In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
Analytical solutions for contaminant transport are widely used for both theoretical and practical purposes.However,many existing solutions are obtained subject to an initial condition of zero concentration,which is of...Analytical solutions for contaminant transport are widely used for both theoretical and practical purposes.However,many existing solutions are obtained subject to an initial condition of zero concentration,which is often unrealistic in many practical cases.This article proposed a stepwise superposition approximation approach to solve the non-zero initial concentration problem for first-type and third-type boundary conditions by using the existing zero initial concentration solution.Theoretical examples showed that the approach was highly efficient if a proper superposition scheme with relative concentration increments was constructed.The key parameter that controlled the convergence speed was the time increment（△t） multiplied by the rate constant（λ）.The approach served also as an alternative way to make a convenient concentration calculation even if the non-zero initial concentration solution of a problem was known.展开更多
We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis main...We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.展开更多
This paper gives the rank of matrix and equalities and inequalities of the difference number of non-zero eigenvalue, and discuss the equivalent description of multi angle of equalities for upper and lower bounds of th...This paper gives the rank of matrix and equalities and inequalities of the difference number of non-zero eigenvalue, and discuss the equivalent description of multi angle of equalities for upper and lower bounds of the inequality.展开更多
There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin partic...There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin particle and other spin particles. This paper shows: in Spin Topological Space, STS [1], the third component of zero spin particle possesses non-zero eigenvalues besides original zero value, this leads to a miraculous spin interaction phenomenon between zero spin particle and other spin particles. In STS, zero spin particle could "dissolve other spin particles", degrade the values of their Casimir operator, and decay these spin particles into other forms of spin particle.展开更多
Industrial robot system is a kind of dynamic system w ith strong nonlinear coupling and high position precision. A lot of control ways , such as nonlinear feedbackdecomposition motion and adaptive control and so o n, ...Industrial robot system is a kind of dynamic system w ith strong nonlinear coupling and high position precision. A lot of control ways , such as nonlinear feedbackdecomposition motion and adaptive control and so o n, have been used to control this kind of system, but there are some deficiencie s in those methods: some need accurate and some need complicated operation and e tc. In recent years, in need of controlling the industrial robots, aiming at com pletely tracking the ideal input for the controlled subject with repetitive character, a new research area, ILC (iterative learning control), has been devel oped in the control technology and theory. The iterative learning control method can make the controlled subject operate as desired in a definite time span, merely making use of the prior control experie nce of the system and searching for the desired control signal according to the practical and desired output signal. The process of searching is equal to that o f learning, during which we only need to measure the output signal to amend the control signal, not like the adaptive control strategy, which on line assesses t he complex parameters of the system. Besides, since the iterative learning contr ol relies little on the prior message of the subject, it has been well used in a lot of areas, especially the dynamic systems with strong non-linear coupling a nd high repetitive position precision and the control system with batch producti on. Since robot manipulator has the above-mentioned character, ILC can be very well used in robot manipulator. In the ILC, since the operation always begins with a certain initial state, init ial condition has been required in almost all convergence verification. Therefor e, in designing the controller, the initial state has to be restricted with some condition to guarantee the convergence of the algorithm. The settle of initial condition problem has long been pursued in the ILC. There are commonly two kinds of initial condition problems: one is zero initial error problem, another is non-zero initial error problem. In practice, the repe titive operation will invariably produce excursion of the iterative initial stat e from the desired initial state. As a result, the research on the second in itial problem has more practical meaning. In this paper, for the non-zero initial error problem, one novel robust ILC alg orithms, respectively combining PD type iterative learning control algorithm wit h the robust feedback control algorithm, has been presented. This novel robust ILC algorithm contain two parts: feedforward ILC algorithm and robust feedback algorithm, which can be used to restrain disturbance from param eter variation, mechanical nonlinearities and unmodeled dynamics and to achieve good performance as well. The feedforward ILC algorithm can be used to improve the tracking error and perf ormance of the system through iteratively learning from the previous operation, thus performing the tracking task very fast. The robust feedback algorithm could mainly be applied to make the real output of the system not deviate too much fr om the desired tracking trajectory, and guarantee the system’s robustness w hen there are exterior noises and variations of the system parameter. In this paper, in order to analyze the convergence of the algorithm, Lyapunov st ability theory has been used through properly selecting the Lyapunov function. T he result of the verification shows the feasibility of the novel robust iterativ e learning control in theory. Finally, aiming at the two-freedom rate robot, simulation has been made with th e MATLAB software. Furthermore, two groups of parameters are selected to validat e the robustness of the algorithm.展开更多
In this paper,we analyze the physical layer security(PLS)performance of a free-space optical(FSO)communication system composed of a transmitting satellite and ground users.Specifically,the FSO fading channels follow t...In this paper,we analyze the physical layer security(PLS)performance of a free-space optical(FSO)communication system composed of a transmitting satellite and ground users.Specifically,the FSO fading channels follow the Málaga distribution.Further,we scrutinize the influence of non-zero boresight pointing errors and angle-of-arrival fluctuations on the PLS performance for the first time.We derived the probability density function and cumulative density function of the FSO link,followed by the closed-form expressions of the secrecy outage probability(SOP)and the probability of strictly positive secrecy capacity(SPSC).The asymptotic SOP expression at the high signal-to-noise ratio regime and diversity order are also provided to reveal the physical mechanism of the PLS of the considered system.Finally,Monte Carlo simulation results are presented to verify the correctness of the analytical expressions.The results afford helpful insights for the future design of satellite FSO communication systems.展开更多
平均光强分布是自由空间激光通信(Free Space Optical Communication,FSOC)性能分析中的一个重要参数,非零均值不等方差的跟踪误差场景下平均光强分布理论的封闭表达式尚未得出。采用统计平均的方法对非零均值不等方差跟踪误差下的平均...平均光强分布是自由空间激光通信(Free Space Optical Communication,FSOC)性能分析中的一个重要参数,非零均值不等方差的跟踪误差场景下平均光强分布理论的封闭表达式尚未得出。采用统计平均的方法对非零均值不等方差跟踪误差下的平均光强分布进行建模并推导出其理论的封闭表达式,通过蒙特卡洛模拟对所推导的结果进行验证。在非零均值不等方差跟踪误差的影响下,高斯光束的平均光强分布廓线的形状和中心位置均发生变化。此外,采用相同面积的方形接收孔径代替圆形接收孔径,推导出非零均值不等方差跟踪误差下的平均接收功率。该工作能为非零均值不等方差跟踪误差下的自由空间激光通信系统性能分析和链路设计提供理论指导。展开更多
Thom–Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism ? : H n (L;Z) → H n (M;Z) to be realized by a map f : M → L of degree k for closed (n ? 1)-connected...Thom–Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism ? : H n (L;Z) → H n (M;Z) to be realized by a map f : M → L of degree k for closed (n ? 1)-connected 2n-manifolds M and L, n > 1. A corollary is that each (n ? 1)-connected 2n-manifold admits selfmaps of degree larger than 1, n > 1. In the most interesting case of dimension 4, with the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree k map from a closed orientable 4-manifold M to a closed simply connected 4-manifold L in terms of their intersection forms; in particular, there is a map f : M → L of degree 1 if and only if the intersection form of L is isomorphic to a direct summand of that of M.展开更多
This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays.Not only the state variable,but also control variables of players involv...This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays.Not only the state variable,but also control variables of players involve discrete and distributed delays.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,the author establishes a necessary maximum principle and a sufficient verification theorem.To explain theoretical results,the author applies them to a dynamic advertising game problem.展开更多
An umbilical free oriented hypersurfacex：M→Rnwith non-zero principal curvatures is called a Laguerre isoparametric hypersurface if its Laguerre form C=i Ciωi=iρ1（Ei（logρ）（r ri）Ei（r））ωi vanishes and Lague...An umbilical free oriented hypersurfacex：M→Rnwith non-zero principal curvatures is called a Laguerre isoparametric hypersurface if its Laguerre form C=i Ciωi=iρ1（Ei（logρ）（r ri）Ei（r））ωi vanishes and Laguerre shape operator S=ρ1（S 1 rid）has constant eigenvalues.Hereρ=i（r ri）2,r=r1＋r2＋···＋rn 1n 1is the mean curvature radius andSis the shape operator ofx.{Ei}is a local basis for Laguerre metric g=ρ2III with dual basis{ωi}and III is the third fundamental form ofx.In this paper,we classify all Laguerre isoparametric hypersurfaces in Rn（n〉3）with two distinct non-zero principal curvatures up to Laguerre transformations.展开更多
外辐射源雷达利用直达天线接收的参考信号作为样本滤除目标回波中的杂波,但由于雨、云、树木或其他运动物体等的影响,回波内可能会包含非零频杂波,导致处理后杂波残余较大,影响目标检测。针对上述问题,提出了一种基于杂波识别的扩展最...外辐射源雷达利用直达天线接收的参考信号作为样本滤除目标回波中的杂波,但由于雨、云、树木或其他运动物体等的影响,回波内可能会包含非零频杂波,导致处理后杂波残余较大,影响目标检测。针对上述问题,提出了一种基于杂波识别的扩展最小均方(Least Mean Square,LMS)对消算法。首先利用模糊函数估计杂波的频率和时延分布,构建含频率信息的多个参考信号。再把多个参考信号插入LMS算法中推导了扩展LMS算法,利用扩展LMS算法可以同时对消静、动杂波。扩展LMS算法能降低对消剩余,提高目标的信噪比,仿真分析和实测数据处理验证了算法的有效性。展开更多
随着双有源桥开关频率的不断提高,开关损耗在总损耗中的占比逐渐增大。零电压开关(zero voltage switching,ZVS)控制策略已成为降低开关损耗的主要手段。然而,传统ZVS控制策略在考虑死区时间时,存在ZVS区域不连续和移相比突变的问题,影...随着双有源桥开关频率的不断提高,开关损耗在总损耗中的占比逐渐增大。零电压开关(zero voltage switching,ZVS)控制策略已成为降低开关损耗的主要手段。然而,传统ZVS控制策略在考虑死区时间时,存在ZVS区域不连续和移相比突变的问题,影响系统稳定。为了解决该问题,提出一种在全功率范围内移相比非突变的ZVS和电流应力优化策略。在中等功率范围内,由于死区时间的影响,所有开关器件的ZVS无法完全实现,以牺牲第1个桥臂开关器件的ZVS为代价,确保移相比的连续变化。在高功率范围内,以移相比连续变化为目标,重新调整分界线,实现中等功率范围与高功率范围的无缝切换。理论分析表明,提出的优化策略能够在全功率范围内保证移相比的连续性。通过搭建小功率实验平台,实验结果验证了所提优化策略的正确性和有效性。展开更多
基金Foundation item： Supported by the Sichuan Educational Comittee Science Foundation for Youths（08ZB002） Supported by the National Secience Foundation of Yibin University（2008Z02）
文摘In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
基金supported by the National Natural Science Foundation of China (No. 40872151)the Key Project in the National Science and Technology Pillar Program of China (No. 2006BAC06B05)
文摘Analytical solutions for contaminant transport are widely used for both theoretical and practical purposes.However,many existing solutions are obtained subject to an initial condition of zero concentration,which is often unrealistic in many practical cases.This article proposed a stepwise superposition approximation approach to solve the non-zero initial concentration problem for first-type and third-type boundary conditions by using the existing zero initial concentration solution.Theoretical examples showed that the approach was highly efficient if a proper superposition scheme with relative concentration increments was constructed.The key parameter that controlled the convergence speed was the time increment（△t） multiplied by the rate constant（λ）.The approach served also as an alternative way to make a convenient concentration calculation even if the non-zero initial concentration solution of a problem was known.
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.
文摘This paper gives the rank of matrix and equalities and inequalities of the difference number of non-zero eigenvalue, and discuss the equivalent description of multi angle of equalities for upper and lower bounds of the inequality.
文摘There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin particle and other spin particles. This paper shows: in Spin Topological Space, STS [1], the third component of zero spin particle possesses non-zero eigenvalues besides original zero value, this leads to a miraculous spin interaction phenomenon between zero spin particle and other spin particles. In STS, zero spin particle could "dissolve other spin particles", degrade the values of their Casimir operator, and decay these spin particles into other forms of spin particle.
文摘Industrial robot system is a kind of dynamic system w ith strong nonlinear coupling and high position precision. A lot of control ways , such as nonlinear feedbackdecomposition motion and adaptive control and so o n, have been used to control this kind of system, but there are some deficiencie s in those methods: some need accurate and some need complicated operation and e tc. In recent years, in need of controlling the industrial robots, aiming at com pletely tracking the ideal input for the controlled subject with repetitive character, a new research area, ILC (iterative learning control), has been devel oped in the control technology and theory. The iterative learning control method can make the controlled subject operate as desired in a definite time span, merely making use of the prior control experie nce of the system and searching for the desired control signal according to the practical and desired output signal. The process of searching is equal to that o f learning, during which we only need to measure the output signal to amend the control signal, not like the adaptive control strategy, which on line assesses t he complex parameters of the system. Besides, since the iterative learning contr ol relies little on the prior message of the subject, it has been well used in a lot of areas, especially the dynamic systems with strong non-linear coupling a nd high repetitive position precision and the control system with batch producti on. Since robot manipulator has the above-mentioned character, ILC can be very well used in robot manipulator. In the ILC, since the operation always begins with a certain initial state, init ial condition has been required in almost all convergence verification. Therefor e, in designing the controller, the initial state has to be restricted with some condition to guarantee the convergence of the algorithm. The settle of initial condition problem has long been pursued in the ILC. There are commonly two kinds of initial condition problems: one is zero initial error problem, another is non-zero initial error problem. In practice, the repe titive operation will invariably produce excursion of the iterative initial stat e from the desired initial state. As a result, the research on the second in itial problem has more practical meaning. In this paper, for the non-zero initial error problem, one novel robust ILC alg orithms, respectively combining PD type iterative learning control algorithm wit h the robust feedback control algorithm, has been presented. This novel robust ILC algorithm contain two parts: feedforward ILC algorithm and robust feedback algorithm, which can be used to restrain disturbance from param eter variation, mechanical nonlinearities and unmodeled dynamics and to achieve good performance as well. The feedforward ILC algorithm can be used to improve the tracking error and perf ormance of the system through iteratively learning from the previous operation, thus performing the tracking task very fast. The robust feedback algorithm could mainly be applied to make the real output of the system not deviate too much fr om the desired tracking trajectory, and guarantee the system’s robustness w hen there are exterior noises and variations of the system parameter. In this paper, in order to analyze the convergence of the algorithm, Lyapunov st ability theory has been used through properly selecting the Lyapunov function. T he result of the verification shows the feasibility of the novel robust iterativ e learning control in theory. Finally, aiming at the two-freedom rate robot, simulation has been made with th e MATLAB software. Furthermore, two groups of parameters are selected to validat e the robustness of the algorithm.
基金National Natural Science Foundation of China(Grant No.62271202,62027802)Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ25F010004)。
文摘In this paper,we analyze the physical layer security(PLS)performance of a free-space optical(FSO)communication system composed of a transmitting satellite and ground users.Specifically,the FSO fading channels follow the Málaga distribution.Further,we scrutinize the influence of non-zero boresight pointing errors and angle-of-arrival fluctuations on the PLS performance for the first time.We derived the probability density function and cumulative density function of the FSO link,followed by the closed-form expressions of the secrecy outage probability(SOP)and the probability of strictly positive secrecy capacity(SPSC).The asymptotic SOP expression at the high signal-to-noise ratio regime and diversity order are also provided to reveal the physical mechanism of the PLS of the considered system.Finally,Monte Carlo simulation results are presented to verify the correctness of the analytical expressions.The results afford helpful insights for the future design of satellite FSO communication systems.
文摘平均光强分布是自由空间激光通信(Free Space Optical Communication,FSOC)性能分析中的一个重要参数,非零均值不等方差的跟踪误差场景下平均光强分布理论的封闭表达式尚未得出。采用统计平均的方法对非零均值不等方差跟踪误差下的平均光强分布进行建模并推导出其理论的封闭表达式,通过蒙特卡洛模拟对所推导的结果进行验证。在非零均值不等方差跟踪误差的影响下,高斯光束的平均光强分布廓线的形状和中心位置均发生变化。此外,采用相同面积的方形接收孔径代替圆形接收孔径,推导出非零均值不等方差跟踪误差下的平均接收功率。该工作能为非零均值不等方差跟踪误差下的自由空间激光通信系统性能分析和链路设计提供理论指导。
文摘Thom–Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism ? : H n (L;Z) → H n (M;Z) to be realized by a map f : M → L of degree k for closed (n ? 1)-connected 2n-manifolds M and L, n > 1. A corollary is that each (n ? 1)-connected 2n-manifold admits selfmaps of degree larger than 1, n > 1. In the most interesting case of dimension 4, with the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree k map from a closed orientable 4-manifold M to a closed simply connected 4-manifold L in terms of their intersection forms; in particular, there is a map f : M → L of degree 1 if and only if the intersection form of L is isomorphic to a direct summand of that of M.
基金the National Natural Science Foundation of China under Grant No.11701214Shandong Provincial Natural Science FoundationChina under Grant No.ZR2019MA045。
文摘This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays.Not only the state variable,but also control variables of players involve discrete and distributed delays.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,the author establishes a necessary maximum principle and a sufficient verification theorem.To explain theoretical results,the author applies them to a dynamic advertising game problem.
基金Supported by National Natural Science Foundation of China(Grant No.10826062)Natural Science Foundation of Fujian Province of China(Grant No.2012J01020)the Fundamental Research Funds for the Central Universities(Grant No.2011121040)
文摘An umbilical free oriented hypersurfacex：M→Rnwith non-zero principal curvatures is called a Laguerre isoparametric hypersurface if its Laguerre form C=i Ciωi=iρ1（Ei（logρ）（r ri）Ei（r））ωi vanishes and Laguerre shape operator S=ρ1（S 1 rid）has constant eigenvalues.Hereρ=i（r ri）2,r=r1＋r2＋···＋rn 1n 1is the mean curvature radius andSis the shape operator ofx.{Ei}is a local basis for Laguerre metric g=ρ2III with dual basis{ωi}and III is the third fundamental form ofx.In this paper,we classify all Laguerre isoparametric hypersurfaces in Rn（n〉3）with two distinct non-zero principal curvatures up to Laguerre transformations.
文摘外辐射源雷达利用直达天线接收的参考信号作为样本滤除目标回波中的杂波,但由于雨、云、树木或其他运动物体等的影响,回波内可能会包含非零频杂波,导致处理后杂波残余较大,影响目标检测。针对上述问题,提出了一种基于杂波识别的扩展最小均方(Least Mean Square,LMS)对消算法。首先利用模糊函数估计杂波的频率和时延分布,构建含频率信息的多个参考信号。再把多个参考信号插入LMS算法中推导了扩展LMS算法,利用扩展LMS算法可以同时对消静、动杂波。扩展LMS算法能降低对消剩余,提高目标的信噪比,仿真分析和实测数据处理验证了算法的有效性。
文摘随着双有源桥开关频率的不断提高,开关损耗在总损耗中的占比逐渐增大。零电压开关(zero voltage switching,ZVS)控制策略已成为降低开关损耗的主要手段。然而,传统ZVS控制策略在考虑死区时间时,存在ZVS区域不连续和移相比突变的问题,影响系统稳定。为了解决该问题,提出一种在全功率范围内移相比非突变的ZVS和电流应力优化策略。在中等功率范围内,由于死区时间的影响,所有开关器件的ZVS无法完全实现,以牺牲第1个桥臂开关器件的ZVS为代价,确保移相比的连续变化。在高功率范围内,以移相比连续变化为目标,重新调整分界线,实现中等功率范围与高功率范围的无缝切换。理论分析表明,提出的优化策略能够在全功率范围内保证移相比的连续性。通过搭建小功率实验平台,实验结果验证了所提优化策略的正确性和有效性。
