Synthesis of new 1,2,3-triazolo[1,2-a]benzotriazole derivatives or substituted 2,3-benzo-1,3a,6,6a-tetraazapentalenes. II

This paper continues the synthesis of new 1,2,3-triazolo[1,2-a]benzotriazoles or 2,3-benzo-1,3a,6,6a-tetrazapentalenes to submit to biological assays. The derivatives were obtained by deoxycyclization reactions of appropriate nitrophenyl-1,2,3-triazole derivatives and by thermal decomposition of appropriate azidophenyl-1,2,3-triazoles (Schemes 1 and 2). Some attempts to extend these synthetic routes to the preparation of 1,2,4-triazolo[1,2-a]benzotriazoles (Scheme 3) and 1,2,3-triazolo[1,2-b]-4H-1,2,3-benzo-triazines (Scheme 4) completely failed.     

New 1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidine derivatives II

The 7‐chloro‐3‐(2‐chlorobenzyl)‐ and 7‐chloro‐3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐d]pyrimidines ( 1 and 4 ), by nucleophilic replacement with some hydrazides, gave the corresponding 7‐hydrazidoderivatives ( 2a‐e and 5a‐e ). These, by heating in Dowtherm, underwent an intramolecular cyclization to form the new tricyclic 7‐substituted‐3‐(2‐chlorobenzyl)‐ and 3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidines ( 3a‐d and 6a‐d ). The 7‐hydrazino‐3‐(2‐chlorobenzyl)‐ and 7‐hydrazino‐3‐(2‐fluorobenzyl)‐triazolo‐pyrimidines ( 9a and 9b ) were also prepared via the corresponding mercapto ( 7a and 7b ) and thiomethyl ( 8a and 8b ) derivatives.     

Synthesis of some 3,7-disubstituted quino[3,2-c][1,8]naphthyridines

The preparation of some 3,7-disubstituted-5,6-dihydroquino[3,2-c][1,8]naphthyridines ( 6 ) by the condensation of 7-substituted-2,3-dihydro-1,8-naphthyridin-4-(1H)ones ( 5 ) with o-aminoacetophenone or o-aminobenzophenone is described. All the 5,6-dihydroderivatives 6 were transformed into the fully aromatic compounds 7 by heating with nitrobenzene. Only a few quino[3,2-c][1,8]naphthyridines were previously described.     

1,2,3-Triazolo[4,5-d]-1,2,4-triazolo[4,3-b]pyridazines

Some new 1,2,3-triazolo[4,5-d]-1,2,4-triazolo[4,3-b]pyridazines were prepared starting from the corresponding 1,2,3-triazolo[4,5-d]pyridazines via the formation of the 1,2,4-triazole ring, by condensation of an appropriate monocarbon fragment with the 4-hydrazino substituent and the nitrogen atom in the 5 position of the heterocycle. Condensation of 4-phenylhydrazino substituted derivatives with formic acid gave zwitterionic compounds.     

New N6‐substituted 8‐alkyl‐2‐phenylmethylsulfanyl‐adenines. II

Title compounds bearing substituents on C(2), C(6) and C(8) were prepared from a newly synthesized pyrimidine derivative 11. The new pyrimidine 11 was generated from compound 2 through two different synthetic schemes. In one pathway, compound 2 was nitrosated, reduced and alkylated to produce com pounds 9 , 10 and 11 respectively (Scheme). In an alternate route using compound 2 as the starting material, a coupling reaction using the diazonium salt derived from p‐methylaniline afforded the azo derivative 7 , which was subsequently alkylated and reductively cleaved to form compounds 8 and 11 respectively (See Scheme). Compound 11 was annulated to the corresponding hypoxanthine derivatives 12–14 ; compounds 12 and 13 were chlorinated with phosphorus oxychloride, then reacted with amines to yield compound 17 and 20 respectively. Compounds 21 , 22 and 23 were obtained by oxidation of the corresponding sulfide as depicted in Scheme. Alkylation of the thiol function of 1 gave a mixture of 3 and 4. Compound 3 was chlo rinated to 5. Nitration of 5 resulted in electrophilic aromatic substitution of the aryl ring and concomitant oxidation of the sulfide to the sulfoxide, producing 6.     

New 4-(benzotriazol-1-yl)-1,2,3-triazole derivatives

A new 4-(benzotriazol-1-yl)-1,2,3-triazole structure was obtained by the diazotization reaction of either of 1-(2-aminophenyl)-4-carboxamido-5-amino-1H-1,2,3-triazole ( 1c ) or of the corresponding Dimroth isomer 1d . It underwent some common reactions to evaluate its chemical behaviour and structure. An analogous reaction sequence was carried out from the 2-nitro-4-methylphenyl azide, to assign the structure to the nitro derivatives prepared. The structure of the new compounds prepared was confirmed by chemical and spectroscopic methods.     

Large Deviation Approach to the Randomly Forced Navier--Stokes Equation

The random forced Navier--Stokes equation can be obtained as a variational problem of a proper action. By virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large deviation functional. Since the hydrodynamic operator is nonlinear, the functional integral yielding the statistics of fluctuations can be practically computed by linearizing around a physical solution of the hydrodynamic equation. We show that this procedure yields the dimensional scaling predicted by K41 theory at the lowest perturbative order, where the perturbation parameter is the inverse Reynolds number. Moreover, an explicit expression of the prefactor of the scaling law is obtained.     

Localization of Bose-Einstein condensates in optical lattices

The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, addressing the study of the discrete nonlinear Schrödinger dynamics, have predicted the spontaneous generation of (classical) breathers in coupled condensates. In the present contribute, we shall focus on localized solutions (quantum breathers) of the full Bose-Hubbard model. We will show that solutions exponentially localized in space and periodic in time exist also in absence of randomness. Thus, this kind of states, reproduce a novel quantum localization phenomenon due to the interplay between bounded energy spectrum and non-linearity.     

On the semiclassical density of states of quasi-integrable mechanical systems

For a class of quasi-integrable mechanical systems, we show that in the semiclassical limit the Bohr-Sommerfeld quantization applied to successive truncations of the Birkhoff series and a power series expansion of Weyl's formula give the same asymptotic number of states below a given energy.

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Sommario Si mostra che per una classe di sistemi quasi integrabili, nel limite semiclassico, la quantizzazione di Bohr-Sommerfeld applicata a successivi troncamenti della serie di Birkhoff e l'espansione in serie di potenze della formula di Weyl danno lo stesso andamento asintotico per la densita' degli stati integrata.