线性

This article gives out the general mathematical model, common characters. some exampes of non linear problems and linearizing methods of them.

本文给出了线性问题的普遍数学模型、特征和一些实例，以及非线性问题的线性化方法。

Parameters of these neural networks can also be divided into two kinds:non linear parameters of the variable basis function and the coefficients of the lin ear combination.

网络的参数也表现为二类：可变基中的参数是非线性的，组合系数是线性的。

We investigate phenomenologically effects of the flavor-dependent quarkonia annihilation on the meson-meson mixing, and find that corrections due to the flavor-dependent quarknoia annihilation can be described by the constituent quark masses in the mixing model which holds for all the meson nonet. We also study the relation between Regge trajectory and meson spectrum, and therefore concluded that the quasi-linear Regge trajectory with the requirements of additivity of intercepts and inverse slopes can describe the meson spectroscopy with good accuracy, and it also holds for the radial excited mesons except for the bbbar mesons.

我们唯象地研究了味道有关的夸克偶素湮灭效应对混合的影响，发现味道有关的夸克偶素间的湮灭引起的修正可以通过组分夸克的质量来描述，考虑这种修正的混合模型可以用于所有的介子九重态；我们也研究了Regge轨迹和介子质量间关系，发现满足截距相加及斜率倒数相加的准线性Regge轨迹可以很好地描述介子的质量，除bbbar外，线性Regge轨迹也可以很好地描述介子激发态的质量；最后，我们借助于赝标介子和标量介子，讨论多个共振态的混合及衰变。

We discuss the completely tr-rank nonincreasing linear maps on finite vN algebras and prove that a unital self-adjoint and surjective linear map on finite vN algebras is completely tr-rank preserving if and only if it is a spatial 〓-automorphism that leaves the central elements fixed.

我们刻画了有限vN代数上完全迹秩不增的线性映射；也证明了有限vN代数上保单位元的自伴线性满射完全保迹秩当且仅当它是空间〓-自同构且限制到中心上是恒等映射。

Linear memoryless state-feedback control law is derived for two classes of uncertain nonlinear interconnection systems with sector restriction or norm-bounded restriction based on Linear Matrix Inequality. This method doesn't require that two input terms are absolutely controllable for nonlinear delay systems.

基于线性矩阵不等式分别导出了具有扇形角约束和范数有界约束的两类非线性关联不确定系统的线性无记忆状态反馈控制律设计方法，该方法不要求系统的两输入项对系统完全可控。

By the analyses on the existing detector generating algorithms, we achieved the improvement of the linear time detector generating algorithm, which was widely used at present. The efficiency of the linear algorithm was improved by eliminating the reluctant detectors, and at the same time the improved algorithm was ensured to cover the nonself space as much as possible.

在分析已有的检测器生成算法的基础上，改进了目前使用最多的线性检测器生成算法，通过消除冗余的检测器提高了线性检测器生成算法的效率，同时还保证了改进后的算法能够尽可能多地覆盖"非我"空间。

Considerable work and progress have been made over the past decades on nonsingular linear systems and linear least squares problems.

最近几年，一批研究工作者在非奇异线性方程组和线性最小二乘问题的条件数方面做了大量的工作，并取得了显著的进展。

A important result is the one-order expression of AR Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR is only a certain more-multivariable power series processAnd, if a process is described as an AR, the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one.

作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了AR的是一个更高维的幂级数的线性过程，从而，说明了AR关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数λ＜1。

Chapter 3, we study the stability of approximate solutions of nonlinear equation problems(the continuous function is defined in the linear normed space).We prove that most of approximate solutions of nonlinear equation problems are stable; all accurate solutions are the essential points of the set of approximate solution; the connected component which contains the accurate solution is the essential component of the set of approximate solution; especially the number of essential components is finite.

第三章，研究定义在线性赋范空间上的非线性方程问题近似解及其解集的稳定性，得到线性赋范空间上在Baire分类下大多数非线性方程问题的近似解都是稳定的；精确解是近似解集的本质解；包含精确解的近似解集的连通区是本质连通区；包含精确解的近似解集的连通区为有限个。

The error growth of numerical method grows linearly with the stage of iterated matrix. A sufficient condition of bounded stability for linear θ-method is proved.

证明了数值方法的计算误差是随着迭代矩阵的级数线性增长的，又进一步给出了线性θ-方法有界稳定的一个充分条件。

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％。