平均

The concept of the weighted logarithmic power mean is introduced; its relation with two-parameter mean is given; the inequality for weighted logarithmic power mean is derived; the magnitude relation among upper bounds of geometric mean and arithmetic mean of geometrically convex functions are made certain.

建立了几何凸函数的对称拟算术平均不等式，对文献[1]提出的不等式进行了推广统一；引进加权对数幂平均的概念，建立起其与双参数平均之间的关系，得到加权对数平均不等式，从而确定了几何凸函数的几何平均、算术平均的上界的大小关系；最后，提出了几何凸函数的对称拟算术平均不等式的推广问题。

Results showed that average lint yield of F1 was 1296.30 kg/hm^2, which was an increase by 214.38 kg/hm^2, compared with CK and its average competitive dominancy was 19.81%; Average lint yield of F2 was 1168.65 kg/hm^2, an increase by 86.73 kg/hm^2, compared with CK and its average competitive domain was 8.01%; Average lint yield of F3 was 1117.65 kg/hm^2, an increase by 35.73 kg/hm^2 compared with CK and its average competitive dominancy was 3.30%. F3 had the highest competitive dominancy, then F2 and F3 whose decreasing ratio is consistent with their competitive dominance, and their average yield decreasing ratios were 12.59% and 17.62%, respectively.

结果表明，F1平均皮棉总产量为1296.30 kg/hm^2，比对照泗棉3号增产214.38 kg/hm^2，平均竞争优势为19.81%；F2平均皮棉产量为1168.65 kg/hm^2，比对照增产86.73 kg/hm^2，平均竞争优势为8.01%；F3平均皮棉产量为1117.65 kg/hm^2，比对照增产35.73 kg/hm^2，平均竞争优势为3.30%。F1竞争优势最大，其次为F2，F3，F2，F3的衰退率与竞争优势一致，其平均优势衰退率分别下降了12.59%和17.62%。

The first part is introduction in which some excellent results are given. For example, LeachandSholander mean of two variables E and its monotonicity, Some results of paper and [4] are also given. In Chapter l,mean function and mean family of n variables in one dimension are given. On the base of mean function of n variables of paper [1], weproof that is mean function and discuss its monotonicity andcontinuity.

第一部分是引言，主要介绍了一些已有的结果，如：一般的两个变元的Leach and Sholander均值B以及它的单调性，又介绍了文[1][4]中一些已有的结果，第一章主要介绍了一维n元平均函数和平均族，在已有的文[1]中给出的参差域K上的n元平均函数概念的基础上，证明一般形式的是平均函数，讨论了它的单调性和连续性，其中还将已有的二元Stolarsky平均推广到了n元平均。

In particular, Stolarsky mean are generalized from two variables to n variables. Moreover,we make ωi become weight function to diversity the kinds of mean function. For the mean family, we discuss mean family with single parameter or multi-parameter .

此外还通过改变权w_i，使之成为权函数，从而使n元平均函数的形式多样化，在n元平均族中给出了单参数和多参数平均族，并讨论了具体的单参数的幂平均族和指数平均族，多参数的Dresher平均以及由此构造的另一种形式的双参数平均族。

3By applying the geometric average to compute the average price of assets which consists of two cases of continuous and discrete,the pricing formula for the Asian option of averag asset and average strike price and the parity relationship are obtained.

3采用几何平均计算资产的平均价格，在连续平均和离散平均两种情形下，分别给出了平均价格型和平均执行价格型亚式期权的定价公式及相应的买权和卖权的平价关系。

Average annual Growth Rate Two methods for calculating average annual growth rate are applied in China, one is often called "level approach" or the method of calculating geometric average, which is derived by comparing the level of the last year of the interval with that of the beginning year; the other is called accumulative approach or algebraic average or equation method, which is derived by the summation of the actual figure of each year in the interval divided by the figure in the base year.

平均增长速度我国计算平均增长速度有两种方法：一种是习惯上经常使用的"水平法"，又称几何平均法，是以间隔期最后一年的水平同基期水平对比来计算平均每年增长速度：另一种是"累计法"，又称代表平均法或方程法，是以间隔期内各年水平的总和同基期水平对比来计算平均每年增长速度。

Annual Average Growth Rate two methods for calculating annual average growth rate are applied in China, one is often called "level approach" or the method of calculating geometric average, which is derived by comparing the level of the last year of the interval with that of the beginning year; the other is called "accumulative approach" or algebraic average or equation method, which is derived by the summation of the actual figure of each year in the interval divided by the figure in the base year.

平均增长速度我国计算平均增长速度有两种方法：一种是习惯上经常使用的"水平法"，又称几何平均法，是以间隔期最后一年的水平同基期水平对比来计算平均每年增长速度；另一种是"累计法"，又称代数平均法或方程法，是以间隔期内各年水平的总和同基期水平对比来计算平均每年增长速度。

In three separate studies, the investigators evaluated 105 adults with type 1 diabetes (mean age, 37 years; mean duration of diabetes, 20 years), 36 adults with type 2 diabetes (mean age, 50 years; mean duration of diabetes, 10 years), and 91 adults with type 1 diabetes (mean age, 39 years; mean duration of diabetes, 20 years). During a four-week period, participants used a hand-held computer to complete 70 trials of cognitive-motor tasks and to enter their current blood glucose reading after each test. Hyperglycemia was defined as blood glucose level higher than 15 mmol/L.

在3个不同的试验中，研究人员评估105位第1型糖尿病患者（平均年龄为37岁；患糖尿病平均时间为20年），36位第2型糖尿病患者（平均年龄为50岁；患糖尿病平均时间为10年），以及91位第1型糖尿病患者（平均年龄为39岁；患糖尿病平均时间为20岁）；在4周期间，受试者使用一种掌上型电脑来完成70种认知运动任务的试验，以及在每次测试后，输入他们目前的血糖读数，血糖高於15 mmolL被定义为高血糖。

The 7 of 14 microsatellites had reached the homozygosis completely in familiesⅡat 18 The results suggested that the average N is decreasing and the genetic homozygosity is increasing with the improving inbred generation of WZSP.

WZSP近交系Ⅰ系F14-F16的14个微卫星座平均每个位点等位基因数为2个、平均杂合度为0.40、多态信息含量为0.26；Ⅱ系F15-F18的平均等位基因数为1.92，平均杂合度分别为0.32，多态信息含量为0.25；Ⅲ系F14-F17的平均等位基因数为2.17，平均杂合度为0.44，平均多态信息含量为0.32。

In this period of time, the mean annual air/ground temperature, mean annual maximum and minimum air/ground temperature, extreme maximum and minimum air/ground temperature, difference between ground-and air temperature, and annual accumulated temperature in the area all had an increasing trend, and the increase of mean annual air temperature, mean annual ground temperature, difference between ground-and air temperature, mean annual minimum air temperature, extreme maximum ground temperature, and extreme minimum ground temperature was more obvious, being 0.32℃, 0.59℃, 0.27℃, 0.39℃, 2.03℃, 1.62℃ per 10 years, respectively.

结果表明：26年来，林区热因子（平均气温、平均地温、平均最高／最低气温、平均最高／最低地温、极端最高／最低气温、极端最高／最低地温、地气温差、年积温）均呈上升趋势，其中平均气温、平均地温、地气温差、平均最低气温和极端最高／最低地温升高趋势明显，每10年分别增加0.32℃、0.59℃、0.27℃、0.39℃、2.03℃、1.62℃，最低温度的升高趋势都大于最高温度的增长速率，说明尖峰岭热带山地雨林区气候变暖来自于最低温度升高的贡献。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。