In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar perce...In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.展开更多
Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challeng...Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.展开更多
In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which ...In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law.We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities.Then,we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem.Moreover,we demonstrate the convergence of a penalty method for this contact problem under consideration.Finally,finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.展开更多
Circumlunar abort trajectories constitute a vital contingency return strategy during the translunar phase of crewed lunar missions.This paper proposes a methodology for constructing the solution set of the circumlunar...Circumlunar abort trajectories constitute a vital contingency return strategy during the translunar phase of crewed lunar missions.This paper proposes a methodology for constructing the solution set of the circumlunar abort trajectory and leverages its advantageous properties to address the optimization design problem of abort trajectories.Initially,a solution set of all feasible abort trajectories,originating from an abort point on the nominal trajectory and complying with fundamental reentry constraints,is formulated through the introduction of two novel design parameters.Subsequently,the geometric characteristics of the solution set,as well as the distributional properties of key iterative constraint responses,including flight time and velocity increment,are analyzed.Finally,the characteristics exhibited in the solution set are employed to directly identify the design parameters of the abort trajectories with minimum flight time and velocity increment,thereby providing solutions to two distinct types of optimization problems.The simulation results for a variety of nominal trajectories,encompassing the reconstruction and redesign of the Apollo13 abort trajectory,validate the proposed method,demonstrating its ability to directly generate optimal abort trajectories.The method proposed in this paper investigates feasible abort trajectories from a global perspective,providing both a framework and convenience for mission planning and iterative optimization in abort trajectory design.展开更多
Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analyt...Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analytical solution to determine the longitudinal mechanical responses of tunnels subjected to the combined effects of seismic waves and strike-slip faulting.Adopting the elastic springbeam model,the seismic waves are modelled as shear horizontal(SH)waves and the fault dislocation follows an S-shaped pattern;the superposition principle for free-fielddisplacements caused by both effects is assumed.In addition,the transmission and reflectionof seismic waves at the fault-rock geological interface and the tangential contact conditions at the tunnel-rock interface are considered.The analytical model is validated against numerical simulations,confirmingits accuracy in calculating tunnel responses.Moreover,a parametric study is conducted to evaluate the impact of key factors,including fault displacement,fault zone width,fault dip angle,earthquake frequency,rock conditions,tunnel lining stiffness,and tangential contact conditions,on tunnel responses.Compared with each effect alone,the combined effects of seismic waves and strike-slip faulting significantlychange the tunnel deformation and internal forces,leading to increased tunnel responses,especially within the fault zone and near the fault-rock interfaces.Depending on specificparameters,tunnel responses can be classifiedinto seismic-dominated,faulting-dominated,and seismic-faulting coupled responses on the basis of the relative contributions of each effect.The proposed analytical solution can be applied to quickly predict the longitudinal mechanical behaviour of tunnels under such combined effects in engineering applications.展开更多
Substrate and nutrient supply are essential for vegetable cultivation in greenhouse.The strategies for plant nutrient supply vary depending on the cultivation methods or substrate dosages employed.With the development...Substrate and nutrient supply are essential for vegetable cultivation in greenhouse.The strategies for plant nutrient supply vary depending on the cultivation methods or substrate dosages employed.With the development of mechanization,wide-row spacing substrate cultivation became an optimize mode of the greenhouse cucumber cultivation,aligning with the trend of intelligent agriculture.To determine the optimal nutrient solution supply amount(NS)and supply frequency(SF)for promoting the integrated growth of cucumber under wide-row spacing substrate cultivation,we explored the effects of substrate supply amount(SS),NS,and SF on cucumber yield,quality,and element utilization efficiency.A five-level quadratic orthogonal rotation combination design with three experimental factors(NS,SF,and SS)was implemented for 23 coupling treatments over three growing seasons,including spring(2022S and 2023S)and autumn(2022A).The technique for order preference by similarity to ideal solution(TOPSIS)combining weights based on game theory was applied to construct cucumber comprehensive growth evaluation model.Single and two experimental factors analyses revealed significant effects of single factors and the coupling of NS-SS,NS-SF and SS-SF on the integrated growth of cucumber for all three growing seasons.For the NS-SF-SS combination,the optimal parameters for comprehensive cucumber growth were determined as follows:levels of^(-1).68 for NS,-0.7 for SF,and^(-1).682 for SS in 2022A;-0.43 for NS,-0.06 for SF,and 0.34 for SS in 2022S;0.3 for NS,-0.02 for SF,and 0.04 for SS in 2023S.Furthermore,for SS ranges of 2.00-3.01,3.01-4.50,4.50-5.99,5.99-7.00(L·plant^(-1)),the corresponding NS and SF intervals maximizing cucumber integrated growth in spring were:0.28-0.30(L·plant^(-1))and 6(times·d^(-1)),0.26-0.30(L·plant^(-1))and 6(times·d^(-1)),0.25-0.30(L·plant^(-1))and 6(times·d^(-1)),0.23-0.30(L·plant^(-1))and 6(times·d^(-1)),respectively.With the same SS,the corresponding NS and SF intervals that maximized cucumber integrated growth in autumn were:0.10(L·plant^(-1))and 8(times·d^(-1)),0.18(L·plant^(-1))and 7(times·d^(-1)),0.30(L·plant^(-1))and 6(times·d^(-1)),0.49(L·plant^(-1))and 5(times·d^(-1)),respectively.The results provide a theoretical basis for solution management,and further in-depth research on cucumber cultivation.展开更多
This study reported the synthesis of magnetic solid solutions V2(A_(x)B_(y)Sn_(1-x-y))C(where A and B are Mn,Fe,or Co)MAX phases.These materials were prepared by incorporating magnetic elements into the V_(2)SnC MAX p...This study reported the synthesis of magnetic solid solutions V2(A_(x)B_(y)Sn_(1-x-y))C(where A and B are Mn,Fe,or Co)MAX phases.These materials were prepared by incorporating magnetic elements into the V_(2)SnC MAX phase via pressure-less sintering at 1000℃for 3 hours.XRD analysis reveals that the composition with x=y=0.2 exhibits a shift of diffraction peaks to higher angles,indicating lattice parameter changes,and achieves the highest phase purity with the maximum solid solution limit,further increases in the dopant content led to the formation of impurities.While the solid solution of magnetic elements preserves the characteristic layered structure of the MAX phase,it successfully induces magnetic properties.The magnetic transition temperatures for these solid solutions ranges from 61 to 200 K.Specifically,V_(2)(Mn_(x)Co_(y)Sn_(1-x-y))C demonstrated hard magnetic characteristics,with a high saturation magnetization(6.536 emu/g)and large remanence(4.236 emu/g).In contrast,V_(2)(Mn_(x)Fe_(y)Sn_(1-x-y))C and V2(Fe_(x)Co_(y)Sn_(1-x-y))C exhibits soft magnetic behavior,evidenced by their narrow hysteresis loops and low coercivity.Their saturation magnetization values are 3.80 and 1.784 emu/g,respectively.The distinctly"S"-shaped hysteresis loop of V_(2)(Fe_(x)Co_(y)Sn_(1-x-y))C further confirms its soft magnetic nature.展开更多
The 15th Five-Year Plan will begin in 2026,amid heightened global technological competition and rapid supply chain changes.At this pivotal moment,the low-altitude economy and commercial aerospace,once seen as futurist...The 15th Five-Year Plan will begin in 2026,amid heightened global technological competition and rapid supply chain changes.At this pivotal moment,the low-altitude economy and commercial aerospace,once seen as futuristic,are quickly transitioning from strategic concepts to large-scale manufacturing industries.These sectors now drive China’s high-quality development and support a new framework for international engagement.展开更多
In-situ stress is a key parameter for underground mine design and rock stability analysis.The borehole overcoring technique is widely used for in-situ stress measurement,but the rheological recovery deformation of roc...In-situ stress is a key parameter for underground mine design and rock stability analysis.The borehole overcoring technique is widely used for in-situ stress measurement,but the rheological recovery deformation of rocks after stress relief introduces errors.To improve accuracy,this study proposes an in-situ stress solution theory that incorporates time-dependent stress relief effects.Triaxial stepwise loadingunloading rheological tests on granite and siltstone established quantitative relationships between instantaneous elastic recovery and viscoelastic recovery under different stress levels,confirming their impact on measurement accuracy.By integrating a dual-class elastic deformation recovery model,an improved in-situ stress solution theory was derived.Additionally,accounting for the nonlinear characteristics of rock masses,a determination method for time-dependent nonlinear mechanical parameters was proposed.Based on the CSIRO hollow inclusion strain cell,time-dependent strain correction equations and long-term confining pressure calibration equations were formulated.Finally,the proposed theory was successfully applied at one iron mine(736 m depth)in Xinjiang,China,and one coal mine(510 m depth)in Ningxia,China.Compared to classical theory,the calculated mean stress values showed accuracy improvements of 6.0%and 9.4%,respectively,validating the applicability and reliability of the proposed theory.展开更多
Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding str...Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding strength in titanium/stainless steel laminated composites were investigated.Results indicate that the hardened layer reduces the interfacial bonding strength from over 261 MPa to less than 204 MPa.During the cold roll-bonding process,the hardened layer fractures,leading to the formation of multi-scale cracks that are difficult for the stainless steel to fill.This not only hinders the development of an interlocking interface but also leads to the presence of numerous microcracks and hardened blocks along the nearly straight interface,consequently weakening the interfacial bonding strength.In metals with high work hardening rates,the conventional approach of enhancing interface interlocking and improving interfacial bonding strength by using a surface-hardened layer becomes less effective.展开更多
Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fund...Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.展开更多
An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solutio...An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.展开更多
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function i...In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.展开更多
We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional(1D)full compressible NavierStokes equations on a half line R_+.Instead of the c...We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional(1D)full compressible NavierStokes equations on a half line R_+.Instead of the classical center manifold approach for the existence of small-amplitude boundary layer solutions in the previous results,the delicate global phase plane analysis,based on the qualitative theory of ODEs,is utilized to obtain the sufficient and necessary conditions for the existence/non-existence of large boundary layer solutions to the half-space inflow problem when the right end state belongs to the supersonic,transonic,and subsonic regions,respectively,which completely answers the existence/nonexistence of boundary layer solutions to the half-space inflow problem of 1D full compressible Navier-Stokes equations.展开更多
This paper mainly studies the following Monge-Ampère type systems{det^(1/n)(ΔuI-D^(2)u)=p(|x|)f(v),x∈R^(n),det^(1/n)(ΔvI-D^(2)v)=q(|x|)g(u),x∈R^(n).The existence of entire radial solutions is obtained by usin...This paper mainly studies the following Monge-Ampère type systems{det^(1/n)(ΔuI-D^(2)u)=p(|x|)f(v),x∈R^(n),det^(1/n)(ΔvI-D^(2)v)=q(|x|)g(u),x∈R^(n).The existence of entire radial solutions is obtained by using monotone iteration method and Arzelà-Ascoli theorem.These results generalize the classical Keller-Osserman condition to fully nonlinear systems.展开更多
Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkho...Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkhoff systems, the character of the characteristic roots of the Fréchet derivative C was obtained. Furthermore the existence theorem of periodic solutions was obtained by using Liapunov center theorem, and an example was presented to illustrate the results.展开更多
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
基金Supported by the Doctoral Research Start-up Project of Yuncheng University(YQ-2023067)Project of Shanxi Natural Science Foundation(202303021211189)+1 种基金Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Provinces(20220036)Shanxi ProvinceIntelligent Optoelectronic Sensing Application Technology Innovation Center and Shanxi Province Optoelectronic Information Science and TechnologyLaboratory,Yuncheng University.
文摘In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.
基金Supported by National Natural Science Foundation of China(Grant No.62173161).
文摘Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.
基金supported by the Project for Outstanding Young Talents in Bagui of Guangxi,the Natural Science Foundation of Guangxi(2021GXNSFFA196004,2024GXNSFBA010337)the NSFC(12371312)+2 种基金the Natural Science Foundation of Chongqing(CSTB2024NSCQ-JQX0033)supported by the Postdoctoral Fellowship Program of CPSF(GZC20241534)the Startup Project of Postdoctoral Scientific Research of Zhejiang Normal University(ZC304023924).
文摘In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law.We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities.Then,we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem.Moreover,we demonstrate the convergence of a penalty method for this contact problem under consideration.Finally,finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.
文摘Circumlunar abort trajectories constitute a vital contingency return strategy during the translunar phase of crewed lunar missions.This paper proposes a methodology for constructing the solution set of the circumlunar abort trajectory and leverages its advantageous properties to address the optimization design problem of abort trajectories.Initially,a solution set of all feasible abort trajectories,originating from an abort point on the nominal trajectory and complying with fundamental reentry constraints,is formulated through the introduction of two novel design parameters.Subsequently,the geometric characteristics of the solution set,as well as the distributional properties of key iterative constraint responses,including flight time and velocity increment,are analyzed.Finally,the characteristics exhibited in the solution set are employed to directly identify the design parameters of the abort trajectories with minimum flight time and velocity increment,thereby providing solutions to two distinct types of optimization problems.The simulation results for a variety of nominal trajectories,encompassing the reconstruction and redesign of the Apollo13 abort trajectory,validate the proposed method,demonstrating its ability to directly generate optimal abort trajectories.The method proposed in this paper investigates feasible abort trajectories from a global perspective,providing both a framework and convenience for mission planning and iterative optimization in abort trajectory design.
基金supported by the National Natural Science Foundation of China(No.41941018)Shanghai Gaofeng Discipline Construction Funding.
文摘Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analytical solution to determine the longitudinal mechanical responses of tunnels subjected to the combined effects of seismic waves and strike-slip faulting.Adopting the elastic springbeam model,the seismic waves are modelled as shear horizontal(SH)waves and the fault dislocation follows an S-shaped pattern;the superposition principle for free-fielddisplacements caused by both effects is assumed.In addition,the transmission and reflectionof seismic waves at the fault-rock geological interface and the tangential contact conditions at the tunnel-rock interface are considered.The analytical model is validated against numerical simulations,confirmingits accuracy in calculating tunnel responses.Moreover,a parametric study is conducted to evaluate the impact of key factors,including fault displacement,fault zone width,fault dip angle,earthquake frequency,rock conditions,tunnel lining stiffness,and tangential contact conditions,on tunnel responses.Compared with each effect alone,the combined effects of seismic waves and strike-slip faulting significantlychange the tunnel deformation and internal forces,leading to increased tunnel responses,especially within the fault zone and near the fault-rock interfaces.Depending on specificparameters,tunnel responses can be classifiedinto seismic-dominated,faulting-dominated,and seismic-faulting coupled responses on the basis of the relative contributions of each effect.The proposed analytical solution can be applied to quickly predict the longitudinal mechanical behaviour of tunnels under such combined effects in engineering applications.
基金supported by the China Agriculture Research System(Grant No.CARS-23-D06)the Key Research and Development Program of Shaanxi Province(Grant Nos.2024NC2-GJHX-29 and 2024NC-ZDCYL-05-08)Shaanxi Agricultural Collaborative Innovation and Extension Alliance Project(Grant No.LMZD202202).
文摘Substrate and nutrient supply are essential for vegetable cultivation in greenhouse.The strategies for plant nutrient supply vary depending on the cultivation methods or substrate dosages employed.With the development of mechanization,wide-row spacing substrate cultivation became an optimize mode of the greenhouse cucumber cultivation,aligning with the trend of intelligent agriculture.To determine the optimal nutrient solution supply amount(NS)and supply frequency(SF)for promoting the integrated growth of cucumber under wide-row spacing substrate cultivation,we explored the effects of substrate supply amount(SS),NS,and SF on cucumber yield,quality,and element utilization efficiency.A five-level quadratic orthogonal rotation combination design with three experimental factors(NS,SF,and SS)was implemented for 23 coupling treatments over three growing seasons,including spring(2022S and 2023S)and autumn(2022A).The technique for order preference by similarity to ideal solution(TOPSIS)combining weights based on game theory was applied to construct cucumber comprehensive growth evaluation model.Single and two experimental factors analyses revealed significant effects of single factors and the coupling of NS-SS,NS-SF and SS-SF on the integrated growth of cucumber for all three growing seasons.For the NS-SF-SS combination,the optimal parameters for comprehensive cucumber growth were determined as follows:levels of^(-1).68 for NS,-0.7 for SF,and^(-1).682 for SS in 2022A;-0.43 for NS,-0.06 for SF,and 0.34 for SS in 2022S;0.3 for NS,-0.02 for SF,and 0.04 for SS in 2023S.Furthermore,for SS ranges of 2.00-3.01,3.01-4.50,4.50-5.99,5.99-7.00(L·plant^(-1)),the corresponding NS and SF intervals maximizing cucumber integrated growth in spring were:0.28-0.30(L·plant^(-1))and 6(times·d^(-1)),0.26-0.30(L·plant^(-1))and 6(times·d^(-1)),0.25-0.30(L·plant^(-1))and 6(times·d^(-1)),0.23-0.30(L·plant^(-1))and 6(times·d^(-1)),respectively.With the same SS,the corresponding NS and SF intervals that maximized cucumber integrated growth in autumn were:0.10(L·plant^(-1))and 8(times·d^(-1)),0.18(L·plant^(-1))and 7(times·d^(-1)),0.30(L·plant^(-1))and 6(times·d^(-1)),0.49(L·plant^(-1))and 5(times·d^(-1)),respectively.The results provide a theoretical basis for solution management,and further in-depth research on cucumber cultivation.
基金Funded by the National Natural Science Foundation for Young Scholars of China(No.51302073)the Hubei Provincial Key Laboratory of Green Materials for Light Industry,Hubei University of Technology(No.202509B13)。
文摘This study reported the synthesis of magnetic solid solutions V2(A_(x)B_(y)Sn_(1-x-y))C(where A and B are Mn,Fe,or Co)MAX phases.These materials were prepared by incorporating magnetic elements into the V_(2)SnC MAX phase via pressure-less sintering at 1000℃for 3 hours.XRD analysis reveals that the composition with x=y=0.2 exhibits a shift of diffraction peaks to higher angles,indicating lattice parameter changes,and achieves the highest phase purity with the maximum solid solution limit,further increases in the dopant content led to the formation of impurities.While the solid solution of magnetic elements preserves the characteristic layered structure of the MAX phase,it successfully induces magnetic properties.The magnetic transition temperatures for these solid solutions ranges from 61 to 200 K.Specifically,V_(2)(Mn_(x)Co_(y)Sn_(1-x-y))C demonstrated hard magnetic characteristics,with a high saturation magnetization(6.536 emu/g)and large remanence(4.236 emu/g).In contrast,V_(2)(Mn_(x)Fe_(y)Sn_(1-x-y))C and V2(Fe_(x)Co_(y)Sn_(1-x-y))C exhibits soft magnetic behavior,evidenced by their narrow hysteresis loops and low coercivity.Their saturation magnetization values are 3.80 and 1.784 emu/g,respectively.The distinctly"S"-shaped hysteresis loop of V_(2)(Fe_(x)Co_(y)Sn_(1-x-y))C further confirms its soft magnetic nature.
文摘The 15th Five-Year Plan will begin in 2026,amid heightened global technological competition and rapid supply chain changes.At this pivotal moment,the low-altitude economy and commercial aerospace,once seen as futuristic,are quickly transitioning from strategic concepts to large-scale manufacturing industries.These sectors now drive China’s high-quality development and support a new framework for international engagement.
基金supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China(No.2024ZD1700201)the National Natural Science Foundation of China(Nos.U2034206,51974014 and 51574014)+1 种基金the Guangdong Basic and Applied Basic Research Foundation(No.2024A1515011631)the National Key Research and Development Project of China(No.2022YFC3004601)。
文摘In-situ stress is a key parameter for underground mine design and rock stability analysis.The borehole overcoring technique is widely used for in-situ stress measurement,but the rheological recovery deformation of rocks after stress relief introduces errors.To improve accuracy,this study proposes an in-situ stress solution theory that incorporates time-dependent stress relief effects.Triaxial stepwise loadingunloading rheological tests on granite and siltstone established quantitative relationships between instantaneous elastic recovery and viscoelastic recovery under different stress levels,confirming their impact on measurement accuracy.By integrating a dual-class elastic deformation recovery model,an improved in-situ stress solution theory was derived.Additionally,accounting for the nonlinear characteristics of rock masses,a determination method for time-dependent nonlinear mechanical parameters was proposed.Based on the CSIRO hollow inclusion strain cell,time-dependent strain correction equations and long-term confining pressure calibration equations were formulated.Finally,the proposed theory was successfully applied at one iron mine(736 m depth)in Xinjiang,China,and one coal mine(510 m depth)in Ningxia,China.Compared to classical theory,the calculated mean stress values showed accuracy improvements of 6.0%and 9.4%,respectively,validating the applicability and reliability of the proposed theory.
基金supported by the National Key R&D Program of China (No. 2018YFA0707300)the National Natural Science Foundation of China (No. 52374376)the Introduction Plan for High end Foreign Experts, China (No. G2023105001L)。
文摘Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding strength in titanium/stainless steel laminated composites were investigated.Results indicate that the hardened layer reduces the interfacial bonding strength from over 261 MPa to less than 204 MPa.During the cold roll-bonding process,the hardened layer fractures,leading to the formation of multi-scale cracks that are difficult for the stainless steel to fill.This not only hinders the development of an interlocking interface but also leads to the presence of numerous microcracks and hardened blocks along the nearly straight interface,consequently weakening the interfacial bonding strength.In metals with high work hardening rates,the conventional approach of enhancing interface interlocking and improving interfacial bonding strength by using a surface-hardened layer becomes less effective.
文摘In this paper,by using the method of Lyapunov-Schmidt reduction,we obtain the existence of multi-bump solutions for planar Schrödinger-Poisson system.
文摘Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.
基金Supported by Scientific Research Fund of Hunan Provincial Education Departmen(t23A0361)。
文摘An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
文摘In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.
基金partially supported by the NSFC(12171459,12288201,12090014,12421001)CAS Project for Young Scientists in Basic Research(YSBR-031)。
文摘We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional(1D)full compressible NavierStokes equations on a half line R_+.Instead of the classical center manifold approach for the existence of small-amplitude boundary layer solutions in the previous results,the delicate global phase plane analysis,based on the qualitative theory of ODEs,is utilized to obtain the sufficient and necessary conditions for the existence/non-existence of large boundary layer solutions to the half-space inflow problem when the right end state belongs to the supersonic,transonic,and subsonic regions,respectively,which completely answers the existence/nonexistence of boundary layer solutions to the half-space inflow problem of 1D full compressible Navier-Stokes equations.
文摘This paper mainly studies the following Monge-Ampère type systems{det^(1/n)(ΔuI-D^(2)u)=p(|x|)f(v),x∈R^(n),det^(1/n)(ΔvI-D^(2)v)=q(|x|)g(u),x∈R^(n).The existence of entire radial solutions is obtained by using monotone iteration method and Arzelà-Ascoli theorem.These results generalize the classical Keller-Osserman condition to fully nonlinear systems.
文摘Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkhoff systems, the character of the characteristic roots of the Fréchet derivative C was obtained. Furthermore the existence theorem of periodic solutions was obtained by using Liapunov center theorem, and an example was presented to illustrate the results.
