In this article,we study the existence and asymptotic behavior of multi-bump solutions for nonlinear Choquard equation with a general nonlinearity-Δu+(λa(x)+1)u=(1/|x|α*F(u))f(u)in R^N,where N≥3,0<α<min{N,...In this article,we study the existence and asymptotic behavior of multi-bump solutions for nonlinear Choquard equation with a general nonlinearity-Δu+(λa(x)+1)u=(1/|x|α*F(u))f(u)in R^N,where N≥3,0<α<min{N,4},λis a positive parameter and the nonnegative potential function a(x)is continuous.Using variational methods,we prove that if the potential well int(a^-1(0))consists of k disjoint components,then there exist at least 2^k-1 multi-bump solutions.The asymptotic behavior of these solutions is also analyzed asλ→+∞.展开更多
The Schrodinger equation -△u＋λ2u=｜u｜2q-2u has a unique positive radial solution Uλ, which decays exponentially at infinity. Hence it is reasonable that the Schrolinger system -△u1＋u1=｜u1｜2q-1u1-εb（x）｜u2...The Schrodinger equation -△u＋λ2u=｜u｜2q-2u has a unique positive radial solution Uλ, which decays exponentially at infinity. Hence it is reasonable that the Schrolinger system -△u1＋u1=｜u1｜2q-1u1-εb（x）｜u2｜1｜u1｜q-1u1,-△u2＋u2=｜u2｜2q-2u2-εb（x）｜u1｜1｜u2｜q-1u2 has multiple-bump solutions which behave like Uλ in the neighborhood of some points. For u=（u1,u2）∈H1（R3）×H1（R3）, a nonlinear functional Iε（u）=I1（u1）＋I2（u2）-ε/q∫R3b（x）｜u1｜q｜u2｜qdx,is defined,where I1（u1）=1/2｜｜u1｜｜2-1/2q∫R3｜u1｜2qdx and I2（u2）=1/2｜｜u2｜｜2ω-1/2q∫R3｜u2｜2qdx. It is proved that the solutions of the system are the critical points of I,. Let Z be the smooth solution manifold of the unperturbed problem and TzZ is the tangent space. The critical point of I is rewritten as the form of z ＋ w, where w ∈ （TzZ）⊥. Using some properties of Iε, it is proved that there exists a critical point of I, close to the form which is a multi-bump solution.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
In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solu...In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solution sequence with negative energy for the system via a variant Clark’s theorem.Then we get the asymptotical property of the solution sequence by L∞norm.展开更多
This study investigates the dimensionless quasi-geostrophic potential vorticity(QG-PV)equation with external sources.Employing the Gardner-Morikawa transformation and weakly nonlinear perturbation expansion,we derive ...This study investigates the dimensionless quasi-geostrophic potential vorticity(QG-PV)equation with external sources.Employing the Gardner-Morikawa transformation and weakly nonlinear perturbation expansion,we derive the nonlinear Boussinesq equation with external sources.We demonstrate the existence of explicit zero-order and first-order Wronskian solutions for the model equation whenα_4=0.Furthermore,using a modified Jacobi elliptic function method,we obtain soliton-like solutions for bothα_4=0 andα_4≠0.Analysis of these solutions reveals that the generalizedβ-plane approximation and shear flow are significant factors in inducing nonlinear Rossby waves,and that external sources play a crucial role in influencing Rossby wave behavior.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
This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic fie...This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.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
Composite resin restorations are routinely exposed to acidic and chromogenic beverages that may alter their surface integrity over time.This in-vitro study evaluated the surface roughness behavior of two universal sin...Composite resin restorations are routinely exposed to acidic and chromogenic beverages that may alter their surface integrity over time.This in-vitro study evaluated the surface roughness behavior of two universal single-shade(Unishade)composites and two conventionalmulti-shade composites following immersion in commonly consumed staining solutions and assessed whether repolishing could restore smoothness after degradation.A total of 120 standardized disc specimens were fabricated and allocated to fourmaterial groups,with each group subdivided into distilled water,cola,and coffee immersion subgroups.Surface roughness was recorded at baseline,after one week,after one month,and following a final repolishing step using a standardized multi-step system.The findings demonstrated that Unishade composites exhibited more stable surface characteristics across all immersion periods,with changes consistently remaining below the threshold associated with biofilm accumulation.Conventional composites showed greater variability,particularly in cola,where roughness values increased significantly compared with distilled water and coffee.Repolishing substantially reduced immersion-induced roughness in all materials,although its effectiveness varied depending on composite formulation and beverage acidity.Cola produced the greatest surface alterations across all groups,highlighting the erosive potential of low-pH beverages.These results indicate that Unishade composites possess superior resistance to surface degradation,likely due to their nano-structured filler configuration and less hydrophilic resin matrices,while conventional materials appear more susceptible to acidic challenge.Within the limitations of this study,selecting surface-stable material types and applying appropriate finishing and repolishing protocols may enhance the long-term performance and esthetics of composite restorations.展开更多
Community-pioneered Nature-based Solutions(NbS)have become the main strategies in climate adaptation,although the evidence of their effectiveness and the governing conditions is still fragmented across hazards,ecosyst...Community-pioneered Nature-based Solutions(NbS)have become the main strategies in climate adaptation,although the evidence of their effectiveness and the governing conditions is still fragmented across hazards,ecosystems,and disciplines.The current review is a synthesis of the worldwide empirical research based on the concept of community-led NbS,meaning those interventions where communities have significant decision-making power and responsibility concerning the design,stewardship,sharing of benefits,and learning.On a taxonomy that differentiates between proximal ecosystem functionality and hazard modulation and distal human vulnerability reduction,and procedural,distributional,and recognition justice,we systematize the evidence-based findings according to hazardecosystem-intervention type(coastal storms and sea-level rise,flooding,drought and water insecurity,urban heat,and emerging compound risks)and we compare the outcomes.The results are reported to have the co-benefits of biodiversity gain,livelihood diversification,and better well-being,though they can be neutralized by elite capture,exclusion,tenure insecurity,as well as,in cities,green gentrification and displacement.The analysis of governance indicates repeating bundles related to longer-lasting and fairer results:hedge rights and tenure,community-enforceable and legitimizing representation institutions,financing institutions with longer horizons of maintenance and active adaptation,protection,and grievance,ethical supervision,and data governance.Our findings conclude that to scale community-led NbS,we need to switch the targets of areas to the target of governance quality and design of evaluation that would connect a change in the ecosystem to lived risk reduction and distributional change.展开更多
In this paper,a class of discontinuous Cohen-Grossberg neural networks with timevarying delays is considered.Firstly,under the extended Filippov differential inclusions framework,the problem of periodic solutions of t...In this paper,a class of discontinuous Cohen-Grossberg neural networks with timevarying delays is considered.Firstly,under the extended Filippov differential inclusions framework,the problem of periodic solutions of the considered neural networks with more relaxed conditions imposed on the amplification functions is analyzed by using set-valued mapping and Kakutani's fixed point theorem,which has rarely been used to study such problem.Secondly,the fixed-time synchronization of the error system of the considered neural networks is also investigated by designing a novel control strategy,which can improve not only the previous ones with sign function greatly,but also can reduce the chattering phenomenon.Finally,two numerical examples are presented to further illustrate the validity of the obtained results.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
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
Colorectal cancer(CRC)is a prevalent malignancy worldwide,posing a significant public health concern.Mounting evidence has confirmed that timely early screening facilitates the detection of incipient CRC,thereby enhan...Colorectal cancer(CRC)is a prevalent malignancy worldwide,posing a significant public health concern.Mounting evidence has confirmed that timely early screening facilitates the detection of incipient CRC,thereby enhancing patient prognosis.Obviously,non-participation of asymptomatic individuals in screening programs hampers early diagnosis and may adversely affect long-term outcomes for CRC patients.In this letter,we provide a comprehensive overview of the current status of early screening practices,while also thoroughly examine the dilemmas and potential solutions associated with early screening for CRC.In response to these issues,we proffer a set of recommendations directed at governmental authorities and the general public,which focus on augmenting financial investment,establishing standardized screening protocols,advancing technological capabilities,and bolstering public awareness campaigns.The importance of collaborative efforts from various stakeholders cannot be overstated in the quest to enhance early detection rates and alleviate the societal burden of CRC.展开更多
Background:Isotonic crystalloids are recommended as the first choice for fluid therapy in acute pan-creatitis(AP),with normal saline(NS)and lactate Ringer’s(LR)used most often.Evidence based recom-mendations on the t...Background:Isotonic crystalloids are recommended as the first choice for fluid therapy in acute pan-creatitis(AP),with normal saline(NS)and lactate Ringer’s(LR)used most often.Evidence based recom-mendations on the type of fluid are conflicting and generally come from small single-center randomized controlled trials(RCTs).We therefore conducted a systematic review and meta-analysis to compare the effect of balanced solutions(BS)versus NS on patient-centered clinical outcomes in AP.Methods:From four databases searched up to October 2024,we included only RCTs of adult patients with AP that compared the use of BS(including LR,acetate Ringer’s,etc.)with NS.The primary out-come was the disease advances from AP to moderately severe and severe AP(MSAP/SAP).Trial sequential analyses(TSA)were conducted to control for type-I and type-II errors and Grading of Recommendations Assessment,Development,and Evaluation(GRADE)was used to assess the quality of evidence.Results:Six RCTs were identified and included,involving 260 patients treated with BS and 298 patients with NS.Patients who received the BS had less MSAP/SAP[odds ratio(OR)=0.50,95%confidence in-terval(CI):0.29 to 0.85,P=0.01,I^(2)=0%;5 studies,299 patients],reduced the need of ICU admission(OR=0.60,95%CI:0.39 to 0.93,P=0.02,I^(2)=0%;5 studies,507 patients)and shorter length of hospital stay[mean difference(MD)=-0.88,95%CI:-1.48 to-0.28,P=0.004,I^(2)=0%;6 studies,558 patients;confirmed by TSA with high certainty]compared with those who received NS.The evidence for most of the clinical outcomes was rated as moderate to low due to the risk of bias,imprecision and inconsistency.Conclusions:BS,compared with NS,was associated with improved clinical outcomes in patients with AP.However,given the moderate to low quality of evidence for most of the outcomes assessed,further trials are warranted.展开更多
In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations,numerous tricks have been proposed.The goal of this short review is to explain how a theorem of Eremenko on meromorphic...In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations,numerous tricks have been proposed.The goal of this short review is to explain how a theorem of Eremenko on meromorphic solutions of some nonlinear ODEs together with some classical,19th-century results,can be turned into algorithms(thus avoiding ad hoc assumptions)which provide all(as opposed to some)solutions in a precise class.To illustrate these methods,we present some new such exact solutions,physically relevant.展开更多
In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)...In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)ϕ=u^(2),in R^(3),where s∈(3/4,1),t∈(0,1),q∈(1,2),p∈(4,2_(s)^(*)),2_(s)^(*):=6/3-2s is the fractional critical exponent in dimension 3,V_(λ)(x)=λV(x)+1 withλ>0.Under the case of steep potential well,we obtain the existence of the sign-changing solutions for the above system by using the constraint variational method and the quantitative deformation lemma.Furthermore,we prove that the energy of ground state sign-changing solution is strictly more than twice of the energy of the ground state solution.Our results improve the recent results in the literature.展开更多
This paper focuses on the preparation of rare earth oxide products from rare earth chloride solutions during the rare earth extraction and separation processes,as well as the recycling of magnesium chloride solutions....This paper focuses on the preparation of rare earth oxide products from rare earth chloride solutions during the rare earth extraction and separation processes,as well as the recycling of magnesium chloride solutions.It proposes the idea of introducing spray pyrolysis technology into the rare earth extraction and separation processes.This paper briefly describes the development history of chloride spray pyrolysis technology,focusing on the research status and application progress of rare earth chloride solution and magnesium chloride solution spray pyrolysis technology,as well as spray pyrolysis equipment.The paper also analyzes the challenges and technical intricacies associated with applying spray pyrolysis technology to chloride solutions in the rare earth extraction and separation processes.Additionally,it explores future trends and proposes strategies to facilitate the full recycling of acids and bases,streamline the process flow,and enhance the prospects for green and low-carbon rare earth metallurgy.展开更多
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.
基金L.Guo is supported by the Fundamental Research Funds for the Central Universities(2662018QD039)T.Hu is supported by the Project funded by China Postdoctoral Science Foundation(2018M643389).
文摘In this article,we study the existence and asymptotic behavior of multi-bump solutions for nonlinear Choquard equation with a general nonlinearity-Δu+(λa(x)+1)u=(1/|x|α*F(u))f(u)in R^N,where N≥3,0<α<min{N,4},λis a positive parameter and the nonnegative potential function a(x)is continuous.Using variational methods,we prove that if the potential well int(a^-1(0))consists of k disjoint components,then there exist at least 2^k-1 multi-bump solutions.The asymptotic behavior of these solutions is also analyzed asλ→+∞.
基金The National Natural Science Foundation of China(No.11171063)the Natural Science Foundation of Jiangsu Province(No.BK2010404)
文摘The Schrodinger equation -△u＋λ2u=｜u｜2q-2u has a unique positive radial solution Uλ, which decays exponentially at infinity. Hence it is reasonable that the Schrolinger system -△u1＋u1=｜u1｜2q-1u1-εb（x）｜u2｜1｜u1｜q-1u1,-△u2＋u2=｜u2｜2q-2u2-εb（x）｜u1｜1｜u2｜q-1u2 has multiple-bump solutions which behave like Uλ in the neighborhood of some points. For u=（u1,u2）∈H1（R3）×H1（R3）, a nonlinear functional Iε（u）=I1（u1）＋I2（u2）-ε/q∫R3b（x）｜u1｜q｜u2｜qdx,is defined,where I1（u1）=1/2｜｜u1｜｜2-1/2q∫R3｜u1｜2qdx and I2（u2）=1/2｜｜u2｜｜2ω-1/2q∫R3｜u2｜2qdx. It is proved that the solutions of the system are the critical points of I,. Let Z be the smooth solution manifold of the unperturbed problem and TzZ is the tangent space. The critical point of I is rewritten as the form of z ＋ w, where w ∈ （TzZ）⊥. Using some properties of Iε, it is proved that there exists a critical point of I, close to the form which is a multi-bump solution.
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 the National Natural Science Foundation of China(12226412)Natural Science Foundation of Jiangsu Province(BK20221339)。
文摘In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solution sequence with negative energy for the system via a variant Clark’s theorem.Then we get the asymptotical property of the solution sequence by L∞norm.
基金supported by the National Natural Science Foundation of China(Grant No.12362027)the Scientific Research Ability of Youth Teachers of Inner Mongolia Agricultural University(Grant No.BR230110)+3 种基金Inner Mongolia National Science Fund for Excellent Young Scholars(Grant No.2025YQ033)Foundation for Basic Science Research Initiation at Inner Mongolia Agricultural University(Grant No.JC2021001)The Natural Science Foundation of Inner Mongolia Autonomous Region(2025MS01020)Supported by the Basic and Applied Basic Research Science and Technology Program Projects of Hohhot(2025-rule-basic-60)。
文摘This study investigates the dimensionless quasi-geostrophic potential vorticity(QG-PV)equation with external sources.Employing the Gardner-Morikawa transformation and weakly nonlinear perturbation expansion,we derive the nonlinear Boussinesq equation with external sources.We demonstrate the existence of explicit zero-order and first-order Wronskian solutions for the model equation whenα_4=0.Furthermore,using a modified Jacobi elliptic function method,we obtain soliton-like solutions for bothα_4=0 andα_4≠0.Analysis of these solutions reveals that the generalizedβ-plane approximation and shear flow are significant factors in inducing nonlinear Rossby waves,and that external sources play a crucial role in influencing Rossby wave behavior.
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 National Natural Science Foundation of China(12401279,12371219)the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027).
文摘This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.
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.
文摘Composite resin restorations are routinely exposed to acidic and chromogenic beverages that may alter their surface integrity over time.This in-vitro study evaluated the surface roughness behavior of two universal single-shade(Unishade)composites and two conventionalmulti-shade composites following immersion in commonly consumed staining solutions and assessed whether repolishing could restore smoothness after degradation.A total of 120 standardized disc specimens were fabricated and allocated to fourmaterial groups,with each group subdivided into distilled water,cola,and coffee immersion subgroups.Surface roughness was recorded at baseline,after one week,after one month,and following a final repolishing step using a standardized multi-step system.The findings demonstrated that Unishade composites exhibited more stable surface characteristics across all immersion periods,with changes consistently remaining below the threshold associated with biofilm accumulation.Conventional composites showed greater variability,particularly in cola,where roughness values increased significantly compared with distilled water and coffee.Repolishing substantially reduced immersion-induced roughness in all materials,although its effectiveness varied depending on composite formulation and beverage acidity.Cola produced the greatest surface alterations across all groups,highlighting the erosive potential of low-pH beverages.These results indicate that Unishade composites possess superior resistance to surface degradation,likely due to their nano-structured filler configuration and less hydrophilic resin matrices,while conventional materials appear more susceptible to acidic challenge.Within the limitations of this study,selecting surface-stable material types and applying appropriate finishing and repolishing protocols may enhance the long-term performance and esthetics of composite restorations.
文摘Community-pioneered Nature-based Solutions(NbS)have become the main strategies in climate adaptation,although the evidence of their effectiveness and the governing conditions is still fragmented across hazards,ecosystems,and disciplines.The current review is a synthesis of the worldwide empirical research based on the concept of community-led NbS,meaning those interventions where communities have significant decision-making power and responsibility concerning the design,stewardship,sharing of benefits,and learning.On a taxonomy that differentiates between proximal ecosystem functionality and hazard modulation and distal human vulnerability reduction,and procedural,distributional,and recognition justice,we systematize the evidence-based findings according to hazardecosystem-intervention type(coastal storms and sea-level rise,flooding,drought and water insecurity,urban heat,and emerging compound risks)and we compare the outcomes.The results are reported to have the co-benefits of biodiversity gain,livelihood diversification,and better well-being,though they can be neutralized by elite capture,exclusion,tenure insecurity,as well as,in cities,green gentrification and displacement.The analysis of governance indicates repeating bundles related to longer-lasting and fairer results:hedge rights and tenure,community-enforceable and legitimizing representation institutions,financing institutions with longer horizons of maintenance and active adaptation,protection,and grievance,ethical supervision,and data governance.Our findings conclude that to scale community-led NbS,we need to switch the targets of areas to the target of governance quality and design of evaluation that would connect a change in the ecosystem to lived risk reduction and distributional change.
基金Supported by the National Natural Science Foundation of China(62576008)University Annual Scientific Research Plan of Anhui Province(2022AH030023)。
文摘In this paper,a class of discontinuous Cohen-Grossberg neural networks with timevarying delays is considered.Firstly,under the extended Filippov differential inclusions framework,the problem of periodic solutions of the considered neural networks with more relaxed conditions imposed on the amplification functions is analyzed by using set-valued mapping and Kakutani's fixed point theorem,which has rarely been used to study such problem.Secondly,the fixed-time synchronization of the error system of the considered neural networks is also investigated by designing a novel control strategy,which can improve not only the previous ones with sign function greatly,but also can reduce the chattering phenomenon.Finally,two numerical examples are presented to further illustrate the validity of the obtained results.
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.
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.
文摘Colorectal cancer(CRC)is a prevalent malignancy worldwide,posing a significant public health concern.Mounting evidence has confirmed that timely early screening facilitates the detection of incipient CRC,thereby enhancing patient prognosis.Obviously,non-participation of asymptomatic individuals in screening programs hampers early diagnosis and may adversely affect long-term outcomes for CRC patients.In this letter,we provide a comprehensive overview of the current status of early screening practices,while also thoroughly examine the dilemmas and potential solutions associated with early screening for CRC.In response to these issues,we proffer a set of recommendations directed at governmental authorities and the general public,which focus on augmenting financial investment,establishing standardized screening protocols,advancing technological capabilities,and bolstering public awareness campaigns.The importance of collaborative efforts from various stakeholders cannot be overstated in the quest to enhance early detection rates and alleviate the societal burden of CRC.
文摘Background:Isotonic crystalloids are recommended as the first choice for fluid therapy in acute pan-creatitis(AP),with normal saline(NS)and lactate Ringer’s(LR)used most often.Evidence based recom-mendations on the type of fluid are conflicting and generally come from small single-center randomized controlled trials(RCTs).We therefore conducted a systematic review and meta-analysis to compare the effect of balanced solutions(BS)versus NS on patient-centered clinical outcomes in AP.Methods:From four databases searched up to October 2024,we included only RCTs of adult patients with AP that compared the use of BS(including LR,acetate Ringer’s,etc.)with NS.The primary out-come was the disease advances from AP to moderately severe and severe AP(MSAP/SAP).Trial sequential analyses(TSA)were conducted to control for type-I and type-II errors and Grading of Recommendations Assessment,Development,and Evaluation(GRADE)was used to assess the quality of evidence.Results:Six RCTs were identified and included,involving 260 patients treated with BS and 298 patients with NS.Patients who received the BS had less MSAP/SAP[odds ratio(OR)=0.50,95%confidence in-terval(CI):0.29 to 0.85,P=0.01,I^(2)=0%;5 studies,299 patients],reduced the need of ICU admission(OR=0.60,95%CI:0.39 to 0.93,P=0.02,I^(2)=0%;5 studies,507 patients)and shorter length of hospital stay[mean difference(MD)=-0.88,95%CI:-1.48 to-0.28,P=0.004,I^(2)=0%;6 studies,558 patients;confirmed by TSA with high certainty]compared with those who received NS.The evidence for most of the clinical outcomes was rated as moderate to low due to the risk of bias,imprecision and inconsistency.Conclusions:BS,compared with NS,was associated with improved clinical outcomes in patients with AP.However,given the moderate to low quality of evidence for most of the outcomes assessed,further trials are warranted.
基金partially supported by RGC(No.17307420)supported by NSFC(No.12471077)。
文摘In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations,numerous tricks have been proposed.The goal of this short review is to explain how a theorem of Eremenko on meromorphic solutions of some nonlinear ODEs together with some classical,19th-century results,can be turned into algorithms(thus avoiding ad hoc assumptions)which provide all(as opposed to some)solutions in a precise class.To illustrate these methods,we present some new such exact solutions,physically relevant.
基金supported by the Natural Science Foundation of Sichuan(No.2023NSFSC0073)。
文摘In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)ϕ=u^(2),in R^(3),where s∈(3/4,1),t∈(0,1),q∈(1,2),p∈(4,2_(s)^(*)),2_(s)^(*):=6/3-2s is the fractional critical exponent in dimension 3,V_(λ)(x)=λV(x)+1 withλ>0.Under the case of steep potential well,we obtain the existence of the sign-changing solutions for the above system by using the constraint variational method and the quantitative deformation lemma.Furthermore,we prove that the energy of ground state sign-changing solution is strictly more than twice of the energy of the ground state solution.Our results improve the recent results in the literature.
基金supported by the National Key Research and Development Program of China(2022YFB3504501)the National Natural Science Foundation of China(52274355)。
文摘This paper focuses on the preparation of rare earth oxide products from rare earth chloride solutions during the rare earth extraction and separation processes,as well as the recycling of magnesium chloride solutions.It proposes the idea of introducing spray pyrolysis technology into the rare earth extraction and separation processes.This paper briefly describes the development history of chloride spray pyrolysis technology,focusing on the research status and application progress of rare earth chloride solution and magnesium chloride solution spray pyrolysis technology,as well as spray pyrolysis equipment.The paper also analyzes the challenges and technical intricacies associated with applying spray pyrolysis technology to chloride solutions in the rare earth extraction and separation processes.Additionally,it explores future trends and proposes strategies to facilitate the full recycling of acids and bases,streamline the process flow,and enhance the prospects for green and low-carbon rare earth metallurgy.
