Papers by Keyword: Non-Isomorphism

Abstract: This paper clarifies the basic idea of design and construct for non-isomorphism block. The method of using standard edge matrix to structure block design is proposed, the whole process to design and construct (14, 8, 7, 4, 3) and (18, 9, 8, 4, 3) is introduced. It uses the side of each column of the standard edge matrix exactly, and also constitutes a complete graph by arranging the edge of complete graph to the initial matrix and re-arranging it to the standard edge matrix. According to the set of edge in standard edge matrix, 14 blocks of designing (14,8,7,4,3) and 18 blocks of designing (18,9,8,4,3) are obtained. Finally, it proved the number of design non-isomorphism (14, 8, 7, 4, 3) is 5, and (14, 8, 7, 4, 3) is 1.

Abstract: The Green’s functions technique suitable for broken symmetry structure analysis was developed. With the help of this new technique the phonon subsystem was analysed in ultrathin films and in cylindrical nanotubes with finite height. The most interesting results of mentioned analyses are spatial dependence of thermodynamical characteristics, existence of phonon gap and extremely low specific heat and thermal conductivity at low temperatures. This promises wide application of films and finite nanotubes in technology. The same technique was applied to investigate electron subsystems in rectangular nanostructures of all dimensions as well as in simple and full nanotubes. The most interesting conclusion of these analyses is the presence of autoreduction effect being the consequence of nonisomorphic transition configuration – momentum space. This effect represents a qualitative difference between nano and macroscopic structures. The skin effect is present in all types of nanostructures except nano-parallelepiped where antiskin effect takes place. The latter is quite understandable, since in nano-parallelepiped nodes are on boundaries.