实数

We have to distinguish between the propagating modes with real valued , and the evanescent modes with imaginary

我们必须分别考虑具有实数β的导模和具有虚数β的消失模。

And if we have some regex for, example, real number in exponential format?

如果我们有一定的正则表达式，例如，在指数格式的实数？

Math real but not expressible as the quotient of two integers.

是实数但是不能变成整数之比的形式的。

The controllability and observability of a system over F always means the controllability and observability of the system over the field R of real numbers.

一个F上的系统是能控能观的，即结构能控能观的，则意味着实数域上该系统实际上总是能控能观的。

And we know by study, so long as system is controllable and observable at the structure over the field F(z of the rational functions in multi-parameters, it is always controllable and observable over the field R of real numbers.

通过研究我们知道，一个系统只要在结构上多元有理函数域(F上是能控能观的，则意味着实数域上该系统实际上总是能控能观的。

The five characteristics of the system are exploiting the ordered decomposition of problems in the structure of networks; using the Hasse graph to map the transfer network to the field of real numbers homomorphically; distinguishing the production rules as strong rules and weak rules; using the method of scheduling among stations to balance the search by weak rules in every station; searching in the best-first way both in the large and in the small, but with the different aims respectively, which can be regarded as a BF′-BF strategy in which the macro guides the micro.

该系统有五个特点：利用了一种网络结构的有序分解；采用Hasse图将中转站网络同态地映射到实数域上；将产生式规则区分为强规则和弱规则；采用站间调度的方法系统地平衡了各站弱规则的搜索；全局和局部都为最佳优搜索，只是目标指向不一样，是一种宏观引导微观的BF′-BF混合策略。

Through the operation of formal power series, we set up the expansion of Ar, a popularizing of the common polynomial theorem, where r is a non-zero real number.

通过形式幂级数A的幂运算，建立了Ar的展开式，这里r为非零实数，这是常见的多项式定理的推广。

Research results: Kolmogorov entropy is more than zero, lyapunov exponents tend to zero, correlation dimension is real number of more than 3, negative power appears partially in power spectrum in lower frequency and the FCA diagram as certain inclination.

研究结果：kolmogorov熵大于0，Lyapunov指数趋于0，关联维为大于3的实数，功率谱图中在低谱部分出现负幂，PCA图具有一定的斜率。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

These constants define the general format of the character representation of a real number.

这些常量定义了实数在使用字符表达时较为普遍的格式。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。