Atrial fibrillation is the most common sustained arrhythmia and results in significant morbidity, especially in the elderly. The prevalence of atrial fibrillation increases dramatically with advancing age to almost 6%...Atrial fibrillation is the most common sustained arrhythmia and results in significant morbidity, especially in the elderly. The prevalence of atrial fibrillation increases dramatically with advancing age to almost 6% in individuals older than 65 years. In fact, 84% of people with atrial fibrillation are over 65 years of age.1 Additionally, the risk of stroke increases with advancing age, such that one-third of strokes in patients over the age of 65 are caused by atrial fibrillation.展开更多
In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain...In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain number p, this number p would be prime. And being m an integer number higher than (the lowest, the most efficient the operation). . If the result is an integer, this result will tell us how many permutations of two divisors, the input number has. As you can check, no recurrent division by odd or prime numbers is done, to check if the number is prime or has divisors. To get to this point, we will do the following. First, we will create a domain with all the composite numbers. This is easy, as you can just multiply one by one all the integers (greater or equal than 2) in that domain. So, you will get all the composite numbers (not getting any prime) in that domain. Then, we will use the Fourier transform to change from this original domain (called discrete time domain in this regards) to the frequency domain. There, we can check, using Parseval’s theorem, if a certain number is there or not. The use of Parseval’s theorem leads to the above integral. If the number p that we want to check is not in the domain, the result of the integral is zero and the number is a prime. If instead, the result is an integer, this integer will tell us how many permutations of two divisors the number p has. And, in consequence information how many factors, the number p has. So, for any number p lower than 2m?- 1, you can check if it is prime or not, just making the numerical definite integration. We will apply this integral in a computer program to check the efficiency of the operation. We will check, if no further developments are done, the numerical integration is inefficient computing-wise compared with brute-force checking. To be added, is the question regarding the level of accuracy needed (number of decimals and number of steps in the numerical integration) to have a reliable result for large numbers. This will be commented on the paper, but a separate study will be needed to have detailed conclusions. Of course, the best would be that in the future, an analytical result (or at least an approximation) for the summation or for the integration is achieved.展开更多
文摘Atrial fibrillation is the most common sustained arrhythmia and results in significant morbidity, especially in the elderly. The prevalence of atrial fibrillation increases dramatically with advancing age to almost 6% in individuals older than 65 years. In fact, 84% of people with atrial fibrillation are over 65 years of age.1 Additionally, the risk of stroke increases with advancing age, such that one-third of strokes in patients over the age of 65 are caused by atrial fibrillation.
文摘为实现弹道视景准实时仿真,建立了导弹弹道仿真模型,使用Multigen Creator创建了导弹三维模型及地形场景模型。基于Vega Prime分析了弹道视景准实时仿真流程及其关键技术,在Windows平台下通过定制高精度多媒体定时器实现了仿真的准实时性,以内存映射文件技术实现了弹道仿真程序与视景仿真程序跨进程的数据交互。在.NET框架下选用C++调用Vega Prime API函数编程完成了弹道视景准实时仿真程序的开发,验证了该方法的可用性。通过弹道视景准实时仿真,设计人员可以直观的观察和分析导弹飞行过程和飞行姿态的变化,为弹道分析与设计提供了参考。
文摘In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain number p, this number p would be prime. And being m an integer number higher than (the lowest, the most efficient the operation). . If the result is an integer, this result will tell us how many permutations of two divisors, the input number has. As you can check, no recurrent division by odd or prime numbers is done, to check if the number is prime or has divisors. To get to this point, we will do the following. First, we will create a domain with all the composite numbers. This is easy, as you can just multiply one by one all the integers (greater or equal than 2) in that domain. So, you will get all the composite numbers (not getting any prime) in that domain. Then, we will use the Fourier transform to change from this original domain (called discrete time domain in this regards) to the frequency domain. There, we can check, using Parseval’s theorem, if a certain number is there or not. The use of Parseval’s theorem leads to the above integral. If the number p that we want to check is not in the domain, the result of the integral is zero and the number is a prime. If instead, the result is an integer, this integer will tell us how many permutations of two divisors the number p has. And, in consequence information how many factors, the number p has. So, for any number p lower than 2m?- 1, you can check if it is prime or not, just making the numerical definite integration. We will apply this integral in a computer program to check the efficiency of the operation. We will check, if no further developments are done, the numerical integration is inefficient computing-wise compared with brute-force checking. To be added, is the question regarding the level of accuracy needed (number of decimals and number of steps in the numerical integration) to have a reliable result for large numbers. This will be commented on the paper, but a separate study will be needed to have detailed conclusions. Of course, the best would be that in the future, an analytical result (or at least an approximation) for the summation or for the integration is achieved.
