Polyimide thin films were prepared by vapor-deposition polymerization. Naphthalene carboxylic dianhydride (NTCDA) was coevaporated with either diamino naphthalene (DAN) or diamino benzophenone (DAB). Coevaporation of dianhydride and diamines yielded thin films of polyamic acids. A polyimide thin film was obtained by annealing the codeposited film of NTCDA-DAB. On the other hand, the codeposited film of NTCDA-DAN was not imidized by annealing. In both cases, chemical structures of the products were not largely influenced by the molar ratio of depositing monomers if sufficient amount of diamine molecules are supplied in the coevaporation process.

Graph products have important role in constructing many useful networks. It is known that there are four basic graph products. Properties of each product have been studied individually. We propose a unified approach to these products based on the distance in graphs, and new two products on graphs. The viewpoint of products based on the distance introduced here provides a family of products that includes almost known graph products as extremal ones and suggests new products. Also,we study relations among these six products. Finally, we investigate several classes of graph products in those context.

This paper deals with graph colouring games, an example of pseudo-telepathy, in which two players can convince a verifier that a graph G is c-colourable where c is less than the chromatic number of the graph. They win the game if they convince the verifier. It is known that the players cannot win if they share only classical information, but they can win in some cases by sharing entanglement. The smallest known graph where the players win in the quantum setting, but not in the classical setting, was found by Galliard, Tapp and Wolf and has 32,768 vertices. It is a connected component of the Hadamard graph GN with N=c=16. Their protocol applies only to Hadamard graphs where N is a power of 2. We propose a protocol that applies to all Hadamard graphs. Combined with a result of Frankl, this shows that the players can win on any induced subgraph of G12 having 1609 vertices, with c=12. Moreover combined with a result of Godsil and Newman, our result shows that all Hadamard graphs GN (N ≥ 12) and c=N yield pseudo-telepathy games.

In this paper we give a simple algorithm to generate all partitions of a positive integer n. The problem is one of the basic problems in combinatorics, and has been extensively studied for a long time. Our algorithm generates each partition of a given integer in constant time for each without repetition, while best known algorithm generates each partition in constant time on "average." Also, we propose some algorithms to generate all partitions of an integer with some additional property in constant time.