Hardware/software partitioning is an important step in the design of embedded systems. In this paper, the hardware/software partitioning problem is modeled as a constrained binary integer programming problem, which is...Hardware/software partitioning is an important step in the design of embedded systems. In this paper, the hardware/software partitioning problem is modeled as a constrained binary integer programming problem, which is further converted equivalently to an unconstrained binary integer programming problem by a penalty method. A local search method, HSFM, is developed to obtain a discrete local minimizer of the unconstrained binary integer programming problem. Next, an auxiliary function, which has the same global optimal solutions as the unconstrained binary integer programming problem, is constructed, and its properties are studied. We show that applying HSFM to minimize the auxiliary function can escape from previous local optima by the increase of the parameter value successfully. Finally, a discrete dynamic convexized method is developed to solve the hardware/software partitioning problem. Computational results and comparisons indicate that the proposed algorithm can get high-quality solutions.展开更多
Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequent...Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequential Convex Programming(SFC-SCP)to improve the computation efficiency and reliability of trajectory generation.SFC-SCP combines the front-end convex polyhedron SFC construction and back-end SCP-based trajectory optimization.A Sparse A^(*)Search(SAS)driven SFC construction method is designed to efficiently generate polyhedron SFC according to the geometric relation among obstacles and collision-free waypoints.Via transforming the nonconvex obstacle-avoidance constraints to linear inequality constraints,SFC can mitigate infeasibility of trajectory planning and reduce computation complexity.Then,SCP casts the nonlinear trajectory optimization subject to SFC into convex programming subproblems to decrease the problem complexity.In addition,a convex optimizer based on interior point method is customized,where the search direction is calculated via successive elimination to further improve efficiency.Simulation experiments on dense obstacle scenarios show that SFC-SCP can generate dynamically feasible safe trajectory rapidly.Comparative studies with state-of-the-art SCP-based methods demonstrate the efficiency and reliability merits of SFC-SCP.Besides,the customized convex optimizer outperforms off-the-shelf optimizers in terms of computation time.展开更多
An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of c...An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.展开更多
In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total vari...In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.展开更多
Given an undirected graph with edge weights,the max-cut problem is to find a partition of the vertices into twosubsets,such that the sumof theweights of the edges crossing different subsets ismaximized.Heuristics base...Given an undirected graph with edge weights,the max-cut problem is to find a partition of the vertices into twosubsets,such that the sumof theweights of the edges crossing different subsets ismaximized.Heuristics based on auxiliary function can obtain high-quality solutions of the max-cut problem,but suffer high solution cost when instances grow large.In this paper,we combine clustered adaptive multistart and discrete dynamic convexized method to obtain high-quality solutions in a reasonable time.Computational experiments on two sets of benchmark instances from the literature were performed.Numerical results and comparisons with some heuristics based on auxiliary function show that the proposed algorithm is much faster and can obtain better solutions.Comparisons with several state-ofthe-science heuristics demonstrate that the proposed algorithm is competitive.展开更多
In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with lin...In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.展开更多
Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient c...Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.展开更多
This study aims to develop a high-precision and cost-efficient method for the threedimensional reconstruction of large particles in natural gravel and blasted rock fragments,utilizing Structure from Motion(SfM)and Mul...This study aims to develop a high-precision and cost-efficient method for the threedimensional reconstruction of large particles in natural gravel and blasted rock fragments,utilizing Structure from Motion(SfM)and Multi-View Stereo(MVS)techniques.The proposed approach was applied to characterize the three-dimensional morphology of rockfill dam materials at a real construction site.Particle shape was quantitatively analyzed using shape indices of sphericity,convexity,and angularity.The predominant morphology of natural gravel is characterized as slightly elongated and slightly flat,while rock fragments are slightly elongated and not flat.Probability density distributions of shape indices follow a skewed normal distribution:sphericity and convexity show leftward skewness,whereas angularity is right-skewed.Skewness parameters of sphericity and angularity are consistent between natural gravel and blasted rock fragments,indicating comparable shape asymmetry.Convexity skewness is significantly higher in natural gravel compared to rock fragments,by approximately an order of magnitude.The relationship between size and particle shape shows that form ratios and associated shape descriptors change linearly with the logarithm of size;larger particles approach spherical or cubic forms.The innovative measurements contribute to the particle shape data set of rockfill dam materials,providing valuable insights into the three-dimensional and statistical morphological characteristics of relatively large particles in natural gravel and blasted rock fragments.This approach enhances understanding of particle morphology's impact on the mechanical behavior of granular materials.展开更多
In this paper,we consider the distributed online optimization problem on a time-varying network,where each agent on the network has its own time-varying objective function and the goal is to minimize the overall loss ...In this paper,we consider the distributed online optimization problem on a time-varying network,where each agent on the network has its own time-varying objective function and the goal is to minimize the overall loss accumulated.Moreover,we focus on distributed algorithms which do not use gradient information and projection operators to improve the applicability and computational efficiency.By introducing the deterministic differences and the randomized differences to substitute the gradient information of the objective functions and removing the projection operator in the traditional algorithms,we design two kinds of gradient-free distributed online optimization algorithms without projection step,which can economize considerable computational resources as well as has less limitations on the applicability.We prove that both of two algorithms achieves consensus of the estimates and regrets of\(O\left(\log(T)\right)\)for local strongly convex objective,respectively.Finally,a simulation example is provided to verify the theoretical results.展开更多
Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
With the development of integrated power and gas distribution systems(IPGS)incorporating renewable energy sources(RESs),coordinating the restoration processes of the power distribution system(PS)and the gas distributi...With the development of integrated power and gas distribution systems(IPGS)incorporating renewable energy sources(RESs),coordinating the restoration processes of the power distribution system(PS)and the gas distribution system(GS)by utilizing the benefits of RESs enhances service restoration.In this context,this paper proposes a coordinated service restoration framework that considers the uncertainty in RESs and the bi-directional restoration interactions between the PS and GS.Additionally,a coordinated service restoration model is developed considering the two systems’interdependency and the GS’s dynamic characteristics.The objective is to maximize the system resilience index while adhering to operational,dynamic,restoration logic,and interdependency constraints.A method for managing uncertainties in RES output is employed,and convexification techniques are applied to address the nonlinear constraints arising from the physical laws of the IPGS,thereby reducing solution complexity.As a result,the service restoration optimization problem of the IPGS can be formulated as a computationally tractable mixed-integer second-order cone programming problem.The effectiveness and superiority of the proposed framework are demonstrated through numerical simulations conducted on the interdependent IEEE 13-bus PS and 9-node GS.The comparative results show that the proposed framework improves the system resilience index by at least 65.07%compared to traditional methods.展开更多
In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are...In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are more accurate than those obtained by Srivastava.展开更多
In this paper,an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed.Firstly,the affine system is used to build a dynamic model and analyze the state constraints.The midcourse ...In this paper,an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed.Firstly,the affine system is used to build a dynamic model and analyze the state constraints.The midcourse guidance problem is transformed into a continuous time optimization problem.Secondly,the problem is transformed into a discrete convex programming problem by affine control variable relaxation,Gaussian pseudospectral discretization and constraints linearization.Then,the off-line midcourse guidance trajectory is generated before midcourse guidance.It is used as the initial reference trajectory for online correction of midcourse guidance.An online guidance framework is used to eliminate the error caused by calculation of guidance instruction time.And the design of discrete points decreases with flight time to improve the solving efficiency.In addition,it is proposed that the terminal guidance capture is used innovatively space to judge the success of midcourse guidance.Numerical simulation shows the feasibility and effectiveness of the proposed method.展开更多
Towards optimal k-prototype discovery,k-means-like algorithms give us inspirations of central samples collection,yet the unstable seed samples selection,the hypothesis of a circle-like pattern,and the unknown K are st...Towards optimal k-prototype discovery,k-means-like algorithms give us inspirations of central samples collection,yet the unstable seed samples selection,the hypothesis of a circle-like pattern,and the unknown K are still challenges,particularly for non-predetermined data patterns.We propose an adaptive k-prototype clustering method(kProtoClust)which launches cluster exploration with a sketchy division of K clusters and finds evidence for splitting and merging.On behalf of a group of data samples,support vectors and outliers from the perspective of support vector data description are not the appropriate candidates for prototypes,while inner samples become the first candidates for instability reduction of seeds.Different from the representation of samples in traditional,we extend sample selection by encouraging fictitious samples to emphasize the representativeness of patterns.To get out of the circle-like pattern limitation,we introduce a convex decomposition-based strategy of one-cluster-multiple-prototypes in which convex hulls of varying sizes are prototypes,and accurate connection analysis makes the support of arbitrary cluster shapes possible.Inspired by geometry,the three presented strategies make kProtoClust bypassing the K dependence well with the global and local position relationship analysis for data samples.Experimental results on twelve datasets of irregular cluster shape or high dimension suggest that kProtoClust handles arbitrary cluster shapes with prominent accuracy even without the prior knowledge K.展开更多
In this paper,we investigate the application of the Unmanned Aerial Vehicle(UAV)-enabled relaying system in emergency communications,where one UAV is applied as a relay to help transmit information from ground users t...In this paper,we investigate the application of the Unmanned Aerial Vehicle(UAV)-enabled relaying system in emergency communications,where one UAV is applied as a relay to help transmit information from ground users to a Base Station(BS).We maximize the total transmitted data from the users to the BS,by optimizing the user communication scheduling and association along with the power allocation and the trajectory of the UAV.To solve this non-convex optimization problem,we propose the traditional Convex Optimization(CO)and the Reinforcement Learning(RL)-based approaches.Specifically,we apply the block coordinate descent and successive convex approximation techniques in the CO approach,while applying the soft actor-critic algorithm in the RL approach.The simulation results show that both approaches can solve the proposed optimization problem and obtain good results.Moreover,the RL approach establishes emergency communications more rapidly than the CO approach once the training process has been completed.展开更多
We prove that for a smooth convex body K⊂ℝ^(d),d≥2,with positive Gauss curvature,its homothety with a certain associated convex body implies that K is either a ball or an ellipsoid,depending on the associated body co...We prove that for a smooth convex body K⊂ℝ^(d),d≥2,with positive Gauss curvature,its homothety with a certain associated convex body implies that K is either a ball or an ellipsoid,depending on the associated body considered.展开更多
The hydrodynamic response of overland flow to vegetation coverage on convex slopes remains inadequately quantified despite it is critical for soil erosion control in terrains dominated by such topography.This study sy...The hydrodynamic response of overland flow to vegetation coverage on convex slopes remains inadequately quantified despite it is critical for soil erosion control in terrains dominated by such topography.This study systematically investigated the influence of varying vegetation coverage(0%,1.08%,3.24%,4.69%and 9.81%)on the hydrodynamic characteristics of convex slopes through indoor flume experiments under diverse flow discharges(5.5-13.5 m^(3)/h)and slopes(5°-25°).The results revealed three key hydrodynamic mechanisms:(1)Flow retardation and energy dissipation:Increasing vegetation coverage significantly reduced overland flow velocity and promoted higher flow depth,thereby enhancing water retention and energy dissipation.Both stream power(Ω)and unit stream power(ω)declined by 13.9%-30.1%compared to bare slopes.(2)Flow Regime Transition:Froude number(Fr)decreased with increasing vegetation coverage,promoting the transition from supercritical to subcritical flow.The Reynolds number(Re)consistently exceeded 500,indicating the absence of laminar flow.(3)Modification of flow resistance:Vegetation resistance increased nonlinearly with coverage.Maximum bed shear stress was observed at 4.69%coverage(23.5%higher than bare slopes).However,Manning’s(n)and Darcy-Weisbach(f)coefficients did not correlate clearly with Re,indicating that vegetation coverage and slope type feedback significantly change flow resistance mechanisms.展开更多
In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) i...In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.展开更多
基金Supported by the National Natural Science Foundation of China(11301255)the Fund by Collaborative Innovation Center of IoT Industrialization and Intelligent Production,Minjiang University(IIC1703)+1 种基金Foundation of Minjiang University(MYK17032)the Program for New Century Excellent Talents in Fujian Province University
文摘Hardware/software partitioning is an important step in the design of embedded systems. In this paper, the hardware/software partitioning problem is modeled as a constrained binary integer programming problem, which is further converted equivalently to an unconstrained binary integer programming problem by a penalty method. A local search method, HSFM, is developed to obtain a discrete local minimizer of the unconstrained binary integer programming problem. Next, an auxiliary function, which has the same global optimal solutions as the unconstrained binary integer programming problem, is constructed, and its properties are studied. We show that applying HSFM to minimize the auxiliary function can escape from previous local optima by the increase of the parameter value successfully. Finally, a discrete dynamic convexized method is developed to solve the hardware/software partitioning problem. Computational results and comparisons indicate that the proposed algorithm can get high-quality solutions.
基金supported by the National Natural Science Foundation of China(No.62203256)。
文摘Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequential Convex Programming(SFC-SCP)to improve the computation efficiency and reliability of trajectory generation.SFC-SCP combines the front-end convex polyhedron SFC construction and back-end SCP-based trajectory optimization.A Sparse A^(*)Search(SAS)driven SFC construction method is designed to efficiently generate polyhedron SFC according to the geometric relation among obstacles and collision-free waypoints.Via transforming the nonconvex obstacle-avoidance constraints to linear inequality constraints,SFC can mitigate infeasibility of trajectory planning and reduce computation complexity.Then,SCP casts the nonlinear trajectory optimization subject to SFC into convex programming subproblems to decrease the problem complexity.In addition,a convex optimizer based on interior point method is customized,where the search direction is calculated via successive elimination to further improve efficiency.Simulation experiments on dense obstacle scenarios show that SFC-SCP can generate dynamically feasible safe trajectory rapidly.Comparative studies with state-of-the-art SCP-based methods demonstrate the efficiency and reliability merits of SFC-SCP.Besides,the customized convex optimizer outperforms off-the-shelf optimizers in terms of computation time.
基金supported by the NSFC(12171378)supported by the Characteristic innovation projects of universities in Guangdong province(2023K-TSCX381)+3 种基金supported by the Young Top-Talent program of Chongqing(CQYC2021059145)the Major Special Project of NSFC(12141101)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937).
文摘An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.
文摘A survey of recent progress on the multiplicity and stability problems for closed characteristics on compact convex hypersurfaces in R^(2n) is given.
基金Supported in part by NSFC(No.11971005)the Fundamental Research Funds for the Central Universities(Nos.GK202101008,GK202102012)。
文摘In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.
基金supported partially by the National Natural Science Foundation of China(Nos.11226236 and 11301255)the Natural Science Foundation of Fujian Province of China(No.2012J05007)the Science and Technology Project of the Education Bureau of Fujian,China(Nos.JA13246 and JK2012037).
文摘Given an undirected graph with edge weights,the max-cut problem is to find a partition of the vertices into twosubsets,such that the sumof theweights of the edges crossing different subsets ismaximized.Heuristics based on auxiliary function can obtain high-quality solutions of the max-cut problem,but suffer high solution cost when instances grow large.In this paper,we combine clustered adaptive multistart and discrete dynamic convexized method to obtain high-quality solutions in a reasonable time.Computational experiments on two sets of benchmark instances from the literature were performed.Numerical results and comparisons with some heuristics based on auxiliary function show that the proposed algorithm is much faster and can obtain better solutions.Comparisons with several state-ofthe-science heuristics demonstrate that the proposed algorithm is competitive.
基金supported by the National Natural Science Foundation of China(12171106)the Guangxi Science and Technology Program(AD23023001)+4 种基金the Natural Science Foundation of Guangxi Province(2023GXNSFBA026029)the National Natural Science Foundation of China(12401403,12361063)the Research Project of Guangxi Minzu University(2022KJQD03)the Middle-aged and Young Teachers’Basic Ability Promotion Project of Guangxi Province(2023KY0168)the Xiangsihu Young Scholars Innovative Research Team of Guangxi Minzu University(2022GXUNXSHQN04).
文摘In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.
基金supported by the project Disuguaglianze analitiche e geometriche,funded by the Gruppo per Analisi Matematica la Probabilitàe le loro Applicazioni.
文摘Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.
基金National Natural Science Foundation of China,Grant/Award Numbers:51809290,51979093,52239009Project funded by Tibet Autonomous Region Key R&D Plan,Grant/Award Number:XZ202101ZY0002GPostgraduate Research&Practice Innovation Program of Jiangsu Province,Grant/Award Number:No.KYCX22_0656。
文摘This study aims to develop a high-precision and cost-efficient method for the threedimensional reconstruction of large particles in natural gravel and blasted rock fragments,utilizing Structure from Motion(SfM)and Multi-View Stereo(MVS)techniques.The proposed approach was applied to characterize the three-dimensional morphology of rockfill dam materials at a real construction site.Particle shape was quantitatively analyzed using shape indices of sphericity,convexity,and angularity.The predominant morphology of natural gravel is characterized as slightly elongated and slightly flat,while rock fragments are slightly elongated and not flat.Probability density distributions of shape indices follow a skewed normal distribution:sphericity and convexity show leftward skewness,whereas angularity is right-skewed.Skewness parameters of sphericity and angularity are consistent between natural gravel and blasted rock fragments,indicating comparable shape asymmetry.Convexity skewness is significantly higher in natural gravel compared to rock fragments,by approximately an order of magnitude.The relationship between size and particle shape shows that form ratios and associated shape descriptors change linearly with the logarithm of size;larger particles approach spherical or cubic forms.The innovative measurements contribute to the particle shape data set of rockfill dam materials,providing valuable insights into the three-dimensional and statistical morphological characteristics of relatively large particles in natural gravel and blasted rock fragments.This approach enhances understanding of particle morphology's impact on the mechanical behavior of granular materials.
文摘In this paper,we consider the distributed online optimization problem on a time-varying network,where each agent on the network has its own time-varying objective function and the goal is to minimize the overall loss accumulated.Moreover,we focus on distributed algorithms which do not use gradient information and projection operators to improve the applicability and computational efficiency.By introducing the deterministic differences and the randomized differences to substitute the gradient information of the objective functions and removing the projection operator in the traditional algorithms,we design two kinds of gradient-free distributed online optimization algorithms without projection step,which can economize considerable computational resources as well as has less limitations on the applicability.We prove that both of two algorithms achieves consensus of the estimates and regrets of\(O\left(\log(T)\right)\)for local strongly convex objective,respectively.Finally,a simulation example is provided to verify the theoretical results.
文摘Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
基金funded by the Science and Technology Project of State Grid Shanxi Electric Power Company(5205E0230001).
文摘With the development of integrated power and gas distribution systems(IPGS)incorporating renewable energy sources(RESs),coordinating the restoration processes of the power distribution system(PS)and the gas distribution system(GS)by utilizing the benefits of RESs enhances service restoration.In this context,this paper proposes a coordinated service restoration framework that considers the uncertainty in RESs and the bi-directional restoration interactions between the PS and GS.Additionally,a coordinated service restoration model is developed considering the two systems’interdependency and the GS’s dynamic characteristics.The objective is to maximize the system resilience index while adhering to operational,dynamic,restoration logic,and interdependency constraints.A method for managing uncertainties in RES output is employed,and convexification techniques are applied to address the nonlinear constraints arising from the physical laws of the IPGS,thereby reducing solution complexity.As a result,the service restoration optimization problem of the IPGS can be formulated as a computationally tractable mixed-integer second-order cone programming problem.The effectiveness and superiority of the proposed framework are demonstrated through numerical simulations conducted on the interdependent IEEE 13-bus PS and 9-node GS.The comparative results show that the proposed framework improves the system resilience index by at least 65.07%compared to traditional methods.
基金Supported by the Natural Science Foundation of Anhui Provincial Department of Education(Grant Nos.KJ2020A 0993KJ2020ZD74)+2 种基金the High-Level Talent Research Start-Up Project(Grant No.DC2300000286)the Foundation of Guangzhou Civil Aviation College(Grant Nos.22X041824X4412).
文摘In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are more accurate than those obtained by Srivastava.
文摘In this paper,an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed.Firstly,the affine system is used to build a dynamic model and analyze the state constraints.The midcourse guidance problem is transformed into a continuous time optimization problem.Secondly,the problem is transformed into a discrete convex programming problem by affine control variable relaxation,Gaussian pseudospectral discretization and constraints linearization.Then,the off-line midcourse guidance trajectory is generated before midcourse guidance.It is used as the initial reference trajectory for online correction of midcourse guidance.An online guidance framework is used to eliminate the error caused by calculation of guidance instruction time.And the design of discrete points decreases with flight time to improve the solving efficiency.In addition,it is proposed that the terminal guidance capture is used innovatively space to judge the success of midcourse guidance.Numerical simulation shows the feasibility and effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China under Grant No.62162009the Key Technologies R&D Program of He’nan Province under Grant No.242102211065+1 种基金the Scientific Research Innovation Team of Xuchang University under GrantNo.2022CXTD003Postgraduate Education Reform and Quality Improvement Project of Henan Province under Grant No.YJS2024JD38.
文摘Towards optimal k-prototype discovery,k-means-like algorithms give us inspirations of central samples collection,yet the unstable seed samples selection,the hypothesis of a circle-like pattern,and the unknown K are still challenges,particularly for non-predetermined data patterns.We propose an adaptive k-prototype clustering method(kProtoClust)which launches cluster exploration with a sketchy division of K clusters and finds evidence for splitting and merging.On behalf of a group of data samples,support vectors and outliers from the perspective of support vector data description are not the appropriate candidates for prototypes,while inner samples become the first candidates for instability reduction of seeds.Different from the representation of samples in traditional,we extend sample selection by encouraging fictitious samples to emphasize the representativeness of patterns.To get out of the circle-like pattern limitation,we introduce a convex decomposition-based strategy of one-cluster-multiple-prototypes in which convex hulls of varying sizes are prototypes,and accurate connection analysis makes the support of arbitrary cluster shapes possible.Inspired by geometry,the three presented strategies make kProtoClust bypassing the K dependence well with the global and local position relationship analysis for data samples.Experimental results on twelve datasets of irregular cluster shape or high dimension suggest that kProtoClust handles arbitrary cluster shapes with prominent accuracy even without the prior knowledge K.
基金supported in part by the Shenzhen Basic Research Project under Grant JCYJ20220531103008018 and Grant 20200812112423002in part by the Guangdong Basic Research Program under Grant 2019A1515110358,2021A1515012097in part by the open research fund of National Mobile Communications Research Laboratory,Southeast University (No.2021D16)。
文摘In this paper,we investigate the application of the Unmanned Aerial Vehicle(UAV)-enabled relaying system in emergency communications,where one UAV is applied as a relay to help transmit information from ground users to a Base Station(BS).We maximize the total transmitted data from the users to the BS,by optimizing the user communication scheduling and association along with the power allocation and the trajectory of the UAV.To solve this non-convex optimization problem,we propose the traditional Convex Optimization(CO)and the Reinforcement Learning(RL)-based approaches.Specifically,we apply the block coordinate descent and successive convex approximation techniques in the CO approach,while applying the soft actor-critic algorithm in the RL approach.The simulation results show that both approaches can solve the proposed optimization problem and obtain good results.Moreover,the RL approach establishes emergency communications more rapidly than the CO approach once the training process has been completed.
文摘We prove that for a smooth convex body K⊂ℝ^(d),d≥2,with positive Gauss curvature,its homothety with a certain associated convex body implies that K is either a ball or an ellipsoid,depending on the associated body considered.
基金financially supported by the National Natural Science Foundation of China(Grant NO.52279056)Inner Mongolia open list project(Grant NO.2024JBGS0023)。
文摘The hydrodynamic response of overland flow to vegetation coverage on convex slopes remains inadequately quantified despite it is critical for soil erosion control in terrains dominated by such topography.This study systematically investigated the influence of varying vegetation coverage(0%,1.08%,3.24%,4.69%and 9.81%)on the hydrodynamic characteristics of convex slopes through indoor flume experiments under diverse flow discharges(5.5-13.5 m^(3)/h)and slopes(5°-25°).The results revealed three key hydrodynamic mechanisms:(1)Flow retardation and energy dissipation:Increasing vegetation coverage significantly reduced overland flow velocity and promoted higher flow depth,thereby enhancing water retention and energy dissipation.Both stream power(Ω)and unit stream power(ω)declined by 13.9%-30.1%compared to bare slopes.(2)Flow Regime Transition:Froude number(Fr)decreased with increasing vegetation coverage,promoting the transition from supercritical to subcritical flow.The Reynolds number(Re)consistently exceeded 500,indicating the absence of laminar flow.(3)Modification of flow resistance:Vegetation resistance increased nonlinearly with coverage.Maximum bed shear stress was observed at 4.69%coverage(23.5%higher than bare slopes).However,Manning’s(n)and Darcy-Weisbach(f)coefficients did not correlate clearly with Re,indicating that vegetation coverage and slope type feedback significantly change flow resistance mechanisms.
基金supported by the National Natural Science Foundation of China(12061035)the Research Foundation of Jiangxi Science and Technology Normal University of China(2021QNBJRC003)supported by the Graduate Innovation Fund of Jiangxi Science and Technology Normal University(YC2024-X10).
文摘In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.
