The mean value theorem for derivatives says that for a given function over a closed and bounded interval, there is a point <em>P</em> on the graph such that the tangent at <em>P</em> is paralle...The mean value theorem for derivatives says that for a given function over a closed and bounded interval, there is a point <em>P</em> on the graph such that the tangent at <em>P</em> is parallel to the secant through the two endpoints. The mean value theorem for definite integrals says that the area under the function is equal to the area of a rectangle whose base is the length of the interval and height of some point <em>Q</em> on the graph. These two theorems have been studied and utilized extensively and they form the backbone of many important theorems in different branches of mathematics. In this note, we pose the question: for what functions do the two points <em>P </em>and <em>Q</em> always coincide? We find that the only analytic functions satisfying this condition are linear or exponential functions.展开更多
为了便捷求出垂荡式波浪能发电装置垂荡浮子的平均功率,对现有的设计计算方法进行了研究。基于波浪理论和Froude-Krylov假定法求解波浪力,应用单自由度有阻尼系统受迫振动理论,将波浪激励力作为对垂荡浮体的输入动力,将发电机的电磁阻...为了便捷求出垂荡式波浪能发电装置垂荡浮子的平均功率,对现有的设计计算方法进行了研究。基于波浪理论和Froude-Krylov假定法求解波浪力,应用单自由度有阻尼系统受迫振动理论,将波浪激励力作为对垂荡浮体的输入动力,将发电机的电磁阻力作为主要的阻尼力,建立了质量-弹簧-阻尼振动力学模型,确定了垂荡浮子响应的计算方法,并对实际波浪能发电装置垂荡浮子Power Take Off(PTO)系统列举出计算实例。在算例基础上,对假设条件进行了扩展,应用频率响应曲线、MATLAB软件做出不同参数条件下平均功率三维曲线和输出平均功率数值表,清晰地表明了系统响应状况。研究显示,在波高和频率比一定的条件下,PTO系统平均机械功率随着浮体质量和阻尼力矩的变化具有峰值,围绕峰值区域设计装置的各项参数,能够取得较理想的效果。该建模与计算方法可为实际工程优化设计提供参考。展开更多
The non-local means (NLM) denoising method replaces each pixel by the weighted average of pixels with the sur-rounding neighborhoods. In this paper we employ a cosine weighting function instead of the original exponen...The non-local means (NLM) denoising method replaces each pixel by the weighted average of pixels with the sur-rounding neighborhoods. In this paper we employ a cosine weighting function instead of the original exponential func-tion to improve the efficiency of the NLM denoising method. The cosine function outperforms in the high level noise more than low level noise. To increase the performance more in the low level noise we calculate the neighborhood si-milarity weights in a lower-dimensional subspace using singular value decomposition (SVD). Experimental compari-sons between the proposed modifications against the original NLM algorithm demonstrate its superior denoising per-formance in terms of peak signal to noise ratio (PSNR) and histogram, using various test images corrupted by additive white Gaussian noise (AWGN).展开更多
文摘The mean value theorem for derivatives says that for a given function over a closed and bounded interval, there is a point <em>P</em> on the graph such that the tangent at <em>P</em> is parallel to the secant through the two endpoints. The mean value theorem for definite integrals says that the area under the function is equal to the area of a rectangle whose base is the length of the interval and height of some point <em>Q</em> on the graph. These two theorems have been studied and utilized extensively and they form the backbone of many important theorems in different branches of mathematics. In this note, we pose the question: for what functions do the two points <em>P </em>and <em>Q</em> always coincide? We find that the only analytic functions satisfying this condition are linear or exponential functions.
文摘为了便捷求出垂荡式波浪能发电装置垂荡浮子的平均功率,对现有的设计计算方法进行了研究。基于波浪理论和Froude-Krylov假定法求解波浪力,应用单自由度有阻尼系统受迫振动理论,将波浪激励力作为对垂荡浮体的输入动力,将发电机的电磁阻力作为主要的阻尼力,建立了质量-弹簧-阻尼振动力学模型,确定了垂荡浮子响应的计算方法,并对实际波浪能发电装置垂荡浮子Power Take Off(PTO)系统列举出计算实例。在算例基础上,对假设条件进行了扩展,应用频率响应曲线、MATLAB软件做出不同参数条件下平均功率三维曲线和输出平均功率数值表,清晰地表明了系统响应状况。研究显示,在波高和频率比一定的条件下,PTO系统平均机械功率随着浮体质量和阻尼力矩的变化具有峰值,围绕峰值区域设计装置的各项参数,能够取得较理想的效果。该建模与计算方法可为实际工程优化设计提供参考。
文摘The non-local means (NLM) denoising method replaces each pixel by the weighted average of pixels with the sur-rounding neighborhoods. In this paper we employ a cosine weighting function instead of the original exponential func-tion to improve the efficiency of the NLM denoising method. The cosine function outperforms in the high level noise more than low level noise. To increase the performance more in the low level noise we calculate the neighborhood si-milarity weights in a lower-dimensional subspace using singular value decomposition (SVD). Experimental compari-sons between the proposed modifications against the original NLM algorithm demonstrate its superior denoising per-formance in terms of peak signal to noise ratio (PSNR) and histogram, using various test images corrupted by additive white Gaussian noise (AWGN).
