一、主办、承办机构及教学指导委员会主办机构:美国Syracuse大学信息学院(Syracuse University School of Information Studies.网址:http://ischool.syr.edu/)国家科技图书文献中心(NSTL)(网址:http://www.nstl.gov.cn)
The definition of Collatz Operator, the mathematical avatar of the Collatz Algorithm, permits the transformation of the Collatz conjecture, which is delineated over the whole natural number set, into an equivalent inf...The definition of Collatz Operator, the mathematical avatar of the Collatz Algorithm, permits the transformation of the Collatz conjecture, which is delineated over the whole natural number set, into an equivalent inference restricted to the odd prime number set only. Based on this redefinition, one can describe an empirical-heuristic proof of the Collatz conjecture.展开更多
The aim of this paper is to study the 3x + 1 problem based on the Collatz iterative formula. It can be seen from the iterative formula that the necessary condition for the Collatz iteration convergence is that its slo...The aim of this paper is to study the 3x + 1 problem based on the Collatz iterative formula. It can be seen from the iterative formula that the necessary condition for the Collatz iteration convergence is that its slope being less than 1. An odd number N that satisfies the condition of a slope less than 1 after n<sup>th</sup> Collatz iterations is defined as an n-step odd number. Through statistical analysis, it is found that after n<sup>th</sup> Collatz iterations, the iterative value of any n-step odd number N that is greater than 1 is less than N, which proves that the slope less than 1 is a sufficient and necessary condition for Collatz iteration convergence.展开更多
During the Classical period,the Greek tyrants,with Syracuse as their center,established a state that governed most of Sicily and southern Italy.In terms of state structure and organizational methods,the Syracusan city...During the Classical period,the Greek tyrants,with Syracuse as their center,established a state that governed most of Sicily and southern Italy.In terms of state structure and organizational methods,the Syracusan city-state grew strong through its siphoning effect on surrounding areas,while other city-states gradually dissolved.The two formed a hierarchical structure characterized by coercion,utilitarianism,and totality and linked by corresponding political organizational methods,which differed significantly from the logic of city-state governance.In terms of national identity,the Greeks in Sicily lacked the foundation for identification with their native Greek city-states.Memory identification related to the city’s founding myths and regional identification related to the concept of Sikeliotai emerged successively,but in effect,they were subordinated to the tyrant’s identification,marking a shift in the collective identity of the people from essential will to elective will.The Greek state in Sicily was not an isolated,static union of city-state“communities,”but rather a regional,connected“society”that constantly interacted with its surrounding areas.展开更多
文摘一、主办、承办机构及教学指导委员会主办机构:美国Syracuse大学信息学院(Syracuse University School of Information Studies.网址:http://ischool.syr.edu/)国家科技图书文献中心(NSTL)(网址:http://www.nstl.gov.cn)
文摘The definition of Collatz Operator, the mathematical avatar of the Collatz Algorithm, permits the transformation of the Collatz conjecture, which is delineated over the whole natural number set, into an equivalent inference restricted to the odd prime number set only. Based on this redefinition, one can describe an empirical-heuristic proof of the Collatz conjecture.
文摘The aim of this paper is to study the 3x + 1 problem based on the Collatz iterative formula. It can be seen from the iterative formula that the necessary condition for the Collatz iteration convergence is that its slope being less than 1. An odd number N that satisfies the condition of a slope less than 1 after n<sup>th</sup> Collatz iterations is defined as an n-step odd number. Through statistical analysis, it is found that after n<sup>th</sup> Collatz iterations, the iterative value of any n-step odd number N that is greater than 1 is less than N, which proves that the slope less than 1 is a sufficient and necessary condition for Collatz iteration convergence.
文摘During the Classical period,the Greek tyrants,with Syracuse as their center,established a state that governed most of Sicily and southern Italy.In terms of state structure and organizational methods,the Syracusan city-state grew strong through its siphoning effect on surrounding areas,while other city-states gradually dissolved.The two formed a hierarchical structure characterized by coercion,utilitarianism,and totality and linked by corresponding political organizational methods,which differed significantly from the logic of city-state governance.In terms of national identity,the Greeks in Sicily lacked the foundation for identification with their native Greek city-states.Memory identification related to the city’s founding myths and regional identification related to the concept of Sikeliotai emerged successively,but in effect,they were subordinated to the tyrant’s identification,marking a shift in the collective identity of the people from essential will to elective will.The Greek state in Sicily was not an isolated,static union of city-state“communities,”but rather a regional,connected“society”that constantly interacted with its surrounding areas.
