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关键词： discrete cosine transforms   Gaussian distributions   image analysis   image coding   probability statistics  

摘要： Over the past two decades, there have been various studies on the distributions of the DCT coefficients for images. However, they have concentrated only on fitting the empirical data from some standard pictures with a variety of well-known statistical distributions, and then comparing their goodness-of-fit. The Laplacian distribution is the dominant choice balancing simplicity of the model and fidelity to the empirical data. Yet, to the best of our knowledge, there has been no mathematical justification as to what gives rise to this distribution. In this paper, we offer a rigorous mathematical analysis using a doubly stochastic model of the images, which not only provides the theoretical explanations necessary, but also leads to insights about various other observations from the literature. This model also allows us to investigate how certain changes in the image statistics could affect the DCT coefficient distributions.

关键词： action potential duration   atrial fibrillation   ion channels   rate adaptation   regional heterogeneity   mathematical model   INDUCED HEART-FAILURE   OUTWARD CURRENT   VENTRICULAR MYOCYTES   FIBRILLATION   MODEL   MECHANISMS   REPOLARIZATION   CELL   REFRACTORINESS   RECONSTRUCTION  

摘要： Dogs have been used extensively to study atrial arrhythmias, but there are no published mathematical models of the canine atrial action potential (AP). To obtain insights into the ionic mechanisms governing canine atrial AP properties, we incorporated formulations of K+, Na+, Ca2+, and Cl- currents, based on measurements in canine atrial myocytes, into a mathematical model of the AP. The rate-dependent behavior of model APs corresponded to experimental measurements and pointed to a central role for L-type Ca2+ current inactivation in rate adaptation. Incorporating previously described regional ionic current variations into the model largely reproduced AP forms characteristic of the corresponding right atrial regions (appendage, pectinate muscle, crista terminalis, and atrioventricular ring). When ionic alterations induced by tachycardia-dependent remodeling were incorporated, the model reproduced qualitatively the AP features constituting the cellular substrate for atrial fibrillation. We conclude that this ionic model of the canine atrial AP agrees well with experimental measurements and gives potential insights into mechanisms underlying functionally important electrophysiological phenomena in canine atrium.

关键词： 生产设备   经济寿命年限   数学分析   经济曲线  

关键词： 导数   递归数列   近似解   数列极限   应用   方程求解   数学分析   高等数学  

摘要： 本文给出导数在一类数列极限及一类方程近似解的求法中的具体应用

关键词： 数学分析   积分不等式   证明方法   定积分定义   连续函数性质   二重积分   函数凸性  

关键词： 电迁移   金属化   可靠性   数学分析   失效机理   VLSI  

摘要： 针对金属化电迁移 ,进行了失效机理与工艺相关性的研究 ;确定了金属晶粒尺寸与金属化可靠性之间存在着直接关系 .金属平均晶粒直径与金属电迁移寿命受金属化溅射工艺条件的影响完全一致 .提出了平均晶粒直径作为能够表征金属化可靠性的特征工艺参数的概念和金属化可靠性在线评价方法 .

关键词： 产状   数学分析   地质构造  

摘要： 通过对地质构造的系统研究 ,可用数学解析的办法 ,分别求出不同条件下的地质构造面或构造线的产状。只要对所归纳的四类地质构造产状求解灵活掌握 ,配合使用 。

关键词： 单调函数   不等式   辅助函数   证明方法   构造方法   函数单调性   数学分析  

摘要： 阐述了利用函数的单调性证明不等式时，构造辅助函数的几种方法．

关键词： 复合函数   数学性质   数学分析   可积性   周期函数  

关键词： 数学分析   考试   改革   素质教育