Converting homotopies to isotopies and dividing homotopies in half in an effective way

We prove two theorems about homotopies of curves on two-dimensional Riemannian manifolds. We show that, for any \({\epsilon > 0}\) , if two simple closed curves are homotopic through curves of bounded length L, then they are also isotopic through curves of length bounded by \({L + \epsilon}\) . If the manifold is orientable, then for any \({\epsilon > 0}\) we show that, if we can contract a curve \({\gamma}\) traversed twice through curves of length bounded by L, then we can also contract \({\gamma}\) through curves bounded in length by \({L + \epsilon}\) . Our method involves cutting curves at their self-intersection points and reconnecting them in a prescribed way. We consider the space of all curves obtained in this way from the original homotopy, and use a novel approach to show that this space contains a path which yields the desired homotopy.     

相对论性核碰撞中Φ介子产生和弦碎裂函数

用强子和弦级联模型LUCIAE系统研究从AGS到SPS,到RHIC,再到LHC能量核–核碰撞中Φ介子产生.采用与能量有关弦碎裂函数,并通过与荷电粒子多重数实验数据的比较确定其中的参数后,LUCIAE模型给出的Φ介子产额与实验数据也都相近,得到的事件平均弦碎裂变量随能量之增趋饱和规律,可能是核穿透性能量行为的定性表示.     

以LCD为目标的自动定焦判据选择

在光学综合自动测量中 ,使用液晶显示屏作为分划板可以大大简化结构 ,提高效率 ,真正地实现自动测量。由于液晶显示具有对比度低、噪声大等特点 ,所以根据液晶的这些特点以及图像处理和CCD信号接收的特点选择两种适用的判据进行了分析和试验比较 ,并给出了结果。结果表明 ,这两种判别函数都适用于以液晶显示屏为目标和用图像处理方法进行光学参数测量的系统 ,其中锐度判别函数更优于信息熵判别函数 ,前者具有更好的抗干扰性和稳定性 ,而且其判定结果更接近目视清晰度判别     

Revêtements modérés et groupe fondamenttal de graphe de groupes

Let R be a discrete complete valuation ring, with algebraically closedresidue field. Let X be a semi-stable R-curve, with smooth generic fibre. In this paper we study tame coverings of X.     

Turning it off! Disfavouring hydrogen evolution to enhance selectivity for CO production during homogeneous CO2 reduction by cobalt–terpyridine complexes

Understanding the activity and selectivity of molecular catalysts for CO₂ reduction to fuels is an important scientific endeavour in addressing the growing global energy demand. Cobalt–terpyridine compounds have been shown to be catalysts for CO₂ reduction to CO while simultaneously producing H₂ from the requisite proton source. To investigate the parameters governing the competition for H⁺ reduction versus CO₂ reduction, the cobalt bisterpyridine class of compounds is first evaluated as H⁺ reduction catalysts. We report that electronic tuning of the ancillary ligand sphere can result in a wide range of second-order rate constants for H⁺ reduction. When this class of compounds is next submitted to CO₂ reduction conditions, a trend is found in which the less active catalysts for H⁺ reduction are the more selective towards CO₂ reduction to CO. This represents the first report of the selectivity of a molecular system for CO₂ reduction being controlled through turning off one of the competing reactions. The activities of the series of catalysts are evaluated through foot-of-the-wave analysis and a catalytic Tafel plot is provided.     

Agglomerated carbon based phases for anion exchange chromatography

Carbon-clad zirconia particles have been converted into ion exchange media through addition of charged latexes after covalent modification of the carbon surface. A variety of methodologies were investigated to introduce a negative charge to the carbon surface in the form of either sulfonate or oxygen containing functionalities (e.g. hydroxyl or carboxylate). Short analytical sized columns (35 mm × 4 mm I.D.) were packed with modified 2 μm nonporous carbon clad zirconia. Addition of the latex particles after the initial packing produced almost double the efficiency for the system compared to adding the latexes before packing. The optimized system could separate mixtures of common inorganic anions with efficiencies greater than of 41,000 plates/m and retention reproducibility of <2% RSD.     

Incorporation of carbon nanotubes in porous polymer monolithic capillary columns to enhance the chromatographic separation of small molecules

Multiwalled carbon nanotubes have been entrapped in monolithic poly(glycidyl methacrylate-co-ethylene dimethacrylate) capillary columns to afford stationary phases with enhanced liquid chromatographic performance for small molecules in the reversed phase. While the column with no nanotubes exhibited an efficiency of only 1800 plates/m, addition of a small amount of nanotubes to the polymerization mixture increased the efficiency to over 15,000 and 35,000 plates/m at flow rates of 1 and 0.15 μL/min, respectively. Alternatively, the native glycidyl methacrylate-based monolith was functionalized with ammonia and, then, shortened carbon nanotubes, bearing carboxyl functionalities, were attached to the pore surface through the aid of electrostatic interactions with the amine functionalities. Reducing the pore size of the monolith enhanced the column efficiency for the retained analyte, benzene, to 30,000 plates/m at a flow rate of 0.25 μL/min. Addition of tetrahydrofuran to the typical aqueous acetonitrile eluents improved the peak shape and increased the column efficiency to 44,000 plates/m calculated for the retained benzene peak.