广义e-ω-凹算子的不动点及其应用

给出广义e-ω-凹算子的定义,在假设算子A不是锥映射的前提下,得到了广义e-ω-凹算子的不动点的存在唯一性以及单调迭代列.最后,将主要结果应用到一类Hammerstein型积分方程中去.     

多重时滞富营养化生态模型的稳定性与分支分析

本文研究了多重时滞富营养化生态模型的稳定性与分支问题.利用特征值方法,分别研究了具有单时滞和双时滞模型的线性稳定性.发现当模型中的时滞经过一系列临界值时,模型在平衡点附近经历了Hopf分支和Hopf-zero分支,并给出Hopf分支和Hopf-zero分支存在的充分条件.最后数值模拟验证了理论结果.     

儿童额叶癫痫临床和长程视频脑电图特征

目的通过对46例儿童额叶癫痫患儿的临床表现、长程视频脑电图（VEEG）特点进行分析,提高对儿童额叶癫痫的认识。方法收集2008年12月至2014年8月儿科门诊及住院确诊的46例儿童额叶癫痫病例的资料,回顾性分析其临床表现、VEEG及神经影像学等特征。结果本组患儿发病年龄最小11个月,最大15岁。46例患儿共监测到临床发作258次,明确临床发作34例,14.7%仅于清醒期发作,61.8%仅在睡眠期发作,23.5%在清醒、睡眠中均有发作;临床发作形式包括额叶失神、局部阵挛发作、偏转性强直、姿势性强直、过度运动性自动症、口咽自动症、发声、发笑发作、临床下放电和自主神经性发作等。73.9%患儿记录到发作间期额叶为主的癫痫样放电,63.0%患儿记录到发作期额叶为主的癫痫样放电。结论儿童额叶癫痫临床发作频繁、短暂,以睡眠期发作为主,临床表现复杂多样,易漏诊;长程VEEG可监测到儿童额叶癫痫发作期临床及异常脑电图表现,可提供明确诊断率。     

Symmetry breaking of an elliptic equation in expanding annuli

We obtain non-radial bifurcation from radial solutions of a semilinear elliptic equation in expanding annuli of \(\mathbb {R}^N\). To obtain the main results, we use a blow-up argument via the Morse index of the regular entire solutions of the equation

$$\begin{aligned} -\Delta u=\lambda u^p \quad \text {in}\quad \mathbb {R}^N. \end{aligned}$$

(0.1)

The main results of this paper can be seen as applications of the properties of regular entire solutions of (0.1).

     

Switchable [3+2] and [4+2] Heteroannulation of Primary Propargylamines with Isonitriles to Imidazoles and 1,6‐Dihydropyrimidines: Catalyst Loading Enabled Reaction Divergence

Isonitrile 1 due to its carbene‐like reactivity serves generally as a one‐carbon synthon in a diverse set of organic transformations. We report in this article that the isocyano group can also act as a polarized triple bond to undergo, as a two‐atom synthon, heteroannulation with primary propargylamines 15 . In addition, we serendipitously discovered that the reaction pathways can be modulated by simply changing the catalyst loading. In the presence of 0.1 equiv of Yb(OTf)₃ or TfOH, the reaction between 1 and 15 afforded exclusively imidazoles 16 by a formal [3+2] cycloaddition. At a higher catalyst loading (Yb(OTf)₃ (0.4 equiv) or TfOH (0.5 equiv)) under otherwise identical conditions, the same reaction furnished 1,6‐dihydropyrimidines 17 in good to excellent yields by way of a formal [4+2] cycloaddition process. Mechanistic investigations indicated that both annulations went through an amidine intermediate resulting from the insertion of the isocyano group to the NH bond of the primary amine. Subsequent catalyst‐loading‐dependent 5‐exo‐dig or 6‐endo‐dig cyclization provided selectively the two heterocycles, respectively.     

Existence of solutions for an anisotropic elliptic problem with variable exponent and singularity

In this paper, we study the following anisotropic problem with singularity: where is a bounded domain with smooth boundary. Using the critical point theory, we obtain the existence of weak solutions for the problem under suitable conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

冰的熔解热实验装置的改进

将保温杯引入到测定冰熔解热的实验中,提高了实验装置的保温性能;利用马达和风扇自制了搅拌装置,保证了搅拌均匀性;利用单片机、传感器模块和液晶屏实现了温度数显功能,提高了实验精度.通过对比改进前后的实验装置的实验数据可知,改进后的实验装置有效地减小了实验误差.