Synthesis of new polycyclic systems containing the pyrimido[2,1-a]phthalazine skeleton

The synthesis of new polyheterocycles containing the pyrimido[2,1-a]phthalazine system 5, 6 and 7 , obtained by condensation of phthalic anhydride with the appropriate hydrazides 2, 3 and 4 , respectively, are reported. It was also synthesized the 14H-[1]Benzothieno[3′,2′:4,5]pyrimido[2,1-a][1,2,4]triazolo[4,3-c]phthalazin-14-one (16).     

Template evaporation method for controlling anatase nanocrystal size in ordered macroporous TiO2

The importance of pure-phase titanium oxide materials as catalysts, sensors, and photonic band-gap materials has been growing steadily. Recently, more attention has been focused on nanostructured titanium oxide showing controlled and periodic porosity on a nanometric scale. The nanocrystal size control of porous nanostructured titanium oxide in an anatase form is a crucial step for the organic template method. Simple template removal by evaporation in an inert atmosphere is reported in this article and compared with the calcination technique usually reported in the literature. The proposed method allows the formation of a double-porous (macro and meso) anatase phase. We demonstrate that it highly preserves the macropore order into a titanium oxide material and induces narrowly dispersed mesopores by controlling the nano-crystal size that is kept around 6 nm. For the proposed method, polystyrene beads are particularly suitable as templates, being evaporated in the temperature range of anatase existence. The final high surface area makes the materials appealing for applications as photocatalysts or sensors.     

Asymmetric Information in a Capital Accumulation Differential Game with Spillover and Learning Effects

Journal of Optimization Theory and Applications - This paper considers a capital accumulation game where the installation costs of investments are lowered by the firm’s own capital stock...     

Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).