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It is shown that for all auction mechanism, except the second highest bid-price rule, all equilibrium strategies are continuously differential and strict monotonically increasing, and morever the set of Nash-equilibria is completely described by a boundary value problem for a system of singular differential equations.

证明除了次高价格拍卖规则外，所有拍卖机制的均衡策略都是连续可微和严格单调增的，并且Nash均衡集完全由一阶微分方程系统的边值问题所刻划。

It is proved that these two types of fuzzy controllers are equivalent to the variable structural combinations of nonlinear PI controller and nonlinear control offset. Moreover, the outputs of these fuzzy controllers are monotonically increasing, continuous, and bounded with regard to the corresponding universe of discourse.

基于此，深入研究了模糊控制器的解析结构，并证明了这两类模糊控制器等价于一种变结构的非线性 PI 控制器与相应的非线性控制偏置之和，并且在其输入论域上是单调递增、连续且有界的。

The results show that the radiative properties of randomly distributed soot aggregates for a given fractal dimension are complex functions of the monomer diameters, the number of monomers in the aggregates,and the refractive index; For a small value of the monomer diameters, the absorption cross section of soot aggregates tends to be relatively constant when the fractal dimension is small but increases rapidly when the fractal dimension exceeds two. However, a monotonical reduction in light absorption with the increase of the fractal dimension is observed for soot aggregates with sufficiently large monomer diameters, number of monomers,and refractive index. The scattering cross section , extinction cross section and single-scattering albedo increase monotonically with the increase of the fractal dimension. Overall, the results for soot aggregates differ profoundly from those calculated for the equivalent spherical particles, and the discrepancies between them will change small with the increase of the fractal dimension.

研究表明，在给定分形维数的情况下，烟尘団簇粒子的辐射特性取决于原始微粒粒径、数量及复折射率；原始微粒较小的団簇粒子，当分形维数较小时，吸收截面变化不明显，但当分形维数大于二时，吸收截面骤然增大，然而，对于具有比较大的原始微粒粒径、数量及复折射率的烟尘団簇粒子，吸收截面随着分形维数的增大而单调递减；随着分形维数的增大，団簇粒子的散射截面、消光截面及单次散射反照率均单调递增；从整体上来讲，団簇粒子的辐射特性与等效球形粒子的辐射特性存在着比较大的差别，并且这种差别随着分形维数的增大而减小。

And they increase monotonically with the wavelength, and change significantly with different composition.

而消光系数的色散却对薄膜的组分具有很大的依赖性。

In this paper, an efficient approach to ROI extraction based on monotonically marching curve evolution is proposed.

提出了一种基于单调推进曲线进化的感兴趣区域提取新方法。

The striking result is that the weighted variance does not increase monotonically over time.

醒目的结果是，被衡量的变化单调地不增加随时间。

It is shown that these two sequences converge monotonically to a unique solution of the finite difference system.

给出一类求解具时滞边界条件的时滞反应扩散方程的数值方法，证明了迭代序列的单调收敛性以及差分格式的收敛

There is a steadily and monotonically increasing relation between the average area and the amplitude to be detected.

该几何特征量与待测信号幅值之间存在比较稳定的单调递增关系。

In addition, the OAG increases monotonically with the increase of the noise strength and the noise correlation rate.

输出幅度增益随噪声强度、自相关率的增大而单调地增大。

A conclusion is drawn that group sequential decision -making system is a process in which the entropy of the system decreases monotonically, and the gr...

本文的主要结论是：群体决策过程中，系统的熵单调减少；群体决策的结果受选民的影响最大。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。