In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the br...In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.展开更多
Traditionally, in weak interaction, I<sub>3</sub>, Y and four flavour quantum numbers are not conserved but several empirical selection rules work well. Recently, it was found that, in weak interaction, th...Traditionally, in weak interaction, I<sub>3</sub>, Y and four flavour quantum numbers are not conserved but several empirical selection rules work well. Recently, it was found that, in weak interaction, there are three levels of conservation of additive quantum numbers, and fermion quantum number F is conserved in all kinds of interactions. It is known that weak interaction has three types: fermionic, pure hadronic and pure leptonic, corresponding to the first and the second level of conservation of additive quantum numbers respectively. It is demonstrated in this paper that the selection rules in all types of weak interaction can be interpreted by conservation of F, and the formula of relation between Q/e, F and F<sub>0</sub> is more general than Gell-Mann-Nishijima formula. Description of weak interaction becomes simpler, If only we take Q, F<sub>0</sub> and F, based on the conserved physical quantities.展开更多
Refined 3D modeling of mine slopes is pivotal for precise prediction of geological hazards.Aiming at the inadequacy of existing single modeling methods in comprehensively representing the overall and localized charact...Refined 3D modeling of mine slopes is pivotal for precise prediction of geological hazards.Aiming at the inadequacy of existing single modeling methods in comprehensively representing the overall and localized characteristics of mining slopes,this study introduces a new method that fuses model data from Unmanned aerial vehicles(UAV)tilt photogrammetry and 3D laser scanning through a data alignment algorithm based on control points.First,the mini batch K-Medoids algorithm is utilized to cluster the point cloud data from ground 3D laser scanning.Then,the elbow rule is applied to determine the optimal cluster number(K0),and the feature points are extracted.Next,the nearest neighbor point algorithm is employed to match the feature points obtained from UAV tilt photogrammetry,and the internal point coordinates are adjusted through the distanceweighted average to construct a 3D model.Finally,by integrating an engineering case study,the K0 value is determined to be 8,with a matching accuracy between the two model datasets ranging from 0.0669 to 1.0373 mm.Therefore,compared with the modeling method utilizing K-medoids clustering algorithm,the new modeling method significantly enhances the computational efficiency,the accuracy of selecting the optimal number of feature points in 3D laser scanning,and the precision of the 3D model derived from UAV tilt photogrammetry.This method provides a research foundation for constructing mine slope model.展开更多
The generation of good pseudo-random numbers is the base of many important fields in scientific computing, such as randomized algorithms and numerical solution of stochastic differential equations. In this paper, a cl...The generation of good pseudo-random numbers is the base of many important fields in scientific computing, such as randomized algorithms and numerical solution of stochastic differential equations. In this paper, a class of random number generators （RNGs） based on Weyl sequence is proposed. The uniformity of those RNGs is proved theoretically. Statistical and numerical computations show the efficiency of the methods.展开更多
Prime numbers are the integers that cannot be divided exactly by another integer other than one and itself. Prime numbers are notoriously disobedient to rules: they seem to be randomly distributed among natural number...Prime numbers are the integers that cannot be divided exactly by another integer other than one and itself. Prime numbers are notoriously disobedient to rules: they seem to be randomly distributed among natural numbers with no laws except that of chance. Questions about prime numbers have been perplexing mathematicians over centuries. How to efficiently predict greater prime numbers has been a great challenge for many. Most of the previous studies focus on how many prime numbers there are in certain ranges or patterns of the first or last digits of prime numbers. Honestly, although these patterns are true, they help little with accurately predicting new prime numbers, as a deviation at any digit is enough to annihilate the primality of a number. The author demonstrates the periodicity and inter-relationship underlying all prime numbers that makes the occurrence of all prime numbers predictable. This knowledge helps to fish all prime numbers within one net and will help to speed up the related research.展开更多
This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change ...This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change by the Collatz conjecture. 1) This positive integer will change to an odd number;2) The odd number must change to a number of LiKe’s second sequence {3<sup>n</sup> – 1| n ∈ Z<sup>+</sup>};3) Then this 3<sup>n</sup> - 1 will change to a smaller 3<sup>n </sup>– 1 and gradually decrease to 8 (that is 3<sup>2</sup> - 1) then back to 1 in the end. If we can determine each step, the Collatz conjecture will be true. This is certainly more valuable than 2<sup>n</sup> (it might even explain 2<sup>n</sup>). And to illustrate the importance of this rule, introduced some important funny corollaries related to it.展开更多
The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According t...The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According to the fuzzy probability theory and the robust designprinciple, the robust design rule based on fuzzy probability (named fuzzy robust design rule forshort) was put forward and its validity and practicability were analyzed and tested with a designexample. The theoretical analysis and the design examples make clear that, while the fuzzy robustdesign rule was used, the fine design effect can be obtained and the fuzzy robust design rule can bevery suitable for the choice of the membership function of the fuzzy target; so it has a particularadvantage.展开更多
In plasmonic systems, the response of nanoobjects under light illumination can produce complex optical maps. Such plasmonic or resonant systems have interesting characteristics such as sensitivity on parameters and in...In plasmonic systems, the response of nanoobjects under light illumination can produce complex optical maps. Such plasmonic or resonant systems have interesting characteristics such as sensitivity on parameters and initial conditions. In this paper, we show how these complex maps can be cryptographically improved and associated in order to design a secure pseudo random number generator.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12274046,11874094,and 12147102)Chongqing Natural Science Foundation(Grant No.CSTB2022NSCQ-JQX0018)Fundamental Research Funds for the Central Universities(Grant No.2021CDJZYJH-003).
文摘In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.
文摘Traditionally, in weak interaction, I<sub>3</sub>, Y and four flavour quantum numbers are not conserved but several empirical selection rules work well. Recently, it was found that, in weak interaction, there are three levels of conservation of additive quantum numbers, and fermion quantum number F is conserved in all kinds of interactions. It is known that weak interaction has three types: fermionic, pure hadronic and pure leptonic, corresponding to the first and the second level of conservation of additive quantum numbers respectively. It is demonstrated in this paper that the selection rules in all types of weak interaction can be interpreted by conservation of F, and the formula of relation between Q/e, F and F<sub>0</sub> is more general than Gell-Mann-Nishijima formula. Description of weak interaction becomes simpler, If only we take Q, F<sub>0</sub> and F, based on the conserved physical quantities.
基金funded by National Natural Science Foundation of China(Grant Nos.42272333,42277147).
文摘Refined 3D modeling of mine slopes is pivotal for precise prediction of geological hazards.Aiming at the inadequacy of existing single modeling methods in comprehensively representing the overall and localized characteristics of mining slopes,this study introduces a new method that fuses model data from Unmanned aerial vehicles(UAV)tilt photogrammetry and 3D laser scanning through a data alignment algorithm based on control points.First,the mini batch K-Medoids algorithm is utilized to cluster the point cloud data from ground 3D laser scanning.Then,the elbow rule is applied to determine the optimal cluster number(K0),and the feature points are extracted.Next,the nearest neighbor point algorithm is employed to match the feature points obtained from UAV tilt photogrammetry,and the internal point coordinates are adjusted through the distanceweighted average to construct a 3D model.Finally,by integrating an engineering case study,the K0 value is determined to be 8,with a matching accuracy between the two model datasets ranging from 0.0669 to 1.0373 mm.Therefore,compared with the modeling method utilizing K-medoids clustering algorithm,the new modeling method significantly enhances the computational efficiency,the accuracy of selecting the optimal number of feature points in 3D laser scanning,and the precision of the 3D model derived from UAV tilt photogrammetry.This method provides a research foundation for constructing mine slope model.
基金Supported by National Natural Science Foundation of China （19871047）and National Key Basic Research Special Fund（1998020306）.
文摘The generation of good pseudo-random numbers is the base of many important fields in scientific computing, such as randomized algorithms and numerical solution of stochastic differential equations. In this paper, a class of random number generators （RNGs） based on Weyl sequence is proposed. The uniformity of those RNGs is proved theoretically. Statistical and numerical computations show the efficiency of the methods.
文摘Prime numbers are the integers that cannot be divided exactly by another integer other than one and itself. Prime numbers are notoriously disobedient to rules: they seem to be randomly distributed among natural numbers with no laws except that of chance. Questions about prime numbers have been perplexing mathematicians over centuries. How to efficiently predict greater prime numbers has been a great challenge for many. Most of the previous studies focus on how many prime numbers there are in certain ranges or patterns of the first or last digits of prime numbers. Honestly, although these patterns are true, they help little with accurately predicting new prime numbers, as a deviation at any digit is enough to annihilate the primality of a number. The author demonstrates the periodicity and inter-relationship underlying all prime numbers that makes the occurrence of all prime numbers predictable. This knowledge helps to fish all prime numbers within one net and will help to speed up the related research.
文摘This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change by the Collatz conjecture. 1) This positive integer will change to an odd number;2) The odd number must change to a number of LiKe’s second sequence {3<sup>n</sup> – 1| n ∈ Z<sup>+</sup>};3) Then this 3<sup>n</sup> - 1 will change to a smaller 3<sup>n </sup>– 1 and gradually decrease to 8 (that is 3<sup>2</sup> - 1) then back to 1 in the end. If we can determine each step, the Collatz conjecture will be true. This is certainly more valuable than 2<sup>n</sup> (it might even explain 2<sup>n</sup>). And to illustrate the importance of this rule, introduced some important funny corollaries related to it.
文摘The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According to the fuzzy probability theory and the robust designprinciple, the robust design rule based on fuzzy probability (named fuzzy robust design rule forshort) was put forward and its validity and practicability were analyzed and tested with a designexample. The theoretical analysis and the design examples make clear that, while the fuzzy robustdesign rule was used, the fine design effect can be obtained and the fuzzy robust design rule can bevery suitable for the choice of the membership function of the fuzzy target; so it has a particularadvantage.
基金the Region Champagne- Ardennes and the Conseil Regional de l’Aube
文摘In plasmonic systems, the response of nanoobjects under light illumination can produce complex optical maps. Such plasmonic or resonant systems have interesting characteristics such as sensitivity on parameters and initial conditions. In this paper, we show how these complex maps can be cryptographically improved and associated in order to design a secure pseudo random number generator.
