This paper considers an eigenvalue problem containing small stochastic processes. For every fixed is, we can use the Prufer substitution to prove the existence of the random solutions lambda(n) and u(n) in the meaning...This paper considers an eigenvalue problem containing small stochastic processes. For every fixed is, we can use the Prufer substitution to prove the existence of the random solutions lambda(n) and u(n) in the meaning of large probability. These solutions can be expanded in epsilon regularly, and their correction terms can be obtained by solving some random linear differential equations.展开更多
In this paper, we consider the planar multi-facility Weber problem with restricted zones and non-Euclidean distances, propose an algorithm based on the probability changing method (special kind of genetic algorithms) ...In this paper, we consider the planar multi-facility Weber problem with restricted zones and non-Euclidean distances, propose an algorithm based on the probability changing method (special kind of genetic algorithms) and prove its efficiency for approximate solving this problem by replacing the continuous coordinate values by discrete ones. Version of the algorithm for multiprocessor systems is proposed. Experimental results for a high-performance cluster are given.展开更多
The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the water depth is always positiv...The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the water depth is always positive. In this paper, we choose four test problems with exact solutions for the 1D SWEs. Each test problem is a RP with one of the four possible wave patterns as its solution. These problems are numerically solved using schemes from the family of Weighted Essentially Non-Oscillatory (WENO) methods. For comparison purposes, we also include results obtained from the Random Choice Method (RCM). This study has three main objectives. Firstly, we outline the procedures for the implementation of the methods employed in this paper. Secondly, we assess the performance of the schemes in conjunction with a second-order Total Variation Diminishing (TVD) flux on a variety of RPs for the 1D SWEs (for both short- and long-time simulations). Thirdly, we investigate if a single method yields optimal outcomes for all test problems. Optimal outcomes refer to numerical solutions devoid of spurious oscillations, exhibiting high resolution of discontinuities, and attaining high-order accuracy in the smooth parts of the solution.展开更多
Based on decisional Difiie-Hcllman problem, we propose a simpleproxy-protected signature scheme In the random oracle model, we also carry out the strict securityproof for the proposed scheme. The security of the propo...Based on decisional Difiie-Hcllman problem, we propose a simpleproxy-protected signature scheme In the random oracle model, we also carry out the strict securityproof for the proposed scheme. The security of the proposed scheme is not loosely related to thediscrete logarithm assumption hut tightly related to the decisional Diffie-Hellman assumption in therandom oracle model.展开更多
In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for ...In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces are given. As applications, some existence theorems of weak random solutions for the random Cauchy problem of a system of nonlinear random differential equations are obtained, as well as the existence of extremal random solutions and random comparison results for these systems of random equations relative to weak topology in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.展开更多
In this paper, we analyze the effect of both deter- ministic and random perturbations of a regular multi-layered elastic structure on its stop band properties. The tool of choice is the transfer matrix method, which i...In this paper, we analyze the effect of both deter- ministic and random perturbations of a regular multi-layered elastic structure on its stop band properties. The tool of choice is the transfer matrix method, which is both versatile and easy to implement. In both cases, we find that the stop-bands widen. We observe the appearance of very narrow pass-bands within the stop-bands, which can be observed in other instances in optics.展开更多
In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the nu...In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the numerical solutions are studied. The statistical properties of the numerical solutions are computed through numerical case studies.展开更多
The location of the distribution facilities and the routing of the vehicles from these facilities are interdependent in many distribution systems. Such a concept recognizes the interdependence;attempts to integrate th...The location of the distribution facilities and the routing of the vehicles from these facilities are interdependent in many distribution systems. Such a concept recognizes the interdependence;attempts to integrate these two decisions have been limited. Multi-objective location-routing problem (MLRP) is combined with the facility location and the vehicle routing decision and satisfied the different objectives. Due to the problem complexity, simultaneous solution methods are limited, which are given in different objectives with conflicts in functions satisfied. Two kinds of optimal mathematical models are proposed for the solution of MLRP. Three methods have been emphatically developed for MLRP. MGA architecture makes it possible to search the solution space efficiently, which provides a path for searching the solution with two-objective LRP. At last the practical proof is given by random analysis for regional distribution with nine cities.展开更多
<em>k</em>-ary trees are one of the most basic data structures in Computer Science. A new method is presented to determine how many there are with n nodes. This method gives additional insight into their s...<em>k</em>-ary trees are one of the most basic data structures in Computer Science. A new method is presented to determine how many there are with n nodes. This method gives additional insight into their structure and provides a new algo-rithm to efficiently generate such a tree randomly.展开更多
This study attempts to solve vehicle routing problem with time window (VRPTW). The study first identifies the real problems and suggests some recommendations on the issues. The technique used in this study is Genetic ...This study attempts to solve vehicle routing problem with time window (VRPTW). The study first identifies the real problems and suggests some recommendations on the issues. The technique used in this study is Genetic Algorithm (GA) and initialization applied is random population method. The objective of the study is to assign a number of vehicles to routes that connect customers and depot such that the overall distance travelled is minimized and the delivery operations are completed within the time windows requested by the customers. The analysis reveals that the problems experienced in vehicle routing with time window can be solved by GA and retrieved for optimal solutions. After a thorough study on VRPTW, it is highly recommended that a company should implement the optimal routes derived from the study to increase the efficiency and accuracy of delivery with time insertion.展开更多
Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of linear problems are difficult to be managed by the theoreti...Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of linear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an effective tool to investigate the nonlinear problems.展开更多
The simulation of multi-domain,multi-physics mathematical models with uncertain parameters can be quite demanding in terms of algorithm design and com-putation costs.Our main objective in this paper is to examine a ph...The simulation of multi-domain,multi-physics mathematical models with uncertain parameters can be quite demanding in terms of algorithm design and com-putation costs.Our main objective in this paper is to examine a physical interface coupling between two random dissipative systems with uncertain parameters.Due to the complexity and uncertainty inherent in such interface-coupled problems,un-certain diffusion coefficients or friction parameters often arise,leading to consid-ering random systems.We employ Monte Carlo methods to produce independent and identically distributed deterministic heat-heat model samples to address ran-dom systems,and adroitly integrate the ensemble idea to facilitate the fast calcu-lation of these samples.To achieve unconditional stability,we introduce the scalar auxiliary variable(SAV)method to overcome the time constraints of the ensemble implicit-explicit algorithm.Furthermore,for a more accurate and stable scheme,the ensemble data-passing algorithm is raised,which is unconditionally stable and convergent without any auxiliary variables.These algorithms employ the same co-efficient matrix for multiple linear systems and enable easy parallelization,which can significantly reduce the computational cost.Finally,numerical experiments are conducted to support the theoretical results and showcase the unique features of the proposed algorithms.展开更多
This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT prob...This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT problem unsatisfiable with high probability,where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random(k-1,2(k-1)s)-CNF formula.Let F be a regular balanced random(k,2s)-CNF formula where k≥3,then there exists a number so such that F is(1,O)-unsatisfiable with high probability if s>so.A numerical solution of the number so when k e(5,6,...,14)is given to conduct simulated experiments.The simulated experiments verify the theoretical result.Besides,the experiments also suggest that F is(1,O)-satisfiable with high probability if s is less than a certain value.展开更多
文摘This paper considers an eigenvalue problem containing small stochastic processes. For every fixed is, we can use the Prufer substitution to prove the existence of the random solutions lambda(n) and u(n) in the meaning of large probability. These solutions can be expanded in epsilon regularly, and their correction terms can be obtained by solving some random linear differential equations.
文摘In this paper, we consider the planar multi-facility Weber problem with restricted zones and non-Euclidean distances, propose an algorithm based on the probability changing method (special kind of genetic algorithms) and prove its efficiency for approximate solving this problem by replacing the continuous coordinate values by discrete ones. Version of the algorithm for multiprocessor systems is proposed. Experimental results for a high-performance cluster are given.
文摘The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the water depth is always positive. In this paper, we choose four test problems with exact solutions for the 1D SWEs. Each test problem is a RP with one of the four possible wave patterns as its solution. These problems are numerically solved using schemes from the family of Weighted Essentially Non-Oscillatory (WENO) methods. For comparison purposes, we also include results obtained from the Random Choice Method (RCM). This study has three main objectives. Firstly, we outline the procedures for the implementation of the methods employed in this paper. Secondly, we assess the performance of the schemes in conjunction with a second-order Total Variation Diminishing (TVD) flux on a variety of RPs for the 1D SWEs (for both short- and long-time simulations). Thirdly, we investigate if a single method yields optimal outcomes for all test problems. Optimal outcomes refer to numerical solutions devoid of spurious oscillations, exhibiting high resolution of discontinuities, and attaining high-order accuracy in the smooth parts of the solution.
文摘Based on decisional Difiie-Hcllman problem, we propose a simpleproxy-protected signature scheme In the random oracle model, we also carry out the strict securityproof for the proposed scheme. The security of the proposed scheme is not loosely related to thediscrete logarithm assumption hut tightly related to the decisional Diffie-Hellman assumption in therandom oracle model.
文摘In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces are given. As applications, some existence theorems of weak random solutions for the random Cauchy problem of a system of nonlinear random differential equations are obtained, as well as the existence of extremal random solutions and random comparison results for these systems of random equations relative to weak topology in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.
基金a Marie Curie Transfer of Knowledge Fellowship of the European Community's Sixth Framework Programme under contract number(MTKD-CT-2004-509809)
文摘In this paper, we analyze the effect of both deter- ministic and random perturbations of a regular multi-layered elastic structure on its stop band properties. The tool of choice is the transfer matrix method, which is both versatile and easy to implement. In both cases, we find that the stop-bands widen. We observe the appearance of very narrow pass-bands within the stop-bands, which can be observed in other instances in optics.
文摘In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the numerical solutions are studied. The statistical properties of the numerical solutions are computed through numerical case studies.
文摘The location of the distribution facilities and the routing of the vehicles from these facilities are interdependent in many distribution systems. Such a concept recognizes the interdependence;attempts to integrate these two decisions have been limited. Multi-objective location-routing problem (MLRP) is combined with the facility location and the vehicle routing decision and satisfied the different objectives. Due to the problem complexity, simultaneous solution methods are limited, which are given in different objectives with conflicts in functions satisfied. Two kinds of optimal mathematical models are proposed for the solution of MLRP. Three methods have been emphatically developed for MLRP. MGA architecture makes it possible to search the solution space efficiently, which provides a path for searching the solution with two-objective LRP. At last the practical proof is given by random analysis for regional distribution with nine cities.
文摘<em>k</em>-ary trees are one of the most basic data structures in Computer Science. A new method is presented to determine how many there are with n nodes. This method gives additional insight into their structure and provides a new algo-rithm to efficiently generate such a tree randomly.
文摘This study attempts to solve vehicle routing problem with time window (VRPTW). The study first identifies the real problems and suggests some recommendations on the issues. The technique used in this study is Genetic Algorithm (GA) and initialization applied is random population method. The objective of the study is to assign a number of vehicles to routes that connect customers and depot such that the overall distance travelled is minimized and the delivery operations are completed within the time windows requested by the customers. The analysis reveals that the problems experienced in vehicle routing with time window can be solved by GA and retrieved for optimal solutions. After a thorough study on VRPTW, it is highly recommended that a company should implement the optimal routes derived from the study to increase the efficiency and accuracy of delivery with time insertion.
基金This work is supported by the National Natural Science Foundation of China under the Grant 19772037 and 19902014
文摘Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of linear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an effective tool to investigate the nonlinear problems.
文摘The simulation of multi-domain,multi-physics mathematical models with uncertain parameters can be quite demanding in terms of algorithm design and com-putation costs.Our main objective in this paper is to examine a physical interface coupling between two random dissipative systems with uncertain parameters.Due to the complexity and uncertainty inherent in such interface-coupled problems,un-certain diffusion coefficients or friction parameters often arise,leading to consid-ering random systems.We employ Monte Carlo methods to produce independent and identically distributed deterministic heat-heat model samples to address ran-dom systems,and adroitly integrate the ensemble idea to facilitate the fast calcu-lation of these samples.To achieve unconditional stability,we introduce the scalar auxiliary variable(SAV)method to overcome the time constraints of the ensemble implicit-explicit algorithm.Furthermore,for a more accurate and stable scheme,the ensemble data-passing algorithm is raised,which is unconditionally stable and convergent without any auxiliary variables.These algorithms employ the same co-efficient matrix for multiple linear systems and enable easy parallelization,which can significantly reduce the computational cost.Finally,numerical experiments are conducted to support the theoretical results and showcase the unique features of the proposed algorithms.
基金Scientific Research Project for Introduced Talents of Guizhou University of Finance and Economics(No.2021YJ007)National Natural Science Foundation of China(Grant Nos.61862051,61762019,62241206)+2 种基金Top-notch Talent Program of Guizhou Province(No.KY[2018]080)Science and Technology Foundation of Guizhou Province(No.20191299)foundation of Qiannan Normal University for Nationalities(Nos.QNSYRC201715,QNSY2018JS013).
文摘This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT problem unsatisfiable with high probability,where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random(k-1,2(k-1)s)-CNF formula.Let F be a regular balanced random(k,2s)-CNF formula where k≥3,then there exists a number so such that F is(1,O)-unsatisfiable with high probability if s>so.A numerical solution of the number so when k e(5,6,...,14)is given to conduct simulated experiments.The simulated experiments verify the theoretical result.Besides,the experiments also suggest that F is(1,O)-satisfiable with high probability if s is less than a certain value.
