How to impose physically coherent initial conditions to a fractional system?

In this paper, it is shown that neither Riemann–Liouville nor Caputo definitions for fractional differentiation can be used to take into account initial conditions in a convenient way from a physical point of view. This demonstration is done on a counter-example. Then the paper proposes a representation for fractional order systems that lead to a physically coherent initialization for the considered systems. This representation involves a classical linear integer system and a system described by a parabolic equation. It is thus also shown that fractional order systems are halfway between these two classes of systems, and are particularly suited for diffusion phenomena modelling.     

Synthesis of GaN nanospindles via a facile solid-state reaction route

Gallium nitride (GaN) nanospindles have been synthesized via a solid-state reaction at a low-temperature condition. X-ray powder diffraction (XRD), Raman spectrum and high-resolution transmission electron microscopy (HRTEM) revealed that the synthesized GaN crystallized in a hexagonal structure and displaying spindly particles morphology has an average diameter of 100 nm and length of 400 nm X-ray photoelectron spectroscopy (XPS) of the sample gave the atomic ratio of Ga and N of 1.04:1. Room-temperature photoluminescence (PL) spectrum showed that the as-prepared product had a peak emission at 372 nm. The possible formation mechanism of the wurtzite GaN is briefly discussed.     

Nanostructured Ni/Ti_3C_2T_x MXene hybrid as cathode for lithium-oxygen battery

Ti_3C_2 belongs to MXenes family,which is a new two-dimensional material and has been applied in many fields.With simple method of hydrothermal and high temperature calcination,nano structured Ni/Ti_3C_2T_x hybrid was synthesized.The stable layer structure of Ti_3C_2 MXene providing high surface area as well as excellent electronic conductivity are beneficial for deposition and decomposition of discharge product Li_2O_2.Furthermore,possessing special catalytic activity,Ni nanoparticles with size of about 20 nm could accelerate Li_2O_2 breaking down.Taking advantage of two kinds of materials,Ni/Ti_3C_2T_x hybrid as cathode of Li-O_2 battery can achieve a maximal specific capacity of 20,264 mAh/g in 100 mA/g and 10,699 mAh/g in 500 mA/g at the first cycle.This work confirms that the prepared Ni/Ti_3C_2T_x hybrid exhibiting better cycling stability points out a new guideline to improve the electrochemical performance of lithium-oxygen batteries.     

The first synthesis of a water-soluble α-cyclodextrin/C60 supramolecular complex using anionic C60 as a building block

A novel supramolecular inclusion complex of α-CD/C₆₀ was synthesized using anionic C₆₀. The reaction progress was monitored in situ by visible and near-IR spectroscopy. The obtained complex was characterized by UV-vis, ¹³C NMR, MALDI-TOF, and cyclic voltammetry. The induction and dispersion forces are considered to be the major driving forces for the formation of a resulting α-CD/ inclusion complex.     

用于检测多硫化氢和亚硝酰氢的小分子荧光探针

多硫化氢（H₂S_n）和亚硝酰氢（HNO）在一系列生理病理过程中起着重要的作用,包括调节细胞内氧化还原信号传递过程、增强心肌的收缩能力、抑制血小板聚集等。H₂S_n可以通过硫化氢（H₂S）与活性氧物种反应得到。一氧化氮（NO）和HNO可以在超氧化物歧化酶（SOD）作用下相互转化,H₂S和NO反应可以生成H₂S_n和HNO,调控酶的活性以及蛋白与蛋白之间的相互作用,从而影响蛋白质的生理功能。因此,实时检测生物体内H₂S_n和HNO的浓度具有十分重要的生物医学意义。在各种生物检测技术中,荧光探针具有选择性好,灵敏度高,可以实时原位检测,对样品损伤小等优点,受到了广泛关注。本文将按照探针响应基团的反应类型,将近几年用于定性定量检测H₂S_n和HNO荧光探针进行分类和总结,重点概述探针的设计理念、响应机制和生物应用,并对探针的应用前景进行了展望。同时,本文也关注了硫化氢和其他硫烷硫类物种荧光检测的近期进展。     

噻唑烷类配体的手性结构及其在催化苯乙酮不对称硅氢化反应中的应用研究

用分级结晶或柱层析方法对2-(2-吡啶基)-4-羧甲基-1,3-噻唑烷(A)及2-甲基-2-(2-吡啶基)-4-羧甲基-1,3-噻唑烷(B)两种手性配体进行提纯,分别考察了其与[Rh(COD)Cl]₂制备的在位催化剂催化苯乙酮的不对称硅氢化反应,发现只有噻唑烷环上的C4位手性中心对催化反应结果有影响,其C2位手性中心在Rh(1)催化下发生了快速差向异构化反应.     

Optimal internal pricing and capacity planning for service facility with finite buffer

An economic model is developed for exploring optimal internal pricing and capacity planning for service facility with finite buffer capacity. Because of the limited buffer capacity, jobs finding the system full upon their arrival would be rejected. Such rejections create a gap between the value collectively perceived by users and the actual achievement of the organizational value. This gap, called a loss externality, has never been studied before and plays an important role for designing optimal pricing scheme. In general, the underlying economic structure may involve multiple equilibria and it is unclear whether or not the system can be controlled through internal pricing. In this regard, a sufficient condition is given under which the system administrator can find two separate prices for accepted and rejected users at any demand level to be desired so that the desired demand level becomes the unique equilibrium of the system. For a short-run problem, it is shown that the optimal pricing scheme can be expressed as the sum of the congestion and the loss externalities. For a long-run problem, the optimal pricing scheme is expressed in a unified manner so that a structural relationship between the short-run problem and the long-run problem at optimality can be readily observed. A necessary and sufficient condition is also given for the marginal capacity pricing to be optimal, i.e., the optimal long-run pricing consists of the marginal cost for processing capacity and the marginal cost for buffer capacity without involving any externality at all.     

与Faa di Bruno公式相关的一些奇异恒等式

文[1]用Faa di Bruno公式找到了一些关于分拆集上求和奇异的恒等式,本文利用类似的方法找到了另外的一些奇异恒等式,并且利用Lagrange公演公式得到一个论。     

Controllable dissipative soliton and Q-switched pulse emission in a normal dispersion fiber laser using SESAM and cavity loss tuning mechanism

We report on the controllable generation of the dissipative soliton and the Q-switched pulse in a normal dispersion fiber ring laser. The hybrid saturable absorber is used to obtain the dissipative soliton or the Q-switched pulse by slightly adjusting the polarization controller. Based on the experimental results and theoretical analysis, the controllable dissipative soliton and Q-switched pulse emission can be induced by the cavity loss tuning mechanism of the fiber laser.     

任意形状光栅皱阶光波导的分布反馈耦合系数

根据转移矩阵理论,在弱周期结构近似下获得了任意形状光栅皱阶光波导的TE模分布反馈耦合系数的计算公式,同时给出了几种典型的周期型皱阶光波导耦合系数的简洁解析表达式。