Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applyin...Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.展开更多
We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of...We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.展开更多
The paper deals with the study of two different aspects of stability in the given space as well as the image space,where the solution concepts are based on a partial order relation on the family of bounded subsets of ...The paper deals with the study of two different aspects of stability in the given space as well as the image space,where the solution concepts are based on a partial order relation on the family of bounded subsets of a real normed linear space.The first aspect of stability deals with the topological set convergence of families of solution sets of perturbed problems in the image space and Painlevé–Kuratowski set convergence of solution sets of the perturbed problems in the given space.The convergence in the given space is also established in terms of solution sets of scalarized perturbed problems.The second aspect of stability deals with semicontinuity of the solution set maps of parametric perturbed problems in both the spaces.展开更多
We investigated the critical dynamical scalarization and descalarization of black holes within the framework of the EinsteinMaxwell-scalar theory featuring higher-order coupling functions.Both the critical scalarizati...We investigated the critical dynamical scalarization and descalarization of black holes within the framework of the EinsteinMaxwell-scalar theory featuring higher-order coupling functions.Both the critical scalarization and descalarization displayed first-order phase transitions.When examining the nonlinear dynamics near the threshold,we always observed critical solutions that are linearly unstable static scalarized black holes.The critical dynamical scalarization and descalarization share certain similarities with the typeⅠcritical gravitational collapse.However,their initial configurations,critical solutions,and final outcomes differ significantly.To provide further insights into the dynamical results,we conducted a comparative analysis involving static solutions and perturbative analysis.展开更多
This paper focuses on the vector traffic network equilibrium problem with demands uncertainty and capacity constraints of arcs, in which, the demands are not exactly known and assumed as a discrete set that contains f...This paper focuses on the vector traffic network equilibrium problem with demands uncertainty and capacity constraints of arcs, in which, the demands are not exactly known and assumed as a discrete set that contains finite scenarios. For different scenario, the demand may be changed, which seems much more reasonable in practical programming. By using the linear scalarization method,we introduce several definitions of parametric equilibrium flows and reveal their mutual relations. Meanwhile, the relationships between the scalar variational inequality as well as the(weak) vector equilibrium flows are explored, meanwhile, some necessary and sufficient conditions that ensure the(weak) vector equilibrium flows are also considered. Additionally, by means of nonlinear scalarization functionals, two kinds of equilibrium principles are derived. All of the derived conclusions contain the demands uncertainty and capacity constraints of arcs, thus the results proposed in this paper improved some existing works. Finally, some numerical examples are employed to show the merits of the improved conclusions.展开更多
We study the critical dynamics in scalarization and descalarization in the fully nonlinear dynamical evolution in the class of theories with a scalar field coupling with both Gauss-Bonnet(GB) invariant and Ricci scala...We study the critical dynamics in scalarization and descalarization in the fully nonlinear dynamical evolution in the class of theories with a scalar field coupling with both Gauss-Bonnet(GB) invariant and Ricci scalar. We explore the manner in which the GB term triggers black hole(BH) scalarization. A typical type Ⅰ critical phenomenon is observed, in which an unstable critical solution emerges at the threshold and acts as an attractor in the dynamical scalarization. For the descalarization, we reveal that a marginally stable attractor exists at the threshold of the first-order phase transition in shedding off BH hair. This is a new type Ⅰ critical phenomenon in the BH phase transition. Implications of these findings are discussed from the perspective of thermodynamic properties and perturbations for static solutions. We examine the effect of scalar-Ricci coupling on the hyperbolicity in the fully nonlinear evolution and observe that such coupling can suppress the elliptic region and enlarge parameter space in computations.展开更多
In this paper,by reviewing two standard scalarization techniques,a new necessary and sufficient condition for characterizing(ε,.ε)-quasi(weakly)efficient solutions of multiobjective optimization problems is presente...In this paper,by reviewing two standard scalarization techniques,a new necessary and sufficient condition for characterizing(ε,.ε)-quasi(weakly)efficient solutions of multiobjective optimization problems is presented.The proposed procedure for the computation of(ε,.ε)-quasi efficient solutions is given.Note that all of the provided results are established without any convexity assumptions on the problem under consideration.And our results extend several corresponding results in multiobjective optimization.展开更多
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired ...In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.展开更多
In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary varia...In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.展开更多
From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430...From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.展开更多
Nonlinear scalarization is a very important method to deal with the vector optimization problems.In this paper,some conic nonlinear scalarization characterizations of E-optimal points,weakly E-optimal points,and E-Be...Nonlinear scalarization is a very important method to deal with the vector optimization problems.In this paper,some conic nonlinear scalarization characterizations of E-optimal points,weakly E-optimal points,and E-Benson properly efficient points proposed via improvement sets are established by a new scalarization function,respectively.These results improved and generalized some previously known results.As a special case,the scalarization of Benson properly efficient points is also given.Some examples are given to illustrate the main results.展开更多
The aim of this paper is to investigate the continuity of solution mappings for para-metric set optimization problems with upper and lower set less order relations by scalarization methods.First,we recall some linear ...The aim of this paper is to investigate the continuity of solution mappings for para-metric set optimization problems with upper and lower set less order relations by scalarization methods.First,we recall some linear and nonlinear scalarization prop-erties used to characterize the set order relations.Subsequently,we introduce new monotonicity concepts of the set-valued mapping by linear and nonlinear scalarization methods.Finally,we obtain the semicontinuity and closedness of solution mappings for parametric set optimization problems(both convex and nonconvex cases)under the monotonicity assumption and other suitable conditions.The results achieved do not impose the continuity of the set-valued objective mapping,which are obviously different from the related ones in the literature.展开更多
We study the linear instability and nonlinear dynamical evolution of the Reissner-Nordstrom(RN)black hole in the Einstein-Maxwell-scalar theory in asymptotic flat spacetime.We focus on the coupling function f(φ)=e^(-...We study the linear instability and nonlinear dynamical evolution of the Reissner-Nordstrom(RN)black hole in the Einstein-Maxwell-scalar theory in asymptotic flat spacetime.We focus on the coupling function f(φ)=e^(-bφ^(2)),which facilitates both scalar-free RN and scalarized black hole solutions.We first present the evolution of system parameters during dynamic scalarization.For parameter regions in which spontaneous scalarization occurs,we observe that the evolution of the scalar field at the horizon is dominated by the fundamental unstable mode from linear analysis at early times.At late times,the nonlinear evolution can be considered to be the perturbation of scalarized black holes.展开更多
QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interes...QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interest in the theoretical and experimental exploration of LSW(longitudinal scalar waves)solutions that are often omitted in CED(classical electrodynamics)but may have physical significance in nontrivial vacuum conditions.This paper delves into the theoretical foundation of LSW,their role in QED,and the associated mathematical equations governing their dynamics.展开更多
Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form fact...Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form factors related to charge and mass densities;and distributions in the impact parameter space.To this end,we employ an algebraically viable framework that is based upon the valence-quark generalized parton distribution expressed explicitly in terms of the associated distribution function and a profile function that governs the off-forward dynamics.The predominantly analytical nature of this scheme yields several algebraic results and relations while also facilitating the exploration of insightful limiting cases.With a suitable input distribution function,guided either by experiment or theory,and with an appropriate choice of the profile function,it is possible to provide testable predictions for spatial distributions of valence quarks inside pseudoscalar mesons.When comparison is possible,these predictions align well with existing experimental data as well as the findings of reliable theoretical approaches and lattice QCD.展开更多
In this paper,we prove that for certain fiber bundles there is a k-Futaki-Ono conformally Kahler metric related to a metric in any given Kahler class for any k≥2.
Air quality is a critical factor in maintaining health and well-being, influencing both current conditions and future outcomes. Hospitals are one of the sensitive areas of our society, for they are built as sanctuarie...Air quality is a critical factor in maintaining health and well-being, influencing both current conditions and future outcomes. Hospitals are one of the sensitive areas of our society, for they are built as sanctuaries for treatment and recovery, making the quality of paramount importance. This study investigates the impact of traffic-related emissions on indoor air quality within a Level 5 Hospital outpatient ward. Measurements were taken over five consecutive days, revealing that while CO2 levels generally remained within safe limits, there were instances where concentrations exceeded 3000 ppm, categorizing them as “Hazardous.” Notably, particulate matter (PM2.5 and PM10) levels fluctuated significantly, with peak concentrations observed during working hours correlating with increased vehicle activity. The data indicated that PM2.5 levels reached as high as 75 µg/m3, with 91.68% of recorded values exceeding the World Health Organization’s (WHO) and Environmental Protection Agency 24-hour mean threshold of 25 µg/m3. Similarly, PM10 concentrations peaked at 120 µg/m3, with 61.19% of values surpassing the WHO threshold of 50 µg/m3, both of which pose serious health risks, particularly to vulnerable populations such as pregnant women, infants, and the elderly. Additionally, the study highlighted the critical role of wind direction in pollutant dispersion, with specific patterns contributing to elevated indoor concentrations. These findings underscore the urgent need for targeted interventions and proactive air quality management strategies in healthcare facilities, including the strategic design of hospital wards away from primary emission sources and the promotion of electric vehicle use to mitigate traffic-related emissions.展开更多
In this paper,we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant.We prove that if the scalar curvature is not less than the Yamabe invariant in the distribu...In this paper,we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant.We prove that if the scalar curvature is not less than the Yamabe invariant in the distributional sense,then the manifold must be isometric to an Einstein manifold.This result extends Theorem 1.4 in Jiang,Sheng and Zhang[27],from a special case where the manifolds have zero Yamabe invariant to general cases where the manifolds have non-positive Yamabe invariant.展开更多
An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into ...An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into an equivalent system,and the k-order backward differentiation formula(BDF k)and central difference formula are used to discretize the temporal and spatial derivatives,respectively.Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms,the proposed scheme is based on the SAV idea and can be treated semi-implicitly,taking into account both accuracy and effectiveness.Numerical results are presented to demonstrate the high-order convergence(up to fourth-order)of the developed schemes and it is computationally efficient in long-time computations.展开更多
基金Supported by the National Natural Science Foundation of China (10571035,10871141)
文摘Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.
文摘We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.
基金supported by MATRICS scheme of Department of Science and Technology,India(No.MTR/2017/00016).
文摘The paper deals with the study of two different aspects of stability in the given space as well as the image space,where the solution concepts are based on a partial order relation on the family of bounded subsets of a real normed linear space.The first aspect of stability deals with the topological set convergence of families of solution sets of perturbed problems in the image space and Painlevé–Kuratowski set convergence of solution sets of the perturbed problems in the given space.The convergence in the given space is also established in terms of solution sets of scalarized perturbed problems.The second aspect of stability deals with semicontinuity of the solution set maps of parametric perturbed problems in both the spaces.
基金supported by the National Natural Science Foundation of China(Grant Nos.11975235,12005077,12035016,and 12075202)Guangdong Basic and Applied Basic Research Foundation(Grant No.2021A1515012374)。
文摘We investigated the critical dynamical scalarization and descalarization of black holes within the framework of the EinsteinMaxwell-scalar theory featuring higher-order coupling functions.Both the critical scalarization and descalarization displayed first-order phase transitions.When examining the nonlinear dynamics near the threshold,we always observed critical solutions that are linearly unstable static scalarized black holes.The critical dynamical scalarization and descalarization share certain similarities with the typeⅠcritical gravitational collapse.However,their initial configurations,critical solutions,and final outcomes differ significantly.To provide further insights into the dynamical results,we conducted a comparative analysis involving static solutions and perturbative analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.61573096,61272530 and 61573106)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK2012741)the “333 Engineering” Foundation of Jiangsu Province of China(Grant No.BRA2015286)
文摘This paper focuses on the vector traffic network equilibrium problem with demands uncertainty and capacity constraints of arcs, in which, the demands are not exactly known and assumed as a discrete set that contains finite scenarios. For different scenario, the demand may be changed, which seems much more reasonable in practical programming. By using the linear scalarization method,we introduce several definitions of parametric equilibrium flows and reveal their mutual relations. Meanwhile, the relationships between the scalar variational inequality as well as the(weak) vector equilibrium flows are explored, meanwhile, some necessary and sufficient conditions that ensure the(weak) vector equilibrium flows are also considered. Additionally, by means of nonlinear scalarization functionals, two kinds of equilibrium principles are derived. All of the derived conclusions contain the demands uncertainty and capacity constraints of arcs, thus the results proposed in this paper improved some existing works. Finally, some numerical examples are employed to show the merits of the improved conclusions.
基金supported by the National Key R&D Program of China(Grant No.2020YFC2201400)the National Natural Science Foundation of China(Grant Nos.11975235,12005077,and 12035016)+1 种基金Guangdong Basic and Applied Basic Research Foundation(Grant No.2021A1515012374)partially supported by the National Natural Science Foundation of China(Grant No.12075202)。
文摘We study the critical dynamics in scalarization and descalarization in the fully nonlinear dynamical evolution in the class of theories with a scalar field coupling with both Gauss-Bonnet(GB) invariant and Ricci scalar. We explore the manner in which the GB term triggers black hole(BH) scalarization. A typical type Ⅰ critical phenomenon is observed, in which an unstable critical solution emerges at the threshold and acts as an attractor in the dynamical scalarization. For the descalarization, we reveal that a marginally stable attractor exists at the threshold of the first-order phase transition in shedding off BH hair. This is a new type Ⅰ critical phenomenon in the BH phase transition. Implications of these findings are discussed from the perspective of thermodynamic properties and perturbations for static solutions. We examine the effect of scalar-Ricci coupling on the hyperbolicity in the fully nonlinear evolution and observe that such coupling can suppress the elliptic region and enlarge parameter space in computations.
基金This work was partially supported by the National Natural Science Foundation of China(11201511,11271391).
文摘In this paper,by reviewing two standard scalarization techniques,a new necessary and sufficient condition for characterizing(ε,.ε)-quasi(weakly)efficient solutions of multiobjective optimization problems is presented.The proposed procedure for the computation of(ε,.ε)-quasi efficient solutions is given.Note that all of the provided results are established without any convexity assumptions on the problem under consideration.And our results extend several corresponding results in multiobjective optimization.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Foundation(202203021211129)。
文摘In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.
基金Supported by the Research Project Supported of Shanxi Scholarship Council of China(No.2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Research(202203021211129)。
文摘In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.
文摘From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.
基金the National Natural Science Foundation of China(No.11301574)Chongqing Municipal Education Commission(No.KJ1500310)the Doctor Startup Fund of Chongqing Normal University(No.16XLB010).
文摘Nonlinear scalarization is a very important method to deal with the vector optimization problems.In this paper,some conic nonlinear scalarization characterizations of E-optimal points,weakly E-optimal points,and E-Benson properly efficient points proposed via improvement sets are established by a new scalarization function,respectively.These results improved and generalized some previously known results.As a special case,the scalarization of Benson properly efficient points is also given.Some examples are given to illustrate the main results.
基金This research was supported by the National Natural Science Foundation of China(Nos.11301567 and 11571055)the Fundamental Research Funds for the Central Universities(No.106112017CDJZRPY0020).
文摘The aim of this paper is to investigate the continuity of solution mappings for para-metric set optimization problems with upper and lower set less order relations by scalarization methods.First,we recall some linear and nonlinear scalarization prop-erties used to characterize the set order relations.Subsequently,we introduce new monotonicity concepts of the set-valued mapping by linear and nonlinear scalarization methods.Finally,we obtain the semicontinuity and closedness of solution mappings for parametric set optimization problems(both convex and nonconvex cases)under the monotonicity assumption and other suitable conditions.The results achieved do not impose the continuity of the set-valued objective mapping,which are obviously different from the related ones in the literature.
基金the National Key R&D Program of China(2020YFC2201400)the Natural Science Foundation of China(11805083,11905083,12005077)Guangdong Basic and Applied Basic Research Foundation(2021A1515012374)。
文摘We study the linear instability and nonlinear dynamical evolution of the Reissner-Nordstrom(RN)black hole in the Einstein-Maxwell-scalar theory in asymptotic flat spacetime.We focus on the coupling function f(φ)=e^(-bφ^(2)),which facilitates both scalar-free RN and scalarized black hole solutions.We first present the evolution of system parameters during dynamic scalarization.For parameter regions in which spontaneous scalarization occurs,we observe that the evolution of the scalar field at the horizon is dominated by the fundamental unstable mode from linear analysis at early times.At late times,the nonlinear evolution can be considered to be the perturbation of scalarized black holes.
文摘QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interest in the theoretical and experimental exploration of LSW(longitudinal scalar waves)solutions that are often omitted in CED(classical electrodynamics)but may have physical significance in nontrivial vacuum conditions.This paper delves into the theoretical foundation of LSW,their role in QED,and the associated mathematical equations governing their dynamics.
基金supported by the Spanish MICINN grant PID2022-140440NB-C22the regional Andalusian project P18-FR-5057+3 种基金the Coordinación de la Investigación Científica of the Universidad Michoacana de San Nicolás de Hidalgo,Morelia,Mexico,Grant No.4.10the Consejo Nacional de Humanidades,Ciencias y Tecnologías,Mexico,project CBF2023-2024-3544the Beatriz-Galindo support during his current scientific stay at the University of Huelva,Huelva,Spainthe Chair d'excellence within the program d'Alembert supporting a visiting professorship in the Universitéde Paris-Saclay,France。
文摘Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form factors related to charge and mass densities;and distributions in the impact parameter space.To this end,we employ an algebraically viable framework that is based upon the valence-quark generalized parton distribution expressed explicitly in terms of the associated distribution function and a profile function that governs the off-forward dynamics.The predominantly analytical nature of this scheme yields several algebraic results and relations while also facilitating the exploration of insightful limiting cases.With a suitable input distribution function,guided either by experiment or theory,and with an appropriate choice of the profile function,it is possible to provide testable predictions for spatial distributions of valence quarks inside pseudoscalar mesons.When comparison is possible,these predictions align well with existing experimental data as well as the findings of reliable theoretical approaches and lattice QCD.
基金supported by the Nature Science Foundation of China(12171140).
文摘In this paper,we prove that for certain fiber bundles there is a k-Futaki-Ono conformally Kahler metric related to a metric in any given Kahler class for any k≥2.
文摘Air quality is a critical factor in maintaining health and well-being, influencing both current conditions and future outcomes. Hospitals are one of the sensitive areas of our society, for they are built as sanctuaries for treatment and recovery, making the quality of paramount importance. This study investigates the impact of traffic-related emissions on indoor air quality within a Level 5 Hospital outpatient ward. Measurements were taken over five consecutive days, revealing that while CO2 levels generally remained within safe limits, there were instances where concentrations exceeded 3000 ppm, categorizing them as “Hazardous.” Notably, particulate matter (PM2.5 and PM10) levels fluctuated significantly, with peak concentrations observed during working hours correlating with increased vehicle activity. The data indicated that PM2.5 levels reached as high as 75 µg/m3, with 91.68% of recorded values exceeding the World Health Organization’s (WHO) and Environmental Protection Agency 24-hour mean threshold of 25 µg/m3. Similarly, PM10 concentrations peaked at 120 µg/m3, with 61.19% of values surpassing the WHO threshold of 50 µg/m3, both of which pose serious health risks, particularly to vulnerable populations such as pregnant women, infants, and the elderly. Additionally, the study highlighted the critical role of wind direction in pollutant dispersion, with specific patterns contributing to elevated indoor concentrations. These findings underscore the urgent need for targeted interventions and proactive air quality management strategies in healthcare facilities, including the strategic design of hospital wards away from primary emission sources and the promotion of electric vehicle use to mitigate traffic-related emissions.
基金Supported by the National Key Research and Development Program of China(2022YFA1005501)the Natural Science Foundation of Jiangsu Province(BK20241433).
文摘In this paper,we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant.We prove that if the scalar curvature is not less than the Yamabe invariant in the distributional sense,then the manifold must be isometric to an Einstein manifold.This result extends Theorem 1.4 in Jiang,Sheng and Zhang[27],from a special case where the manifolds have zero Yamabe invariant to general cases where the manifolds have non-positive Yamabe invariant.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12001210 and 12261103)the Natural Science Foundation of Henan(Grant No.252300420308)the Yunnan Fundamental Research Projects(Grant No.202301AT070117).
文摘An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into an equivalent system,and the k-order backward differentiation formula(BDF k)and central difference formula are used to discretize the temporal and spatial derivatives,respectively.Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms,the proposed scheme is based on the SAV idea and can be treated semi-implicitly,taking into account both accuracy and effectiveness.Numerical results are presented to demonstrate the high-order convergence(up to fourth-order)of the developed schemes and it is computationally efficient in long-time computations.
