A simple proof of the Prime Number Theorem

The Prime Number Theorem is proved using only properties of the Dirichlet series Σ_{n = 1}^∞n^?8 in its half plane of convergence, and simple facts of harmonic analysis.     

Interactions of trimethylamine N-oxide and water with cyclo-alanylglycine

The osmolyte trimethylamine N-oxide (TMAO) is one of a family of compounds found in living systems that can stabilize biomolecular tertiary structures. As a step in exploring the interactions between this material and polyamino acids, we have determined intermolecular 1H{1H} nuclear Overhauser effects (NOEs) between the protons of cyclo-alanylglycine and protons of solvent components in TMAO-water solutions. Comparison of the results to effects predicted on the basis of the molecular shape of the dipeptide and experimental translational diffusion coefficients suggests that both water and TMAO molecules have properties in the vicinity of the dipeptide that are different from those in the bulk solution. Changes of local concentrations of water and TMAO and changes in the diffusive behavior of these components near the dipeptide are rejected as possible explanations of the discrepancies between observed and calculated Overhauser effects. Rather, it is concluded that TMAO molecules, and the water molecules associated with them, participate to some extent in the formation of long-lived solute-solvent complexes. The aliphatic alcohol tert-butyl alcohol is structurally similar to TMAO. Overhauser effect studies of its interaction with cyclo-alanylglycine in tert-butyl alcohol-water suggest similar kinds of interactions are present in this system but that they are significantly weaker, presumably because of the lower polarity of this alcohol compared to TMAO.     

Optimization of angular and frequency compounding in ultrasonic attenuation estimations

Previous reports have shown that the variance in ultrasound attenuation measurements is reduced when spatial and frequency compounding were applied in data acquisition and analysis. This paper investigates factors affecting the efficiency of compound attenuation imaging methods. A theoretical expression is derived that predicts the correlation between attenuation versus frequency slope (beta) estimates as a function of the increment between measurement frequencies (deltaf ) and the angular separation between beam lines (Delta (theta)). Theoretical results are compared with those from attenuation measurements on tissue-mimicking phantoms and from simulation data. Both predictions and measurement results show that the correlation between beta estimates as a function of (Delta f ) is independent of the length of the radio frequency (rf) data segment over which beta is derived. However, it decreases with an increase in the length of the data segment used in power spectra estimates. In contrast, the correlation between beta estimates as a function of delta(theta) decreases when the rf data segment length is longer or the frequency of the signal is higher. O 2005 Acoustical Society of America.     

Interactions of 2,2,2‐trifluoroethanol with melittin

Melittin dissolved in 42% trifluoroethanol‐water at pH 2 has been shown to be α‐helical between residues 6 and 12 and between residues 13 and 25, with the two helical regions separated by a bend at the Leu13 residue. The inter‐helix angle was found to be 154 ± 3° at 0 °C and 135 ± 3° at 25 °C. The dominant conformation of the peptide is thus similar to those observed by previous workers for the peptide in a variety of media. At 25 °C, intermolecular nuclear Overhauser effects arising from nuclear spin dipole‐dipole interactions between melittin hydrogens and fluorines of the solvent are essentially those expected for a system that is homogeneous as regards concentration and translational diffusion of the peptide and fluoroalcohol components. However, at 0 °C, peptide‐trifluoroethanol cross‐relaxation terms are negative, a result consistent with the conclusion that fluoroalcohol molecules associate with the peptide for times (～1 ns) that are long compared to the time of a typical peptide‐fluoroalcohol diffusive encounter (～0.2 ns). Such interactions may be responsible for the reduction of the translational diffusion coefficient of trifluoroethanol produced by dissolved peptides. Copyright © 2009 John Wiley & Sons, Ltd.     

Universal laws and economic phenomena

Despite the idiosyncratic behavior of individuals, empirical regularities exist in social and economic systems. These regularities often arise from simple underlying mechanisms which, analogous to the natural sciences, can be expressed as universal principles or laws. In this essay, I discuss the similarities between economic and natural phenomena and argue that it is advantageous for economists to adopt methods from the natural sciences to discover “universal laws” in economic systems. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

Concerted and stepwise proton-coupled electron transfers in aquo/hydroxo complex couples in water: oxidative electrochemistry of [Os(II)(bpy)(2)(py)(OH(2))](2+)

Successive oxidation of transition metal(II) aqua complexes (M(II)OH(2) to M(III)OH) is a domain in which proton-coupled electron transfer reactions are extremely common. The mechanism of these PCET reactions-concerted or stepwise-is an important issue in the understanding and design of natural or artificial systems catalyzing the formation of dioxygen by four-electron oxidation of water. Concerted proton-coupled electron transfer from an aqua metal(II) to a hydroxo metal(III) complex requires the close proximity of a proton-accepting group with a pK value between those of the aqua complexes. Otherwise, stepwise electron-proton or proton-electron pathways involving high-energy intermediates are followed. Concerted proton-electron pathways involving water as proton-acceptor or proton-donor group are inefficient. Cyclic voltammetry of the title complex in buffered aqueous solution and re-examination of previous results for the same complex attached to an electrode surface are used to establish these conclusions, which provide a starting point on the route to higher degrees of oxidation, such as those involved in the catalysis of water oxidation.     

内埋炸药下超高韧性水泥基复合材料的抗爆性能

为研究超高韧性水泥基复合材料(ultra-high toughness cementitious composites, UHTCC)在内埋炸药爆炸下的抗爆性能和损伤破坏规律,对不同炸药埋深下的UHTCC和高强混凝土(high-strength concrete, HSC)进行了内埋炸药抗爆实验。得到了两种材料靶体的破坏状态,并利用接触爆炸的实验结果计算出了两种材料的抗爆性能参数。结果表明,在相同条件下,UHTCC抗爆性能优于高强混凝土。为了进一步探究UHTCC的抗压强度、抗拉强度以及拉伸韧性对靶体在内埋炸药下抗爆性能的影响,首先,采用改进的K&C模型对炸药埋深为40 mm的超高韧性水泥基复合材料靶体进行数值模拟,模拟结果与实验结果基本吻合,并根据数值模拟的结果得到了爆炸冲击波沿靶体径向衰减速度大于轴向衰减速度这一规律,验证了数值模型的有效性;然后,通过调整改进K&C模型中与抗压强度、抗拉强度以及拉伸韧性相关的参数,数值预测了不同抗压强度、抗拉强度以及拉伸韧性下UHTCC靶体的破坏状态,发现增强UHTCC的韧性可以有效防止靶体发生整体性破坏,增大UHTCC的抗拉强度可以减小靶体迎爆面的开坑直径,增大UHTCC的抗压强度对减小开坑直径效果不明显。