using the L^p-Euclidean logarithmic Sobolev inequality. A large deviation result based on a Hamilton-Jacobi equation and also related to the L^p-Euclidean logarithmic Sobolev inequality is then stated.