In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation o...In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H<sup>1</sup> and L<sup>2</sup> norms. Finally, some numerical experiments are carried out to support the theoretical results.展开更多
Shape irregularity,a sub-factor of parcel fragmentation is a problem that hinders sustainable agriculture and is solved using land consolidation projects.Determination of the parcel shape degree contributes significan...Shape irregularity,a sub-factor of parcel fragmentation is a problem that hinders sustainable agriculture and is solved using land consolidation projects.Determination of the parcel shape degree contributes significantly to spatial prioritization where there is also a high probability of achieving positive effects of consolidation projects.This study aims to determine the shape degree of the agricultural parcels both at singular and rural county scales in Tekirdag Province,Turkey in 2020 by combining the parcel shape index(PSI) with the minimum bounding geometry index(MBG) to improve parcel scores.Hot-spot zones of the highly irregular and near optimum parcels were also determined using Getis-Ord G_(i)^(*) statistic.The parcel degrees were classified into four categories,namely highly irregular,irregular,regular and near optimum.The obtained unweighted scores of the parameters exhibit deviations from the expected values.After weighting by pairwise comparison,the values approached ideal scores.Among 346 740 parcels,53% were highly irregular and irregular and 47% were regular and near optimum shapes after weighting whereas these were 70% and 30%,respectively before weighting.The average parcel degree of 63 rural counties was regular while the average parcel degree of the remaining 264 rural counties was irregular.The combined use of PSI and MBG index improved the correctness of the parcel shape score.It could be suggested to use as a tool in land consolidation prioritization.展开更多
In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2...In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2)^(q12)(x)+h_(1)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,(−Δ)_(a2)^(β/2)u2(x)=u_(1)^(q21)(x)+u_(2)^(q22)(x)+h_(2)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,u_(1)(x)=0,u_(2)(x)=0,x∈R^(n)∖Ω.Here(−Δ)_(a1)^(α/2) and(−Δ)_(a2)^(β/2) denote weighted fractional Laplacians andΩ⊂R^(n) is a C^(2) bounded domain.It is shown that under some assumptions on h_(i)(i=1,2),the problem admits at least one positive solution(u_(1)(x),u_(2)(x)).We first obtain the{a priori}bounds of solutions to the system by using the direct blow-up method of Chen,Li and Li.Then the proof of existence is based on a topological degree theory.展开更多
随着全球定位系统的发展和应用,巨量的轨迹数据被实时收集,给数据的传输、存储和分析带来挑战.基于分段线性近似(piecewise linear approximation,PLA)的数据压缩技术因具有简单直观、压缩存储低和传输快的特点被广泛应用和研究.针对现...随着全球定位系统的发展和应用,巨量的轨迹数据被实时收集,给数据的传输、存储和分析带来挑战.基于分段线性近似(piecewise linear approximation,PLA)的数据压缩技术因具有简单直观、压缩存储低和传输快的特点被广泛应用和研究.针对现有轨迹PLA压缩方法不能最优化地在线压缩多维数据的现状,在最大误差限定(maximum error bound,记为L_(∞))下提出多维轨迹数据的最优化PLA压缩问题(记为m DisPLA_(∞)),并给出一种在线MDisPLA算法予以解决.该算法利用“分治-融合”的策略扩展一维最优化PLA算法,以最优化地压缩多维轨迹数据.MDisPLA算法具有线性时间复杂性,可以生成最少的不连续分割,且可以保证生成直线表示的质量,即原始数据点和对应解压缩点之间的同步误差具有上界.通过与基于同步距离锥交(cone intersection using the synchronous Euclidean distance,CISED)的轨迹压缩算法进行理论和实验比较,验证了MDisPLA算法是稳健的,可生成具有保质性的直线表示.MDisPLA算法以更低的内存消耗,较CISED算法提高了14倍左右的处理速度,降低了约48%的分割个数和10.5%的存储个数.MDisPLA算法在保证压缩质量的同时,显著提高了处理速度和降低了存储空间,整体上优于CISED算法.展开更多
In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizi...In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .展开更多
Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the developm...Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices.展开更多
Dear Editor,This letter considers a collision-free trajectory tracking problem for performance-guaranteed mobile robots(MRs)subject to obstacles.We propose a safety-critical performance-guaranteed trajectory tracking ...Dear Editor,This letter considers a collision-free trajectory tracking problem for performance-guaranteed mobile robots(MRs)subject to obstacles.We propose a safety-critical performance-guaranteed trajectory tracking method based on control barrier functions(CBFs).First,an auxiliary system is established to generate the non-negative signals for inflexible bounds such that the performance constraints are not violated when avoiding obstacles.展开更多
This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The...This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The multiple missing measurements are characterized through random variables that obey some given probability distributions,and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable.Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense.To this end,the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers,thus the original design issue is reformulated as that of the augmented system.Subsequently,we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters.With the aid of two well-defined matrix difference equations,we not only obtain upper bounds on filtering error covariances,but also minimize those bounds via carefully designing gain parameters.Finally,an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.展开更多
We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two ty...We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two typical bound states found above and below the energy bands,this system presents an extraordinary chiral bound state located within the energy gap.We use the chirality to quantify the breaking of the mirror symmetry.We find that the chirality value undergoes continuous changes by tuning the coupling strengths.The preferred direction of the chirality is controlled not only by the competition between the intracell and the intercell hoppings in the coupled-resonator array,but also by the coherence between the two coupling points.In the case with one coupling point,the chirality values varies monotonously with difference between the intracell hopping and the intercell hoppings.While in the case with two coupling points,due to the coherence between the two coupling points the perfect chiral states can be obtained.展开更多
Information about electronic excited states of molecular anions plays an important role in investigating electron attachment and detachment processes.Here we present a high-level theoretical study of the electronic st...Information about electronic excited states of molecular anions plays an important role in investigating electron attachment and detachment processes.Here we present a high-level theoretical study of the electronic structures of 12 alkali-metal-containing diatomic anions MX-(MX = LiH,LiF,LiCl,NaF,NaCl,NaBr,RbCl,KCl,KBr,RbI,KI and CsI).The equation-of-motion electron-attachment coupled-cluster singles and doubles(EOM-EA-CCSD) method is used to calculate the electron binding energies(EBEs) of 10 electronic excited states of each of the 12 molecule anions.With addition of different s-/p-/d-type diffusion functions in the basis set,we have identified possible excited dipole bound states(DBSs) of each anion.With the investigation of EBEs on the 12 MXs with dipole moment(DM) up to 12.1 D,we evaluate the dependence of the number of anionic excited DBSs on molecular DM.The results indicate that there are at least two or three DBSs of anions with a molecular DM larger than 7 D and a molecule with DM > 10 D can sustain a π-DBS of the anion.Our study has some implications for the excited DBS electronic states of alkali-metal-containing diatomic molecules.展开更多
One-neutron stripping process between^(6)Li and^(209)Bi was studied at 28,30,and 34 MeV using the in-beamγ-ray spectroscopy method.Theγ-γcoincident analysis clearly identified twoγ-rays feeding the ground and long...One-neutron stripping process between^(6)Li and^(209)Bi was studied at 28,30,and 34 MeV using the in-beamγ-ray spectroscopy method.Theγ-γcoincident analysis clearly identified twoγ-rays feeding the ground and long-lived isomeric states,which were employed to determine the cross section.The one-neutron stripping cross sections were similar to the cross sections of complete fusion in the^(6)Li+^(209)Bi system,but the one-neutron stripping cross sections decreased more gradually at the sub-barrier region.A coupled-reaction-channel calculation was performed to study the detailed reaction mechanism of the one-neutron stripping process in^(6)Li.The calculations indicated that the first excited state of 5 Li is critical in the actual one-neutron transfer mechanism,and the valence proton of 209Bi can be excited to the low-lying excited state in(^(6)Li,^(5)Li)reaction,unlike in the(d,p)reaction.展开更多
文摘In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H<sup>1</sup> and L<sup>2</sup> norms. Finally, some numerical experiments are carried out to support the theoretical results.
文摘Shape irregularity,a sub-factor of parcel fragmentation is a problem that hinders sustainable agriculture and is solved using land consolidation projects.Determination of the parcel shape degree contributes significantly to spatial prioritization where there is also a high probability of achieving positive effects of consolidation projects.This study aims to determine the shape degree of the agricultural parcels both at singular and rural county scales in Tekirdag Province,Turkey in 2020 by combining the parcel shape index(PSI) with the minimum bounding geometry index(MBG) to improve parcel scores.Hot-spot zones of the highly irregular and near optimum parcels were also determined using Getis-Ord G_(i)^(*) statistic.The parcel degrees were classified into four categories,namely highly irregular,irregular,regular and near optimum.The obtained unweighted scores of the parameters exhibit deviations from the expected values.After weighting by pairwise comparison,the values approached ideal scores.Among 346 740 parcels,53% were highly irregular and irregular and 47% were regular and near optimum shapes after weighting whereas these were 70% and 30%,respectively before weighting.The average parcel degree of 63 rural counties was regular while the average parcel degree of the remaining 264 rural counties was irregular.The combined use of PSI and MBG index improved the correctness of the parcel shape score.It could be suggested to use as a tool in land consolidation prioritization.
文摘In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2)^(q12)(x)+h_(1)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,(−Δ)_(a2)^(β/2)u2(x)=u_(1)^(q21)(x)+u_(2)^(q22)(x)+h_(2)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,u_(1)(x)=0,u_(2)(x)=0,x∈R^(n)∖Ω.Here(−Δ)_(a1)^(α/2) and(−Δ)_(a2)^(β/2) denote weighted fractional Laplacians andΩ⊂R^(n) is a C^(2) bounded domain.It is shown that under some assumptions on h_(i)(i=1,2),the problem admits at least one positive solution(u_(1)(x),u_(2)(x)).We first obtain the{a priori}bounds of solutions to the system by using the direct blow-up method of Chen,Li and Li.Then the proof of existence is based on a topological degree theory.
文摘随着全球定位系统的发展和应用,巨量的轨迹数据被实时收集,给数据的传输、存储和分析带来挑战.基于分段线性近似(piecewise linear approximation,PLA)的数据压缩技术因具有简单直观、压缩存储低和传输快的特点被广泛应用和研究.针对现有轨迹PLA压缩方法不能最优化地在线压缩多维数据的现状,在最大误差限定(maximum error bound,记为L_(∞))下提出多维轨迹数据的最优化PLA压缩问题(记为m DisPLA_(∞)),并给出一种在线MDisPLA算法予以解决.该算法利用“分治-融合”的策略扩展一维最优化PLA算法,以最优化地压缩多维轨迹数据.MDisPLA算法具有线性时间复杂性,可以生成最少的不连续分割,且可以保证生成直线表示的质量,即原始数据点和对应解压缩点之间的同步误差具有上界.通过与基于同步距离锥交(cone intersection using the synchronous Euclidean distance,CISED)的轨迹压缩算法进行理论和实验比较,验证了MDisPLA算法是稳健的,可生成具有保质性的直线表示.MDisPLA算法以更低的内存消耗,较CISED算法提高了14倍左右的处理速度,降低了约48%的分割个数和10.5%的存储个数.MDisPLA算法在保证压缩质量的同时,显著提高了处理速度和降低了存储空间,整体上优于CISED算法.
文摘In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .
基金supported by the Australian Research Council(Grant No.DP210101292)the International Technology Center Indo-Pacific (ITC IPAC) via Army Research Office (contract FA520923C0023)。
文摘Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices.
基金supported in part by the National Key R&D Program of China (2022ZD0119901)the Shanghai Science and Technology Program (22015810300)+1 种基金the Hainan Province Science and Technology Special Fund (ZDYF2024GXJS 003)the National Natural Science Foundation of China (U2141234,52201369)。
文摘Dear Editor,This letter considers a collision-free trajectory tracking problem for performance-guaranteed mobile robots(MRs)subject to obstacles.We propose a safety-critical performance-guaranteed trajectory tracking method based on control barrier functions(CBFs).First,an auxiliary system is established to generate the non-negative signals for inflexible bounds such that the performance constraints are not violated when avoiding obstacles.
基金supported in part by the National Natural Science Foundation of China(61933007,U21A2019,U22A2044,61973102,62073180)the Natural Science Foundation of Shandong Province of China(ZR2021MF088)+1 种基金the Hainan Province Science and Technology Special Fund of China(ZDYF2022SHFZ105)the Royal Society of the UK,and the Alexander vonHumboldt Foundation of Germany。
文摘This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The multiple missing measurements are characterized through random variables that obey some given probability distributions,and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable.Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense.To this end,the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers,thus the original design issue is reformulated as that of the augmented system.Subsequently,we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters.With the aid of two well-defined matrix difference equations,we not only obtain upper bounds on filtering error covariances,but also minimize those bounds via carefully designing gain parameters.Finally,an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11975095,12075082,11935006,and 12247105)the Major Sci-Tech Program of Hunan Province,China(Grant No.2023ZJ1010)the Natural Science Foundation of Guangdong Province,China(Grant Nos.2019A1515011400 and 2023A151501223).
文摘We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two typical bound states found above and below the energy bands,this system presents an extraordinary chiral bound state located within the energy gap.We use the chirality to quantify the breaking of the mirror symmetry.We find that the chirality value undergoes continuous changes by tuning the coupling strengths.The preferred direction of the chirality is controlled not only by the competition between the intracell and the intercell hoppings in the coupled-resonator array,but also by the coherence between the two coupling points.In the case with one coupling point,the chirality values varies monotonously with difference between the intracell hopping and the intercell hoppings.While in the case with two coupling points,due to the coherence between the two coupling points the perfect chiral states can be obtained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12274178 and 12174148)Support of High Performance Computing Center of Jilin Universitythe high-performance computing cluster Tiger@IAMP。
文摘Information about electronic excited states of molecular anions plays an important role in investigating electron attachment and detachment processes.Here we present a high-level theoretical study of the electronic structures of 12 alkali-metal-containing diatomic anions MX-(MX = LiH,LiF,LiCl,NaF,NaCl,NaBr,RbCl,KCl,KBr,RbI,KI and CsI).The equation-of-motion electron-attachment coupled-cluster singles and doubles(EOM-EA-CCSD) method is used to calculate the electron binding energies(EBEs) of 10 electronic excited states of each of the 12 molecule anions.With addition of different s-/p-/d-type diffusion functions in the basis set,we have identified possible excited dipole bound states(DBSs) of each anion.With the investigation of EBEs on the 12 MXs with dipole moment(DM) up to 12.1 D,we evaluate the dependence of the number of anionic excited DBSs on molecular DM.The results indicate that there are at least two or three DBSs of anions with a molecular DM larger than 7 D and a molecule with DM > 10 D can sustain a π-DBS of the anion.Our study has some implications for the excited DBS electronic states of alkali-metal-containing diatomic molecules.
基金the National Nature Science Foundation of China(Nos.U2167204,11975040,and U1832130)the Brazilian funding agencies CAPES,CNPq,FAPERJ,and the INCT-FNA(Instituto Nacional de Ciência e Tecnologia-Física Nuclear e Aplicações)+5 种基金research project 464898/2014-5.S.P.Hu was supported by Guang dong Key Research And Development Program(No.2020B040420005)Guang dong Basic and Applied Basic Research Foundation(No.2021B1515120027)Ling Chuang Research Project of China National Nuclear Corporation(No.20221024000072F6-0002-7)Nuclear Energy Development and Research Project(No.HNKF202224(28))the‘111’center(B20065)the U.S.Department of Energy,Office of Science,Office of Nuclear Physics,under contract number DE-AC02-06CH1135.
文摘One-neutron stripping process between^(6)Li and^(209)Bi was studied at 28,30,and 34 MeV using the in-beamγ-ray spectroscopy method.Theγ-γcoincident analysis clearly identified twoγ-rays feeding the ground and long-lived isomeric states,which were employed to determine the cross section.The one-neutron stripping cross sections were similar to the cross sections of complete fusion in the^(6)Li+^(209)Bi system,but the one-neutron stripping cross sections decreased more gradually at the sub-barrier region.A coupled-reaction-channel calculation was performed to study the detailed reaction mechanism of the one-neutron stripping process in^(6)Li.The calculations indicated that the first excited state of 5 Li is critical in the actual one-neutron transfer mechanism,and the valence proton of 209Bi can be excited to the low-lying excited state in(^(6)Li,^(5)Li)reaction,unlike in the(d,p)reaction.
