算子演算

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。

For solving this nonideal problem, the orthogonality between the directional vector and the noise subspace with the same frequency can be used to establish a cost function. After finding the appropriate solution with the minimum cost function value through different optimization methods, the LCMV algorithm can use the result to calculate the optimum weight.

为了解决这项在波束成型上的非理想问题，我们利用了宽频信号的方向向量会和同频率的杂讯子空间正交的特性[4，5]去建立一个目标函数，利用不同的最佳化方法找出适当的解，再带入LCMV演算法中算出最佳权重。

We study the properties of $BR_0$-algebra and the total complication triple I method on complete $BR_0$-algebra, and we apply the results to $R_0$-Unite interval $\overline{W}$. Not only we have simplified the proof of the results of $R_0$-type triple I method on $R_0$-Unite interval $\overline{W}$, but also we make the proof to combine with the formal deductive system for fuzzy propositional calculus. This work also explains that the $R_0$-type triple I method is a matching fuzzy inference with $B{\cal L}^*$ system.

研究了基础$BR_0$-代数的性质和基于完备基础$BR_0$-代数的全蕴涵三I算法，对一般蕴涵算子给出了三I算法解存在的一个充分条件，并将结果应用于$R_0$-单位区间$\overline{W}$，不但极大的简化了$R_0$-单位区间$\overline{W}$的$R_0$-型$\alpha$-三I算法结果的证明，而且使其证明过程与相应的模糊命题演算系统结合起来，说明了$R_0$-型三I算法是与$B{\cal L}^*$系统相匹配的模糊推理方法。

We study the properties of BR0-algebra and the total complication triple I method on complete BR0-algebra, and we apply the results to R0-Unite interval W. Not only we have simplified the proof of the results of R0-type triple I method on R0-Unite interval W, but also we make the proof to combine with the formal deductive system for fuzzy propositional calculus. This work also explains that the R0-type triple I method is a matching fuzzy inference with B?

研究了基础BR0-代数的性质和基于完备基础BR0-代数的全蕴涵三I算法，对—般蕴涵算子给出了三I算法解存在的—个充分条件，并将结果应用于R0-单位区间W，不但极大的简化了R0-单位区间W的R0-型α-三I算法结果的证明，而且使其证明过程与相应的模糊命题演算系统结合起来，说明了R0-型三I算法是与B？

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。