Coleman integration using the Tannakian formalism

We use a new idea to construct a theory of iterated Coleman functions on overconvergent spaces with good reduction in any dimension. A Coleman function in this theory consists of a unipotent differential equation, a functional on the underlying bundle and a solution to the equation on a residue class. The new idea is to use the theory of Tannakian categories and the action of Frobenius to analytically continue solutions of the differential equation to all residue classes. Received: 22 November 2000 / Revised version: 28 March 2001 / Published online: 24 September 2001     

Compensation for atmospheric degradation of optical beam transmission by nonlinear optical mixing

The use of nonlinear optical mixing for compensating for atmospheric propagation distortion is considered.     

Confinement and stability in optical resonators employing mirrors with gaussian reflectivity tapers

Optical resonators with mirrors having gaussian reflectivity profiles are analyzed. This makes it possible to extend the conventional analysis of “stable”, i.e., confining, optical resonators to describe unstable (non-confining) resonators. Problems of mode discrimination, spot sizes, asymmetry and perturbation stability are considered.     

Vibrational relaxation of biacetyl studied by a visible—infrared double resonance technique

The vibrational relaxation of biacetyl following excitation by a highly intense laser pulse at 10.6 micron is studied. The changes in vibrational population are monitored by visible absorption from the ground electronic state to the excited n-π* state. The results indicate that thermal disequilibrium persists for at least 10^?5 seconds after the laser pulse at pressures in the range of 1–40 torr.The implications of these results for the use of high-power infrared lasers in inducing selective chemical reactions are briefly discussed.     

Coupled-mode analysis of periodic dielectric waveguides

The coupled-mode formalism is used to describe the behavior of a corrugated dielectric waveguide. Explicit expressions for the dispersion near the Bragg regime are given. These are compared with the results of an “exact” analysis.     

Self-assembled enzymatic monolayer directly bound to a gold surface: activity and molecular recognition force spectroscopy studies

Escherichia coli dihydrofolate reductase (ecDHFR) has one surface cysteine, C152, located opposite and distal to the active site. Here, we show that the enzyme spontaneously assembles on an ultraflat gold surface as a homogeneous, covalently bound monolayer. Surprisingly, the activity of the gold-immobilized ecDHFR as measured by radiographic analysis was found to be similar to that of the free enzyme in solution. Molecular recognition force spectroscopy was used to study the dissociation forces involved in the rupture of AFM probe-tethered methotrexate (MTX, a tight-binding inhibitor of DHFR) from the gold-immobilized enzyme. Treatment of the ecDHFR monolayer with free MTX diminished the interaction of the functionalized tip with the surface, suggesting that the interaction was indeed active-site specific. These findings demonstrate the viability of a simple and direct enzymatic surface-functionalization without the use of spacers, thus, opening the door to further applications in the area of biomacromolecular force spectroscopy.     

Effects of the donor-acceptor distance and dynamics on hydride tunneling in the dihydrofolate reductase catalyzed reaction

A significant contemporary question in enzymology involves the role of protein dynamics and hydrogen tunneling in enhancing enzyme catalyzed reactions. Here, we report a correlation between the donor-acceptor distance (DAD) distribution and intrinsic kinetic isotope effects (KIEs) for the dihydrofolate reductase (DHFR) catalyzed reaction. This study compares the nature of the hydride-transfer step for a series of active-site mutants, where the size of a side chain that modulates the DAD (I14 in E. coli DHFR) is systematically reduced (I14V, I14A, and I14G). The contributions of the DAD and its dynamics to the hydride-transfer step were examined by the temperature dependence of intrinsic KIEs, hydride-transfer rates, activation parameters, and classical molecular dynamics (MD) simulations. Results are interpreted within the framework of the Marcus-like model where the increase in the temperature dependence of KIEs arises as a direct consequence of the deviation of the DAD from its distribution in the wild type enzyme. Classical MD simulations suggest new populations with larger average DADs, as well as broader distributions, and a reduction in the population of the reactive conformers correlated with the decrease in the size of the hydrophobic residue. The more flexible active site in the mutants required more substantial thermally activated motions for effective H-tunneling, consistent with the hypothesis that the role of the hydrophobic side chain of I14 is to restrict the distribution and dynamics of the DAD and thus assist the hydride-transfer. These studies establish relationships between the distribution of DADs, the hydride-transfer rates, and the DAD's rearrangement toward tunneling-ready states. This structure-function correlation shall assist in the interpretation of the temperature dependence of KIEs caused by mutants far from the active site in this and other enzymes, and may apply generally to C-H→C transfer reactions.     

On the Homology of Completion and Torsion

Let A be a commutative ring, and ${\mathfrak{a}}$ a weakly proregular ideal in A. This includes the noetherian case: if A is noetherian then any ideal in it is weakly proregular; but there are other interesting examples. In this paper we prove the MGM equivalence, which is an equivalence between the category of cohomologically ${\mathfrak{a}}$ -adically complete complexes and the category of cohomologically ${\mathfrak{a}}$ -torsion complexes. These are triangulated subcategories of the derived category of A-modules. Our work extends earlier work by Alonso–Jeremias–Lipman, Schenzel and Dwyer–Greenlees.     

A Separated Cohomologically Complete Module is Complete

We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.     

An Excursion from Normal to Inverted C?C Bonds Shows a Clear Demarcation between Covalent and Charge‐Shift C?C Bonds

What is the nature of the C? C bond? Valence bond and electron density computations of 16 C? C bonds show two families of bonds that flesh out as a phase diagram. One family, involving ethane, cyclopropane and so forth, is typified by covalent C? C bonding wherein covalent spin‐pairing accounts for most of the bond energy. The second family includes the inverted bridgehead bonds of small propellanes, where the bond is neither covalent nor ionic, but owes its existence to the resonance stabilization between the respective structures; hence a charge‐shift (CS) bond. The dual family also emerges from calculated and experimental electron density properties. Covalent C? C bonds are characterized by negative Laplacians of the density, whereas CS‐bonds display small or positive Laplacians. The positive Laplacian defines a region suffering from neighbouring repulsive interactions, which is precisely the case in the inverted bonding region. Such regions are rich in kinetic energy, and indeed the energy‐density analysis reveals that CS‐bonds are richer in kinetic energy than the covalent C? C bonds. The large covalent–ionic resonance energy is precisely the mechanism that lowers the kinetic energy in the bonding region and restores equilibrium bonding. Thus, different degrees of repulsive strain create two bonding families of the same chemical bond made from a single atomic constituent. It is further shown that the idea of repulsive strain is portable and can predict the properties of propellanes of various sizes and different wing substituents. Experimentally (M. Messerschmidt, S. Scheins, L. Bruberth, M. Patzel, G. Szeimies, C. Paulman, P. Luger, Angew. Chem. 2005 , 117, 3993–3997; Angew. Chem. Int. Ed. 2005 , 44, 3925–3928), the C? C bond families are beautifully represented in [1.1.1]propellane, where the inverted C? C is a CS‐bond, while the wings are made from covalent C? C bonds. What other manifestations can we expect from CS‐bonds? Answers from experiment have the potential of recharting the mental map of chemical bonding.