Natural product(NPT)derived from traditional Chinese medicine has a rich history as an integral part of Chinese healthcare for thousands of years.Recently,the application of NPT in sonodynamic antibacterial therapy(SD...Natural product(NPT)derived from traditional Chinese medicine has a rich history as an integral part of Chinese healthcare for thousands of years.Recently,the application of NPT in sonodynamic antibacterial therapy(SDAT)has emerged as a promising area of research.This perspective summarizes the recent NPT-based sonosensitizers in SDAT.Currently,common NPT-based sonosensitizers include curcumin,chlorophyll derivatives,hypericin,and berberine.Compared with other sonosensitizers,natural sources of NPT-based sonosensitizers with reactive oxide species production performance under ultrasound conditions,low biotoxicity,and other additional biological activity make them have application prospects in bacterial removal.Finally,the potential benefits and challenges of NPT-based nanosonosensitizers were also discussed.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
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
The exact solutions for deterministic chaos,stochastic chaos,and wave turbulence have been developed in terms of exponential oscillons and pulsons,which are governed by the nonstationary three-dimensional Navier-Stoke...The exact solutions for deterministic chaos,stochastic chaos,and wave turbulence have been developed in terms of exponential oscillons and pulsons,which are governed by the nonstationary three-dimensional Navier-Stokes equations.We have already treated theoretical quantization of the deterministic chaos in invariant structures and experimental quantization in spatial and temporal eigenfunctions using the inhomogeneous Fourier expansions.Theoretical quantization of the stochastic chaos and the wave turbulence has been considered together with experimental quantization of the stochastic chaos and the wave turbulence in spatial x-eigenfunctions.In the present paper,experimental quantization of the stochastic chaos and the wave turbulence in temporal eigenfunctions proceeds experimental quantization of the stochastic chaos and the wave turbulence in the spatial x-eigenfunctions.The method of inhomogeneous Fourier expansions in the spatial x-eigenfunctions has been extended to deterministic-random,random-deterministic,random,external,internal,and temporal eigenfunctions.Exact solutions for quantized oscillons and pulsons depend on 1-,2-,3-,4-,5-,6-,8-,9-,12-,13-,16-,and 32-tuples of the temporal eigenfunctions.Similar to spatial quantization,the vector,deterministic-random,external oscillons,the vector,random-deterministic,external oscillons,the vector,deterministic-random,internal oscillons,the vector,turbulent,external oscillons,the vector,turbulent,diagonal oscillons,the vector,turbulent,internal oscillons,and the vector,turbulent pulsons are computed with the help of the random model of oscillatory cn-noise.Computation is performed using experimental and theoretical programming in Maple.The obtained results show a strong dependence of the quantized oscillons and pulsons on the Reynolds number.Contrary to spatial quantization,where oscillons and pulsons are displayed as multi-mode waves,the quantized oscillons and pulsons in the case of temporal quantization are visualized as fringed waves,which quali-tatively correlate with experimental data.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
We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution.As the spatial discretization of the resulting time-do...We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution.As the spatial discretization of the resulting time-domain boundary integral equation we use either the method of fundamental solutions(MFS)or the Galerkin boundary element method(BEM).In time we apply either a standard convolution quadrature(CQ)based on an A-stable linear multistep method or a modified CQ scheme.It is well-known that the standard low-order CQ schemes for hyperbolic problems suffer from strong dissipation and dispersion properties.The modified scheme is designed to avoid these properties.We give a careful description of the modified scheme and its implementation with differences due to different spatial discretizations highlighted.Numerous numerical experiments illustrate the effectiveness of the modified scheme and dramatic improvement with errors up to two orders of magnitude smaller in comparison with the standard scheme.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
基金supported by the Innovation and Entrepreneurship Training Program for College Students(X2025102911746,X2025102910483).
文摘Natural product(NPT)derived from traditional Chinese medicine has a rich history as an integral part of Chinese healthcare for thousands of years.Recently,the application of NPT in sonodynamic antibacterial therapy(SDAT)has emerged as a promising area of research.This perspective summarizes the recent NPT-based sonosensitizers in SDAT.Currently,common NPT-based sonosensitizers include curcumin,chlorophyll derivatives,hypericin,and berberine.Compared with other sonosensitizers,natural sources of NPT-based sonosensitizers with reactive oxide species production performance under ultrasound conditions,low biotoxicity,and other additional biological activity make them have application prospects in bacterial removal.Finally,the potential benefits and challenges of NPT-based nanosonosensitizers were also discussed.
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.
文摘The exact solutions for deterministic chaos,stochastic chaos,and wave turbulence have been developed in terms of exponential oscillons and pulsons,which are governed by the nonstationary three-dimensional Navier-Stokes equations.We have already treated theoretical quantization of the deterministic chaos in invariant structures and experimental quantization in spatial and temporal eigenfunctions using the inhomogeneous Fourier expansions.Theoretical quantization of the stochastic chaos and the wave turbulence has been considered together with experimental quantization of the stochastic chaos and the wave turbulence in spatial x-eigenfunctions.In the present paper,experimental quantization of the stochastic chaos and the wave turbulence in temporal eigenfunctions proceeds experimental quantization of the stochastic chaos and the wave turbulence in the spatial x-eigenfunctions.The method of inhomogeneous Fourier expansions in the spatial x-eigenfunctions has been extended to deterministic-random,random-deterministic,random,external,internal,and temporal eigenfunctions.Exact solutions for quantized oscillons and pulsons depend on 1-,2-,3-,4-,5-,6-,8-,9-,12-,13-,16-,and 32-tuples of the temporal eigenfunctions.Similar to spatial quantization,the vector,deterministic-random,external oscillons,the vector,random-deterministic,external oscillons,the vector,deterministic-random,internal oscillons,the vector,turbulent,external oscillons,the vector,turbulent,diagonal oscillons,the vector,turbulent,internal oscillons,and the vector,turbulent pulsons are computed with the help of the random model of oscillatory cn-noise.Computation is performed using experimental and theoretical programming in Maple.The obtained results show a strong dependence of the quantized oscillons and pulsons on the Reynolds number.Contrary to spatial quantization,where oscillons and pulsons are displayed as multi-mode waves,the quantized oscillons and pulsons in the case of temporal quantization are visualized as fringed waves,which quali-tatively correlate with experimental data.
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.
文摘We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution.As the spatial discretization of the resulting time-domain boundary integral equation we use either the method of fundamental solutions(MFS)or the Galerkin boundary element method(BEM).In time we apply either a standard convolution quadrature(CQ)based on an A-stable linear multistep method or a modified CQ scheme.It is well-known that the standard low-order CQ schemes for hyperbolic problems suffer from strong dissipation and dispersion properties.The modified scheme is designed to avoid these properties.We give a careful description of the modified scheme and its implementation with differences due to different spatial discretizations highlighted.Numerous numerical experiments illustrate the effectiveness of the modified scheme and dramatic improvement with errors up to two orders of magnitude smaller in comparison with the standard scheme.
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.
