The Bergman‐Shelah preorder on transformation semigroups

Let $\mathbb {N}^\mathbb {N}Let $\mathbb {N}^\mathbb {N}$ be the semigroup of all mappings on the natural numbers $\mathbb {N}$, and let U and V be subsets of $\mathbb {N}^\mathbb {N}$. We write U?V if there exists a countable subset C of $\mathbb {N}^\mathbb {N}$ such that U is contained in the subsemigroup generated by V and C. We give several results about the structure of the preorder ?. In particular, we show that a certain statement about this preorder is equivalent to the Continuum Hypothesis. The preorder ? is analogous to one introduced by Bergman and Shelah on subgroups of the symmetric group on $\mathbb {N}$. The results in this paper suggest that the preorder on subsemigroups of $\mathbb {N}^\mathbb {N}$ is much more complicated than that on subgroups of the symmetric group.     

第一性原理研究富勒烯衍生物PCBM的近边X射线吸收精细结构谱

富勒烯衍生物^{[6, 6]}-苯基-C₆₁-丁酸甲酯(PCBM)在有机聚合物太阳能电池的电子输运方面扮演着非常重要的角色.利用密度泛函理论计算了PCBM的近边X射线吸收精细结构谱及未占据分子轨道.通过对比计算得到的PCBM分子中不等价碳原子的谱线总和,将该分子的主要共振吸收峰进行了标定.我们分析了第一个π^*共振吸收峰高能区右肩吸收峰的来源,并确定了该吸收峰主要来自于C₆₀笼子中碳原子能量较高的未占据分子轨道的跃迁.     

迭代的多组态相互作用方法

本文提出了迭代的组态相互作用方法(IMRCI). IMRCI被用来计算H₂O和CH₂(单重态和三重态)在平衡态和远离平衡时的电子能量. IMRCI、MP2、MP3、MP4、CCSD和CCSD(T)还用来计算H₂O、CH₂(单重态和双重态)和N₂的势能曲线. 这些计算结果表明IMRCI的结果不依赖初始的多参考态组态函数,并能较快地收敛到完全组态相互作用的计算结果. 相比完全组态相互作用的结果,仅需2至4次迭代,IMRCI的误差就能达到10^-5 hartree数量级. 另外,IMRCI还提供了寻找势能面上主要电子组态的一个有效途径. 这将有助于单参考态和多参考态理论模型得到准确的计算结果.     

Bidirectional Whitham equations as models of waves on shallow water

Hammack & Segur (1978) conducted a series of surface water-wave experiments in which the evolution of long waves of depression was measured and studied. This present work compares time series from these experiments with predictions from numerical simulations of the KdV, Serre, and five unidirectional and bidirectional Whitham-type equations. These comparisons show that the most accurate predictions come from models that contain accurate reproductions of the Euler phase velocity, sufficient nonlinearity, and surface tension effects. The main goal of this paper is to determine how accurately the bidirectional Whitham equations can model data from real-world experiments of waves on shallow water. Most interestingly, the unidirectional Whitham equation including surface tension provides the most accurate predictions for these experiments. If the initial horizontal velocities are assumed to be zero (the velocities were not measured in the experiments), the three bidirectional Whitham systems examined herein provide approximations that are significantly more accurate than the KdV and Serre equations. However, they are not as accurate as predictions obtained from the unidirectional Whitham equation.     

Physical Layer Framework for the Multi-Gigabit Copper-Fiber Access Networks

In future, Internet access speeds beyond 1 Gbit/s will be required, which is mainly provided by fiber connections in the fixed access network. A high-performance copper-based transmission technology can enable fiber to the building and fiber to the home installations in a cost-effective copper/fiber hybrid network. ITU has started a project for multi-gigabit copper access (MGfast), as a successor of the G.fast technology with the goal to provide symmetric services with 10 Gbit/s aggregated rate for each subscriber. Besides the use of higher bandwidth up to 424 MHz or 848 MHz, full duplex transmission with echo cancellation is another major improvement in MGfast. Line bonding and frequency bonding allow the use of the same physical layer architecture for different media types. This paper discusses network topologies for the hybrid network and technology options for copper transmission to achieve the desired rate and reach.     

Self-Adaptive Learning of Task Offloading in Mobile Edge Computing Systems

Mobile edge computing (MEC) focuses on transferring computing resources close to the user’s device, and it provides high-performance and low-delay services for mobile devices. It is an effective method to deal with computationally intensive and delay-sensitive tasks. Given the large number of underutilized computing resources for mobile devices in urban areas, leveraging these underutilized resources offers tremendous opportunities and value. Considering the spatiotemporal dynamics of user devices, the uncertainty of rich computing resources and the state of network channels in the MEC system, computing resource allocation in mobile devices with idle computing resources will affect the response time of task requesting. To solve these problems, this paper considers the case in which a mobile device can learn from a neighboring IoT device when offloading a computing request. On this basis, a novel self-adaptive learning of task offloading algorithm (SAda) is designed to minimize the average offloading delay in the MEC system. SAda adopts a distributed working mode and has a perception function to adapt to the dynamic environment in reality; it does not require frequent access to equipment information. Extensive simulations demonstrate that SAda achieves preferable latency performance and low learning error compared to the existing upper bound algorithms.     

A NOTE ON THE GRADIENT PROJECTION METHOD WITH EXACT STEPSIZE RULE

In this paper, we give some convergence results on the gradient projection method with exact stepsize rule for solving the minimization problem with convex constraints. Especially, we show that if the objective function is convex and its gradient is Lipschitz continuous, then the whole sequence of iterations produced by this method with bounded exact stepsizes converges to a solution of the concerned problem.     

邻苯二钾酸氢铊晶体积分衍射效率的标定

 以北京同步辐射实验室4B7中能束线为光源,在2.1~6.0 keV的范围内对邻苯二钾酸氢铊(TlAP)平面晶体一、二 、三级衍射的积分衍射效率进行了精确的实验标定。标定结果表明：TlAP晶体有较高的峰值衍射率; 其一级衍射的积分衍射效率向低能端有增加的趋势,而在2.6~5.4 keV的范围内大约为1.53×10^-4 rad;随着衍射级次的提高,衍射效率逐渐减小,二级衍射的积分衍射效率约为一级衍射效率的1/4,三级衍射结果比一级衍射下降一个量级。实验所标定的TlAP晶体可用于平晶谱仪对激光等离子体X射线光谱的定量分析。     

Global convergence of inexact Newton methods for transonic flow

In computational fluid dynamics, non-linear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these non-linear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modelled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.     

The full evaporation technique: a promising alternative for residual solvents analysis in solid samples

The static headspace technique is the most common approach to residual solvent analysis in pharmaceutical and environmental matrices. This paper presents an alternative tool where the volatile impurities are released from the matrix by working directly on a small amount of sample at a high equilibration temperature: the so-called Full Evaporation Technique (FET). The capability of this method was evaluated on a mixture of nine solvents, which belong to Class 3 in the classification of the European Pharmacopoeia Agency for residual solvents, at various levels of concentration: ethanol, acetone, 2-propanol, methyl acetate, 2-butanone, ethyl acetate, tetrahydrofuran, 2-methyl-1-propanol, 1-butanol. Data on linearity, accuracy, precision and sensitivity are reported. Use of an internal standard proved to be necessary when using such a method. The method is then successfully applied to the analysis of solvent traces in permethylated beta-cyclodextrin.