Existence of Periodic Solution for Nonlinear Neutral Delay Differential Equation

利用抽象连续定理,研究了一类非线性多时滞中立型泛函微分方程周期解问题,并在滞量的不同范围内分别得到了周期解存在的充分条件,推广了相关研究的主要结论。     

Differential effects of learning games on mathematics proficiency

This study examined the effects of a learning game, [The Math App] on the mathematics proficiency of middle school students. For the study, researchers recruited 306 students, Grades 6–8, from two schools in rural southwest Virginia. Over a nine-week period, [The Math App] was deployed as an intervention for investigation. Students were assigned to game intervention treatment, and paper-and-pencil control conditions. For the game intervention condition, students learned fractions concepts by playing [The Math App]. In the analysis, students’ mathematical proficiency levels prior to the intervention were taken into account. Results indicate that students in the game intervention group showed higher mathematics proficiency than those in the paper-and-pencil group. Particularly, the significantly higher performances of intervention groups were noted among 7th graders and inclusion groups. The empirically derived results of the reported study could contribute to the field of educational video game research, which has not reached a consensus on the effects of games on students’ mathematics performance in classroom settings.     

Integrating different tracking systems in football: multiple camera semi-automatic system,local position measurement and GPS technologies

Abstract

During the past decade substantial development of computer-aided tracking technology has occurred. Therefore, we aimed to provide calibration equations to allow the interchangeability of different tracking technologies used in soccer. Eighty-two highly trained soccer players (U14–U17) were monitored during training and one match. Player activity was collected simultaneously with a semi-automatic multiple-camera (Prozone), local position measurement (LPM) technology (Inmotio) and two global positioning systems (GPSports and VX). Data were analysed with respect to three different field dimensions (small, <30 m² to full-pitch, match). Variables provided by the systems were compared, and calibration equations (linear regression models) between each system were calculated for each field dimension. Most metrics differed between the 4 systems with the magnitude of the differences dependant on both pitch size and the variable of interest. Trivial-to-small between-system differences in total distance were noted. However, high-intensity running distance (>14.4 km · h^?1) was slightly-to-moderately greater when tracked with Prozone, and accelerations, small-to-very largely greater with LPM. For most of the equations, the typical error of the estimate was of a moderate magnitude. Interchangeability of the different tracking systems is possible with the provided equations, but care is required given their moderate typical error of the estimate.     

一类带有p—Laplace算子的方程解的有界性

研究方程（Фp（x＇））＇＋λ2Фp（x）＋f（x）=e（t）的拉格朗目稳定性,其中Фp（s）=｜s｜p-2s,p≥2为常数;当x→∞时,扰动项f（x）=o（x）;e（t）为2πp周期函数,且πp=2π（p-1）1/p/psinπ/p.     

差别化的贷款利率定价模型设计及系统实现

随着经济社会的发展,银行贷款品种日益增多,如何灵活地控制每种贷款品种的利率浮动水平,以及针对每位客户科学、合理地给出贷款利率价格,具有非常重要的意义.为此,提出一种差别化的贷款利率定价模型,该模型不仅可以实现差别化的利率定价,而且可以严格控制各种贷款品种的最低及最高上浮比例.同时,在该模型中引入信用等级机制,可激励客户向优质客户转变.     

6轮ARIA的最优不可能差分分析

研究了ARIA在不可能差分分析下的安全性.通过对算法扩散层的分析,给出了ARIA中间状态在加密过程的差分传递性质.在此基础上证明了6轮ARIA不存在使得输入输出差分重量小于10的不可能差分路径,同时证明了在输入输出差分重量为10的情况下6轮ARIA只存在2类形式的不可能差分路径.利用构造出的这2类不可能差分路径,从理论上证明了6轮ARIA不可能差分攻击的最优结果为:2¹²⁰个选择明文和2^94.5次6轮加密.     

常数变易法求二阶常系数线性微分方程的特解

针对二阶常系数非齐次线性微分方程求特解的现有方法的局限性,提出常数变易法求二阶常系数非齐次线性微分方程的特解的方法．并给出四个求特解的公式。     

关于悬链线的一点注记

悬链线是微积分、微分方程、微分几何、变分计算及数值分析中的一个重要课题.本文通过一些诸如方轮自行车、旋转的最小面积等有趣的例子,计算悬链线和相应半圆下面的面积,证明悬链线到处都有,但并不是无处不在.     

二阶延迟微分方程Runge-Kutta方法的稳定性

研究二阶延迟微分方程Runge-Kutta方法的稳定性.首先,引入新变量,将二阶延迟微分方程化为一阶方程组.然后,应用Runge-Kuta 方法于一阶方程组,给出了Runge-Kutta稳定的充分条件,进而得到了二阶延迟微分方程Runge-Kutta方法稳定的充分条件.最后,通过数值试验验证所得结论的正确性.