This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
We are developing an optical layer-2s witch network that uses both wavelength-division multiplexing and time-division multiplexing technologies for efficient traffic aggregation in metro networks.For efficient traffic...We are developing an optical layer-2s witch network that uses both wavelength-division multiplexing and time-division multiplexing technologies for efficient traffic aggregation in metro networks.For efficient traffic aggregation,path bandwidth control is key because it strongly affects bandwidth efficiency.For this paper,we propose a dynamic time-slot allocation method that uses periodic information of difference values of traffic variation.This method can derive near-optimal allocation with lower computational cost,which enlarges the maximum available network size compared with conventional time-slot allocation methods.Numerical results show that the proposed method enables dynamic path control in 1K-node-scale optical layer-2s witch network,which leads to cost-effective metro networks.展开更多
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
文摘We are developing an optical layer-2s witch network that uses both wavelength-division multiplexing and time-division multiplexing technologies for efficient traffic aggregation in metro networks.For efficient traffic aggregation,path bandwidth control is key because it strongly affects bandwidth efficiency.For this paper,we propose a dynamic time-slot allocation method that uses periodic information of difference values of traffic variation.This method can derive near-optimal allocation with lower computational cost,which enlarges the maximum available network size compared with conventional time-slot allocation methods.Numerical results show that the proposed method enables dynamic path control in 1K-node-scale optical layer-2s witch network,which leads to cost-effective metro networks.
