KdV方程的显式精确解

将非线性方程的解表示成修正的三角函数的有限级数 ,从而将非线性方程的求解问题转化为代数方程求解问题 ,借助 Mathematica软件 ,采用修正的三角函数法和吴文俊消元法 ,得到了 Kd V方程的多组显式精确解 .     

与给定切线多边形相切的三角样条曲线

用三角样条论述与给定切线多边形相切的曲线,所得曲线是G3连续、保形的,通过切点的调节参数λi可调配曲线的形状.此方法与与传统的Bezier方法、B样条方法相比,所构造的曲线具有光滑性好,以及所需额外信息更少,逼近性好等优点.最后,通过实例加以比较说明.图6,参6.     

DENOISING AND HARMONIC DETECTION USING NONORTHOGONAL WAVELET PACKETS IN INDUSTRIAL APPLICATIONS

New industrial applications call for new methods and new ideas in signal analysis. Wavelet packets are new tools in industrial applications and they have just recently appeared in projects and patents. In training neural networks, for the sake of dimensionality and of ratio of time, compact information is needed. This paper deals with simultaneous noise suppression and signal compression of quasi-harmonic signals. A quasi-harmonic signal is a signal with one dominant harmonic and some more sub harmonics in superposition. Such signals often occur in rail vehicle systems, in which noisy signals are present. Typically, they are signals which come from rail overhead power lines and are generated by intermodulation phenomena and radio interferences. An important task is to monitor and recognize them. This paper proposes an algorithm to differentiate discrete signals from their noisy observations using a library of nonorthonormal bases. The algorithm combines the shrinkage technique and techniques in regression analysis using Shannon Entropy function and Cross Entropy function to select the best discernable bases. Cosine and sine wavelet bases in wavelet packets are used. The algorithm is totally general and can be used in many industrial applications. The effectiveness of the proposed method consists of using as few as possible samples of the measured signal and in the meantime highlighting the difference between the noise and the desired signal. The problem is a difficult one, but well posed. In fact, compression reduces the level of the measured noise and undesired signals but introduces the well known compression noise. The goal is to extract a coherent signal from the measured signal which will be “well represented” by suitable waveforms and a noisy signal or incoherent signal which cannot be “compressed well” by the waveforms. Recursive residual iterations with cosine and sine bases allow the extraction of elements of the required signal and the noise. The algorithm that has been developed is utilized as a filter to extract features for training neural networks. It is currently integrated in the inferential modelling platform of the unit for Advanced Control and Simulation Solutions within ABB’s industry division. An application using real measured data from an electrical railway line is presented to illustrate and analyze the effectiveness of the proposed method. Another industrial application in fault detection, in which coherent and incoherent signals are univocally visible, is also shown.     

在Hlder度量下一类三角插值多项式的逼近

研究了在Hlder度量下,一类三角插值多项式的逼近和饱和问题,确定了饱和类和饱和阶。     

高职校园数字化测量控制网构建方法的研究

构建测量实训课程使用的数字化控制网,应明确控制网的用途,有针对性的建设。根据实训项目对控制网进行分级与规划设计,埋设并标记控制点,并对控制点的坐标进行采集,最后建立完整的数据库。     

关于余弦的一个含参双边不等式及其应用

借助于多项式判别系统和maple数学软件,建立了关于余弦的一个含参双边不等式及含参三角函数不等式链,由此得到两条关于Seiffert平均的不等式链,并给出杨乐不等式的一个拓广.     

CORDIC算法的优化及实现

为提高坐标旋转数字计算(CORDIC)算法的精度并降低硬件资源消耗,对CORDIC算法收敛性以及旋转序列的选取进行了研究.针对圆周系统下CORDIC算法的角度覆盖范围、硬件资源和运算精度等问题提出了进一步的优化措施.利用经过优化后的CORDIC算法,在FPGA中实现了流水线结构的正余弦函数和反正切函数,并把运算精度与硬件资源消耗与Xilinx IP核进行了比较.比较结果表明该优化算法在提高运算精度的同时能够有效降低硬件资源消耗.      

高考三角函数题型探析

三角函数的图象与性质、三角恒等变换和解三角形问题都是高考数学三角函数部分主要考查对象,考生如何把握命题意图与考点,找到突破方法技巧,获得正确的结论,笔者结合自己的教学经验和学生的实际情况提出一些自己的观点.     

组合箱梁调平层裂缝防治技术

介绍了高速公路桥梁建设中组合箱梁调平层裂缝的情况,针对调平层裂缝产生的原因,提出了调平层裂缝防治措施和处理方法。