Fractal relaxed Dirichlet problems

Given aself similar fractal K ? ? ⁿ of Hausdorff dimension α>n?2, andc ₁>0, we give an easy and explicit construction, using the self similarity properties ofK, of a sequence of closed sets? _h such that for every bounded open setΩ?? ⁿ and for everyf ∈ L²(Ω) the solutions to $$\left\{ \begin{gathered} - \Delta u_h = f in \Omega \backslash \varepsilon _h \hfill \\ u_h = 0 on \partial (\Omega \backslash \varepsilon _h ) \hfill \\ \end{gathered} \right.$$ converge to the solution of the relaxed Dirichlet boundary value problem $$\left\{ \begin{gathered} - \Delta u + uc_1 \mathcal{H}_{\left| K \right.}^\alpha = f in \Omega \hfill \\ u = 0 on \partial \Omega \hfill \\ \end{gathered} \right.$$ (H _∣ ^α denotes the restriction of the α-dimensional Hausdorff measure toK). The condition α>n?2 is strict.     

Recognition of guests bearing donor and acceptor hydrogen bonding groups by heteroditopic calix[4]arene receptors

The synthesis of new hosts specifically designed for the recognition of neutral guests bearing donor-acceptor hydrogen bonding groups is described. These hosts are characterized by the presence of two distinct binding region in close proximity: the rigid π-donor cavity and the H-bond donor N-methylene-N′-phenylureido group inserted onto the upper rim of the calix[4]arene skeleton. The binding abilities of these receptors were investigated toward a series of neutral ditopic organic molecules in CDCl₃ solution by ¹H NMR spectroscopy. The results obtained show that rigidity of the calix[4]arene apolar cavity is the control element in determining efficiency. In fact, compared with the more rigid 2, host 10, where the rigidity of the cone structure is maintained by hydrogen bonding of the OH of the lower rim, a decrease of efficiency of almost one order of magnitude was observed. The cooperative effect of the two binding region of host 2 was verified with different classes of ditopic guests. Good efficiency in the recognition of urea derivatives and dimethylsulfoxide was achieved.     

Synthesis of new tren-based tris-macrocycles. Anion cluster assembling inside the cavity generated by a bowl-shaped receptor

The synthesis of three new tris-macrocycles, containing three [12]aneN(4) (L1), [12]aneN(3)O (L2), or [14]aneN(4) (L3) moieties appended to a tren unit, is reported. The crystal structure of the [(Na(ClO(4))(6)) subset L1(2)H(13)]Na(6)Cl(2)(ClO(4))(12) compound shows the anionic cluster [Na(ClO(4))(6)](5)(-) assembled inside the cavity defined by two bowl-shaped polyammonium receptors, held by multiple charge-charge and hydrogen bond interactions.     

Photocleavage studies of fluorescent amino acid conjugates bearing different types of linkages

The synthesis and photochemistry of 3-oxo-3H-benzopyran derivatives linked through ester, anhydride, urethane and carbonate bonds to representative l-amino acids, at the amino and carboxylic acid groups at the main chain or the hydroxyl group at the side chain, were carried out. The stability to photolysis of the resulting conjugates was studied at different wavelengths of irradiation (254, 300 and 350 nm), the anhydride and ester linkages being the most sensitive in the studied conditions.     

A comparative analysis of various gradient methods for geometry optimization at the ab initio SCF-MO level

Various techniques, already suggested for improving the computational efficiency of the force relaxation method, have been applied here in conjunction with the variable metric algorithms suggested by Murtagh and Sargent and by Fletcher. Various tests have been performed to assess the computational efficiency of the resulting minimization procedures. In addition, procedures where the steps are defined in terms of a parabolic fitting of the forces in approximated normal coordinates have been tested. In all cases the forces are computed analytically.     

Matrix-isolation FT-IR spectra and theoretical study of dimethyl sulfate

The preferred conformations of dimethyl sulfate and their vibrational spectra were studied by matrix-isolation FT-IR spectroscopy and theoretical methods (DFT and MP2, with basis sets of different sizes, including the quadruple-zeta, aug-cc-pVQZ basis). Conformer GG (of C2 symmetry and exhibiting OSOC dihedral angles of 74.3 degrees ) was found to be the most stable conformer in both the gaseous phase and isolated in argon. Upon annealing of the matrix, the less stable observed conformer (GT; with C1 symmetry) quickly converts to the GG conformer, with the resulting species being embedded in a matrix-cage which corresponds to the most stable matrix-site for GG form. The highest energy TT conformer, which was assumed to be the most stable conformer in previous studies, is predicted by the calculations to have a relative energy of ca. 10 kJ mol-1 and was not observed in the spectra of the matrix-isolated compound.     

Chemo‐ and Enzyme‐Catalyzed Reactions Revealing a Common Temperature‐Dependent Dynamic Solvent Effect on Enantioselectivity

The enantiomeric ratio E of enzyme‐catalyzed (Candida antarctica lipase and lipase PS) and chemo‐catalyzed (L ‐proline‐based diamines) acylation reactions of 1‐(naphthalen‐2‐yl)ethanol, 2‐phenylpropanol, and 2‐benzylpropane‐1,3‐diol is dependent on solvent and temperature. Plots of ln E vs. 1/T showed the presence of inversion temperatures (T_inv). The T_inv values for the bio‐catalyzed and the chemo‐catalyzed reactions are fairly in agreement, and correspond as well to the T_NMR values obtained by variable‐temperature ¹³C‐NMR experiments on the substrates in the same solvent of the resolution. This result demonstrates that clustering effects in the substrate solvation manage the chemical and the enzymatic enantioselectivity, and, moreover, that the solute? solvent cluster is always the real reacting species in solution for chemical as well as for enzymatic reactions.     

Simplified chemical and radiochemical synthesis of 2-arachidonoyl-glycerol, an endogenous ligand of cannabinoid receptors

Endocannabinoids have emerged as a new class of lipid mediators, with manifold roles in the central nervous system and in the periphery. Several studies have identified 2-arachidonoyl-glycerol (2-AG) as a major endogenous agonist of cannabinoid receptors. Here, the chemical synthesis of 2-AG is reported, along with the synthesis of its tritium-labeled derivative. These unlabeled and radiolabeled compounds are suitable tools for unravelling some metabolic routes and biological activities of 2-AG in various cells and tissues.     

Synthesis of Pyrrolidine Analogues of N-Acetylneuraminic Acid as Potential Sialidase Inhibitors

The pyrrolidine derivatives 3 , 4 , and 5 were prepared from the methyl ester 7 of Neu2en5Ac via lie pyrrolidine-borane adduct 33 . They inhibit Vibrio cholerae sialidase competitively with K_i = 4. 4 10^?3 M, 5. 3 10^?3 M, and 4. 0 10^?2 M, respectively. Benzylation of 7 gave the fully O-benzylated 8 besides 9, 10 , and 11. Ozonolysis and reduction with NaBH₄ of 8 and 9 gave the 1, 4-diols 12 and 15 , the hydroxy acetates 13 and 16 , and the furanoses 14 and 17 (Scheme 1), respectively. The diol 12 was selectively protected (→ 19 → 20 → 23 ) and transformed into the azide 27 by a Mitsunobu reaction. Selective base-catalysed deprotection of the diacetate 22 , obtained from 12 , was hampered by an easy acetyl-group migration. The mesylate 28 proved unstable. The azide 27 was transformed via 29 into the ketone 30 (Scheme 2). Hydrogenation of 30 gave the dihydropyrrole 31 and, hence, the pyrrole 32. The adduct 33 was obtained from 30 by a Staudinger reaction (→31) and reduction with LiBH₄/HBF⁴. It was transformed into the pyrroudine 34 . The structure of 34 was established by X-ray analysis. Reductamination of the pyrrolidine-borane adduct with glyoxylic acid gave 40 and, hence, 3. N-Alkylation afforded 44 and, hence, the phosphonate 4. The acid 5 was obtained from 33 by acylation (→ 47 ) and deprotection (Scheme 4).     

Baeyer-Villiger oxidation with potassium peroxomonosulfate supported on acidic silica gel

[reaction: see text] Potassium peroxomonosulfate deposited onto silica SiO2 x KHSO5 efficiently reacts with ketones in dichloromethane at room temperature to give the corresponding esters or lactones in quantitative yields. This method avoids hydrolysis of the reaction products. The Baeyer-Villiger reaction is catalyzed by potassium hydrogensulfate present in the supported reagent.