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Simple Zeros of the Riemann Zeta-Function 总被引:1,自引:0,他引:1
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. 相似文献
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This paper concerns a Markov operator T on a space L1, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:
- a the existence of invariant probabilitydensities (IPDs)
- b the existence of strictly positive IPDs,and
- c the existence and uniqueness of IPDs.
- b the existence of strictly positive IPDs,and
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Broderick R. Wilks Won J. Chung Peter J. Ludovice Mary E. Rezac Pavla Meakin Anita J. Hill 《Journal of Polymer Science.Polymer Physics》2006,44(1):215-233
Increasing the length of an alkyl side chain on a rigid polynorbornene (PNB) backbone is shown to decrease the glass‐transition temperature of the resultant polymer, decrease the density of the bulk polymer, decrease the number and average free‐volume element size present, and decrease the permeability of gases through the polymer. Methyl‐, butyl‐, and hexyl‐substituted PNBs were investigated. Experimental results were compared with predictions based on molecular modeling. By using models that provided good agreement between the experimental and simulated wide‐angle diffraction patterns, the distributions of free‐volume elements were predicted. These predictions clearly indicate that the number of large free‐volume elements decreases as the length of the side chain increases, suggesting that the flexible aliphatic side chains can be largely accommodated within the free volume between the rigid PNB backbones. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 215–233, 2006 相似文献
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This article evaluates the influence of temperature on the sorption of gases in two isomers of polynorbornene. The subject polymers were stereoisomers with nearly identical bulk density and total free volume. Because of differences in the mobility of the polymer backbone, the isomers packed differently resulting in differences in the average free‐volume element size within the matrix. The influence of these differences on free‐volume element size was characterized by the heat of sorption of gases in the matrix. The most pronounced differences were observed in the isosteric heats of sorption of condensable carbon dioxide and methane in the polymer isomers. This analysis suggests that the relative space available for sorption into free‐volume elements is higher in the methyl II isomer relative to methyl III. These conclusions support the physical characterizations reported in Part I of this series suggesting that the methyl II isomer has larger average free‐volume elements but fewer of them than the methyl III isomer. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1939–1946, 2003 相似文献
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Rebecca Hanscam Eric M. Shepard Joan B. Broderick Valérie Copié Robert K. Szilagyi 《Journal of computational chemistry》2019,40(2):515-526
Peptides coordinated to iron–sulfur clusters, referred to as maquettes, represent a synthetic strategy for constructing biomimetic models of iron–sulfur metalloproteins. These maquettes have been successfully employed as building blocks of engineered heme-containing proteins with electron-transfer functionality; however, they have yet to be explored in reactivity studies. The concept of iron–sulfur nesting in peptides is a leading hypothesis in Origins-of-Life research as a plausible path to bridge the discontinuity between prebiotic chemical transformations and extant enzyme catalysis. Based on past biomimetic and biochemical research, we put forward a mechanism of maquette reconstitution that guides our development of computational tools and methodologies. In this study, we examined a key feature of the first stage of maquette formation, which is the secondary structure of aqueous peptide models using molecular dynamics simulations based on the AMBER99SB empirical force field. We compared and contrasted S…S distances, [2Fe-2S] and [4Fe-4S] nests, and peptide conformations via Ramachandran plots for dissolved Cys and Gly amino acids, the CGGCGGC 7-mer, and the GGCGGGCGGCGGW 16-mer peptide. Analytical tools were developed for following the evolution of secondary structural features related to [Fe-S] cluster nesting along 100 ns trajectories. Simulations demonstrated the omnipresence of peptide nests for preformed [2Fe-2S] clusters; however, [4Fe-4S] cluster nests were observed only for the 16-mer peptide with lifetimes of a few nanoseconds. The origin of the [4Fe-4S] nest and its stability was linked to a “kinked-ribbon” peptide conformation. Our computational approach lays the foundation for transitioning into subsequent stages of maquette reconstitution, those being the formation of iron ion/iron–sulfur coordinated peptides. © 2018 Wiley Periodicals, Inc. 相似文献
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Scott R. Broderick Changwon Suh J Provine Christopher S. Roper Roya Maboudian Roger T. Howe Krishna Rajan 《Surface and interface analysis : SIA》2012,44(3):365-371
We have demonstrated an informatics methodology for finding correlations between the full profile Fourier transform infrared spectra of polycrystalline 3C‐silicon carbide (poly‐SiC) films and their growth conditions, thereby developing high‐throughput structure‐process relationships. Because SiC films are a structural element in photonic sensors, this paper focuses on the interpretation of their optical response, the multivariate tracking of critical processing pathways, and the identification of controlling processing mechanisms. Using principal component analysis, we have developed a data analysis tool to aid in the assessment of the relative contributions of experimental parameters in low‐pressure chemical vapor deposition processes to optical responses on the basis of the size of eigenvalues of the spectral data set. The applied methodology for identifying spectral relationships of stoichiometry, dopant chemistry, and microstructure of poly‐SiC provides more effective guidelines to manipulate optical responses by controlling multiple experimental parameters. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统. 相似文献
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