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).     

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.     

Die Massenspektren der Pyrrolidide einiger aliphatisch-alicyclischer Carbonsäuren

The mass spectra of the pyrrolidides of some long-chain carboxylic acids with alicyclic residues attached to their ω-end are discussed and compared with the spectra of the corresponding esters. Fragmentation triggered by the pyrrolidide group generates a series of peaks, which clearly exhibits the size and the structure of the carbon chain.     

Conformational studies by dynamic NMR. 94.1 cogwheel pathway for the stereomutations of durene derivatives containing the mesityl ring

The low-temperature NMR spectra of 1,4-bis(mesitoyl)durene, 1, and of 1,4-bis(mesitylethenyl)durene, 2, reveal the presence of syn and anti rotamers at the equilibrium, their relative proportions depending on the dielectric constant of the solvent. In solution the more stable rotamer of 1 is the anti whereas, in the case of 2, the more stable is the syn. Depending on the crystallization solvent employed the more (anti) and the less stable (syn) rotamers were both observed (X-ray diffraction) in the solid state of 1. On the other hand, only the less stable rotamer (anti) was found to be present in the solid state of 2. As shown by MM calculations, the syn-to-anti interconversion occurs via a correlated process (cogwheel pathway) involving the mesityl-C and durene-C bond rotations: the dynamic NMR technique yields an experimental barrier of 8.2 kcal mol(-)(1) for 1 and 13.1 kcal mol(-)(1) for 2. In the case of derivative 2 a second barrier, due to a second type of correlated rotation process (torsion), was also determined (8.6 kcal mol(-)(1)). As a consequence of the restriction of this second torsional motion the anti rotamer of 2 displays two distinguishable NMR spectra at -133 degrees C, corresponding to a pair of conformers with different symmetry (anti C(i)() and anti C(2)).     

Synthesis of 1,2-cis-Configurated Glycosylphosphonates

A synthesis of 1,2-cis-configurated, non-isosteric phosphonate analogues of aldose-1-phosphates is described. Treatment of 1-O-acyl-glycoses 1 , 7 , 13 , and 19 with trialkyl phosphite in the presence of trimethylsilyl trifluoromethanesulfonate gave the 1,2-cis-configurated glycosylphosphonates 2 , 4 , 8 , 10 , 14 , 16 , 20 , and 22 as the major anomers and the 1,2-trans-configurated glycosylphosphonates 3 , 5 , 9 , 11 , 15 , 17 , 21 , and 23 as the minor anomers. The 1,2-cis-configurated phosphonates 4 , 10 , 16 , and 22 were deprotected to give the (β-D -glucopyranosyl)phosphonate 6 , the (β-D -mannopyranosyl)phosphonate 12 , the (β-D -ribofuranosyl)phosphonate 18 , and the (β-D -arabinofuranosyl)phosphonate 24 , respectively, in high yields. The preferred formation of 1,2-cis-configurated phosphonates is explained by postulating an equilibrium between the anomeric phosphonium-salt intermediates (such as 25 and 26 ) and a stabilization of the cis-configurated salts through formation of a pentacoordinated species (such as 28 ).     

A convenient protocol for selective cleavage of 2-hydroxy acid amides. Application to semisynthesis of the cyclic heptapeptide aza HUN-7293

A two-step protocol for the first chemoselective cleavage of 2-hydroxy acid amides has been developed. Mesylation of the model substrate 2-(hydroxypropionylamino)-4-methylpentanoic acid methyl ester (11) followed by treatment with N-ethylthiourea (13) allows cleavage of 2-hydroxy acid amides under smooth conditions. Successful application of this methodology to the open-chain transesterification product 15 (methylester) of the cyclic heptadepsipeptide HUN-7293, a potent inhibitor of inducible cell adhesion molecule expression, delivered the corresponding hexapeptide 18 with unprotected N-terminus in 70-75% yield. This result demonstrates that the protocol developed even works in the presence of an ester and several methylated and unmethylated amide bonds. Finally, a sequence of ligation of methyl D-dehydroglutaminate (20) to the C-terminus of the saponification product 21, followed by the degradation protocol and ring closure, allowed chemical "point mutation" at the DGCN site affording the aza analogue of HUN-7293 (24) in 15% overall yield. To the best of our knowledge this is the first report on chemoselective cleavage of 2-hydroxy acid amides.     

Polarographie schwefelhaltiger Proteine

Zusammenfassung An kristallisierten Enzymen des biologischen Stoffwechsel wird gezeigt, daß bei der Polarographie nur die schwefelhaltigen Proteine katalytische Wasserstoffwellen geben. Von den in der Literatur beschriebenen Doppelstufen der Proteine besitzt nur die im negativeren Potentialbereich liegende Welle die eigentliche katalytische Funktion. Die erste Vorwelle von Proteinen verschwindet, wenn die polarographische Messung bei 0° C durchgeführt wird.In Proteinen sind nur Disulfidgruppen katalytisch wirksam. Sogenannte reine Sulfhydryl-Enzyme haben keinen katalytischen Effekt. Typische SH-Enzyme können jedoch polarographisch als p-Chloromercuribenzoatkomplexe gemessen werden.Durch Harnstoffzusatz bei der polarographischen Messung von Proteinen gelingt es, zwischen maskierten und freien Sulfhydryl- oder Disulfidgruppen an Enzymen zu definieren.Auszug aus der Dissertationsschrift H. Katzlmeier, Technische Hochschule München (1959).     

Nanoscale borromeates

[Structure: See text] In addition to a parent zinc(II) Borromean ring (BR) complex, the preparation and characterization of two hexasubstituted BR complexes with either 4-acetoxymethylphenyl or 4-methylthiophenyl substituents associated in turn with all six pyridyl rings has been achieved convergently in good yields by appealing to the dynamic features of the reactions between primary amino groups in a preformed acyclic ligand and 2,6-diformylpyridine. Two molecules of the acyclic ligands react with two molecules of 2,6-diformylpyridine to form a cyclic [2 + 2] tetraimine in the presence of Zn(II) ions as templates in 2-propanol at 70 degrees C. The successful preparation of the two derivatives by convergent template-directed syntheses opens up opportunities to self-assemble, under equilibrium control, numerous nanoscale metallo-organic particles with potentially useful properties.     

Partial Synthesis and Characterization of the Mono-and Diepoxides of β-Cryptoxanthin

β-Cryptoxanthin ( 1 ) was acetylated and then epoxidized with monoperoxyphthalic acid. After hydrolysis, repeated chromatography, and crystallization, (3S,5R,6S)-5,6-epoxy-β-cryptoxanthin ( 3 ), (3S,5S,6R)-5,6-epoxy-β-cryptoxanthin ( 4 ), (3R,5′R,6′R)-5′,6′-epoxy-β-cryptoxanthin ( 5 ), (3S,5R,6S,5′R,6′S)-5,6:5′,6′-diepoxy-β-cryp-toxanthin ( 6 ), and (3S,5S,6R,5′S,6′R)-5,6:5′,6′-diepoxy-β-cryptoxanthin ( 7 ) were isolated as main products and characterized by their UV/VIS, CD, ¹H- and ¹³C-NMR, and mass spectra. The comparison of the carotenoid isolated from yellow, tomato-shaped paprika (Capsicum annuum var. lycopersiciforme flavum) with 3–5 strongly supports the structure of 3 for the natural product.