As expounded in some recent mathematical conferences, this research on that amazing source of algebraic ideas known as Fermat＇s equation is aimed to prove how Fermat triples can be limited until the impossible existe...As expounded in some recent mathematical conferences, this research on that amazing source of algebraic ideas known as Fermat＇s equation is aimed to prove how Fermat triples can be limited until the impossible existence through a criterion of incompatible parities related to unexplored properties of the binomial coefficients. In this paper, the authors use a technique based on the analysis of four numbers and their internal relations with three basic compulsory factors. It leads to the practical impossibility to find any triple of natural numbers candidate to satisfy Fermat＇s equation, because when the authors try to meet a condition between parity and range the authors are compelled to violate the other one, so that they are irreducibly alternative. In particular, there is a parity violation when the authors choose all the basic factors in the allowed range and the authors obtain exceeding values of one of the involved variables when the authors try to restore the parity. Since Fermat＇s last theorem would consequently be demonstrated, many readers could recall the never found elementary proof of FLT （Fermat＇s last theorem） claimed by Pierre de Fermat. The authors are not encouraging such an interpretation because this paper is intended as a journey into Fermat＇s equation and the reader＇s attitude should be towards the algebraic achievements here proposed, with their possible hidden flaws and future developments, rather than to legendary problems like Fermat＇s riddle.展开更多
With the advent of Internet services, big data and cloud computing, high-throughput computing has generated much research interest, especially on high-throughput cloud servers. However, three basic questions are still...With the advent of Internet services, big data and cloud computing, high-throughput computing has generated much research interest, especially on high-throughput cloud servers. However, three basic questions are still not satis-factorily answered： （1） What are the basic metrics （what throughput and high-throughput of what）？ （2） What are the main factors most beneficial to increasing throughput？ （3） Are there any fundamental constraints and how high can the throughput go？ This article addresses these issues by uti- lizing the fifty-year progress in Little＇s law, to reveal three fundamental relations among the seven basic quantities of throughput （2）, number of active threads （L）, waiting time （W）, system power （P）, thread energy （E）, Watts per thread to, threads per Joule 0. In addition to Little＇s law L = λW, we obtain P =λE and λ = Lto0, under reasonable assumptions. These equations help give a first order estimation of per- formance and power consumption targets for billion-thread cloud servers.展开更多
文摘As expounded in some recent mathematical conferences, this research on that amazing source of algebraic ideas known as Fermat＇s equation is aimed to prove how Fermat triples can be limited until the impossible existence through a criterion of incompatible parities related to unexplored properties of the binomial coefficients. In this paper, the authors use a technique based on the analysis of four numbers and their internal relations with three basic compulsory factors. It leads to the practical impossibility to find any triple of natural numbers candidate to satisfy Fermat＇s equation, because when the authors try to meet a condition between parity and range the authors are compelled to violate the other one, so that they are irreducibly alternative. In particular, there is a parity violation when the authors choose all the basic factors in the allowed range and the authors obtain exceeding values of one of the involved variables when the authors try to restore the parity. Since Fermat＇s last theorem would consequently be demonstrated, many readers could recall the never found elementary proof of FLT （Fermat＇s last theorem） claimed by Pierre de Fermat. The authors are not encouraging such an interpretation because this paper is intended as a journey into Fermat＇s equation and the reader＇s attitude should be towards the algebraic achievements here proposed, with their possible hidden flaws and future developments, rather than to legendary problems like Fermat＇s riddle.
文摘With the advent of Internet services, big data and cloud computing, high-throughput computing has generated much research interest, especially on high-throughput cloud servers. However, three basic questions are still not satis-factorily answered： （1） What are the basic metrics （what throughput and high-throughput of what）？ （2） What are the main factors most beneficial to increasing throughput？ （3） Are there any fundamental constraints and how high can the throughput go？ This article addresses these issues by uti- lizing the fifty-year progress in Little＇s law, to reveal three fundamental relations among the seven basic quantities of throughput （2）, number of active threads （L）, waiting time （W）, system power （P）, thread energy （E）, Watts per thread to, threads per Joule 0. In addition to Little＇s law L = λW, we obtain P =λE and λ = Lto0, under reasonable assumptions. These equations help give a first order estimation of per- formance and power consumption targets for billion-thread cloud servers.
