不变性

Duality invariance is the core of the space theory of functional analysis.

对偶不变性结果是泛函分析空间理论的核心内容。

Then the momentum P in the acquired motion equation is replaced by quantum operator, thus we obtain Schrodinger equation for charged particle moving in magnetic fields in Quantum Mechanics. Then we discuss the Gauge transformation and gauge invariance of Schrodinger equation, following which the Dirac phase is introduced.

然后把经典力学中的哈密顿量量子化，得到量子化的带电粒子在磁场中运动的薛定谔方程，之后是薛定谔方程的规范变换和规范不变性，并引入Dirac不可积相因子的概念。

During the transition from global gauge transformation to local gauge one,field interaction undergoes a 'nothing'-to-'something' change,thus affecting gauge invariance.

当使自由粒子整体规范变换向局域规范变换过渡时，场的相互作用发生了从"无"到"有"的变化，规范不变性遭到了破坏。

A relativistic transformation of generalized coordinates is discussed and it is found that the first law of thermodynamics and the equation of state of an ideal gas are invariant with respect to the relativistic transformation of generalized coordinates , so that the existence of relativistic transformation of generalized coordinates is reasonable.

讨论了一个涉及热力学的广义坐标的相对论变换，发现热力学第一定律和理想气体状态方程对广义坐标的相对论变换具有不变性，表明广义坐标的相对论变换有其存在的理由

Finally, the calculation process of CGR graphic's multi-fractal analysis was studied. the scope of choice of the weight factor and the scale invariance range were discussed, the weight factor can be chosen as ? 15≤q≤50; multi-fractal spectrum and generalized dimension of different sequence were calculated, multi-fractal spectrum and generalized dimension in different scales of different sequences were compared, it was found that multi-fractal spectrum and generalized dimension can show different levels of fractal characteristics of CGR graphics of DNA sequence, which can distinguish more complex structure of sequences.

最后，研究了DNA序列CGR图形的多重分形的计算过程，讨论了权重因子及满足标度不变性的范围选择等问题，得到结论：对CGR图形进行多重分形时权重因子可以选择为-15≤q≤50；计算了不同序列的多重分形谱和广义维数，比较了不同序列不同尺度的多重分形谱和广义维数，发现多重分形谱和广义维数能够表现DNA序列CGR图形的不同层次的分形特征，能够区分更复杂的序列结构。

In SLDMINV the invariance of the Krylov subspace is invoked, making the main computation reduced into almost real arithmetic, and thus lowering the computation amount markedly. In the meantime, the iteration is performed in the Krylov subspace generated from the inverse of the coefficient matrix and so the convergent speed is enhanced greatly, leading to two orders of the magnitude improvement over standard SLDM.

SLDMINV中运用了Krylov子空间不变性技巧，这使得计算基本化为实运算，显著降低了计算量；同时在由系数矩阵的逆构成的子空间上进行迭代，收敛速度大大加快，较之SLDM提高两个量级。

Based on geodesic distance invariance of nonlinear reduced dimension algorithm source code, the text published...

基于测地距离不变性的非线性降维算法源码，原文发表在2000年的Science杂志上，需要了解具体原理者请先看其论文。

By means of the language of mathematical logic the invariance of Hamilton principle under canonical transformation is expressed and proved.

用数理逻辑的语言表述了哈密顿原理及其在正则变换下的不变性，并给以证明。

Based on the definition of Boolean function on set and positive extension, The sufficient and necessary condition of PBF is proven. At last, an algorithm of generating MSP expression of stack filter positive Boolean function is presented taking advantage of Hasse diagram.

通过定义布尔函数开、闭集和最小项正、负扩展，证明了布尔函数具有层叠性的充要条件是布尔函数开集的正扩展或闭集的负扩展具有不变性，在此基础上，提出了一种通过Hasse图确定层叠滤波器最简正布尔函数的算法。

Based on the definition of Boolean function on set and positive extension, The sufficient and necessary condition of PBF is proven. At last,an algorithm of generating MSP expression of stack filter positive Boolean function ispresented taking advantage of Hasse diagram.

通过定义布尔函数开、闭集和最小项正、负扩展，证明了布尔函数具有层叠性的充要条件是布尔函数开集的正扩展或闭集的负扩展具有不变性，在此基础上，提出了一种通过Hasse图确定层叠滤波器最简正布尔函数的算法。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。