Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I ex...Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.展开更多
Scalability is an important issue in the design of interconnection networks for massively parallel systems. In this paper a scalable class of interconnection network of Hex-Cell for massively parallel systems is intro...Scalability is an important issue in the design of interconnection networks for massively parallel systems. In this paper a scalable class of interconnection network of Hex-Cell for massively parallel systems is introduced. It is called Multilayer Hex-Cell (MLH). A node addressing scheme and routing algorithm are also presented and discussed. An interesting feature of the proposed MLH is that it maintains a constant network degree regardless of the increase in the network size degree which facilitates modularity in building blocks of scalable systems. The new addressing node scheme makes the proposed routing algorithm simple and efficient in terms of that it needs a minimum number of calculations to reach the destination node. Moreover, the diameter of the proposed MLH is less than Hex-Cell network.展开更多
文摘Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.
文摘Scalability is an important issue in the design of interconnection networks for massively parallel systems. In this paper a scalable class of interconnection network of Hex-Cell for massively parallel systems is introduced. It is called Multilayer Hex-Cell (MLH). A node addressing scheme and routing algorithm are also presented and discussed. An interesting feature of the proposed MLH is that it maintains a constant network degree regardless of the increase in the network size degree which facilitates modularity in building blocks of scalable systems. The new addressing node scheme makes the proposed routing algorithm simple and efficient in terms of that it needs a minimum number of calculations to reach the destination node. Moreover, the diameter of the proposed MLH is less than Hex-Cell network.
