| 1. | In general, experience has shown that third-to fifth-degree polynomials produce sufficiently low residuals and monotonically increasing derivatives .
实践证明，三至五次多项式就能产生足够小的残差和单调递增的导数。 |
| 2. | Strictly increase monotonically
严格单调递增 |
| 3. | Monotonic increasing function
单调递增函数 |
| 4. | A conspicuous monotonic increase could be found in the influence of domestic economic situation to the elderly " s health and their use of medical resources
家庭经济状况对老年人口健康和医疗资源利用都具有明显的单调递增影响趋势。 |
| 5. | Given a new concept - gametal inbreeding relation coefficient , and proved it is a increase function by inbreeding coefficient f , it ' s reflect the relating degree from the aspect of informatics
提出了配子间的近交关联系数的概念，并证明了它是近交系数f的单调递增函数，从信息论的角度刻画了配子间的关联程度。 |
| 6. | The relation between the chemical potential and the density of a nuclear matter is firstly given here , which is that the density of a nuclear matter monotonously increases with the increasing of the chemical potential
在此，化学势和核物质密度之间的关系第一次被给出：核物质密度随着化学势的增加而单调递增。 |
| 7. | Between 1996 and 2005 , the land use index of chuzhou showed no trend of monotonic increasing or decreasing , but inclined to fluctuation , which reflected the open and dynamic character of the land use system
2005年滁州市土地利用指数并没有呈现出单调递增或递减的趋势，而是呈现出波动的趋势，这也反映了土地利用系统开放性和动态性的特征。 |
| 8. | Given the size and the minimum degree of scale - free networks , it is shown that nse reached a minimum value when scaling exponent is about equal to 1 . 7 and the nse increases with increasing scaling exponent after the minimum value
在给定网络规模及最小度条件下，无标度网络的网络结构熵在标度指数等于1 . 7附近取最小值，即此时网络最不均匀，当标度指数大于1 . 7时，无标度网络的网络结构熵随标度指数单调递增。 |
| 9. | One of its most important applications is to improve the optimization algorithms by evaluating the relevant derivatives information efficiently the aim of the work includes : to establish and study new algorithms - - cf - pcg algorithrns with ad ; to establish and study the extended cf - pcg algorithm ( ecfpcg ) . cf - pcg algorithms with ad is proposed on the basis of cf - pcg algorithms with sd , in addition to replace sd with ad , there are other significant modification to the algorithms . the results by theoretical analysis and numerical experiments implicate that cf - pcg algo - rithm with ad is an improvement to newton method with ad
论文首次将自动微分应用于牛顿- pcg型算法，构造了新算法，并从理论上比较了新算法与牛顿法的效率，证明了新算法的效率严格大于牛顿法的效率，而且新算法与牛顿法的效率比分别是问题维数n和目标函数复杂性的严格单调递增函数，当n趋于无穷大时，这个效率比的下界以ln ( n ) ln2的速率趋于无穷大。 |
| 10. | Because the polynomial function has the merit that its monotonicity lies in different range , it makes the non - linear input - output model with polynomial function break through the restriction of the direct consumption coefficients which decrease or increase monotonically , so the model is more practical and realizable
由于多项式函数具有分段区间单调性的特点，使得多项式型的非线性投入产出模型突破了以往的研究中要求直接消耗系数仅仅是关于部门总产品的单调递减或单调递增的函数的限制，使建立非线性投入产出模型的条件更为宽松，更能描述现实的经济系统。 |
