This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and ...This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.展开更多
In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existenc...In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.展开更多
AIM To compare the outcomes of displaced distal radius fractures treated with volar locking plates and with immediate postoperative mobilisation with the outcomes of these fractures treated with modalities that necess...AIM To compare the outcomes of displaced distal radius fractures treated with volar locking plates and with immediate postoperative mobilisation with the outcomes of these fractures treated with modalities that necessitate 6 wk wrist immobilisation.METHODS A prospective,randomised controlled single-centre trial was conducted with 56 patients who had a displaced radius fracture were randomised to treatment either with a volar locking plate(n=29),or another treatment modality(n=27;cast immobilisation with or without wires or external fixator).Outcomes were measured at 12 wk.Functional outcome scores measured were the Patient-Rated Wrist Evaluation(PRWE)Score;Disabilities of the Arm,Shoulder and Hand and activities of daily living(ADLs).Clinical outcomes were wrist range of motion and grip strength.Radiographic parameters were volar inclination and ulnar variance.RESULTS Patients in the volar locking plate group had significantly better PRWE scores,ADL scores,grip strength and range of extension at three months compared with the control group.All radiological parameters were significantly better in the volar locking plate group at 3 mo.CONCLUSION The present study suggests that volar locking plates produced significantly better functional and clinical outcomes at 3 mo compared with other treatment modalities.Anatomical reduction was significantly more likely to be preserved in the plating group.Level of evidence:Ⅱ.展开更多
In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where ...In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.展开更多
In this paper,we consider the existence of nontrivial weak solutions to a double critical problem involving a fractional Laplacian with a Hardy term:(−Δ)s u−γu|x|2s=|u|2∗s(β)−2 u|x|β+[Iμ∗Fα(⋅,u)](x)fα(x,u),u∈H...In this paper,we consider the existence of nontrivial weak solutions to a double critical problem involving a fractional Laplacian with a Hardy term:(−Δ)s u−γu|x|2s=|u|2∗s(β)−2 u|x|β+[Iμ∗Fα(⋅,u)](x)fα(x,u),u∈H˙s(R n),(0.1)(1)where s∈(0,1),0≤α,β<2s<n,μ∈(0,n),γ<γH,Iμ(x)=|x|−μ,Fα(x,u)=|u(x)|2#μ(α)|x|δμ(α),fα(x,u)=|u(x)|2#μ(α)−2 u(x)|x|δμ(α),2#μ(α)=(1−μ2n)⋅2∗s(α),δμ(α)=(1−μ2n)α,2∗s(α)=2(n−α)n−2s andγH=4 sΓ2(n+2s4)Γ2(n−2s4).We show that problem(0.1)admits at least a weak solution under some conditions.To prove the main result,we develop some useful tools based on a weighted Morrey space.To be precise,we discover the embeddings H˙s(R n)↪L 2∗s(α)(R n,|y|−α)↪L p,n−2s2 p+pr(R n,|y|−pr),(0.2)(2)where s∈(0,1),0<α<2s<n,p∈[1,2∗s(α))and r=α2∗s(α).We also establish an improved Sobolev inequality,(∫R n|u(y)|2∗s(α)|y|αdy)12∗s(α)≤C||u||θH˙s(R n)||u||1−θL p,n−2s2 p+pr(R n,|y|−pr),∀u∈H˙s(R n),(0.3)(3)where s∈(0,1),0<α<2s<n,p∈[1,2∗s(α)),r=α2∗s(α),0<max{22∗s(α),2∗s−12∗s(α)}<θ<1,2∗s=2nn−2s and C=C(n,s,α)>0 is a constant.Inequality(0.3)is a more general form of Theorem 1 in Palatucci,Pisante[1].By using the mountain pass lemma along with(0.2)and(0.3),we obtain a nontrivial weak solution to problem(0.1)in a direct way.It is worth pointing out that(0.2)and 0.3)could be applied to simplify the proof of the existence results in[2]and[3].展开更多
Jeep problem is a kind of model of logistics in extreme situation, which has application in exploration and aircraft problems. The optimal distance and driving strategy of multiple jeeps problem are known. We consider...Jeep problem is a kind of model of logistics in extreme situation, which has application in exploration and aircraft problems. The optimal distance and driving strategy of multiple jeeps problem are known. We consider multiple jeeps problem with container restriction, which is more complicated in the proof of feasibility and optimality of a driving strategy. We investigate when it can achieve the same optimal distance as without restriction.Based on the non-restricted optimal distance, a new driving strategy is proposed. We provide the necessary and sufficient condition to ensure the feasibility of the strategy, and obtain the maximal feasible distance.展开更多
We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X.This kind of map is a generalization of maps such as topologically expansive Lorenz map,unimodal map wi...We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X.This kind of map is a generalization of maps such as topologically expansive Lorenz map,unimodal map without homtervals and so on.Under the finiteness and basin conditions,we provide a leveled A-R pair decomposition for such maps,and characterize α-limit set of each point.Based on weak Morse decomposition of X,we construct a bounded Lyapunov function V(x),which gives a clear description of orbit behavior of each point in X except a meager set.展开更多
The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain ...The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.展开更多
In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri...In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.展开更多
In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume a...In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho＇s conjecture. We show that the linear finite element solution uh and the linear interpolation uI have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to Vu. A numerical example is presented to verify the theoretical result.展开更多
We consider the vibration of elastic thin plates under certain reasonable assumptions. We derive the nonlinear equations for this model by the Hamilton Principle. Under the conditions on the hyperbolicity for the init...We consider the vibration of elastic thin plates under certain reasonable assumptions. We derive the nonlinear equations for this model by the Hamilton Principle. Under the conditions on the hyperbolicity for the initial data, we establish the local time wellposedness for the initial and boundary value problem by Picard iteration scheme, and obtain the estimates for the solutions.展开更多
An efficient and accurate method for solving the two-dimensional Helmholtz equation in domains exterior to elongated obstacles is developed in this paper.The method is based on the so called transformed field expansio...An efficient and accurate method for solving the two-dimensional Helmholtz equation in domains exterior to elongated obstacles is developed in this paper.The method is based on the so called transformed field expansion(TFE) coupled with a spectral-Galerkin solver for elliptical domain using Mathieu functions.Numerical results are presented to show the accuracy and stability of the proposed method.展开更多
In this paper,we introduce new non-polynomial basis functions for spectral approximation of time-fractional partial differential equations (PDEs). Different from many other approaches,the nonstandard singular basis fu...In this paper,we introduce new non-polynomial basis functions for spectral approximation of time-fractional partial differential equations (PDEs). Different from many other approaches,the nonstandard singular basis functions are defined from some generalised Birkhoff interpolation problems through explicit inversion of some prototypical fractional initial value problem (FIVP) with a smooth source term. As such,the singularity of the new basis can be tailored to that of the singular solutions to a class of time-fractional PDEs,leading to spectrally accurate approximation. It also provides the acceptable solution to more general singular problems.展开更多
In previous articles,the exact solutions for deterministic chaos,stochastic chaos,and wave turbulence have been developed in terms of exponential os-cillons and pulsons,which are governed by the nonstationary three-di...In previous articles,the exact solutions for deterministic chaos,stochastic chaos,and wave turbulence have been developed in terms of exponential os-cillons and pulsons,which are governed by the nonstationary three-dimen-sional Navier-Stokes equations.We have later considered theoretical quanti-zation of the deterministic chaos in invariant structures and experimental quantization in spatial and temporal eigenfunctions with the help of inhomo-geneous Fourier expansions.The study of exact wave turbulence was also con-tinued with the theoretical quantization of stochastic chaos and wave turbu-lence.The current paper proceeds with experimental quantization of the sto-chastic chaos and the wave turbulence in spatial x-eigenfunctions.The method of inhomogeneous Fourier expansions in the deterministic eigenfunctions has been extended to deterministic-random,random-deterministic,random,ex-ternal,and internal eigenfunctions.The previous results on theoretical quan-tization in invariant structures have been confirmed,analyzed,and visualized in this work using experimental quantization in the novel eigenfunctions.Ar-guments of exact solutions for quantized oscillons and pulsons are given by 1-,2-,3-,4-,5-,6-,8-,12-,15-,16,and 32-tuples of the spatial eigenfunctions.The exact solutions are grouped into the vector,deterministic-random,exter-nal oscillons,the vector,random-deterministic,external oscillons,the vector,deterministic-random,internal oscillons,the vector,turbulent,external oscil-lons,the vector,turbulent,diagonal oscillons,the vector,turbulent,internal,oscillons,and the vector,turbulent pulsons.We compute independent ran-dom parameters with the help of the random model of oscillatory cn-noise.Computation is performed by experimental and theoretical programming in Maple.The obtained results demonstrate a strong dependence of the quan-tized oscillons and pulsons on the Reynolds number.展开更多
This paper examines a recently developed statistical approach for evaluating the effectiveness of vaccination campaigns in terms of deaths averted.The statistical approach makes predictions by comparing death rates in...This paper examines a recently developed statistical approach for evaluating the effectiveness of vaccination campaigns in terms of deaths averted.The statistical approach makes predictions by comparing death rates in the vaccinated and unvaccinated populations.The statistical approach is preferred for its simplicity and straightforwardness,especially when compared to the difficulties involved when fitting the many parameters of a dynamic SIRD-type model,which may even be an impossible task.We compared the estimated number of deaths averted by the statistical approach to the“ground truth”number of deaths averted in a relatively simple scheme(e.g.,constant vaccination,constant R_(0),pure SIR dynamics,no age stratification)through mathematical analysis,and quantified the difference and degree of underestimation.The results indicate that the statistical approach consistently produces conservative estimates and will always underestimate the number of deaths averted by the direct effect of vaccination,and thus obviously the combined total effect(direct and indirect effect).For high R_(0)values(e.g.R_(0)8),the underestimation is relatively small as long as the vaccination level(v)remains below the herd immunity vaccination threshold.However,for low R_(0)values(e.g.R_(0)1.5),the statistical approach significantly underestimates the number of deaths averted by vaccination,with the underestimation greater than 20%.Applying an approximate correction to the statistical approach,however,can improve the accuracy of estimates for low R_(0)and low v.In conclusion,the statistical approach can provide reasonable estimates in scenarios involving high R_(0)values and low v,such as during the Omicron variant epidemic in Australia.For low R_(0)values and low v,applying an approximate correction to the statistical approach can lead to more accurate estimates,although there are caveats even for this.These results suggest that the statistical method needs to be used with caution.展开更多
Single-value prediction such as the End of Life and Remaining Useful Life is a common method of estimating the lifetime of Li-ion batteries.Information from such prediction is limited when the entire degradation patte...Single-value prediction such as the End of Life and Remaining Useful Life is a common method of estimating the lifetime of Li-ion batteries.Information from such prediction is limited when the entire degradation pattern is needed for practical applications such as dynamic adjustment of battery warranty,improved maintenance scheduling,and battery stock management.In this research,a predictive,semi-parametric survival model called the Cox Proportional Hazards is proposed for the prediction of cell degradation in the form of survival probability(battery reliability)and cumulative hazard(battery risk)functions.Once this model is trained,the two functions can be obtained directly for a new cell without having to predict several cogent points.The model is trained on the first 50 cycles of only the voltage profile from either the charge or discharge data regime,implying that our methodology is data region agnostic.The signature method with both desirable mathematical and machine learning properties was adopted as a feature extraction technique.展开更多
The southeastern margin of the Tibetan Plateau is a crucial region to understand the mechanisms of plateau uplift and deformation.This region is seismically active and has experienced multiple large earthquakes,result...The southeastern margin of the Tibetan Plateau is a crucial region to understand the mechanisms of plateau uplift and deformation.This region is seismically active and has experienced multiple large earthquakes,resulting in significant human and economic losses.Constructing velocity and anisotropic tomography models is crucial for understanding the seismogenic mechanism and deep structural deformation in this area.In this study,we extract high-quality P-wave first-arrival data from the earthquake catalog of the China Earthquake Administration and use them to construct both common-receiver and commonsource differential traveltime datasets.We then apply a novel adjoint-state traveltime tomography approach to obtain new Pwave velocity and azimuthal anisotropy models for the region.This method eliminates the need for ray tracing,thereby reducing the potential bias from the ray theory and ray tracing.A comparison between our results and previous imaging models and shearwave splitting measurements reveals several new details.The results indicate weak anisotropy in the shallow depth of the central Chuandian block.Two low-velocity anomalies are identified beneath the Songpan-Ganzi and Lijiang-Xiaojinhe fault zones,as well as beneath the Xiaojiang Fault.The distinct anisotropic characteristics of these two low-velocity anomalies suggest different tectonic contexts:Beneath the Songpan-Ganzi and Lijiang-Xiaojinhe fault zones,the azimuthal anisotropy aligns north-south and northeast-southwest,while beneath the Xiaojiang Fault,it aligns northwest-southeast.In addition,the anisotropy of the upper mantle in the southern part of the study area has a significant east-west feature.The earthquake relocation results reveal intensified seismic activity in regions with significant velocity contrasts and near fault zones.Segmental seismic activity is observed along some major fault zones,and seismicity is also more pronounced in fault intersection areas.The new imaging results provide new perspectives and insights for understanding the seismogenic mechanisms and regional tectonic deformation in the region.展开更多
Three-dimensional(3D)printing allows for the construction of complex structures.However,3D-printing vertical structures with a high aspect ratio remains a pending challenge,especially when a high lateral resolution is...Three-dimensional(3D)printing allows for the construction of complex structures.However,3D-printing vertical structures with a high aspect ratio remains a pending challenge,especially when a high lateral resolution is required.Here,to address this challenge,we propose and demonstrate micro-3D sculptured metastructures with deep trenches of 1:4(width:height)aspect ratio for sub-10µm resolution.Our construction relies on two-photon polymerization for a 3D-pattern with its trenches,followed by electroplating of a thick metal film and its dry etching to remove the seed layer.To test the proposed fabrication process,we built up three-dimensional RF metastructures showcasing the depth effect as the third dimension.Using the numerical solutions,we custom-tailored these metastructure resonators to fall within a specific resonance frequency range of 4-6 GHz while undertaking comparative analyses regarding overall footprint,quality factor,and resonance frequency shift as a function of their cross-sectional aspect ratio.The proposed process flow is shown to miniaturize metal footprint and tune the resonance frequency of these thick 3Dmetastructures while increasing their quality factor.These experimental findings indicate that this method of producing trenches via 3D-printing provides rich opportunities to implement high-aspect-ratio,complex structures.展开更多
Traditional operational research methods have been the primary means of solving combinatorial optimization problems(COPs)for the past few decades.However,with the rapid increase in the scale of problems in real-world ...Traditional operational research methods have been the primary means of solving combinatorial optimization problems(COPs)for the past few decades.However,with the rapid increase in the scale of problems in real-world scenarios and the demand for online optimization,these methods face persistent challenges including computational complexity and optimality.In recent years,combinatorial optimization methods based on deep learning have rapidly evolved,progressing from tackling solely small-scale problems(e.g.,the traveling salesman problem(TSP)with fewer than 100 cities)to swiftly delivering high-quality solutions for graphs containing up to a million nodes.Particularly,in the last two years,a multitude of studies has surfaced,demonstrating the ability to generalize learned models to large-scale problems with diverse distributions.This capability empowers deep learning-based methods to demonstrate robust competitiveness,even when challenged by professional solvers.Consequently,this review summarizes the methods employed in recent years for solving COPs through deep learning(including prompt learning),scrutinizes the strengths and weaknesses of these methods,and concludes by highlighting potential directions for mitigating these weaknesses.展开更多
文摘This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.
基金supported by Natural Science Foundation of China(11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT 17R46financially supported by funding for basic research business in Central Universities(innovative funding projects)(2018CXZZ090)。
文摘In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.
文摘AIM To compare the outcomes of displaced distal radius fractures treated with volar locking plates and with immediate postoperative mobilisation with the outcomes of these fractures treated with modalities that necessitate 6 wk wrist immobilisation.METHODS A prospective,randomised controlled single-centre trial was conducted with 56 patients who had a displaced radius fracture were randomised to treatment either with a volar locking plate(n=29),or another treatment modality(n=27;cast immobilisation with or without wires or external fixator).Outcomes were measured at 12 wk.Functional outcome scores measured were the Patient-Rated Wrist Evaluation(PRWE)Score;Disabilities of the Arm,Shoulder and Hand and activities of daily living(ADLs).Clinical outcomes were wrist range of motion and grip strength.Radiographic parameters were volar inclination and ulnar variance.RESULTS Patients in the volar locking plate group had significantly better PRWE scores,ADL scores,grip strength and range of extension at three months compared with the control group.All radiological parameters were significantly better in the volar locking plate group at 3 mo.CONCLUSION The present study suggests that volar locking plates produced significantly better functional and clinical outcomes at 3 mo compared with other treatment modalities.Anatomical reduction was significantly more likely to be preserved in the plating group.Level of evidence:Ⅱ.
基金supported by Natural Science Foundation of China(11371159 and 11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT_17R46
文摘In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.
基金Natural Science Foundation of China(11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46.
文摘In this paper,we consider the existence of nontrivial weak solutions to a double critical problem involving a fractional Laplacian with a Hardy term:(−Δ)s u−γu|x|2s=|u|2∗s(β)−2 u|x|β+[Iμ∗Fα(⋅,u)](x)fα(x,u),u∈H˙s(R n),(0.1)(1)where s∈(0,1),0≤α,β<2s<n,μ∈(0,n),γ<γH,Iμ(x)=|x|−μ,Fα(x,u)=|u(x)|2#μ(α)|x|δμ(α),fα(x,u)=|u(x)|2#μ(α)−2 u(x)|x|δμ(α),2#μ(α)=(1−μ2n)⋅2∗s(α),δμ(α)=(1−μ2n)α,2∗s(α)=2(n−α)n−2s andγH=4 sΓ2(n+2s4)Γ2(n−2s4).We show that problem(0.1)admits at least a weak solution under some conditions.To prove the main result,we develop some useful tools based on a weighted Morrey space.To be precise,we discover the embeddings H˙s(R n)↪L 2∗s(α)(R n,|y|−α)↪L p,n−2s2 p+pr(R n,|y|−pr),(0.2)(2)where s∈(0,1),0<α<2s<n,p∈[1,2∗s(α))and r=α2∗s(α).We also establish an improved Sobolev inequality,(∫R n|u(y)|2∗s(α)|y|αdy)12∗s(α)≤C||u||θH˙s(R n)||u||1−θL p,n−2s2 p+pr(R n,|y|−pr),∀u∈H˙s(R n),(0.3)(3)where s∈(0,1),0<α<2s<n,p∈[1,2∗s(α)),r=α2∗s(α),0<max{22∗s(α),2∗s−12∗s(α)}<θ<1,2∗s=2nn−2s and C=C(n,s,α)>0 is a constant.Inequality(0.3)is a more general form of Theorem 1 in Palatucci,Pisante[1].By using the mountain pass lemma along with(0.2)and(0.3),we obtain a nontrivial weak solution to problem(0.1)in a direct way.It is worth pointing out that(0.2)and 0.3)could be applied to simplify the proof of the existence results in[2]and[3].
基金supported by the Fundamental Research Funds for the Central Universities(WUT:2017 IVA 073)。
文摘Jeep problem is a kind of model of logistics in extreme situation, which has application in exploration and aircraft problems. The optimal distance and driving strategy of multiple jeeps problem are known. We consider multiple jeeps problem with container restriction, which is more complicated in the proof of feasibility and optimality of a driving strategy. We investigate when it can achieve the same optimal distance as without restriction.Based on the non-restricted optimal distance, a new driving strategy is proposed. We provide the necessary and sufficient condition to ensure the feasibility of the strategy, and obtain the maximal feasible distance.
基金supported by the National Key Re-search and Development Program of China(2020YFA0714200)supported by the Excellent Dissertation Cultivation Funds of Wuhan University of Technology(2018-YS-077)。
文摘We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X.This kind of map is a generalization of maps such as topologically expansive Lorenz map,unimodal map without homtervals and so on.Under the finiteness and basin conditions,we provide a leveled A-R pair decomposition for such maps,and characterize α-limit set of each point.Based on weak Morse decomposition of X,we construct a bounded Lyapunov function V(x),which gives a clear description of orbit behavior of each point in X except a meager set.
基金the National Natural Science Foundation of China(No.10571017)supported in part by the National Natural Science Foundation of China(No.60533020)supported in part by NSF DMS 0712744
文摘The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.
基金supported by the Natural Science Foundation of China(11771166,12071169)the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。
文摘In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.
基金supported by Singapore AcRF RG59/08 (M52110092)Singapore NRF 2007 IDM-IDM002-010.
文摘In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho＇s conjecture. We show that the linear finite element solution uh and the linear interpolation uI have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to Vu. A numerical example is presented to verify the theoretical result.
基金supported in part by Innovation Award by Wuhan University of Technology under a project Grant 20410771supported in part by China Scholarship Council under Grant 201306230035
文摘We consider the vibration of elastic thin plates under certain reasonable assumptions. We derive the nonlinear equations for this model by the Hamilton Principle. Under the conditions on the hyperbolicity for the initial data, we establish the local time wellposedness for the initial and boundary value problem by Picard iteration scheme, and obtain the estimates for the solutions.
基金supported in part by NSF grant DMS-0610646supported by AcRF Tier 1 Grant RG58/08+1 种基金Singapore MOE Grant T207B2202Singapore NRF2007IDM-IDM002-010
文摘An efficient and accurate method for solving the two-dimensional Helmholtz equation in domains exterior to elongated obstacles is developed in this paper.The method is based on the so called transformed field expansion(TFE) coupled with a spectral-Galerkin solver for elliptical domain using Mathieu functions.Numerical results are presented to show the accuracy and stability of the proposed method.
基金the China Postdoctoral Science Foundation Funded Project (No.2017M620113)the National Natural Science Foundation of China (Nos.11801120,71773024 and 11771107)+4 种基金the Fundamental Research Funds for the Central Universities (Grant No.HIT.NSRIF.2019058)the Natural Science Foundation of Heilongjiang Province of China (No.G2018006)Singapore MOE AcRF Tier 2 Grants (MOE2017-T2-2-014 and MOE2018-T2-1-059)National Science Foundation of China (No.11371376)the Innovation-Driven Project and Mathematics.
文摘In this paper,we introduce new non-polynomial basis functions for spectral approximation of time-fractional partial differential equations (PDEs). Different from many other approaches,the nonstandard singular basis functions are defined from some generalised Birkhoff interpolation problems through explicit inversion of some prototypical fractional initial value problem (FIVP) with a smooth source term. As such,the singularity of the new basis can be tailored to that of the singular solutions to a class of time-fractional PDEs,leading to spectrally accurate approximation. It also provides the acceptable solution to more general singular problems.
文摘In previous articles,the exact solutions for deterministic chaos,stochastic chaos,and wave turbulence have been developed in terms of exponential os-cillons and pulsons,which are governed by the nonstationary three-dimen-sional Navier-Stokes equations.We have later considered theoretical quanti-zation of the deterministic chaos in invariant structures and experimental quantization in spatial and temporal eigenfunctions with the help of inhomo-geneous Fourier expansions.The study of exact wave turbulence was also con-tinued with the theoretical quantization of stochastic chaos and wave turbu-lence.The current paper proceeds with experimental quantization of the sto-chastic chaos and the wave turbulence in spatial x-eigenfunctions.The method of inhomogeneous Fourier expansions in the deterministic eigenfunctions has been extended to deterministic-random,random-deterministic,random,ex-ternal,and internal eigenfunctions.The previous results on theoretical quan-tization in invariant structures have been confirmed,analyzed,and visualized in this work using experimental quantization in the novel eigenfunctions.Ar-guments of exact solutions for quantized oscillons and pulsons are given by 1-,2-,3-,4-,5-,6-,8-,12-,15-,16,and 32-tuples of the spatial eigenfunctions.The exact solutions are grouped into the vector,deterministic-random,exter-nal oscillons,the vector,random-deterministic,external oscillons,the vector,deterministic-random,internal oscillons,the vector,turbulent,external oscil-lons,the vector,turbulent,diagonal oscillons,the vector,turbulent,internal,oscillons,and the vector,turbulent pulsons.We compute independent ran-dom parameters with the help of the random model of oscillatory cn-noise.Computation is performed by experimental and theoretical programming in Maple.The obtained results demonstrate a strong dependence of the quan-tized oscillons and pulsons on the Reynolds number.
基金supported by the Australian Research Council(Grant No.:DP240102585)。
文摘This paper examines a recently developed statistical approach for evaluating the effectiveness of vaccination campaigns in terms of deaths averted.The statistical approach makes predictions by comparing death rates in the vaccinated and unvaccinated populations.The statistical approach is preferred for its simplicity and straightforwardness,especially when compared to the difficulties involved when fitting the many parameters of a dynamic SIRD-type model,which may even be an impossible task.We compared the estimated number of deaths averted by the statistical approach to the“ground truth”number of deaths averted in a relatively simple scheme(e.g.,constant vaccination,constant R_(0),pure SIR dynamics,no age stratification)through mathematical analysis,and quantified the difference and degree of underestimation.The results indicate that the statistical approach consistently produces conservative estimates and will always underestimate the number of deaths averted by the direct effect of vaccination,and thus obviously the combined total effect(direct and indirect effect).For high R_(0)values(e.g.R_(0)8),the underestimation is relatively small as long as the vaccination level(v)remains below the herd immunity vaccination threshold.However,for low R_(0)values(e.g.R_(0)1.5),the statistical approach significantly underestimates the number of deaths averted by vaccination,with the underestimation greater than 20%.Applying an approximate correction to the statistical approach,however,can improve the accuracy of estimates for low R_(0)and low v.In conclusion,the statistical approach can provide reasonable estimates in scenarios involving high R_(0)values and low v,such as during the Omicron variant epidemic in Australia.For low R_(0)values and low v,applying an approximate correction to the statistical approach can lead to more accurate estimates,although there are caveats even for this.These results suggest that the statistical method needs to be used with caution.
基金funded by an industry-academia collaborative grant EPSRC EP/R511687/1 awarded by EPSRC&University of Edinburgh,United Kingdom program Impact Acceleration Account(IAA)R.Ibraheem is a Ph.D.student in EPSRC’s MAC-MIGS Centre for Doctoral Training.MAC-MIGS is supported by the UK’s Engineering and Physical Science Research Council(grant number EP/S023291/1)+2 种基金G.dos Reis acknowledges partial support from the FCT-Fundação para a Ciência e a Tecnologia,PortugalI.P.,under the scope of the projects UIDB/00297/2020(https://doi.org/10.54499/UIDB/00297/2020)and UIDP/00297/2020(https://doi.org/10.54499/UIDP/00297/2020)(Center for Mathematics and Applications,NOVA Math)G.dos Reis acknowledges support from the Faraday Institution,United dom King-(grant number FIRG049).
文摘Single-value prediction such as the End of Life and Remaining Useful Life is a common method of estimating the lifetime of Li-ion batteries.Information from such prediction is limited when the entire degradation pattern is needed for practical applications such as dynamic adjustment of battery warranty,improved maintenance scheduling,and battery stock management.In this research,a predictive,semi-parametric survival model called the Cox Proportional Hazards is proposed for the prediction of cell degradation in the form of survival probability(battery reliability)and cumulative hazard(battery risk)functions.Once this model is trained,the two functions can be obtained directly for a new cell without having to predict several cogent points.The model is trained on the first 50 cycles of only the voltage profile from either the charge or discharge data regime,implying that our methodology is data region agnostic.The signature method with both desirable mathematical and machine learning properties was adopted as a feature extraction technique.
基金supported by the National Key R&D Program of China(Grant No.2022YFF0800601)the China National Science and Technology Major Project(Grant 2024ZD1001101)。
文摘The southeastern margin of the Tibetan Plateau is a crucial region to understand the mechanisms of plateau uplift and deformation.This region is seismically active and has experienced multiple large earthquakes,resulting in significant human and economic losses.Constructing velocity and anisotropic tomography models is crucial for understanding the seismogenic mechanism and deep structural deformation in this area.In this study,we extract high-quality P-wave first-arrival data from the earthquake catalog of the China Earthquake Administration and use them to construct both common-receiver and commonsource differential traveltime datasets.We then apply a novel adjoint-state traveltime tomography approach to obtain new Pwave velocity and azimuthal anisotropy models for the region.This method eliminates the need for ray tracing,thereby reducing the potential bias from the ray theory and ray tracing.A comparison between our results and previous imaging models and shearwave splitting measurements reveals several new details.The results indicate weak anisotropy in the shallow depth of the central Chuandian block.Two low-velocity anomalies are identified beneath the Songpan-Ganzi and Lijiang-Xiaojinhe fault zones,as well as beneath the Xiaojiang Fault.The distinct anisotropic characteristics of these two low-velocity anomalies suggest different tectonic contexts:Beneath the Songpan-Ganzi and Lijiang-Xiaojinhe fault zones,the azimuthal anisotropy aligns north-south and northeast-southwest,while beneath the Xiaojiang Fault,it aligns northwest-southeast.In addition,the anisotropy of the upper mantle in the southern part of the study area has a significant east-west feature.The earthquake relocation results reveal intensified seismic activity in regions with significant velocity contrasts and near fault zones.Segmental seismic activity is observed along some major fault zones,and seismicity is also more pronounced in fault intersection areas.The new imaging results provide new perspectives and insights for understanding the seismogenic mechanisms and regional tectonic deformation in the region.
基金the financial support in part from TUBITAK 20AG001,and 121C266HVD also acknowledges the support from TUBA and TUBITAK 2247-A National Leader Researchers Program(121C266)。
文摘Three-dimensional(3D)printing allows for the construction of complex structures.However,3D-printing vertical structures with a high aspect ratio remains a pending challenge,especially when a high lateral resolution is required.Here,to address this challenge,we propose and demonstrate micro-3D sculptured metastructures with deep trenches of 1:4(width:height)aspect ratio for sub-10µm resolution.Our construction relies on two-photon polymerization for a 3D-pattern with its trenches,followed by electroplating of a thick metal film and its dry etching to remove the seed layer.To test the proposed fabrication process,we built up three-dimensional RF metastructures showcasing the depth effect as the third dimension.Using the numerical solutions,we custom-tailored these metastructure resonators to fall within a specific resonance frequency range of 4-6 GHz while undertaking comparative analyses regarding overall footprint,quality factor,and resonance frequency shift as a function of their cross-sectional aspect ratio.The proposed process flow is shown to miniaturize metal footprint and tune the resonance frequency of these thick 3Dmetastructures while increasing their quality factor.These experimental findings indicate that this method of producing trenches via 3D-printing provides rich opportunities to implement high-aspect-ratio,complex structures.
基金supported by National Natural Science Foundation of China(Grant Nos.T2350003,31930022,12131020 and T2341007)the National Basic Research Program of China(Grant No.2022YFA1004800)Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB38040400)。
文摘Traditional operational research methods have been the primary means of solving combinatorial optimization problems(COPs)for the past few decades.However,with the rapid increase in the scale of problems in real-world scenarios and the demand for online optimization,these methods face persistent challenges including computational complexity and optimality.In recent years,combinatorial optimization methods based on deep learning have rapidly evolved,progressing from tackling solely small-scale problems(e.g.,the traveling salesman problem(TSP)with fewer than 100 cities)to swiftly delivering high-quality solutions for graphs containing up to a million nodes.Particularly,in the last two years,a multitude of studies has surfaced,demonstrating the ability to generalize learned models to large-scale problems with diverse distributions.This capability empowers deep learning-based methods to demonstrate robust competitiveness,even when challenged by professional solvers.Consequently,this review summarizes the methods employed in recent years for solving COPs through deep learning(including prompt learning),scrutinizes the strengths and weaknesses of these methods,and concludes by highlighting potential directions for mitigating these weaknesses.
