In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.展开更多
A novel aperiodically intermittent impulse control(AIIC)method is proposed to investigate the exponential synchronization in mean square(ESMS)of a class of impulsive stochastic infinite-dimensional systems with Poisso...A novel aperiodically intermittent impulse control(AIIC)method is proposed to investigate the exponential synchronization in mean square(ESMS)of a class of impulsive stochastic infinite-dimensional systems with Poisson jumps(ISIDSP).The AIIC control strategy inherits the flexibility of aperiodically intermittent control,including the variable control period,adjustable control interval length,and the discretization of impulsive control.In addition,this article introduces a novel mild Itô's formula.By leveraging semigroup theory,the contraction mapping principle,and graph theory,along with constructing the Lyapunov function,the criterion for the existence and uniqueness of a mild solution of ISIDSP is thereby established.Furthermore,the mean-square exponential synchronization problem of the above systems is resolved,and the constraints within the mild solution domain are alleviated.These criteria clarify the impact of control parameters,control intervals and network topology on ESMS.The theoretical results are subsequently applied to a class of neural networks with reaction-diffusion processes,and the validity of the results is verified using numerical simulations.展开更多
With the rapid development of generative artificial intelligence(GenAI),the task of story visualization,which transforms natural language narratives into coherent and consistent image sequences,has attracted growing r...With the rapid development of generative artificial intelligence(GenAI),the task of story visualization,which transforms natural language narratives into coherent and consistent image sequences,has attracted growing research attention.However,existing methods still face limitations in balancing multi-frame character consistency and generation efficiency,which restricts their feasibility for large-scale practical applications.To address this issue,this study proposes a modular cloud-based distributed system built on Stable Diffusion.By separating the character generation and story generation processes,and integratingmulti-feature control techniques,a cachingmechanism,and an asynchronous task queue architecture,the system enhances generation efficiency and scalability.The experimental design includes both automated and human evaluations of character consistency,performance testing,and multinode simulation.The results show that the proposed system outperforms the baseline model StoryGen in both CLIP-I and human evaluation metrics.In terms of performance,under the experimental environment of this study,dual-node deployment reduces average waiting time by approximately 19%,while the four-node simulation further reduces it by up to 65%.Overall,this study demonstrates the advantages of cloud-distributed GenAI in maintaining character consistency and reducing generation latency,highlighting its potential value inmulti-user collaborative story visualization applications.展开更多
A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance con...A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.展开更多
Li_(7)La_(3)Zr_(2)O_(12)-based electrolytes have got great promise for solid-state lithium(Li)metal batteries because of their high elastic modulus and wide electrochemical stability window.However,the insufficient co...Li_(7)La_(3)Zr_(2)O_(12)-based electrolytes have got great promise for solid-state lithium(Li)metal batteries because of their high elastic modulus and wide electrochemical stability window.However,the insufficient contact and heterogeneous Li deposition severely hinder their practical applications.Here,a flexible ternary polymethacrylate(PMA)matrix is designed to incorporate with Ta-doped Li_(7)La_(3)Zr_(2)O_(12)(LLZTO-PMA).The PMA matrix ensures excellent interfacial contact,while the synergistic effects of its polar carbonyl groups and its interaction with LLZTO creating fast interfacial Li^(+)pathways yield a high ionic conductivity of 0.266 mS cm^(-1)at 20℃.Moreover,the interaction between LLZTO and PMA matrix further guides the formation of a hybrid LiF/Li_(3)N-rich solid electrolyte interphase,which allows a fast Li^(+)interfacial kinetic due to its lowered Li^(+)diffusion barrier.Consequently,the LLZTO-PMA electrolyte contributes an ultra-stable Li anode interphase,attaining a lifespan exceeding 10,000 h in symmetric cells and retaining over 96%capacity after 600 cycles in full battery,demonstrating a breakthrough for high-performance solid-state batteries.展开更多
The zigzag nitrogen chain,similar to the Ch-N structure,has long been considered as a potential high-energy-density structure.However,all the previously predicted zigzag N-chain structures,similar to Ch-N,exhibited im...The zigzag nitrogen chain,similar to the Ch-N structure,has long been considered as a potential high-energy-density structure.However,all the previously predicted zigzag N-chain structures,similar to Ch-N,exhibited imaginary frequencies in their phonon spectra at 0 GPa.Here,we conducted a systematic investigation of P-N compounds using first-principles calculations,uncovering a series of structurally similar stable phases,C2/m-PN_(x)(x=6,8,10,12,and 14),in which N forms zigzag N chains similar to those in Ch-N.In P-N compounds,the longest zigzag N-chain,which can theoretically remain stable under ambient pressure,is the N-chain composed of 14 N atoms in C2/m-PN14.If the N-chain continues to grow,imaginary interchain vibrational frequencies arise in the system.Notably,N chains with an even number of atoms were more likely to be energetically favorable.The five C2/m-PN_(x) phases and one metastable phase(R-PN_(6))exhibited remarkable stability and excellent detonability at ambient pressure,indicating that they are promising candidates for high-energy-density materials.In addition,R-PN_(6) was the first structure to stabilize the N_(6) ring through covalent bonding,with the covalent network contributing to its high hardness(47.59 GPa).展开更多
In this paper,the necessary and sufficient conditions for generalone-step m ethods to be exponentially fitted atq0∈C aregiven.A classofm ultiderivative hybrid one-step m ethods of order at leasts+ 1 is constructed ...In this paper,the necessary and sufficient conditions for generalone-step m ethods to be exponentially fitted atq0∈C aregiven.A classofm ultiderivative hybrid one-step m ethods of order at leasts+ 1 is constructed w ith s+ 1 param eters,w here sis the order of derivative.The necessary and sufficient conditions for these m ethods to be A-stable and exponentially fitted is proved.Furtherm ore,a class ofA-stable 2 param eters hybrid one-step m ethods oforderatleast 8 are constructed,w hich use 4th order derivative.These m ethods are exponentially fitted atq0 if and only if its fitted function f(q) satisfies f(q0)= 0.Finally,an A-stable exponentially fitted m ethod oforder 8 is obtained.展开更多
In this paper, we are concerned with output feedback stabilization for a one-dimensional anti-stable wave equation with disturbance. First, we design a disturbance estimator for the original system. Then, we propose a...In this paper, we are concerned with output feedback stabilization for a one-dimensional anti-stable wave equation with disturbance. First, we design a disturbance estimator for the original system. Then, we propose an output feedback controller for the original system. By calculation, the closed-loop of original system is proved to be exponentially stable and well-posed. Finally, this paper is summarized.展开更多
The properties of electrolytes are critical for fast-charging and stable-cycling applications in lithium metal batteries(LMBs).However,the slow kinetics of Li^(+)transport and desolvation in commercial carbonate elect...The properties of electrolytes are critical for fast-charging and stable-cycling applications in lithium metal batteries(LMBs).However,the slow kinetics of Li^(+)transport and desolvation in commercial carbonate electrolytes,cou pled with the formation of unstable solid electrolyte interphases(SEI),exacerbate the degradation of LMB performance at high current densities.Herein,we propose a versatile electrolyte design strategy that incorporates cyclohexyl methyl ether(CME)as a co-solvent to reshape the Li^(+)solvation environment by the steric-hindrance effect of bulky molecules and their competitive coordination with other solvent molecules.Simulation calculations and spectral analysis demonstrate that the addition of CME molecules reduces the involvement of other solvent molecules in the Li solvation sheath and promotes the formation of Li^(+)-PF_(6)^(-)coordination,thereby accelerating Li^(+)transport kinetics.Additionally,this electrolyte composition improves Li^(+)desolvation kinetics and fosters the formation of inorganic-rich SEI,ensuring cycle stability under fast charging.Consequently,the Li‖LiNi_(0.8)Co_(0.1)Mn_(0.1)O_(2)battery with the modified electrolyte retains 82% of its initial capacity after 463 cycles at 1 C.Even under the extreme fast-charging condition of 5 C,the battery can maintain 80% capacity retention after 173 cycles.This work provides a promising approach for the development of highperformance LMBs by modulating solvation environment of electrolytes.展开更多
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
文摘In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
基金supported in part by the National Natural Science Foundation of China(12471422,62573274,12371173)the Natural Science Foundation of Shandong Province of China(ZR2022LLZ003,ZR2024MF001)the Funding for Visiting Studies and Research by Teachers in Ordinary Undergraduate Colleges and Universities in Shandong Province。
文摘A novel aperiodically intermittent impulse control(AIIC)method is proposed to investigate the exponential synchronization in mean square(ESMS)of a class of impulsive stochastic infinite-dimensional systems with Poisson jumps(ISIDSP).The AIIC control strategy inherits the flexibility of aperiodically intermittent control,including the variable control period,adjustable control interval length,and the discretization of impulsive control.In addition,this article introduces a novel mild Itô's formula.By leveraging semigroup theory,the contraction mapping principle,and graph theory,along with constructing the Lyapunov function,the criterion for the existence and uniqueness of a mild solution of ISIDSP is thereby established.Furthermore,the mean-square exponential synchronization problem of the above systems is resolved,and the constraints within the mild solution domain are alleviated.These criteria clarify the impact of control parameters,control intervals and network topology on ESMS.The theoretical results are subsequently applied to a class of neural networks with reaction-diffusion processes,and the validity of the results is verified using numerical simulations.
文摘With the rapid development of generative artificial intelligence(GenAI),the task of story visualization,which transforms natural language narratives into coherent and consistent image sequences,has attracted growing research attention.However,existing methods still face limitations in balancing multi-frame character consistency and generation efficiency,which restricts their feasibility for large-scale practical applications.To address this issue,this study proposes a modular cloud-based distributed system built on Stable Diffusion.By separating the character generation and story generation processes,and integratingmulti-feature control techniques,a cachingmechanism,and an asynchronous task queue architecture,the system enhances generation efficiency and scalability.The experimental design includes both automated and human evaluations of character consistency,performance testing,and multinode simulation.The results show that the proposed system outperforms the baseline model StoryGen in both CLIP-I and human evaluation metrics.In terms of performance,under the experimental environment of this study,dual-node deployment reduces average waiting time by approximately 19%,while the four-node simulation further reduces it by up to 65%.Overall,this study demonstrates the advantages of cloud-distributed GenAI in maintaining character consistency and reducing generation latency,highlighting its potential value inmulti-user collaborative story visualization applications.
文摘A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.
基金supported by the National Natural Science Foundation of China(No.22305106)the Postdoctoral Fellowship Program of CPSF(GZC20230682)Beijing Key Laboratory of High-Entropy Energy materials and Devices,Beijing Institute of Nanoenergy and Nanosystems(No.GS 2025ZD005)。
文摘Li_(7)La_(3)Zr_(2)O_(12)-based electrolytes have got great promise for solid-state lithium(Li)metal batteries because of their high elastic modulus and wide electrochemical stability window.However,the insufficient contact and heterogeneous Li deposition severely hinder their practical applications.Here,a flexible ternary polymethacrylate(PMA)matrix is designed to incorporate with Ta-doped Li_(7)La_(3)Zr_(2)O_(12)(LLZTO-PMA).The PMA matrix ensures excellent interfacial contact,while the synergistic effects of its polar carbonyl groups and its interaction with LLZTO creating fast interfacial Li^(+)pathways yield a high ionic conductivity of 0.266 mS cm^(-1)at 20℃.Moreover,the interaction between LLZTO and PMA matrix further guides the formation of a hybrid LiF/Li_(3)N-rich solid electrolyte interphase,which allows a fast Li^(+)interfacial kinetic due to its lowered Li^(+)diffusion barrier.Consequently,the LLZTO-PMA electrolyte contributes an ultra-stable Li anode interphase,attaining a lifespan exceeding 10,000 h in symmetric cells and retaining over 96%capacity after 600 cycles in full battery,demonstrating a breakthrough for high-performance solid-state batteries.
基金supported by the Anhui Provincial Natural Science Foundation (Grant No.2508085J006)CASHIPS Director's Fund (Grant No.YZJJ202207-CX)。
文摘The zigzag nitrogen chain,similar to the Ch-N structure,has long been considered as a potential high-energy-density structure.However,all the previously predicted zigzag N-chain structures,similar to Ch-N,exhibited imaginary frequencies in their phonon spectra at 0 GPa.Here,we conducted a systematic investigation of P-N compounds using first-principles calculations,uncovering a series of structurally similar stable phases,C2/m-PN_(x)(x=6,8,10,12,and 14),in which N forms zigzag N chains similar to those in Ch-N.In P-N compounds,the longest zigzag N-chain,which can theoretically remain stable under ambient pressure,is the N-chain composed of 14 N atoms in C2/m-PN14.If the N-chain continues to grow,imaginary interchain vibrational frequencies arise in the system.Notably,N chains with an even number of atoms were more likely to be energetically favorable.The five C2/m-PN_(x) phases and one metastable phase(R-PN_(6))exhibited remarkable stability and excellent detonability at ambient pressure,indicating that they are promising candidates for high-energy-density materials.In addition,R-PN_(6) was the first structure to stabilize the N_(6) ring through covalent bonding,with the covalent network contributing to its high hardness(47.59 GPa).
文摘In this paper,the necessary and sufficient conditions for generalone-step m ethods to be exponentially fitted atq0∈C aregiven.A classofm ultiderivative hybrid one-step m ethods of order at leasts+ 1 is constructed w ith s+ 1 param eters,w here sis the order of derivative.The necessary and sufficient conditions for these m ethods to be A-stable and exponentially fitted is proved.Furtherm ore,a class ofA-stable 2 param eters hybrid one-step m ethods oforderatleast 8 are constructed,w hich use 4th order derivative.These m ethods are exponentially fitted atq0 if and only if its fitted function f(q) satisfies f(q0)= 0.Finally,an A-stable exponentially fitted m ethod oforder 8 is obtained.
文摘In this paper, we are concerned with output feedback stabilization for a one-dimensional anti-stable wave equation with disturbance. First, we design a disturbance estimator for the original system. Then, we propose an output feedback controller for the original system. By calculation, the closed-loop of original system is proved to be exponentially stable and well-posed. Finally, this paper is summarized.
基金supported by the Lithium Resources and Lithium Materials Key Laboratory of Sichuan Province(LRMKF202405)the National Natural Science Foundation of China(52402226)+3 种基金the Natural Science Foundation of Sichuan Province(2024NSFSC1016)the Scientific Research Startup Foundation of Chengdu University of Technology(10912-KYQD2023-10240)the opening funding from Key Laboratory of Engineering Dielectrics and Its Application(Harbin University of Science and Technology)(KFM202507,Ministry of Education)the funding provided by the Alexander von Humboldt Foundation。
文摘The properties of electrolytes are critical for fast-charging and stable-cycling applications in lithium metal batteries(LMBs).However,the slow kinetics of Li^(+)transport and desolvation in commercial carbonate electrolytes,cou pled with the formation of unstable solid electrolyte interphases(SEI),exacerbate the degradation of LMB performance at high current densities.Herein,we propose a versatile electrolyte design strategy that incorporates cyclohexyl methyl ether(CME)as a co-solvent to reshape the Li^(+)solvation environment by the steric-hindrance effect of bulky molecules and their competitive coordination with other solvent molecules.Simulation calculations and spectral analysis demonstrate that the addition of CME molecules reduces the involvement of other solvent molecules in the Li solvation sheath and promotes the formation of Li^(+)-PF_(6)^(-)coordination,thereby accelerating Li^(+)transport kinetics.Additionally,this electrolyte composition improves Li^(+)desolvation kinetics and fosters the formation of inorganic-rich SEI,ensuring cycle stability under fast charging.Consequently,the Li‖LiNi_(0.8)Co_(0.1)Mn_(0.1)O_(2)battery with the modified electrolyte retains 82% of its initial capacity after 463 cycles at 1 C.Even under the extreme fast-charging condition of 5 C,the battery can maintain 80% capacity retention after 173 cycles.This work provides a promising approach for the development of highperformance LMBs by modulating solvation environment of electrolytes.
