查询词典 linear relation

First, based on the relations of stress and strain between the whole medium and its macroscopically isotropic constituents, an explicit relation between elastic matrices of the whole medium and its constituents was derived. Combining the explicit relation of elastic matrices with the strain's relation, two coefficient tensors were defined and analyzed to get a general relation between the hulk and shear modulus of the whole medium under the assumption that all the field variables are in a unified coordinate system. Secondly, combining these relations with the classical Hashin-Shtrikman elastic modulus bounds, four new expressions of elastic medium of the whole medium were obtained and compared with the original hounds. Last, these formulae were applied in the computation of effective elastic moduli of clean sandstone saturated with pore water.

首先基于整体介质与宏观各向同性组分满足的应力和应变组分关系，推导出整体介质弹性矩阵与组分弹性矩阵之间的显式关系，联合其应变关系，定义和分析了对应的两个系数张童，并据此导出了相关场变量位于统一坐标系时整体介质体积模量与剪切模量的关系；然后将经典的Hashin-Shtrikman弹性模量边界模型与上述关系式结合，得到4个新的整体介质弹性模量的估算公式，再与原始的Hashin-Shtrikman弹性模量边界进行了比较，最后针对饱和水纯净砂岩介质进行了试算。

In this paper, we deal with the complete extension of a fuzzy relation and obtain the following main conclusion. Every reflexive,*-antisymmetric and *-transitive fuzzy relation can be extended to a complete reflexive,*-antisymmetric and *-transitive fuzzy relation, namely, every partial order can be extended to a linear order.

文章研究了一个模糊关系的完全扩张问题，主要结果为：一个自反的、*-反对称的*、-传递的模糊关系可以扩张成为一个完全的、自反的、*-反对称的、*-传递的模糊关系，即任何一个偏序都可以扩张成一个线性序。

Linear solvation energy relation was firstly introduced in the paper, and the method and step of gaining the special parameters of solvent and solute were introduced in detail, and these special parameters were used to selection and optimization of extractive agent in extractive distillation. The model of predicting activity coefficient at infinite dilution was established by linear solvation energy relation. By the above theory, several candidate solvents were selected to separate C5 fraction, and by experiment of vapor-liquid phase equilibrium at atmosphere pressure, the mixture of N-methyl-pyrrolidone including 4% water was used extractive agent of separating C5 fraction. Then binary vapor-liquid phase equilibrium of the some compound in C5 fraction and N-methyl-pyrolidone were determined at atmosphere pressure and correlated by NRTL equation. Isoprene being objective compound, experiments were operated in the laboratory-scale column; the processes were simulated by RadFrac model in ASPEN PLUS. And by the combination of experiment and simulation, the new process of separation of C5 was established.

本文首先对线性溶剂化能关系进行了分析介绍，也介绍了采用溶剂化能关系得到溶质溶剂特性参数的方法步骤，并将这些参数用于萃取精馏萃取剂的选择与优化；也通过线性溶剂化能关系式建立无限稀释活度系数预测模型，取得了一定的预测精度；将通过上述方法初选的溶剂进行了常压汽液平衡的测定研究，通过实验研究选定含水4%的N-甲基吡咯烷酮溶液做为C5分离的萃取剂，测定了大量N-甲基吡咯烷酮与C5组分的二元平衡数据，并进行关联计算；以异戊二烯为目标产物在实验室规模的精馏塔内进行了C5分离的实验研究，取得大量塔内数据；通过选用合适的热力学模型，采用ASPEN中RadFrac模块对分离过程进行模拟研究，通过实验与模拟相结合，建立了C5分离的新工艺，为将来的工业化打下了坚实的基础。

Both theoretical and experimental results show that compaction properties and heating rates do not alter this linear relation, but influence the slope of the linear relation, and therefore it is concluded that large dihedral angle, high green density, narrow particle and pore size distributions are beneficial to the achievement of the grain size-density trajectory with promoted densification and minimized grain growth.

理论分析和实验结果表明，成型体性质不改变这一线性关系，但可以改变直线的斜率，而升温速率对直线斜率的影响不大。较大的二面角、较高的素坯密度、较窄的颗粒和气孔尺寸分布有利于获得较小的晶粒生长和较高的烧结密度。

In order to avoid the repetition, we find a group of coefficients that are generated with field and its gradient data. To establish explicit linear relation between structural index based on the linear relation, depth is calculated when calculated parameters are given without touching the field data. Accordingly, it can avoid the repetition of Euler's equation calculation and greatly reduce the works load as well as enhance efficiency.

为了避免这种重复，这里找到了一组系数，该系数与场值及其梯度值有关，并直接建立起场源位置与构造指数N简单的对应关系，从而把解欧拉方程的最小二乘问题转化成了解线性方程的问题，避免了解欧拉方程组时的重复计算，大大地减少了计算工作量，有效地提高了工作效率。

For the thrashing due to true sharing of data, we thoroughly study the relationship between array element accesses and loop indices of a nested loop, present a complete set of ideas, theories, and methods with which the staggering relation and the compacting relation between the threads of the nested loop (either with a single linear function or with multiple linear functions) can be determined at compile-time, and accordingly the nested loop (either perfectly nested or imperfectly nested) can be restructured to avoid the thrashing problem.

使用这套理论和方法，我们在编译时就可以确定出嵌套循环（含单线性函数或多线性函数，紧嵌套或非紧嵌套）各线索间的错位关系，一致错位关系和压缩关系，根据这种关系对嵌套循环进行重构可以使真共享抖动问题得到很好的解决。

This paper consider centrifugal force and coriolis force for ideas of Planetary LabCD Valve Model and Single Point Fluid Separation Model, then the relation of critical rotation speed and planetary angle is linear which control parameter of critical rotation speeding in the Planetary LabCD Valve Model and compare with James Lee theory, and define γR in SPFS Valve Model to show the relation of the low rotation speed is linear and is fixed where the high rotation speed for utilizes any rotation speed.

本论文考虑离心力与科氏力之影响，且提出行星式碟片阀门模式与单点流体分离阀门模式两模式，其中行星式碟片阀门模式，其临界转速与行星角之大小近於线性变化，可当於控制阀门之临界转速之设计参数，且比较在阀门设计上考虑行星角来控制阀门临界转速与James Lee之阀门临界转速理论可以得知，从吾人所提出行星式碟片阀门模式可以得到与实验结果相同的趋势。

Experimental result showed that under the wavelength of 460 nm,there was good linear relation between absorbency and content of SO42-;and stationary time that absorbency value needed became longer along with the increase of sample quantity of phosphoric acid.When absorbency become stationary,there is good linear relation between the phosphoric acid sample quantity and the content ofSO42-.So the content of SO42- can be adjusted by turning the sample quantity to make it in scope of standard curve.

实验结果表明，在波长为460 nm处，硫酸根含量与吸光度成良好的线性关系；随着磷酸取样量的增加，吸光度达到稳定值所需的时间相应增加，稳定后磷酸取样量与硫酸根含量成良好线性关系，因此实验过程中可通过调整磷酸的取样量来调节硫酸根含量，使之在标准曲线的测定范围内。

The linear dispersion relation of the enhanced equations is the Pad\'{e} [4,4] expansion of the linear Stokes dispersion relation, the accuracy of which is acceptable even when the relative water depth is as large as 1.0. Its nonlinear property and shoaling gradient are also improved.

改进后方程的线性色散关系达到了一阶Stokes波色散关系的Pad\'{e}[4，4]近似，在相对水深达1.0的强色散波浪时仍保持较高的准确性，并且方程的非线性和线性变浅率都得到了不同程度的改善。

Secondly,the author puts emphasis on "the simple linear programming"----the teaching design's whole blueprint in high school, the strategy on how to deal with the relation between dual inequality and linear programming; how to establish the linear programming model; the strategy on how to find the optimal solution; the several situations of the optimal solution's positions.

其次重点研究了"高中简单的线性规划"教学设计的总体构想；处理线性规划与二元一次不等式关系的策略；如何建立线性规划模型；线性规划问题中最优解的找法策略，最优解的位置的几种情况。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。