Numerical experiments on billiards

We investigate decay properties of correlation functions in a class of chaotic billiards. First we consider the statistics of Poincaré recurrences (induced by a partition of the billiard): the results are in agreement with theoretical bounds by Bunimovich, Sinai, and Bleher, and are consistent with a purely exponential decay of correlations out of marginality. We then turn to the analysis of the velocity-velocity correlation function: except for intermittent situations, the decay is purely exponential, and the decay rates scale in a simple way with the (uniform) curvature of the dispersing arcs. A power-law decay is instead observed when the system is equivalent to an infinite-horizon Lorentz gas. Comments are given on the behaviour of other types of correlation functions, whose decay, during the observed time scale, appears slower than exponential.     

On the finiteness of optimal partitions

We prove that, under appropriate assumptions on the domain Ω and on the datumg, any optimal partition of Ω (minimizing the sum of the total perimeter and the approximation term is finite. Finiteness result for the problem of image segmentation in Artificial Vision can be deduced.

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Sunto Dimostriamo che, in opportune ipotesi sul dominio Ω e sul datog, ogni partizione ottimale di Ω (minimizzante il perimetro totale in Ω più il termine di approssimazione è finita. Se ne deducono risultati di finitezza per il problema della segmentazione di immagini in Visione Artificiale.

     

Excess enthalpies of some aromatic aldehydes in n-hexane, n-heptane and benzene

Calorimetric measurements of molar excess enthalpies, H^E, at 298.15 K, of mixtures containing aromatic aldehydes of general formula C₆H₅(CH₂)_mCHO (with m = 0, 1 and 2) + n-hexane, n-heptane or benzene are reported, together with the values of H^E at equimolar composition compared with the corresponding values of H^E for the aromatic ketones in the same solvents. The experimental results clearly indicate that the intermolecular interactions between the carbonyl groups (CHO) are influenced by the intramolecular interactions between the carbonyl and phenyl groups, particularly for the mixtures containing benzaldehyde.     

Minimal boundaries enclosing a given volume

We prove some facts concerning surfaces of minimal area bounding regions of prescribed volume in ⁿ. The main result we prove is that the mean curvature of such a surface is constant, if possibly a discontinuous function of the enclosed volume. The boundary behaviour of the solutions is also discussed.     

Cyclic guanidines: Synthesis of 4,6,7,8-tetrahydro-1H-imidazo[1,2-a]pyrazolo[3,4-d]pyrimidin-7-ones and 1,4,6,7,8,9-hexahydropyrazolo[3′,4′:4,5]pyrimido[2,1-c] [1,2,4]triazin-7-ones

The synthesis of potential platelet aggregation inhibitors 4,6,7,8-tetrahydroimidazo[1,2-a]pyrazolo[3,4-d]-pyrimidin-7-ones and 1,4,6,7,8,9-hexahydropyrazolo[3′,4′:4,5]pyrimido[2,1-c] [1,2,4]triazin-7-ones derivatives is described starting from 4,6-dichloropyrazolo[3,4-d]pyrimidines.     

Modern Synthetic Strategies with Organoselenium Reagents: A Focus on Vinyl Selenones

In recent years, vinyl selenones were rediscovered as useful building blocks for new synthetic transformations. This review will highlight these advances in the field of multiple-bond-forming reactions, one-pot synthesis of carbo- and heterocycles, enantioselective construction of densely functionalized molecules, and total synthesis of natural products.     

Combining Experimental and Computational Studies to Understand and Predict Reactivities of Relevance to Homogeneous Catalysis

This article showcases three major uses of computational chemistry in reactivity studies: the application after, in combination with, and before experiment. Following a brief introduction of suitable computational tools, challenges and opportunities in the implementation of computational chemistry in reactivity studies are discussed, exemplified with selected case studies from our and other laboratories.