When a cluster of unmanned aerial vehicles (UAVs) is flying in formation, it is crucial to maintain the formation and not to be interfered by external electromagnetic wave signals. In order to maintain the formation, ...When a cluster of unmanned aerial vehicles (UAVs) is flying in formation, it is crucial to maintain the formation and not to be interfered by external electromagnetic wave signals. In order to maintain the formation, this paper proposes to use pure azimuth passive positioning to adjust the position of UAVs, i.e., certain UAVs in the formation transmit signals, the rest of the UAVs receive the signals passively, and extract the orientation information from them to adjust the position of the UAVs [1] [2] [3]. In this paper, the position adjustment problem of UAVs in “circular” formation flight under three models is investigated. To address the problem of “how to obtain the position of the receiving UAV when there are two UAVs with known numbers and evenly distributed on the circumference in addition to the UAV transmitting at the known center of the circle, and the rest of the UAVs with slight deviations in their positions are receiving the signals”, two purely mathematical geometric methods, namely, triangular localization method and polar co-ordinate method, are proposed respectively. We have determined the position of the receiving UAV;we have used the exhaustive method and the construction and disproof method to solve the problem of “how many UAVs are needed to transmit signals in order to realize the effective positioning of the UAVs when it is known that a certain UAV with a slight deviation in its position receives the signals emitted by two UAVs at the same time”, and the results show that: in addition to the known signals emitted by two UAVs, it is also necessary to transmit the signals emitted by two UAVs. The results show that in addition to the known two UAVs transmitting signals, two additional UAVs are required to transmit signals for precise po-sitioning. When the position of UAVs has deviation at the initial moment, the ideal approximation method and the target delimitation method are pro-posed, and the target of nine UAVs uniformly distributed on a circle of a spe-cific radius is achieved through several adjustments, after which the ad-vantages and disadvantages of each model are analyzed, and suggestions for improvement are put forward. The purely azimuthal passive localization method and the constructed model approach proposed in this paper can be extended to other fields, such as spacecraft formations in space and battle-ship formations at sea, as well as other formation flight position adjustment problems.展开更多
Traditional material handling vehicles often use internal combustion engines as their power source, which results in exhaust emissions that pollute the environment. In contrast, automated material handling vehicles ha...Traditional material handling vehicles often use internal combustion engines as their power source, which results in exhaust emissions that pollute the environment. In contrast, automated material handling vehicles have the advantages of zero emissions, low noise, and low vibration, thus avoiding exhaust pollution and providing a more comfortable working environment for operators. In order to achieve the goals of “peaking carbon emissions by 2030 and achieving carbon neutrality by 2060”, the use of environmentally friendly autonomous material handling vehicles for material transportation is an inevitable trend. To maximize the amount of transported materials, consider peak-to-valley electricity pricing, battery pack procurement, and the construction of charging and swapping stations while achieving “minimum daily transportation volume” and “lowest investment and operational cost over a 3-year settlement period” with the shortest overall travel distance for all material handling vehicles, this paper examines two different scenarios and establishes goal programming models. The appropriate locations for material handling vehicle swapping stations and vehicle battery pack scheduling schemes are then developed using the NSGA-II algorithm and ant colony optimization algorithm. The results show that, while ensuring a daily transportation volume of no less than 300 vehicles, the lowest investment and operational cost over a 3-year settlement period is approximately 24.1 million Yuan. The material handling vehicles follow the shortest path of 119.2653 km passing through the designated retrieval points and have two shortest routes. Furthermore, the advantages and disadvantages of the proposed models are analyzed, followed by an evaluation, deepening, and potential extension of the models. Finally, future research directions in this field are suggested.展开更多
In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is ...In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is isomorphic to the C-valued cohomology of the toric manifold.展开更多
The variational quantum eigensolver(VQE) is emerging as a cornerstone algorithm in the era of noisy intermediatescale quantum(NISQ) devices,which offers a practical pathway for solving complex quantum problems using h...The variational quantum eigensolver(VQE) is emerging as a cornerstone algorithm in the era of noisy intermediatescale quantum(NISQ) devices,which offers a practical pathway for solving complex quantum problems using hybrid quantum-classical frameworks.Initially proposed to estimate the ground state energies of quantum systems,VQE combines the quantum circuits with the classical optimization approaches,harnessing the strengths of both computational paradigms [1].展开更多
Let(X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hyt?nen. In this paper, the authors obtain the boundedness of the commutators of θ-...Let(X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hyt?nen. In this paper, the authors obtain the boundedness of the commutators of θ-type Calderón-Zygmund operators with RBMO functions from L∞(μ) into RBMO(μ) and from Hat1,∞(μ) into L1(μ), respectively.As a consequence of these results, they establish the Lp(μ) boundedness of the commutators on the non-homogeneous metric spaces.展开更多
In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy par...In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one.展开更多
We study a stochastic Cahn-Hilliard equation driven by a Poisson random measure with Neumann boundary conditions. The global weak solution is established for the equation. Moreover, the existence of a Lyapunov functio...We study a stochastic Cahn-Hilliard equation driven by a Poisson random measure with Neumann boundary conditions. The global weak solution is established for the equation. Moreover, the existence of a Lyapunov function for the equation and an invariant measure associated with the transition semigroup are proved.展开更多
We use induced orbit covers to define induced orbit data.By studying the space of regular functions on orbit cover,we know that the induced representation has close connection with the induced orbit datum under the me...We use induced orbit covers to define induced orbit data.By studying the space of regular functions on orbit cover,we know that the induced representation has close connection with the induced orbit datum under the meaning of Vogan’s conjecture.Therefore,when verifying Vogan’s conjecture,many cases can be reduced to the case of rigid orbit data.展开更多
文摘When a cluster of unmanned aerial vehicles (UAVs) is flying in formation, it is crucial to maintain the formation and not to be interfered by external electromagnetic wave signals. In order to maintain the formation, this paper proposes to use pure azimuth passive positioning to adjust the position of UAVs, i.e., certain UAVs in the formation transmit signals, the rest of the UAVs receive the signals passively, and extract the orientation information from them to adjust the position of the UAVs [1] [2] [3]. In this paper, the position adjustment problem of UAVs in “circular” formation flight under three models is investigated. To address the problem of “how to obtain the position of the receiving UAV when there are two UAVs with known numbers and evenly distributed on the circumference in addition to the UAV transmitting at the known center of the circle, and the rest of the UAVs with slight deviations in their positions are receiving the signals”, two purely mathematical geometric methods, namely, triangular localization method and polar co-ordinate method, are proposed respectively. We have determined the position of the receiving UAV;we have used the exhaustive method and the construction and disproof method to solve the problem of “how many UAVs are needed to transmit signals in order to realize the effective positioning of the UAVs when it is known that a certain UAV with a slight deviation in its position receives the signals emitted by two UAVs at the same time”, and the results show that: in addition to the known signals emitted by two UAVs, it is also necessary to transmit the signals emitted by two UAVs. The results show that in addition to the known two UAVs transmitting signals, two additional UAVs are required to transmit signals for precise po-sitioning. When the position of UAVs has deviation at the initial moment, the ideal approximation method and the target delimitation method are pro-posed, and the target of nine UAVs uniformly distributed on a circle of a spe-cific radius is achieved through several adjustments, after which the ad-vantages and disadvantages of each model are analyzed, and suggestions for improvement are put forward. The purely azimuthal passive localization method and the constructed model approach proposed in this paper can be extended to other fields, such as spacecraft formations in space and battle-ship formations at sea, as well as other formation flight position adjustment problems.
文摘Traditional material handling vehicles often use internal combustion engines as their power source, which results in exhaust emissions that pollute the environment. In contrast, automated material handling vehicles have the advantages of zero emissions, low noise, and low vibration, thus avoiding exhaust pollution and providing a more comfortable working environment for operators. In order to achieve the goals of “peaking carbon emissions by 2030 and achieving carbon neutrality by 2060”, the use of environmentally friendly autonomous material handling vehicles for material transportation is an inevitable trend. To maximize the amount of transported materials, consider peak-to-valley electricity pricing, battery pack procurement, and the construction of charging and swapping stations while achieving “minimum daily transportation volume” and “lowest investment and operational cost over a 3-year settlement period” with the shortest overall travel distance for all material handling vehicles, this paper examines two different scenarios and establishes goal programming models. The appropriate locations for material handling vehicle swapping stations and vehicle battery pack scheduling schemes are then developed using the NSGA-II algorithm and ant colony optimization algorithm. The results show that, while ensuring a daily transportation volume of no less than 300 vehicles, the lowest investment and operational cost over a 3-year settlement period is approximately 24.1 million Yuan. The material handling vehicles follow the shortest path of 119.2653 km passing through the designated retrieval points and have two shortest routes. Furthermore, the advantages and disadvantages of the proposed models are analyzed, followed by an evaluation, deepening, and potential extension of the models. Finally, future research directions in this field are suggested.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.12201314).
文摘In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is isomorphic to the C-valued cohomology of the toric manifold.
文摘The variational quantum eigensolver(VQE) is emerging as a cornerstone algorithm in the era of noisy intermediatescale quantum(NISQ) devices,which offers a practical pathway for solving complex quantum problems using hybrid quantum-classical frameworks.Initially proposed to estimate the ground state energies of quantum systems,VQE combines the quantum circuits with the classical optimization approaches,harnessing the strengths of both computational paradigms [1].
基金supported by the National Natural Science Foundation of China(No.11671414)
文摘Let(X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hyt?nen. In this paper, the authors obtain the boundedness of the commutators of θ-type Calderón-Zygmund operators with RBMO functions from L∞(μ) into RBMO(μ) and from Hat1,∞(μ) into L1(μ), respectively.As a consequence of these results, they establish the Lp(μ) boundedness of the commutators on the non-homogeneous metric spaces.
基金supported by National Science Foundation of USA(Grant Nos.DMS-1403400 and DMS-1712602)National Natural Science Foundation of China(Grant Nos.11171151,11371200,11525104 and 11531013)
文摘In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one.
基金supported by National Natural Science Foundation of China(Grant Nos.11101222,11101223 and 11271203)the China Scholarship Council(CSC)(Grant No.201208120071)
文摘We study a stochastic Cahn-Hilliard equation driven by a Poisson random measure with Neumann boundary conditions. The global weak solution is established for the equation. Moreover, the existence of a Lyapunov function for the equation and an invariant measure associated with the transition semigroup are proved.
基金supported by National Natural Science Foundation of China(Grant No.10971103)
文摘We use induced orbit covers to define induced orbit data.By studying the space of regular functions on orbit cover,we know that the induced representation has close connection with the induced orbit datum under the meaning of Vogan’s conjecture.Therefore,when verifying Vogan’s conjecture,many cases can be reduced to the case of rigid orbit data.
