本文对线性空间中的凸集上的实值函数定义一种导数，用其研究函数凸性，得到了上述三种凸函数的若干判定定理。
This paper defines a kind of derivative for real function on convex set which is in linear space. By means of the derivative we study convexity of function and obtain some decision theories.
单复变量包含实数和虚数两部分，针对两个实值函数n(x) 和v(x)的表达式为：b(x) = n(x) +iv(x)。
fullprof A complex variable has real and imaginary parts written in the form b(x) = n(x) + iv(x) for two real-valued functions n(x) and v(x)
锥拟凸向量函数的概念是通常实值函数拟凸性的拓广。 由于拓广途径不一，在许多有关文献中各自提出了自己的锥拟凸向量函数概念。
This paper summarizes several different definitions of cone quasiconvex vector functions proposed in different literatures and discusses the relations among them.
函数将目标值的实部设置为源值三个颜色分量的平均值，并将目标值的虚部设置为0。
The VI sets the real portion of the destination value to the average of the three color components of the source, and it sets the imaginary portion of the destination to 0.
函数设置目标的实部分量为源值。函数设置目标的虚部为0。
The VI sets the real component of the destination to the source value. The VI sets the imaginary component of the destination to 0.
在实际中，粗糙变量不一定是实值，他们的值有可能是连续函数、有界变差函数等等。
In practice, rough variables may not be real number values, and their values may be continuous functions, bounded variation functions and so on.
函数设置目标的实部分量为源值。
The VI sets the real component of the destination to the source value.
在等价鞅测度框架下，讨论了(在到期时刻)期权处于实值状态时支付函数为幂型的股票欧式期权定价公式。
Via the framework of equivalent martingale measures, we derive the pricing formulas of European options with power payoffs (if the option is in the money, at the time of maturity).
函数将目标值的实部设置为源值三个颜色分量的平均值，并将目标值的虚部设置为0。
The VI sets the real component of the destination to the source value. The VI sets the imaginary component of the destination to 0.
对系统的特征值进行分类，定义特征值实部函数，并对不同自激电容和转速下的函数值进行计算。
Classifying the eigenvalues of the system, the eigenvalue real part functions are defined and the function values under different self-excited capacitances and rotating speeds are calculated.
对系统的特征值进行分类，定义特征值实部函数，并对不同自激电容和转速下的函数值进行计算。
Classifying the eigenvalues of the system, the eigenvalue real part functions are defined and the function values under different self-excited capacitances and rotating speeds are calculated.
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