Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

A hydration study of (1-->4) and (1-->6) linked alpha-glucans by comparative 10 ns molecular dynamics simulations and 500-MHz NMR

The hydration behavior of two model disaccharides, methyl-alpha-D-maltoside (1) and methyl-alpha-D-isomaltoside (2), has been investigated by a comparative 10 ns molecular dynamics study. The detailed hydration of the two disaccharides was described using three force fields especially developed for modeling of carbohydrates in explicit solvent. To validate the theoretical results the two compounds were synthesized and subjected to 500 MHz NMR spectroscopy, including pulsed field gradient diffusion measurements (1: 4.0. 10(-6) cm(2). s(-1); 2: 4.2. 10(-6) cm(2). s(-1)). In short, the older CHARMM-based force field exhibited a more structured carbohydrate-water interaction leading to better agreement with the diffusional properties of the two compounds, whereas especially the alpha-(1-->6) linkage and the primary hydroxyl groups were inaccurately modeled. In contrast, the new generation of the CHARMM-based force field (CSFF) and the most recent version of the AMBER-based force field (GLYCAM-2000a) exhibited less structured carbohydrate-water interactions with the result that the diffusional properties of the two disaccharides were underestimated, whereas the simulations of the alpha-(1-->6) linkage and the primary hydroxyl groups were significantly improved and in excellent agreement with homo- and heteronuclear coupling constants. The difference between the two classes of force field (more structured and less structured carbohydrate-water interaction) was underlined by calculation of the isotropic hydration as calculated by radial pair distributions. At one extreme, the radial O em leader O pair distribution function yielded a peak density of 2.3 times the bulk density in the first hydration shell when using the older CHARMM force field, whereas the maximum density observed in the GLYCAM force field was calculated to be 1.0, at the other extreme.     

Effects of glycosylation on peptide conformation: a synergistic experimental and computational study

Asparagine-linked glycosylation, the co-translational covalent attachment of carbohydrates to asparagine side chains, has a major effect on the folding, stability, and function of many proteins. The carbohydrate composition in mature glycoproteins is heterogeneous due to modification of the initial oligosaccharide by glycosidases and glycosyltransferases during the glycoprotein passage through the endoplasmic reticulum and Golgi apparatus. Despite the diversity of carbohydrate structures, the core beta-D-(GlcNAc)(2) remains conserved in all N-linked glycoproteins. Previously, results from our laboratory showed that the molecular composition of the core disaccharide has a critical and unique conformational effect on the peptide backbone. Herein, we employ a synergistic experimental and computational approach to study the effect of the stereochemistry of the carbohydrate--peptide linkage on glycopeptide structure. A glycopeptide derived from a hemagglutinin protein fragment was synthesized, with the carbohydrate attached to the peptide with an alpha-linked stereochemistry. Computational and biophysical analyses reveal that the conformations of the peptide and alpha- and beta-linked glycopeptides are uniquely influenced by the attached saccharide. The value of computational approaches for probing the influence of attached saccharides on polypeptide conformation is highlighted.     

First-principle studies of intermolecular and intramolecular catalysis of protonated cocaine

We have performed a series of first-principles electronic structure calculations to examine the reaction pathways and the corresponding free energy barriers for the ester hydrolysis of protonated cocaine in its chair and boat conformations. The calculated free energy barriers for the benzoyl ester hydrolysis of protonated chair cocaine are close to the corresponding barriers calculated for the benzoyl ester hydrolysis of neutral cocaine. However, the free energy barrier calculated for the methyl ester hydrolysis of protonated cocaine in its chair conformation is significantly lower than for the methyl ester hydrolysis of neutral cocaine and for the dominant pathway of the benzoyl ester hydrolysis of protonated cocaine. The significant decrease of the free energy barrier, approximately 4 kcal/mol, is attributed to the intramolecular acid catalysis of the methyl ester hydrolysis of protonated cocaine, because the transition state structure is stabilized by the strong hydrogen bond between the carbonyl oxygen of the methyl ester moiety and the protonated tropane N. The relative magnitudes of the free energy barriers calculated for different pathways of the ester hydrolysis of protonated chair cocaine are consistent with the experimental kinetic data for cocaine hydrolysis under physiologic conditions. Similar intramolecular acid catalysis also occurs for the benzoyl ester hydrolysis of (protonated) boat cocaine in the physiologic condition, although the contribution of the intramolecular hydrogen bonding to transition state stabilization is negligible. Nonetheless, the predictability of the intramolecular hydrogen bonding could be useful in generating antibody-based catalysts that recruit cocaine to the boat conformation and an analog that elicited antibodies to approximate the protonated tropane N and the benzoyl O more closely than the natural boat conformer might increase the contribution from hydrogen bonding. Such a stable analog of the transition state for intramolecular catalysis of cocaine benzoyl-ester hydrolysis was synthesized and used to successfully elicit a number of anticocaine catalytic antibodies.     

Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.     

粉粒体两相流的电容层析成象测量

粉粒体系统中的固相浓度分布的在线测量是十分困难的问题．电容层析成象技术是一种近年来发展起来的非侵入式快速浓度场测量技术．它不干扰流场，不受流动中颗粒浓度、加速度、不透明等因素的制约．本文讨论其测量原理、应用、近期进展、存在的主要问题及其解决的对策．     

ac Conductivity of mixed spinel NiAl0.7Cr0.7Fe0.6O4

ac Conductivity measurements are carried out across the metal to insulator transition in NiAl_0.7Cr_0.7Fe_0.6O₄. The low frequency data is analyzed using Summerfield scaling theory for hopping conductivity. The exponent of the scaling behavior has significantly different values in the conducting and insulating regimes. The hopping frequency and the zero frequency conductivity are found to increase with temperature, slowly in the metallic regime and rapidly in the insulating regime.