查询词典 sum of squares

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

According to the criterion of minimizing the sum of the squares of the states posterior confidence region widths, we get the value of the updated Biscay distribution, then get the states interval estimation.

该方法结合了区间运算和Kalman滤波方法，分别根据状态和观测方程得到的预测值的Biscay分布，融合得到估计的Biscay分布值，进而得到状态的区间估计。

In a right—angled triangle ,the square on the hypotenuse is equal to the sum of the squares on the other two sides.

它是所有几何定理中最有名的，也是仅有的有着广泛流传的笑话。

In a right—angled triangle,the square on the hypotenuse is equal to the sum of the squares on the other two sides.

关于这一特色的定理，下面就是笑话的行文：自动翻译查看资料来源划选1次

The sum of two positive integers is 29, find the minimum value of the sum of their squares.

两个正整数之和为29，求此两数平方和的最小值。

There exist nT-rings R such that every element of R is a sum of 3 squares and a sum of 4 cubes.

还证明了存在该类型的nT-环R，R的每个元素是3平方和和4立方和。

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

举一个例子，10以内的所有自然数的和的平方与它们的平方和的差这样计算

In Chapter 2, we characterize the bipartite graphs with given number of vertices and edges which have the smallest and largest values of the sum of squares of degrees. Meanwhile, we present some bipartite graphs attaining extreme values.

在论文的第二章里，给出了n个顶点m条边的偶图的度平方和的最大值和最小值，同时给出了达到极值的一种极图的构造方法。

The system of linear equations is solved y the method of least squares which minimizes the sum of the squares of the differences between the observed and calculated arrival times.

这个线性方程系统由通过最小方解决的，最小化了观测时间和计算时间之间的不同的方。

Four thin-layer drying models were investigated for the description of FIR-assisted freeze-drying characteristics. The models were exponential model, Page model, diffusion model, and approximation of the diffusion model. Tests were conducted using a three-level, three-factor (drying temperature, distance between sample and FIR heater, and sample thickness) design, and quadratic polynomial analyses were performed to relate the drying parameters of thin-layer drying model. The performance of these thin-layer drying models was evaluated by comparing the coefficient of correlation (R2), the sum of squares, and the RMSE amongst four models. Drying parameter K of the Page model gave the best results in describing freeze-drying with FIR of Tylose and sweet potato.

运用四种薄层乾燥模型（指数、Page、渗透模型及近似渗透模型）研究远红外线冷冻乾燥之乾燥特性，实验采用三阶层、三因子（远红外线加热器设定温度、远红外线加热器至样品表面之距离及样品之厚度）的实验设计，对於薄层乾燥模型的乾燥参数以二次多项式函数表示之，乾燥参数之二次多项式函数的最适性判断主要是藉由决定系数、模式缺乏适合性及均方根误差等值的比较而加以评估，以Tylose及甘薯样品而言，其中四种薄层乾燥模型的乾燥参数以Page模型之K值的结果为最佳。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。