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Synthesis of structures is a very difficult task even with only a small number of components that form a system; yet it is the catalyst of innovation. Molecular structures and nanostructures typically have a large number of similar components but different connections, which manifests a more challenging task for their synthesis. <p> This thesis presents a novel method and its related algorithms and computer programs for the synthesis of structures. This novel method is based on several concepts: (1) the structure is represented by a graph and further by the adjacency matrix; and (2) instead of only exploiting the eigenvalue of the adjacency matrix, both the eigenvalue and the eigenvector are exploited; specifically the components of the eigenvector have been found very useful in algorithm development. This novel method is called the Eigensystem method.<p> The complexity of the Eigensystem method is equal to that of the famous program called Nauty in the combinatorial world. However, the Eigensystem method can work for the weighted and both directed and undirected graph, while the Nauty program can only work for the non-weighted and both directed and undirected graph. The cause for this is the different philosophies underlying these two methods. The Nauty program is based on the recursive component decomposition strategy, which could involve some unmanageable complexities when dealing with the weighted graph, albeit no such an attempt has been reported in the literature. It is noted that in practical applications of structure synthesis, weighted graphs are more useful than non-weighted graphs for representing physical systems. <p> Pivoted at the Eigensystem method, this thesis presents the algorithms and computer programs for the three fundamental problems in structure synthesis, namely the isomorphism/automorphism, the unique labeling, and the enumeration of the structures or graphs.

Synthesis of structures is a very difficult task even with only a small number of components that form a system; yet it is the catalyst of innovation. Molecular structures and nanostructures typically have a large number of similar components but different connections, which manifests a more challenging task for their synthesis. <p> This thesis presents a novel method and its related algorithms and computer programs for the synthesis of structures. This novel method is based on several concepts: (1) the structure is represented by a graph and further by the adjacency matrix; and (2) instead of only exploiting the eigenvalue of the adjacency matrix, both the eigenvalue and the eigenvector are exploited; specifically the components of the eigenvector have been found very useful in algorithm development. This novel method is called the Eigensystem method.<p> The complexity of the Eigensystem method is equal to that of the famous program called Nauty in the combinatorial world. However, the Eigensystem method can work for the weighted and both directed and undirected graph, while the Nauty program can only work for the non-weighted and both directed and undirected graph. The cause for this is the different philosophies underlying these two methods. The Nauty program is based on the recursive component decomposition strategy, which could involve some unmanageable complexities when dealing with the weighted graph, albeit no such an attempt has been reported in the literature. It is noted that in practical applications of structure synthesis, weighted graphs are more useful than non-weighted graphs for representing physical systems. <p> Pivoted at the Eigensystem method, this thesis presents the algorithms and computer programs for the three fundamental problems in structure synthesis, namely the isomorphism/automorphism, the unique labeling, and the enumeration of the structures or graphs.

An epicyclic-type automatic transmission is a device which is connected from engine to driving wheels, and the main purpose is to maintain the revolution speed of engine to be in a desired working range while accelerating or decelerating the automobile. The epicyclic -type automatic transmissions in production are mostly Ravigneaux-type epicyclic mechanisms, and in recent year, the development of automatic transmissions for automobile is oriented to the orientation of setting an single epicyclic gear mechanism instead of the input to bring various inputs of revolution speed to increase the total number of speed ratios of an automatic transmission, and such type of epicyclic is called combinational epicyclic-type automatic transmissions for automobiles. For the incompletion in the relative design methodology, a systematic methodology of designing mechanism and clutching-sequence of combinational epicyclic-type automobile transmission is described. First, fundamental principle of the combination and operations of automatic transmissions are analyzed to establish the design requirements. Second, a procedure of structure synthesis of combinational epicyclic-type automobile transmission is brought up which the planar graphic method is applied for. Third, based on Speed Ratio Relationship of each clutching sequence, a procedure of gearing-sequence is introduced. Finally, on the basis of the analytic method, the teeth of gears is to be clarified. The result of this work obtains five types of the combinational epicyclic-type automatic transmissions which could reach six speeds.