查询词典 logarithm

The rational points of an elliptic curve forms an additive group. The discrete logarithm problem of this group is called elliptic curve discrete logarithm problem.

椭圆曲线上的有理点会形成一个加法群，此加法群上的离散对数问题称为椭圆曲线离散对数问题(elliptic curve discrete logarithm problem)。

For example, 10 3 = 1,000; therefore, log 10 1,000 = 3. The kinds most often used are the common logarithm and the natural logarithm.

如，10 3=1，000；于是log 101，000=3。通常使用的有常用对数和自然对数

Returns the common logarithm (base-10 logarithm) of x .

返回 x 的通用对数（以10为对数）。

In the first chapter , we consider the law of iterated logarithm with finite partial sum. Under certain condition ,we extend the law of iterated logarithm with finite partial sum for the Wiener process to Gaussian process ; In addition, we apply the law of iterated logarithm of Chung to the finite partial sum condition.

第一章考虑有限项部分和的重对数律，在一定条件下，将 Wiener过程下有限项部分和的重对数律推广到高斯过程中，得到高斯过程下的有限项部分和的重对数律；另外，将Chung氏重对数律进一步推广到有限项部分和的情形下。

Of a logarithm, the non-negative fractional part of the represent ation of a logarithm.

对于对数而言，一个对数表示式中的非负的小数部分。

This paper will mainly discuss the Law of Iterated Logarithm for some kind weighted partial sum. It is an extension of "the Law of Iterated Logarithm of Kolmogorov".

本文主要讨论独立随机变量某种加权和重对数律，它是"Kolmogorov重对数律"的推广。

The Law of Iterated Logarithm for independent r.v. has been deeply discussed in all kinds of paper. We have been familiar with "the Law of Iterated Logarithm of Kolmogorov" and "the Law of Iterated Logarithm of Hartman-Wintner".

各种文献中对独立随机变量序列重对数律已有深入讨论，我们已熟知"Kolmogorov重对数律"及"Hartman-Wintner重对数律"。

Fri particular, the Wittmann-type strong law of larg numbers for independent random variables is generalized to the case of NA random variables. We also present the sufficient and necessary condition of the laws of logarithm, and we extend Teicher-type strong law of the large numbers for sequence of NA random variables. Some of the laws of iterated logarithm of Teicher-type, Egorov-type arid Wittmann-type for sequence of NA random variables are obtained. Then we investigate the rate3f ionvergcll( fbr series of NA randonl variables, we obtain soIne results fbr tl1e Iaws of theiterated logarithttl, the laws of logarithm and decreasing order fOr the tail sum.Risk itllttlysis tlleory is a sigIlifica11t part of insurance InatheInatics.

Wittmann（1985a）关于实独立随机变量列的结果，并给出了NA列强大数律成立的若干条件，特别建立了一般NA列对数律成立的充分必要条件，在二阶矩存在的条件下完整的解决了一般NA列对数律的问题，中文摘要2而已有的一些NA列对数律的结果可以由它推出，给出了NA列的Teiclier型强大数律，表明lbiChCI·（1979）给出的实独立随机变量列的强大数律可以减弱其条件等；建立厂不问分布NA列的Teicfl仪；Egorov，Petrov型有界重对数律，以及加权同分布NA列的有界重对数律，进一步推广了NA列的Kolmogory有界重对数律等，特别对NA列建立了Wittm洲型有界重对数律，而其证明方法与独立情形有很大不同，同时通过反例表明在与独立场合类似的条件下，独立列的Wittmann有界重对数律不能完美的推广到NA歹小惰形；最后研究了NA随机变量级数的收敛速度，给出了尾和下降的阶；尾和的有界重对数律，及尾和对数律成立的充要条件等，并通过反例说明 NA随机变量级数与独立随机变量级数在收敛速度方面存在的差异。

Result indicated that this model and the experimental data were inosculated. Good linear relationships were found between the natural logarithm of solution density, the logarithm of reaction duration, the reciprocal temperature and the natural logarithm of medicament concentration.

结果表明在单因素条件下，药剂质量浓度对数、反应时间的对数、反应温度的倒数与溶液中溶质的自然对数之间具有良好的线性关系，该模型可以同试验数据相吻合。

Using augmented Dickey-Fuller test, the result shows that BDI logarithm series is nonstationary but the first difference is stationary, i. e. it is integrated of order one. High-level ARCH effect was certification in the BDI logarithm series by ARCH LM test, and GARCH (1, 1) model was used to eliminate the conditional heteroscedasticity. Through variance ratio test, the result shows, that the random walk hypothesis of BDI logarithm series can be rejected and international dry bulk shipping market is inefficient.

运用ADF检验方法对BDI的对数序列进行平稳性和单整检验，结果证明BDI对数序列是一个非平稳过程，经一阶差分后是平稳过程，即BDI对数序列是一阶单整过程；通过ARCH LM检验认为BDI对数序列存在高阶ARCH效应，并用GARCH(1，1)模型消除了残差序列的条件异方差性；通过方差比检验法对国际干散货航运市场的收益率序列进行了检验，结果显示BDI的对数序列的随机游走假设被拒绝，国际干散货航运市场不是一个有效的市场。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。