Aim To define a mixed redundant model(MRM), improving the reliability of C 3I system. Methods The model combined the technology characters of two? unit system with one warm stand by unit and function substitute s...Aim To define a mixed redundant model(MRM), improving the reliability of C 3I system. Methods The model combined the technology characters of two? unit system with one warm stand by unit and function substitute system. The reliability and availability equations of MRM were deduced. Results and Conclusion Compared with several other reliability models, it has obvious effect upon improving the system reliability. The effect? cost rate is very high among these models. The model can be used in reliability design, evaluation and check of C 3I system. Only a little attached cost is needed to improve C 3I system reliability effectively.展开更多
In this paper, we describe all the divisible semiring congruences on a distributive semiring S and also establish a one_to_one, inclusion_preserving mapping from the set of full, closed, self_conjagate, ideal subsemir...In this paper, we describe all the divisible semiring congruences on a distributive semiring S and also establish a one_to_one, inclusion_preserving mapping from the set of full, closed, self_conjagate, ideal subsemirings of S to the set of all divisible semiring congruences on S.展开更多
Reliability and remaining useful life(RUL)estimation for a satellite rechargeable lithium battery(RLB)are significant for prognostic and health management(PHM).A novel Bayesian framework is proposed to do reliability ...Reliability and remaining useful life(RUL)estimation for a satellite rechargeable lithium battery(RLB)are significant for prognostic and health management(PHM).A novel Bayesian framework is proposed to do reliability analysis by synthesizing multisource data,including bivariate degradation data and lifetime data.Bivariate degradation means that there are two degraded performance characteristics leading to the failure of the system.First,linear Wiener process and Frank Copula function are used to model the dependent degradation processes of the RLB's temperature and discharge voltage.Next,the Bayesian method,in combination with Markov Chain Monte Carlo(MCMC)simulations,is provided to integrate limited bivariate degradation data with other congeneric RLBs'lifetime data.Then reliability evaluation and RUL prediction are carried out for PHM.A simulation study demonstrates that due to the data fusion,parameter estimations and predicted RUL obtained from our model are more precise than models only using degradation data or ignoring the dependency of different degradation processes.Finally,a practical case study of a satellite RLB verifies the usability of the model.展开更多
Nine targets which stand both for the static characteristic of produced formations and the dynamic parameter of wells including the average permeability,variation coefficient of permeability,moving capability,remainin...Nine targets which stand both for the static characteristic of produced formations and the dynamic parameter of wells including the average permeability,variation coefficient of permeability,moving capability,remaining recoverable reserves,coefficient of flooding,daily oil production,increasing rate of water cut,cumulative liquid production per unit meter and efficiency index of oil production are selected as the evaluation indexes,a novel model to evaluate the porous formations in long-term waterflooding sand reservoir was established by using the support vector machine and clustering analysis. Data of 57 wells from Shentuo 21 block Shengli oilfield was analyzed by using the model. Four kinds of formation groups were gained. According to the analysis result,different adjustment solutions were put forward to develop the relevant formations. The Monthly oil production increased 7.6 % and the water cut decreased 8.9 % after the adjusted solutions. Good results indicate that the learning from this method gained will be valuable adding to other long-term waterflooding sand reservoirs in Shengli oilfield and other similar reservoirs worldwide.展开更多
Surveying control network optimization design is related to standards, such as precision, reliability, sensitivity and the cost, and these standards are related closely to each other. A new method for surveying contro...Surveying control network optimization design is related to standards, such as precision, reliability, sensitivity and the cost, and these standards are related closely to each other. A new method for surveying control network simulation optimization design is proposed. This method is based on the inner reliability index of the observation values.展开更多
In order to solve reliability-redundancy allocation problems more effectively, a new hybrid algorithm named CDEPSO is proposed in this work, which combines particle swarm optimization (PSO) with differential evoluti...In order to solve reliability-redundancy allocation problems more effectively, a new hybrid algorithm named CDEPSO is proposed in this work, which combines particle swarm optimization (PSO) with differential evolution (DE) and a new chaotic local search. In the CDEPSO algorithm, DE provides its best solution to PSO if the best solution obtained by DE is better than that by PSO, while the best solution in the PSO is performed by chaotic local search. To investigate the performance of CDEPSO, four typical reliability-redundancy allocation problems were solved and the results indicate that the convergence speed and robustness of CDEPSO is better than those of PSO and CPSO (a hybrid algorithm which only combines PSO with chaotic local search). And, compared with the other six improved meta-heuristics, CDEPSO also exhibits more robust performance. In addition, a new performance was proposed to more fairly compare CDEPSO with the same six improved recta-heuristics, and CDEPSO algorithm is the best in solving these problems.展开更多
In order to improve the reliability of an electronic or a computer system, redundant components always need to be added as part of the system. When an active component falls, a standby component will be activated to g...In order to improve the reliability of an electronic or a computer system, redundant components always need to be added as part of the system. When an active component falls, a standby component will be activated to guarantee the system in operation continuously. The standby component and the switching device have been usually assumed to be continuously functional duriv,g the setup of the reliability model. In fact, it is these two asstuxtptions that induce deviations during modeling and introduce variances for the system reliability design. Through modeling and optiming the dependability of the synchronous clock system that decomposed from a multi-node system, a new reliability model which takes these two elements into consideration has been developed. Simulation results demonstrate that the upgraded reliability model is closer Io the actual dependability of the real system. The capability of the system reliability design is also improved as a result.展开更多
The problems of current highly redundant flight control system are analyzed in this paper. Our study gives methods of utilizing other information to reduce physical components on the condition of meeting the reliabili...The problems of current highly redundant flight control system are analyzed in this paper. Our study gives methods of utilizing other information to reduce physical components on the condition of meeting the reliability requirements for flight control system. The strategies presented in this paper mainly include information redundancy, multi-thread, time redundancy, geometry space redundancy, etc.. Analysis and simulation show these non-hardware based methods can reduce the requirement of system hardware level and thus reduce the system complexity, weight, space, costs and R&D (research and development) time.展开更多
In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existenc...In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existence of the strictly dominant eigenvalue,and show the linear stability of solution.展开更多
AIM:To evaluate the efficacy of cola treatment for gastric phytobezoars,including diospyrobezoars.METHODS:A total of 17 patients(range:48 to 78 years) with symptomatic gastric phytobezoars treated with cola and adjuva...AIM:To evaluate the efficacy of cola treatment for gastric phytobezoars,including diospyrobezoars.METHODS:A total of 17 patients(range:48 to 78 years) with symptomatic gastric phytobezoars treated with cola and adjuvant endoscopic therapy were reviewed.Three liters of cola lavage(10 cases) or drink(7 cases) were initially used,and then endoscopic fragmentation was done for the remnant bezoars by using a lithotripsy basket or a polypectomy snare.The overall success of dissolving a gastric phytobezoars with using three liters of cola and the clinical and endoscopic findings were compared retrospectively between four cases of complete dissolution by using only cola and 13 cases of partial dissolution with cola.RESULTS:After 3 L of cola lavage or drinking,a complete dissolution of bezoars was achieved in four patients(23.5%),while 13 cases(76.5%) were only partially dissolved.Phytobezoars(4 of 6 cases) were observed more frequently than diospyrobezoars(0 of 11) in the group that underwent complete dissolution(P = 0.006).Gender,symptom duration,size of bezoar and method of cola administration were not significantly different between the two groups.Twelve of 13 patients with residual bezoars were completely treated with a combination of cola and endoscopic fragmentation.CONCLUSION:The rate of complete dissolution with three liters of cola was 23.5%,but no case of diospyrobezoar was completely dissolved using this method.However,pretreatment with cola may be helpful and facilitate endoscopic fragmentation of gastric phytobezoars.展开更多
With the progress of the railway technology, the railway transportation is becoming more efficient, intelligent and faster. High speed trains, as a major part of the railway transportation, are engaged with passenger&...With the progress of the railway technology, the railway transportation is becoming more efficient, intelligent and faster. High speed trains, as a major part of the railway transportation, are engaged with passenger's safety, and therefore the reliability issue is very important in such vital systems. In this paper, a dependable speed controller core based on FPGA has been developed for high speed trains. To improve the reliability and mitigate single upset faults on basic speed controller, this paper proposes a new effective method which is based on hardware redundancy. In the proposed Hybrid Dual Duplex Redundancy(HDDR) method, the original controller is quadruplicated and correct values are voted through the comparator and error detection unit. We have analyzed the proposed system with Reliability, Availability, Mean time to failure and Security(RAMS) theory in order to evaluate the effectiveness of proposed scheme. Theoretical analysis shows that the Mean Time To Failure(MTTF) of the proposed system is 2.5 times better than the traditional Triple Modular Redundancy(TMR). Furthermore, the fault injection experimental results reveal that the capability of tolerating Single Event Upsets(SEUs) in the proposed method increases up to 7.5 times with respect to a regular speed controller.展开更多
Today's industry requires more reliable information on the current status of their hard assets; prognosis for continued usability of systems and better predictability of equipment life cycle maintenance. Therefore, a...Today's industry requires more reliable information on the current status of their hard assets; prognosis for continued usability of systems and better predictability of equipment life cycle maintenance. Therefore, an innovative technique for early detection of potential failure and condition monitoring is urgently required by many engineers. This document describes a novel approach to improve industrial equipment safety, reliability and life cycle management. A new field portable instrument called the "IMS (indicator of mechanical stresses)" utilizes magneto-anisotropic ("cross") transducers to measure anisotropy of magnetic properties in ferromagnetic material. Mechanical stresses including residual stresses in Ferro-magnetic parts, are "not visible" to most traditional NDT (non-destructive testing) methods; for example, radiography and ultrasonic inspection. Stress build-up can be the first indicator that something is faulty with a structure. This can be the result of a manufacturing defect; or as assets age and fatigue, stress loads can become unevenly distributed throughout the metal. We outline the evaluation of IMS as a fast screening tool to provide structural condition or deterioration feedback in novel applications for pipelines, petrochemical refinery, cranes, and municipal infrastructure.展开更多
Currently, most visual servoing system must be calibrated, while it is impossible to calibrate cameras and robot models precisely in industrial practice, so a novel dynamic uncalibrated eye-in-hand visual servoing sys...Currently, most visual servoing system must be calibrated, while it is impossible to calibrate cameras and robot models precisely in industrial practice, so a novel dynamic uncalibrated eye-in-hand visual servoing system of tracking a moving target is proposed. The method does not require calibration of camera and robot kinematic models. Vision guided algorithm for tracking dynamic image is developed through minimizing nonlinear objective function. For the large residual has not been approximated in dynamic environment and the change of composite image Jacobian with time increment has not been computed in visual servoing system now,large residuals are dynamic approximated and the change of composite image Jacobian at each iterative step is computed. Simulation results demonstrate the validity of these approaches.展开更多
In this paper, we study some categoricities of reflexivity and coreflexivity. The main results are as follows: (1). A and C are a pair of equivalent categories.(2). Reflexivity and coreflexivity can be extended as m...In this paper, we study some categoricities of reflexivity and coreflexivity. The main results are as follows: (1). A and C are a pair of equivalent categories.(2). Reflexivity and coreflexivity can be extended as mentioned in the paper. Those can be used to simplify and generalize some results of .展开更多
We propose a method to determine the solvability of the diophantine equation x^2 - Dy^2 = n for the following two cases:the following two cases:(1) D = pq, where p, q ≡ 1 mod 4 are distinct primes with (q) = 1 ...We propose a method to determine the solvability of the diophantine equation x^2 - Dy^2 = n for the following two cases:the following two cases:(1) D = pq, where p, q ≡ 1 mod 4 are distinct primes with (q) = 1 and p q (p/q(q/p)4 = -1.(2) D = 2p1P2 ... Pro, where Pi ≡ 1 mod 8, 1 ≤ i ≤m are distinct primes and D = r2 +s2 with r, s ≡±3 mod 8.展开更多
This paper proves three conjectures on congruences involving central binomial coefficients or Lucas sequences.Let p be an odd prime and let a be a positive integer.It is shown that if p=1(mod 4)or a〉1then [3/4pa]∑...This paper proves three conjectures on congruences involving central binomial coefficients or Lucas sequences.Let p be an odd prime and let a be a positive integer.It is shown that if p=1(mod 4)or a〉1then [3/4pa]∑k=0≡(2/pa)(mod p^2)where(—)denotes the Jacobi symbol.This confirms a conjecture of the second author.A conjecture of Tauraso is also confirmed by showing that p-1∑k=1 Lk/k^2≡0(mod p) provided p〉5.where the Lucas numbers Lo,L1,L2,...are defined by L_0=2,L1=1 and Ln+1=Ln+Ln-l(n=1,2,3,...).The third theorem states that if p=5 then Fp^a-(p^a/5)mod p^3 can be determined in the following way: p^a-1∑k=0(-1)^k(2k k)≡(p^a/5)(1-2F p^a-(pa/5))(mod p^3)which appeared as a conjecture in a paper of Sun and Tauraso in 2010.展开更多
Distributed coordinated control of networked robotic systems formulated by Lagrange dynamics has recently been a subject of considerable interest within science and technology communities due to its broad engineering ...Distributed coordinated control of networked robotic systems formulated by Lagrange dynamics has recently been a subject of considerable interest within science and technology communities due to its broad engineering applications involving complex and integrated production processes,where high flexibility,manipulability,and maneuverability are desirable characteristics.In this paper,we investigate the distributed coordinated adaptive tracking problem of networked redundant robotic systems with a dynamic leader.We provide an analysis procedure for the controlled synchronization of such systems with uncertain dynamics.We also find that the proposed control strategy does not require computing positional inverse kinematics and does not impose any restriction on the self-motion of the manipulators;therefore,the extra degrees of freedom are applicable for other sophisticated subtasks.Compared with some existing work,a distinctive feature of the designed distributed control algorithm is that only a subset of followers needs to access the position information of the dynamic leader in the task space,where the underlying directed graph has a spanning tree.Subsequently,we present a simulation example to verify the effectiveness of the proposed algorithms.展开更多
文摘Aim To define a mixed redundant model(MRM), improving the reliability of C 3I system. Methods The model combined the technology characters of two? unit system with one warm stand by unit and function substitute system. The reliability and availability equations of MRM were deduced. Results and Conclusion Compared with several other reliability models, it has obvious effect upon improving the system reliability. The effect? cost rate is very high among these models. The model can be used in reliability design, evaluation and check of C 3I system. Only a little attached cost is needed to improve C 3I system reliability effectively.
文摘In this paper, we describe all the divisible semiring congruences on a distributive semiring S and also establish a one_to_one, inclusion_preserving mapping from the set of full, closed, self_conjagate, ideal subsemirings of S to the set of all divisible semiring congruences on S.
基金Project(71371182) supported by the National Natural Science Foundation of China
文摘Reliability and remaining useful life(RUL)estimation for a satellite rechargeable lithium battery(RLB)are significant for prognostic and health management(PHM).A novel Bayesian framework is proposed to do reliability analysis by synthesizing multisource data,including bivariate degradation data and lifetime data.Bivariate degradation means that there are two degraded performance characteristics leading to the failure of the system.First,linear Wiener process and Frank Copula function are used to model the dependent degradation processes of the RLB's temperature and discharge voltage.Next,the Bayesian method,in combination with Markov Chain Monte Carlo(MCMC)simulations,is provided to integrate limited bivariate degradation data with other congeneric RLBs'lifetime data.Then reliability evaluation and RUL prediction are carried out for PHM.A simulation study demonstrates that due to the data fusion,parameter estimations and predicted RUL obtained from our model are more precise than models only using degradation data or ignoring the dependency of different degradation processes.Finally,a practical case study of a satellite RLB verifies the usability of the model.
基金supported by funds from the Key Pro-ject of Chinese National Programs for Fundamental Research and Development (863 Program) under thenumber 2007AA090701the Young and Mid-dle-aged Researchers Innovation and Technology Foun-dation of CNPC under the number 04E7029
文摘Nine targets which stand both for the static characteristic of produced formations and the dynamic parameter of wells including the average permeability,variation coefficient of permeability,moving capability,remaining recoverable reserves,coefficient of flooding,daily oil production,increasing rate of water cut,cumulative liquid production per unit meter and efficiency index of oil production are selected as the evaluation indexes,a novel model to evaluate the porous formations in long-term waterflooding sand reservoir was established by using the support vector machine and clustering analysis. Data of 57 wells from Shentuo 21 block Shengli oilfield was analyzed by using the model. Four kinds of formation groups were gained. According to the analysis result,different adjustment solutions were put forward to develop the relevant formations. The Monthly oil production increased 7.6 % and the water cut decreased 8.9 % after the adjusted solutions. Good results indicate that the learning from this method gained will be valuable adding to other long-term waterflooding sand reservoirs in Shengli oilfield and other similar reservoirs worldwide.
文摘Surveying control network optimization design is related to standards, such as precision, reliability, sensitivity and the cost, and these standards are related closely to each other. A new method for surveying control network simulation optimization design is proposed. This method is based on the inner reliability index of the observation values.
基金Project(20040533035)supported by the National Research Foundation for the Doctoral Program of Higher Education of ChinaProject(60874070)supported by the National Natural Science Foundation of China
文摘In order to solve reliability-redundancy allocation problems more effectively, a new hybrid algorithm named CDEPSO is proposed in this work, which combines particle swarm optimization (PSO) with differential evolution (DE) and a new chaotic local search. In the CDEPSO algorithm, DE provides its best solution to PSO if the best solution obtained by DE is better than that by PSO, while the best solution in the PSO is performed by chaotic local search. To investigate the performance of CDEPSO, four typical reliability-redundancy allocation problems were solved and the results indicate that the convergence speed and robustness of CDEPSO is better than those of PSO and CPSO (a hybrid algorithm which only combines PSO with chaotic local search). And, compared with the other six improved meta-heuristics, CDEPSO also exhibits more robust performance. In addition, a new performance was proposed to more fairly compare CDEPSO with the same six improved recta-heuristics, and CDEPSO algorithm is the best in solving these problems.
文摘In order to improve the reliability of an electronic or a computer system, redundant components always need to be added as part of the system. When an active component falls, a standby component will be activated to guarantee the system in operation continuously. The standby component and the switching device have been usually assumed to be continuously functional duriv,g the setup of the reliability model. In fact, it is these two asstuxtptions that induce deviations during modeling and introduce variances for the system reliability design. Through modeling and optiming the dependability of the synchronous clock system that decomposed from a multi-node system, a new reliability model which takes these two elements into consideration has been developed. Simulation results demonstrate that the upgraded reliability model is closer Io the actual dependability of the real system. The capability of the system reliability design is also improved as a result.
文摘The problems of current highly redundant flight control system are analyzed in this paper. Our study gives methods of utilizing other information to reduce physical components on the condition of meeting the reliability requirements for flight control system. The strategies presented in this paper mainly include information redundancy, multi-thread, time redundancy, geometry space redundancy, etc.. Analysis and simulation show these non-hardware based methods can reduce the requirement of system hardware level and thus reduce the system complexity, weight, space, costs and R&D (research and development) time.
基金Supported by the Nature Science Foundation of Henan Education Committee(2008A110022)
文摘In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existence of the strictly dominant eigenvalue,and show the linear stability of solution.
文摘AIM:To evaluate the efficacy of cola treatment for gastric phytobezoars,including diospyrobezoars.METHODS:A total of 17 patients(range:48 to 78 years) with symptomatic gastric phytobezoars treated with cola and adjuvant endoscopic therapy were reviewed.Three liters of cola lavage(10 cases) or drink(7 cases) were initially used,and then endoscopic fragmentation was done for the remnant bezoars by using a lithotripsy basket or a polypectomy snare.The overall success of dissolving a gastric phytobezoars with using three liters of cola and the clinical and endoscopic findings were compared retrospectively between four cases of complete dissolution by using only cola and 13 cases of partial dissolution with cola.RESULTS:After 3 L of cola lavage or drinking,a complete dissolution of bezoars was achieved in four patients(23.5%),while 13 cases(76.5%) were only partially dissolved.Phytobezoars(4 of 6 cases) were observed more frequently than diospyrobezoars(0 of 11) in the group that underwent complete dissolution(P = 0.006).Gender,symptom duration,size of bezoar and method of cola administration were not significantly different between the two groups.Twelve of 13 patients with residual bezoars were completely treated with a combination of cola and endoscopic fragmentation.CONCLUSION:The rate of complete dissolution with three liters of cola was 23.5%,but no case of diospyrobezoar was completely dissolved using this method.However,pretreatment with cola may be helpful and facilitate endoscopic fragmentation of gastric phytobezoars.
文摘With the progress of the railway technology, the railway transportation is becoming more efficient, intelligent and faster. High speed trains, as a major part of the railway transportation, are engaged with passenger's safety, and therefore the reliability issue is very important in such vital systems. In this paper, a dependable speed controller core based on FPGA has been developed for high speed trains. To improve the reliability and mitigate single upset faults on basic speed controller, this paper proposes a new effective method which is based on hardware redundancy. In the proposed Hybrid Dual Duplex Redundancy(HDDR) method, the original controller is quadruplicated and correct values are voted through the comparator and error detection unit. We have analyzed the proposed system with Reliability, Availability, Mean time to failure and Security(RAMS) theory in order to evaluate the effectiveness of proposed scheme. Theoretical analysis shows that the Mean Time To Failure(MTTF) of the proposed system is 2.5 times better than the traditional Triple Modular Redundancy(TMR). Furthermore, the fault injection experimental results reveal that the capability of tolerating Single Event Upsets(SEUs) in the proposed method increases up to 7.5 times with respect to a regular speed controller.
文摘Today's industry requires more reliable information on the current status of their hard assets; prognosis for continued usability of systems and better predictability of equipment life cycle maintenance. Therefore, an innovative technique for early detection of potential failure and condition monitoring is urgently required by many engineers. This document describes a novel approach to improve industrial equipment safety, reliability and life cycle management. A new field portable instrument called the "IMS (indicator of mechanical stresses)" utilizes magneto-anisotropic ("cross") transducers to measure anisotropy of magnetic properties in ferromagnetic material. Mechanical stresses including residual stresses in Ferro-magnetic parts, are "not visible" to most traditional NDT (non-destructive testing) methods; for example, radiography and ultrasonic inspection. Stress build-up can be the first indicator that something is faulty with a structure. This can be the result of a manufacturing defect; or as assets age and fatigue, stress loads can become unevenly distributed throughout the metal. We outline the evaluation of IMS as a fast screening tool to provide structural condition or deterioration feedback in novel applications for pipelines, petrochemical refinery, cranes, and municipal infrastructure.
文摘Currently, most visual servoing system must be calibrated, while it is impossible to calibrate cameras and robot models precisely in industrial practice, so a novel dynamic uncalibrated eye-in-hand visual servoing system of tracking a moving target is proposed. The method does not require calibration of camera and robot kinematic models. Vision guided algorithm for tracking dynamic image is developed through minimizing nonlinear objective function. For the large residual has not been approximated in dynamic environment and the change of composite image Jacobian with time increment has not been computed in visual servoing system now,large residuals are dynamic approximated and the change of composite image Jacobian at each iterative step is computed. Simulation results demonstrate the validity of these approaches.
文摘In this paper, we study some categoricities of reflexivity and coreflexivity. The main results are as follows: (1). A and C are a pair of equivalent categories.(2). Reflexivity and coreflexivity can be extended as mentioned in the paper. Those can be used to simplify and generalize some results of .
基金supported by National Natural Science Foundation of China(Grant No.10901150)the Deutsche Forschungsgemeinschaft(Grant No.DE 1646/2-1)
文摘We propose a method to determine the solvability of the diophantine equation x^2 - Dy^2 = n for the following two cases:the following two cases:(1) D = pq, where p, q ≡ 1 mod 4 are distinct primes with (q) = 1 and p q (p/q(q/p)4 = -1.(2) D = 2p1P2 ... Pro, where Pi ≡ 1 mod 8, 1 ≤ i ≤m are distinct primes and D = r2 +s2 with r, s ≡±3 mod 8.
基金supported by National Natural Science Foundation of China(Grant Nos.10901078 and 11171140)
文摘This paper proves three conjectures on congruences involving central binomial coefficients or Lucas sequences.Let p be an odd prime and let a be a positive integer.It is shown that if p=1(mod 4)or a〉1then [3/4pa]∑k=0≡(2/pa)(mod p^2)where(—)denotes the Jacobi symbol.This confirms a conjecture of the second author.A conjecture of Tauraso is also confirmed by showing that p-1∑k=1 Lk/k^2≡0(mod p) provided p〉5.where the Lucas numbers Lo,L1,L2,...are defined by L_0=2,L1=1 and Ln+1=Ln+Ln-l(n=1,2,3,...).The third theorem states that if p=5 then Fp^a-(p^a/5)mod p^3 can be determined in the following way: p^a-1∑k=0(-1)^k(2k k)≡(p^a/5)(1-2F p^a-(pa/5))(mod p^3)which appeared as a conjecture in a paper of Sun and Tauraso in 2010.
基金supported by the National Natural Science Foundation of China(Grant Nos.1127219110972129 and 10832006)+1 种基金Specialized Research Foundation for the Doctoral Program of Higher Education(Grant No.200802800015)University Natural Science Research Program of Anhui Province(Grant No.KJ2013B216)
文摘Distributed coordinated control of networked robotic systems formulated by Lagrange dynamics has recently been a subject of considerable interest within science and technology communities due to its broad engineering applications involving complex and integrated production processes,where high flexibility,manipulability,and maneuverability are desirable characteristics.In this paper,we investigate the distributed coordinated adaptive tracking problem of networked redundant robotic systems with a dynamic leader.We provide an analysis procedure for the controlled synchronization of such systems with uncertain dynamics.We also find that the proposed control strategy does not require computing positional inverse kinematics and does not impose any restriction on the self-motion of the manipulators;therefore,the extra degrees of freedom are applicable for other sophisticated subtasks.Compared with some existing work,a distinctive feature of the designed distributed control algorithm is that only a subset of followers needs to access the position information of the dynamic leader in the task space,where the underlying directed graph has a spanning tree.Subsequently,we present a simulation example to verify the effectiveness of the proposed algorithms.