本文研究动力系统的线性群作用，该群的李代数与系统的向量场作用，以及两者间的关系．并将其结果应用于n阶旋转群，给出了n阶旋转对称非线性系统的一般结构表达式。

We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root–of-Not (i.e. Controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and uses group theory. We devise a novel technique that transforms the quantum logic synthesis problem from a multi-valued constrained optimization problem to a group permutation problem. The transformation enables us to utilize group theory to exploit the properties of the synthesis problem. Assuming a cost of one for each two-qubit gate, we found all reversible circuits with quantum costs of 4, 5, 6, etc, and give another algorithm to realize these reversible circuits with quantum gates.

In this paper, terminal sliding mode control design is considered. A control method, different from many existing terminal sliding model control design methods, is proposed based on a new switching law and continuous finite-time control ideas. Then terminal sliding mode control laws are constructed for some classes of nonlinear systems.

Reversible logic plays an important role in the synthesis of circuits for quantum computing. In this paper, we introduce families of reversible gates based on the majority Boolean function (MBF) and we prove their properties in reversible circuit synthesis. These gates can be used to synthesize reversible circuits of minimum "scratchpad register width" for arbitrary reversible functions.We show that, given a MBF f with 2k+1 inputs, f can be implemented by a reversible logic gate with 2k+1 inputs and 2k+1 outputs, i.e., without any constant inputs.We also demonstrate new gates from this family with very efficient quantum realizations for majority-based applications. They can be used to synthesize any reversible function of the same width in conjunction with inverters and Feynman (2-qubit controlled-NOT) gates. The gate universality problem is formulated in terms of elementary group theory and solved using the algebraic software GAP.

This paper investigates the synthesis of quantum networks built to realize ternary switching circuits in the absence of ancilla bits. The results we established are twofold. The first shows that ternary Swap, ternary Not and ternary Toffoli gates are universal for the realization of arbitrary n × n ternary quantum switching networks without ancilla bits. The second result proves that all n × n quantum ternary networks can be generated by Not, Controlled-Not, Multiply-Two, and Toffoli gates. Our approach is constructive.