Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

Formation of spanning water networks on protein surfaces via 2D percolation transition

The formation of spanning hydrogen-bonded water networks on protein surfaces by a percolation transition is closely connected with the onset of their biological activity. To analyze the structure of the hydration water at this important threshold, we performed the first computer simulation study of the percolation transition of water in a model protein powder and on the surface of a single protein molecule. The formation of an infinite water network in the protein powder occurs as a 2D percolation transition at a critical hydration level, which is close to the values observed experimentally. The formation of a spanning 2D water network on a single rigid protein molecule can be described by adapting the cluster analysis of conventional percolation studies to the characterization of the connectivity of the hydration water on the surface of finite objects. Strong fluctuations of the surface water network are observed close to the percolation threshold. Our simulations also furnish a microscopic picture for understanding the specific values of the experimentally observed hydration levels, where different steps of increasing mobility in the hydrated powder are observed.     

Enzymatic synthesis of neopentylpolyol esters in organic media

Utilization of lipases for synthesis of esters of hydrophilic polyols has been investigated. The choice of a suitable solvent is crucial in this type of reaction. An interesting case is fatty acid esters from neopentylpolyols, such as trimethylolpropane, which are of great interest as high temperature lubricants. Enzymatic synthesis of trimethylolpropane tricaprylate was studied as an alternative to chemical manufacturing. Triester production occurred only if the water produced by esterification was continuously removed from the medium. In these condition, kinetics of appearance and transformation of mono-, di- and triesters were determined in order to define optimal conditions.     

Fourier interferometric stimulation (FIS) in biology and medicine

A continuously scanning Michelson interferometer was developed to modulate an intensive light source spectrally. The interferogram is used as a stimulus to investigate spectral sensitivities in insects and man. The FIS-method is fast and precise and shows many advantages which are partly based on the advantages of Fourier spectroscopy. The existing applications are summarized.     

New example of a non-heme mononuclear iron(IV) oxo complex. Spectroscopic data and oxidation activity

The green complex S=1 [(TPEN)FeO]2+ [TPEN=N,N,N',N'-tetrakis(2-pyridylmethyl)ethane-1,2-diamine] has been obtained by treating the [(TPEN)Fe]2+ precursor with meta-chloroperoxybenzoic acid (m-CPBA). This high-valent complex belongs to the emerging family of synthetic models of Fe(IV)=O intermediates invoked during the catalytic cycle of biological systems. This complex exhibits spectroscopic characteristics that are similar to those of other models reported recently with a similar amine/pyridine environment. Thanks to its relative stability, vibrational data in solution have been obtained by Fourier transform infrared. A comparison of the Fe=O and Fe=(18)O wavenumbers reveals that the Fe-oxo vibration is not a pure one. The ability of the green complex to oxidize small organic molecules has been studied. Mixtures of oxygenated products derived from two- or four-electron oxidations are obtained. The reactivity of this [FeO]2+ complex is then not straightforward, and different mechanisms may be involved.     

Oligosaccharide analogues of polysaccharides. Part 14:. Carbocyclic cyclodextrin analogues. Synthesis of all trimeric and tetrameric isomers by homo- and heterocoupling of 1,4-cis-diethynylated 1,5-anhydroglucitols

Hetero- or homocoupling of protected 1,4-cis-diethynylated 1,5-anhydroglucitols leads to two isomeric cyclotrimers and to four isomeric cyclotetramers. The C₃-symmetric cyciotrimer 31 , the C₄-symmetric cyclotetramer 35 , and the D₂-symmetric cyclotetramer 6 have been prepared before. We have now synthesized the C₁-symmetric cyciotrimer 13 , and the C₁- and the C₂-symmetric cyclotetramers 22 and 27 , respectively. The cyclotrimer 13 was prepared by intramolecular, oxidative homocoupling and, alternatively, by a one-pot trimerization/cyclization of the monomer 36 (Schemes 1 and 5, resp.). Oxidative homocoupling was used for the cyclization of the tetramers 19 and 25 , leading to 22 and 27. The tetramer 19 was made by sequential Cadiot-Chod-kiewicz coupling (Scheme 2)and the tetramer 25 by a combination of a Cadiot-Chodkiewicz reaction and an intermolecular, oxidalive homocoupling (Scheme 3). The acetates 34 and 38 , corresponding to 35 and 27 , respectively, were also made by a one-pot dimerization/cyclization of the dimer 37 (Scheme 5). Intramolecular oxidative heterocoupling is also feasible and results in an alternative, more convenient synthesis of the acetylated cyclotrimer 30 and the acetylated cyclotetramer 34 (corresponding to 31 and 35 , resp.; Scheme 4). The solid-state conformation of the C₄-symmetric cyclotetramer 34 corresponds well to the one predicted by force-field calculations. We compared the water-solubilities of the cyclotrimers 13 and 31 and the tetramers 6, 22, 27 , and 35 , their calculated conformations (MM3*), and the D -adenosine binding properties of the cyclotetramers 6, 27 , and 35 .     

The synthesis and chemical reactions of certain pyrazolo[1,5-a]-1,3,5-triazines

3-Aminopyrazole was utilized as a starting material for the preparation of certain pyrazolo-[1,5-a]-1,3,5-triazines. 4-Chloro-2-methylthiopyrazolo[1,5-a]-1,3,5-triazine was prepared and used for studies of nucleophilic displacement reactions, and it has been found that both the chloro and methylthio groups may be displaced by nucleophiles. By modifications of these procedures we have prepared the adenine, hypoxanthine, and xanthine analogs of the pyrazolo-[1,5-a]-1,3,5-triazine ring system. Electrophilic substitution occurs in the 8-position of this ring system. The methyl group was introduced into the 4-position by a novel ring opening and ring closing of the 1,3,5-triazine ring.