A CALPHAD-type Young's modulus database of Ti-rich Ti–Nb–Zr–Mo system

Accurate Young's modulus is the necessity for the design of biomedical Ti alloys. A combinatorial method of the diffusion couple, nanoindentation, electron probe microanalysis (EPMA), and CALculation of PHAse Diagrams (CALPHAD) techniques has been utilized to construct the Young's modulus database of Ti alloys with various compositions in the present work. Two groups of body-centered cubic (bcc) Ti–Nb–Zr–Mo quaternary diffusion couples annealed at 1273 K for 25 h were experimentally prepared. Subsequently, the composition-dependent mechanical properties in the wide compositional range of Ti-based alloys were obtained by using EPMA and nanoindentation probes. Finally, on the basis of the measured Young's moduli in the present and previous work and the modeling parameters of Young's modulus of Ti–Nb–Zr system, the Young's modulus database of bcc Ti–Nb–Zr–Mo system was established through the CALPHAD approach. The CALPHAD-type database of bcc Ti–Nb–Zr–Mo system can provide the accurate Young's moduli of Ti alloys with wide compositions.     

Kinetics of volume expansion during infusion of Ringer’s solution based on two volume model

In this work mathematical models were developed to represent the kinetics of volume changes of fluid spaces associated with infusion of Ringer’s solution. During infusion of Ringer’s solution, the human body is assumed to be characterized by the two-fluid space model which has second volume space in addition to the first volume so that fluid exchanges between these two spaces are possible. Various infusion types were tested to accommodate different medical situations. Volunteers were given Ringer’s solution and the changes in blood hemoglobin were detected. From the comparison with experimental data, the two-fluid space model was found to represent adequately the kinetics of human volume expansion during infusion of Ringer’s solution.     

A conservative discontinuous Galerkin scheme for the 2D incompressible Navier–Stokes equations

In this paper we consider a conservative discretization of the two-dimensional incompressible Navier–Stokes equations. We propose an extension of Arakawa’s classical finite difference scheme for fluid flow in the vorticity–stream function formulation to a high order discontinuous Galerkin approximation. In addition, we show numerical simulations that demonstrate the accuracy of the scheme and verify the conservation properties, which are essential for long time integration. Furthermore, we discuss the massively parallel implementation on graphic processing units.     

Recommending suitable learning scenarios according to learners’ preferences: An improved swarm based approach

The paper presents a new approach for recommending suitable learning paths for different learners groups. Selection of the learning path is considered as recommendations to choosing and combining the sequences of learning objects (LOs) according to learners’ preferences. Learning path can be selected by applying artificial intelligence techniques, e.g. a swarm intelligence model. If we modify and/or change some LOs in the learning path, we should rearrange the alignment of new and old LOs and reallocate pheromones to achieve effective learning recommendations. To solve this problem, a new method based on the ant colony optimisation algorithm and adaptation of the solution to the changing optimum is proposed. A simulation process with a dynamic change of learning paths when new LOs are inserted was chosen to verify the method proposed. The paper contributes with the following new developments: (1) an approach of dynamic learning paths selection based on swarm intelligence, and (2) a modified ant colony optimisation algorithm for learning paths selection. The elaborated approach effectively assist learners by helping them to reach most suitable LOs according to their preferences, and tutors – by helping them to monitor, refine, and improve e-learning modules and courses according to the learners’ behaviour.     

广义KDV-MKDV方程的精确解

利用直接积分方法将广义KDV-MKDV方程化为一阶变系数非线性常微分方程组,然后用待定系数法确定相应的常数获得了广义KDV-MKDV方程新的精确解;利用先作假设变换后选取试探函数的方法来直接构造广义KDV-MKDV方程新的精确解.     

Zipf定律在划定经济区域内的实证研究——以长江三角洲经济区为例

国外关于Zipf定律的实证研究的区域空间多采用国家层次,而国内关于Zipf定律的实证研究则涉及国家、跨省的经济区及行政省的不同层次,于是这就有可能存在经济区域空间划定是否合理的问题。现以长江三角洲地区为例,通过修正的引力模型计算城市之间的经济联系强度及潜能,以此进行长江三角洲经济区域的空间划定,并在划定的经济区域内进行Zipf定律的实证研究,以验证经济区域空间划定是否合理。研究结果显示了经济区域空间划定的合理性。     

高维力学系统的能量方程

在低维系统中,能量方程因其明晰的物理意义而得到广泛的应用,而研究高维力学系统的能量方程也同样具有理论价值和实际意义,如位移对时间的导数是速度,速度对时间的导数是加速度,这些具有明显的物理意义,而加速度的导数其物理意义就不是很清晰了,但具有理论上的意义.本文应用广义经典力学中关于广义拉格朗日函数、广义动量和广义哈密顿函数等概念,推导了高维系统的能量方程,文中举了实例具体说明新方程的应用,为力学数学系统能量方程的推广提供了一种途经.     

广义分布式天线系统上行分集性能分析

针对广泛存在于无线通信环境中的阴影效应对系统性能影响非常大的问题,采用与传统的微分集技术相比,能够有效地对抗这种阴影衰落的分布式天线技术来解决这个问题.为了获得该条件下系统的理论性能,分析了采用最大比合并和相干等增益合并分集的广义分布式天线系统.借助lognormal近似法,给出了其中断概率和误码率性能的高精度解析结果.分析表明,在存在阴影衰落的情况下,这种广义分布式天线系统能够同时获得较大的微/宏分集增益,非常适合未来的无线小区环境.     

可信性空间上基于复模糊变量的学习理论的关键定理

给出了可信性测度空间上复模糊变量定义及一些性质;给出了复模糊变量的经验风险泛函、期望风险泛函以及经验风险最小化原则严格一致收敛的定义。在此基础上给出并证明了基于复模糊变量的学习理论的关键定理,为系统建立可信性空间上的复统计学习理论奠定了理论基础。     

浅谈解的存在唯一性定理在《偏微分方程数值解》中的应用

从一个新的角度讨论常微分方程中解的存在唯一性定理在偏微分方程数值解法中的重要应用。给出一类伪双曲型偏微分方程的新的分裂混合有限元数值格式,将该格式转化成常微分方程系统,利用解的存在唯一性定理证明该系统是存在唯一解的。通过简短的讨论、概述明确解的存在唯一定理在偏微分方程数值解中的应用方法．并希望能够在教学科研未来的发展中有新的观念。