碳纳米管增强型复合材料功能梯度板的自由振动模型与尺度效应

基于一种新的各向异性修正偶应力理论，建立了碳纳米管增强复合材料功能梯度板的自由振动模型。该模型能够描述尺度效应，且仅包含一个尺度参数。基于一阶剪切变形理论和哈密顿原理推演了板的运动微分方程，并以四边简支板为例给出了自振频率的解析解。讨论了板的几何尺寸、碳纳米管体分比含量和分布方式等因素对板的自振频率的影响。结果表明，本文模型所预测的板的自振基频总是高于经典弹性理论的Mindlin板模型的预测结果，两者间的差异在板的几何尺寸接近尺度参数的值时非常明显，且会随着板的几何尺寸的增大而逐渐消失。     

Occupation times for the finite buffer fluid queue with phase-type ON-times

In this short communication we study a fluid queue with a finite buffer. The performance measure we are interested in is the occupation time over a finite time period, i.e., the fraction of time the workload process is below some fixed target level. Using an alternating renewal sequence, we determine the double transform of the occupation time; the occupation time for the finite buffer M/G/1 queue with phase-type jumps follows as a limiting case.     

Time allocated to mathematics in post-primary schools in Ireland: are we in double trouble?

Mathematics educators and legislators worldwide have begun placing a greater emphasis on teaching mathematics for understanding and through the use of real-life applications. Revised curricula have led to the time allocated to mathematics in effected countries being scrutinised. This has resulted in policy-makers and educationalists worldwide calling for the inclusion of double class periods on the mathematics timetable. Research from the United States suggests that the introduction of double or block periods allow for the objectives of revised curricula to be realized. The aim of this study, which is set in the school context, is first to ascertain if schools in Ireland are scheduling double periods for mathematics at both lower post-primary level (Junior Cycle) and upper post-primary level (Senior Cycle). It also seeks to determine if there is a link between teachers’ levels of satisfaction with the time allocated to mathematics and the provision of double periods and to get insights from teachers in relation to their opinions on what can be achieved through the introduction of such classes. Questionnaires were sent to 400 post-primary schools (approximately 1600 teachers) which were selected using stratified sampling techniques. It was found that 8.7% of mathematics teachers reported the provision of double periods at Junior Cycle while 55% reported that double periods were included on their timetable at Senior Cycle. The study also identified a link between teachers’ levels of satisfaction with the time allocated to mathematics and the provision of double periods. Finally, teachers felt that double periods allowed for new teaching methodologies, which were promoted by the revised curricula, to be implemented and teaching for understanding was also more feasible. In essence, it was found that double periods have an influence on the mathematical experience of post-primary students as well as the teaching approaches employed.     

Approximating total weighted completion time on identical parallel machines with precedence constraints and release dates

We present a $(2+2ln2+\epsilon )$-approximation algorithm for the classical nonpreemptive scheduling problem to minimize the total weighted completion time of jobs on identical parallel machines subject to release dates and precedence constraints, improving upon the previously best known 4-approximation algorithm from 1998. The result carries over to the more general problem with precedence delays and generalizes a recent result by Li (2017) for the problem without release dates or delays.     

单发太赫兹时域光谱技术

太赫兹时域光谱技术(THz-TDS)广泛应用于材料、生物医学、化学、药学、安检等诸多领域。传统扫描式THz-TDS技术需要通过改变探测光延时逐点扫描并重构时域信号，仅适合于具有较高重复频率且稳定的太赫兹辐射源情形下的样品探测。在低重复频率或涨落较大的太赫兹辐射源情形下和不可逆过程中样品的探测，扫描式THz-TDS不再适用，需要使用单发THz-TDS技术，单发THz-TDS技术原则上仅需要一个激光脉冲就可以获取一个完整的太赫兹时域脉冲波形。介绍几种主要的单发THz-TDS探测技术，这些技术都利用了电光晶体的泡克尔斯效应，通过测量探测光的某个物理量的变化来提取太赫兹信号。根据探测方法不同可分为光谱编码、空间编码和互相关等技术。在光谱编码技术中，探测光不同频率成分在时间上发生分离，不同时间成分分别被太赫兹脉冲不同时刻电场调制，通过测量探测光各个频率被太赫兹脉冲调制前后的光谱的变化提取太赫兹脉冲波形。该方法光路简单，测量结果直观，有较高的信噪比，但其时间分辨率较低，且被测太赫兹信号容易产生失真。为提高被测信号的时间分辨率，有人提出了空间编码技术，即不同位置探测光分别被太赫兹脉冲不同时刻电场调制，通过测量探测光各个位置太赫兹脉冲调制前后的光强变化提取太赫兹脉冲波形。根据不同空间展开方法可分为一维空间编码技术和二维空间编码技术。空间编码技术中虽然有较高的时间分辨率，但由于探测光在空间展开能量分散使得其信噪比相对较低。此外，还有一种较高时间分辨率的技术即互相关技术，可分为共线互相关和非共线互相关技术。在非共线互相关技术中，被太赫兹脉冲调制的激光啁啾脉冲与短脉冲互相关作用产生二次谐波，通过太赫兹脉冲调制前后二次谐波空间分布变化来提取太赫兹信号；在共线互相关技术中被太赫兹脉冲调制的啁啾脉冲与短脉冲共线入射到光谱仪，通过干涉条纹提取太赫兹信号，该技术提高了时间分辨率和信噪比，但光路布置复杂，不能进行实时监测。回顾了这几种单发THz-TDS探测技术的发展历程，综述探测技术的原理、实验方案和测量结果，并讨论了这些探测技术的优势和不足。     

Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

Nonexistence of nontrivial global solutions for nonlocal in time differential inequalities

In this paper, some nonlocal in time differential inequalities of Sobolev type are considered. Using the nonlinear capacity method, sufficient conditions for the nonexistence of nontrivial global classical solutions are provided.     

Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.     

Molecular Design Tactics for Highly Efficient Thermally Activated Delayed Fluorescence Emitters for Organic Light Emitting Diodes

Recently, pure organic thermally activated delayed fluorescence (TADF) emitters have attracted considerable interest from the scientific community in the field of organic light emitting diodes (OLEDs) as they can theoretically realize 100 % of the internal quantum efficiency by exploiting both the singlet and triplet excitons via the reverse intersystem crossing enabled by small singlet‐triplet energy splitting. Currently, the external quantum efficiency of the TADF emitters is reaching the level of phosphorescent emitters. Therefore, the TADF approach is considered as a potential alternative to the low efficiency conventional fluorescent and expensive phosphorescent emitters. In this account, we summarized our recent development of blue and green TADF molecular designs to improve the device performances of the TADF devices.