线性

The definitions of intrinsical linear nonholonomic constrain and intrinsical nonlinear nonholonomic constrain are put forward in this paper. The nonholonomic systems are divided into intrinsical linear nonholonomic system and intrinsical nonlinear nonholonomic system.The rational spectrums of all kinds of virtual displacement definitions and commutativity of d,?

本文研究了非完整动力学中使不定性问题确定化的交换关系和将非线性问题线性化的虚位移定义，首次证明并给出了在非完系统中各种虚位移定义与交换关系的合理适用范围，指出完整动力学与本质线性非完整动力学在研究方法上具有相同性。

As we know, with the exception of the Haar function, uni-real-valued orthogonal wavelet filter banks with compact support lack symmetry and do not possess linear phase.

我们知道，紧支撑正交的单一小波除Hair小波外不具有任何对称性，它用作滤波器不可能有线性相位，而由实单一紧支撑正交的尺度函数构造出的二重尺度函数却是对称的，对应的二重小波可以是对称或反对称的，从而使得这种小波在信号处理的过程中具有线性相位。

The aim of this paper is to study the existence of solution and multiply results for quasilinear elliptic system in bounded domain and the whole space, semilinear elliptic equation in two dimension space, second order nonlinear difference equation by variational methods. The main results are listed in the following:1. An abstract compactness theorem is proved, and then, under weak Boccardo and De.

本文主要利用变分法，分别研究了有界区域和全空间上拟线性椭圆型方程组、二维空间上半线性椭圆型方程和二阶非线性差分方程问题的解与多重解的存在性，具体内容如下： 1。

It has some advantages over the previous methods, for instance, simplicity in complementation and high accuracy in estimation.

其次提出了基于基础矩阵的三线性约束关系估计方法，该方法与以往的三线性估计方法相比，具有简单易实现，且估计精度比较高的优点。

This paper studys the stability of nonlinear systems in two particular critical cases. In a case, the linear systems at the equilibrium point of interest is assumed to possess a simple zero eigenvalue. In the other case, it is assumed to possess a complex conjugate pair of simple pure imaginary eigenvalue.

本文基于中心流形定理研究了非线性系统在两种特殊临界情形下的稳定性问题，一种是与它相应的线性系统在平衡点仅有零特征根，另一种是与它相应的线性系统在平衡点仅有一对共轭的纯虚数特征根。

The linear manifold-learning algorithms represented by PCA, with their substantial mathematical foundation and simple implementation, but they are not able to show complex nonlinear manifold structure with their linear essence, which gives rise to nonlinear manifold-learning algorithms such as Isomap, SIE etc.

以PCA为代表的线性流形学习算法有较强的数学基础，实现简单，但是其线性本质并不能揭示复杂的非线性流形结构；于是又出现了以Isomap、SIE等为代表的非线性流形学习算法。

Graph theory is one of the unified modelling methods. Based on the traditional linear graph theory, the paper proposed the Extensible Elementary Linear Graph method, which could realize composable simulation for multidiscipline system, and perform inter-energy domain expression in a unified way.

图论方法是多领域统一建模方法之一，本文基于线性图建模方法，研究和发展了一种模块化的多领域建模方法——可扩展单元线性图复合仿真方法，以实现跨能量域的统一模型表达。

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。

The experimental results show that for most continuous optimization problems, the strategy of concave function gains an advantage over the linear strategy, while the linear strategy outperforms strategy of convex function with the identical initial and final weights.

试验结果表明，对于多数连续优化问题，在初始权值和最终权值相同的情况下，凹函数递减策略优于线性策略，而线性策略优于凸函数策略，凹函数递减策略能够在不影响收敛精度的情况下较大幅度地提高粒子群算法的收敛速度。

Based on the analysis of the relationship between vegetable and meteorological condition,the regression equation to guide the Beijing vegetable carriage by temperature and relative humidity was derived.

中文摘要：在分析蔬菜与气象条件关系及北京地区气候条件下温湿日变化特征的基础上，应用线性二元回归方法建立了蔬菜运输指数与温度、相对湿度之间的线性回归方程。

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％。