Photo-induced ligand substitution at a remote site via electron transfer in a porphyrin-appended rhenium carbonyl supermolecule

The photochemical and electrochemical properties of a Zn-porphyrin appended rhenium(I) tricarbonyl bipyridine 3-Me-pyridine complex have been investigated; visible-light sensitisation of electron transfer results in ligand substitution at a site remote from the chromophore.     

Synthesis of a 56 component library of sugar beta-peptides

Many biological processes of vital importance are triggered by the molecular recognition of small carbohydrate units by proteins and receptors thus leading to the belief that carbohydrates could act as candidates for the design of new drugs. We have developed a new useful synthetic approach, which can be applied in a combinatorial manner, giving access to 1,1-di-substituted pyrans projecting amide side chains in both the alpha- and beta-directions. Thus, treatment of the readily accessible hemiketal (1) with TFA followed by trimethylsilyl trifluoromethanesulfonate (TMSOTf) in the presence of a nitrile gives dihydrooxazinones (2) via a new type of modified intramolecular Ritter reaction. The dihydrooxazinones (2) can either be isolated or used directly in reactions with a broad variety of amines. Final deprotection furnishes the 1,1-di-substituted sugar beta-peptides having the general structure (4).     

Bi-laplacian growth patterns in disordered media

Experiments in quasi-two-dimensional geometry (Hele-Shaw cells) in which a fluid is injected into a viscoelastic medium (foam, clay, or associating polymers) show patterns akin to fracture in brittle materials, very different from standard Laplacian growth patterns of viscous fingering. An analytic theory is lacking since a prerequisite to describing the fracture of elastic material is the solution of the bi-Laplace rather than the Laplace equation. In this Letter we close this gap, offering a theory of bi-Laplacian growth patterns based on the method of iterated conformal maps.     

Smectic membranes in motion: approaching the fast limits of x-ray photon correlation spectroscopy

The dynamics of the layer-displacement fluctuations in smectic membranes have been studied by x-ray photon correlation spectroscopy (XPCS). We report transitions from an oscillatory damping regime to simple exponential decay of the fluctuations, both as a function of membrane thickness and upon changing from specular to off-specular scattering. This behavior is in agreement with recent theories. Employing avalanche photodiode detectors and the uniform filling mode of the synchrotron storage ring, the fast limits of XPCS have been explored down to 50 ns.     

Effects of feedback from collimating, focusing, and spot-array generating outcoupler gratings in surface-emitting semiconductor lasers

We experimentally demonstrate that a grating outcoupler used for complex beam shaping (spot-array generation) can produce unintentional optical feedback that severely disturbs the integrated in-plane laser that illuminates the coupler. Simulations show that these outcouplers, in contrast to conventional collimating or focusing outcouplers, tend to produce high levels of feedback in spite of the detuning used to suppress feedback. Further, this feedback is focused to high intensity in the laser gain medium. This focused light acts as a seed for the nonlinear self-focusing that causes wave-front distortion and filamentation, which degrades the beam quality.     

Changes in orcine muscle water characteristics during growth--an in vitro low-field NMR relaxation study

This study investigates the effects of developmental stage and muscle type on the mobility and distribution of water within skeletal muscles, using low-field (1)H-NMR transverse relaxation measurements in vitro on four different porcine muscles (M. longissimus dorsi, M. semitendinosus, M. biceps femoris, M. vastus intermedius) from a total of 48 pigs slaughtered at various weight classes between 25 kg and 150 kg. Principal component analysis (PCA) revealed effects of both slaughter weight and muscle type on the transverse relaxation decay. Independent of developmental stage and muscle type, distributed exponential analysis of the NMR T(2) relaxation data imparted the existence of three distinct water populations, T(2b), T(21), and T(22), with relaxation times of approximately 1-10, 45-120, and 200-500 ms, respectively. The most profound change during muscle growth was a shift toward faster relaxation in the intermediate time constant, T(21). It decreased by approx. 24% in all four muscle types during the period from 25 to 150 kg live weight. Determination of dry matter, fat, and protein content in the muscles showed that the changes in relaxation time of the intermediate time constant, T(21), during growth should be ascribed mainly to a change in protein content, as the protein content explained 77% of the variation in the T(21) time constant. Partial least squares (PLS) regression revealed validated correlations in the region of 0.58 to 0.77 between NMR transverse relaxation data and muscle development for all the four muscle types, which indicates that NMR relaxation measurements may be used in the prediction of muscle developmental stage.     

Heterocyclization of compounds containing diazo and cyano groups. 6. Theoretical and experimental investigations of cyclization of 2-cyano-2-diazoacetamides to 5-hydroxy-1,2,3-triazole-4-carbonitriles

A series of N-alkyl- and N-aryl-2-cyano-2-diazoacetamides was synthesized by the reaction of 2-amino-2-cyanoacetamides with sodium nitrite in hydrochloric acid. The mechanism of their heteroclectrocyclization to 5-hydroxy-1,2,3-triazoles was investigated kinetically and theoretically by the B3LYP/6-31+G^* method. The conclusion was made on the basis of the determined activation energy of the cyclization process. reaction parameters , and kinetic isotope effects, that there is a difference between the mechanisms of cyclization of the N-alkyl and N-aryl derivatives of 2-cyano-2-diazoacetamide; cyclization of the N-alkyl derivatives takes place by a monorotatory mechanism, while cyclization of the N-aryl derivatives takes place by a mechanism where one of the stages is heteroelectrocyclization of 2-diazoacetimidates.For Communication 5, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 26–41, January, 2000.     

These are the differentials of order

We answer P.-A. Meyer's question ``Qu'est ce qu'une différentielle d'ordre ?'. In fact, we present a general theory of higher order differentials based upon a construction of universal objects for higher order differentials. Applied to successive tangent spaces on a differentiable manifold, our theory gives the higher order differentials of Meyer as well as several new results on differentials on differentiable manifolds. In addition our approach gives a natural explanation of the quite mysterious multiplicative structure on higher order differentials observed by Meyer. Applied to iterations of the first order Kähler differentials our theory gives an algebra of higher order differentials for any smooth scheme. We also observe that much of the recent work on higher order osculation spaces of varieties fits well into the framework of our theory.

     

Trace distributions associated to the Schrödinger operator

Dedicated to Professor Shmuel Agmon     

On the spontaneous magnetization in the Ising model

The equality between the spontaneous magnetization and the long range order is established for the Ising model with nearest neighbour interactions for low and high temperatures. The proof is presented for the two-dimensional lattice but works also in higher dimensions. The result verifies that the valuem*=(1–(Sh)^–4)^1/8 of the spontaneous magnetization below the critical point calculated by Onsager and Yang is the true value, which has been a long standing open question.