比值判别法,设正项级数sum from n=1 to ∞ U_n之后项与前项的比值的极限等于ι,即(i)当ι【1时,级数sum from n=1 to ∞ U_n收敛;(ii)当ι】1时,级数sum from n=1 to ∞ U_n发散;(iii)当ι=1时,级数可能收敛也可能发散,所以当ι=1时此...比值判别法,设正项级数sum from n=1 to ∞ U_n之后项与前项的比值的极限等于ι,即(i)当ι【1时,级数sum from n=1 to ∞ U_n收敛;(ii)当ι】1时,级数sum from n=1 to ∞ U_n发散;(iii)当ι=1时,级数可能收敛也可能发散,所以当ι=1时此法失效,为了使比值判别法得到进一步推广,经过初步探讨,当ι=1时,如果正项级数的项单调递减,可以采用下面两种比式形式得到解决.展开更多
对级数sum from n=1 to ∞(8nbn)的收敛性可用阿贝尔、犹利克雷判别法,而对其绝对收敛性却提文甚少;本文根据比较判别法直接研究级数sum from n=1 to ∞(a_nb_n)的绝对收敛性,并得出结果,用这结果判定了些级数的敛散性显得更加有效和方...对级数sum from n=1 to ∞(8nbn)的收敛性可用阿贝尔、犹利克雷判别法,而对其绝对收敛性却提文甚少;本文根据比较判别法直接研究级数sum from n=1 to ∞(a_nb_n)的绝对收敛性,并得出结果,用这结果判定了些级数的敛散性显得更加有效和方便。 一、定理及推论 1、定理:设sum from n=1 to ∞(a_n)是一无穷级数,{bn}是一序列。【i】若序列{bn}有畀且级数sum from n=1 to ∞(a_n)绝对收敛,则级数sum from n=1 to ∞(a_nb_n)绝对收敛;若序列{1/bn)有界且sum from n=1 to ∞|a_n|发散,则sum from n=1 to ∞n|a_nb_n|发散。 证明:假设sum from n=1 to ∞(a_n)绝对收敛且{b_n}有界,则存在正数M,使得|bn|【M,因此有|a_nb_n|≤M|a_n|因为sum from n=1 to ∞M|a_n|收敛,由比较判别法知sum from n=1 to ∞(a_nb_n)绝对收敛。 设sum from n=1 to ∞|a_n|发散且{1/b_n}有界,若sum from n=1 to ∞|a_nb_n|收敛,于(i)知sum from n=1 to ∞|a_nb_n|/|bn|=sum from n=1 to ∞|a_n|收敛,与条件矛盾,故级数sum from n=1 to ∞|a_nb_n|发散。展开更多
This paper proposes the discriminant analysis on land grading after analyzing the common methods and discussing the Fisher’s discriminant in detail. Actually this method deduces the dimension from multi to single, th...This paper proposes the discriminant analysis on land grading after analyzing the common methods and discussing the Fisher’s discriminant in detail. Actually this method deduces the dimension from multi to single, thus it makes the feature vectors in n \|dimension change to a scalar, and use this scalar to classify samples. This paper illustrates the result by giving an example of the residential land grading by the discriminant analysis.展开更多
Here we use a Discriminant Genetic Algorithm Extended (DGAE) model to diagnose and predict seasonal sand and dust storm (SDS) activities occurring in Northeast Asia. The study employed the regular meteorological data,...Here we use a Discriminant Genetic Algorithm Extended (DGAE) model to diagnose and predict seasonal sand and dust storm (SDS) activities occurring in Northeast Asia. The study employed the regular meteorological data, including surface data, upper air data, and NCEP reanalysis data, collected from 1980–2006. The regional, seasonal, and annual differences of 3-D atmospheric circulation structures and SDS activities in the context of spatial and temporal distributions were given. Genetic algorithms were introduced with the further extension of promoting SDS seasonal predication from multi-level resolution. Genetic probability was used as a substitute for posterior probability of multi-level discriminants, to show the dual characteristics of crossover inheritance and mutation and to build a non-linear adaptability function in line with extended genetic algorithms. This has unveiled the spatial distribution of the maximum adaptability, allowing the forecast field to be defined by the population with the largest probability, and made discriminant genetic extension possible. In addition, the effort has led to the establishment of a regional model for predicting seasonal SDS activities in East Asia. The model was tested to predict the spring SDS activities occurring in North China from 2007 to 2009. The experimental forecast resulted in highly discriminant intensity ratings and regional distributions of SDS activities, which are a meaningful reference for seasonal SDS predictions in the future.展开更多
文摘比值判别法,设正项级数sum from n=1 to ∞ U_n之后项与前项的比值的极限等于ι,即(i)当ι【1时,级数sum from n=1 to ∞ U_n收敛;(ii)当ι】1时,级数sum from n=1 to ∞ U_n发散;(iii)当ι=1时,级数可能收敛也可能发散,所以当ι=1时此法失效,为了使比值判别法得到进一步推广,经过初步探讨,当ι=1时,如果正项级数的项单调递减,可以采用下面两种比式形式得到解决.
文摘对级数sum from n=1 to ∞(8nbn)的收敛性可用阿贝尔、犹利克雷判别法,而对其绝对收敛性却提文甚少;本文根据比较判别法直接研究级数sum from n=1 to ∞(a_nb_n)的绝对收敛性,并得出结果,用这结果判定了些级数的敛散性显得更加有效和方便。 一、定理及推论 1、定理:设sum from n=1 to ∞(a_n)是一无穷级数,{bn}是一序列。【i】若序列{bn}有畀且级数sum from n=1 to ∞(a_n)绝对收敛,则级数sum from n=1 to ∞(a_nb_n)绝对收敛;若序列{1/bn)有界且sum from n=1 to ∞|a_n|发散,则sum from n=1 to ∞n|a_nb_n|发散。 证明:假设sum from n=1 to ∞(a_n)绝对收敛且{b_n}有界,则存在正数M,使得|bn|【M,因此有|a_nb_n|≤M|a_n|因为sum from n=1 to ∞M|a_n|收敛,由比较判别法知sum from n=1 to ∞(a_nb_n)绝对收敛。 设sum from n=1 to ∞|a_n|发散且{1/b_n}有界,若sum from n=1 to ∞|a_nb_n|收敛,于(i)知sum from n=1 to ∞|a_nb_n|/|bn|=sum from n=1 to ∞|a_n|收敛,与条件矛盾,故级数sum from n=1 to ∞|a_nb_n|发散。
文摘This paper proposes the discriminant analysis on land grading after analyzing the common methods and discussing the Fisher’s discriminant in detail. Actually this method deduces the dimension from multi to single, thus it makes the feature vectors in n \|dimension change to a scalar, and use this scalar to classify samples. This paper illustrates the result by giving an example of the residential land grading by the discriminant analysis.
基金supported by National S & T Support Program (Grant No. 2008BAC40B02)National Basic Research Program of China (Grant Nos. 2006CB403703 and 2006CB403701)Basic Research Fund under Chinese Academy of Meteorological Sciences (Grant Nos. 2009Y002, 2009Y001)
文摘Here we use a Discriminant Genetic Algorithm Extended (DGAE) model to diagnose and predict seasonal sand and dust storm (SDS) activities occurring in Northeast Asia. The study employed the regular meteorological data, including surface data, upper air data, and NCEP reanalysis data, collected from 1980–2006. The regional, seasonal, and annual differences of 3-D atmospheric circulation structures and SDS activities in the context of spatial and temporal distributions were given. Genetic algorithms were introduced with the further extension of promoting SDS seasonal predication from multi-level resolution. Genetic probability was used as a substitute for posterior probability of multi-level discriminants, to show the dual characteristics of crossover inheritance and mutation and to build a non-linear adaptability function in line with extended genetic algorithms. This has unveiled the spatial distribution of the maximum adaptability, allowing the forecast field to be defined by the population with the largest probability, and made discriminant genetic extension possible. In addition, the effort has led to the establishment of a regional model for predicting seasonal SDS activities in East Asia. The model was tested to predict the spring SDS activities occurring in North China from 2007 to 2009. The experimental forecast resulted in highly discriminant intensity ratings and regional distributions of SDS activities, which are a meaningful reference for seasonal SDS predictions in the future.
