Tilt-to-length(TTL)coupling noise is a critical issue in space-based gravitational wave detection due to its complex dependence on multiple interacting factors,which complicates the identification of dominant paramete...Tilt-to-length(TTL)coupling noise is a critical issue in space-based gravitational wave detection due to its complex dependence on multiple interacting factors,which complicates the identification of dominant parameters.To address this challenge,we develop a simulation model of the Taiji scientific interferometer,generating noise datasets under multiparameter conditions.Given the uniqueness of the telescope as well as the convergence behavior of the algorithm,the analysis is structured hierarchically:(i)the telescope level and(ii)the optical bench level.A hierarchical framework combining XGBoost and SHapley Additive exPlanations(SHAP)values is employed to model the intricate relationships between parameters and TTL coupling noise,supplemented by sensitivity analysis.Our results identify pointing jitter and telescope radius as the dominant parameters at the telescope level,while the angles of the plane mirrors and beam splitters are most influential at the optical bench level.The parameter space is reduced from 86 dimensions to 14 dimensions without sacrificing model accuracy.This approach offers actionable insights for optimizing the Taiji interferometer design.展开更多
This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit...This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.展开更多
In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.展开更多
We study a finite number of independent random walks with subexponentially distributed increments and negative drifts.We extend the one-dimensional results to finite and fully general stopping times.Assuming that the ...We study a finite number of independent random walks with subexponentially distributed increments and negative drifts.We extend the one-dimensional results to finite and fully general stopping times.Assuming that the distribution of the lengths of these intervals is relatively light compared to the distribution of the increments of the random walks,we derive the asymptotic tail distribution of the partial maximum sum over the random time interval.展开更多
Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,...Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.展开更多
In this paper,we establish and study a single-species logistic model with impulsive age-selective harvesting.First,we prove the ultimate boundedness of the solutions of the system.Then,we obtain conditions for the asy...In this paper,we establish and study a single-species logistic model with impulsive age-selective harvesting.First,we prove the ultimate boundedness of the solutions of the system.Then,we obtain conditions for the asymptotic stability of the trivial solution and the positive periodic solution.Finally,numerical simulations are presented to validate our results.Our results show that age-selective harvesting is more conducive to sustainable population survival than non-age-selective harvesting.展开更多
Let T_(n) and S_(n) be the full transformation semigroup and the symmetric group on X_(n)={1,2,...,n},respectively.Let G be a transitiveimprimitive subgroupof S_(n) with nontrivial blocksΔand letαbe a transformation...Let T_(n) and S_(n) be the full transformation semigroup and the symmetric group on X_(n)={1,2,...,n},respectively.Let G be a transitiveimprimitive subgroupof S_(n) with nontrivial blocksΔand letαbe a transformation in T_(n)\S_(n).The kernel ofαis the partition of X_(n) induced by the equivalence relation{(x,y)|xα=yα};the kernel type ofαis the partition of n given by the sizes of the parts of the kernel.A transformation semigroup is called synchronizing if it contains a constant map.Then a group G synchronizes a transformationαif the semigroup(G,α)contains a constant map.In this paper,we study a transitive imprimitive permutation group G together with a non-invertible transformationαthat generate a synchronizing semigroup.We mainly discuss 7 cases where G synchronizes a special transformationαwith each kernel class A_(i)(A_(1)j)satisfying|A_(i)∩Δ|=1(|A_(1)j∩Δ|=1)for all blocksΔofG,that is,the kernel type ofαis(|A_(1)|,1,...,1),(|A_(1)1|,...,|A_(1m)|,|A_(2)|,...,|Ar|),or(|A_(1)|,...,|A_(t)|,1,...,1),or the rank is 2,3,4,or n-2.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
Groundwater modeling remains challenging due to heterogeneity and complexity of aquifer systems,necessitating endeavors to quantify Groundwater Levels(GWL)dynamics to inform policymakers and hydrogeologists.This study...Groundwater modeling remains challenging due to heterogeneity and complexity of aquifer systems,necessitating endeavors to quantify Groundwater Levels(GWL)dynamics to inform policymakers and hydrogeologists.This study introduces a novel Fuzzy Nonlinear Additive Regression(FNAR)model to predict monthly GWL in an unconfined aquifer in eastern Iran,using a 19-year(1998–2017)dataset from 11 piezometric wells.Under three distinct scenarios with progressively increasing input complexity,the study utilized readily available climate data,including Precipitation(Prc),Temperature(Tave),Relative Humidity(RH),and Evapotranspiration(ETo).The dataset was split into training(70%)and validation(30%)subsets.Results showed that among three input scenarios,Scenario 3(Sc3,incorporating all four variables)achieved the best predictive performance,with RMSE ranging from 0.305 m to 0.768 m,MAE from 0.203 m to 0.522 m,NSE from 0.661 to 0.980,and PBIAS from 0.771%to 0.981%,indicating low bias and high reliability.However,Sc2(excluding ETo)with RMSE ranging from 0.4226 m to 0.9909 m,MAE from 0.3418 m to 0.8173 m,NSE from 0.2831 to 0.9674,and PBIAS from−0.598%to 0.968%across different months offers practical advantages in data-scarce settings.The FNAR model outperforms conventional Fuzzy Least Squares Regression(FLSR)and holds promise for GWL forecasting in data-scarce regions where physical or numerical models are impractical.Future research should focus on integrating FNAR with deep learning algorithms and real-time data assimilation expanding applications across diverse hydrogeological settings.展开更多
In this paper,Schwarz-type lemmas for different classes of quaternion functions are obtained.Firstly,some properties of symmetric points are given.Secondly,the Schwarz-type lemma and the Schwarz-Pick-type theorem for ...In this paper,Schwarz-type lemmas for different classes of quaternion functions are obtained.Firstly,some properties of symmetric points are given.Secondly,the Schwarz-type lemma and the Schwarz-Pick-type theorem for quaternion regular functions are obtained.Finally,the Schwarz-type lemma for quaternion k-regular functions is derived.展开更多
This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural condit...This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural conditions on f,using the Crandall-Rabinowitz bifurcation theorem,we obtain a bifurcation curve emanating from(k,0).Furthermore,we also analyze the local structure of bifurcation curves and stability of solutions on them.Specifically,our results indicate the bifurcation is critical for each k and is subcritical(supercritical)if f'''(0)>0(f'''(0)<0).展开更多
In this paper,we investigate the convex roof measures of quantum coherence,with a focus on their superadditive properties.We propose sufficient conditions and establish a framework for coherence superadditivity in tri...In this paper,we investigate the convex roof measures of quantum coherence,with a focus on their superadditive properties.We propose sufficient conditions and establish a framework for coherence superadditivity in tripartite and multipartite systems.Through theoretical derivation,the relevant theorems are given.These results not only expand our understanding of the superadditivity of pure and mixed states but also characterize the conditions under which the superadditivity relations reach equality.Finally,the proposed methods and conclusions are verified through representative examples,providing new theoretical insights into the distribution of quantum coherence in multipartite systems.展开更多
In the era of massive data,the study of distributed data is a significant topic.Model averaging can be effectively applied to distributed data by combining information from all machines.For linear models,the model ave...In the era of massive data,the study of distributed data is a significant topic.Model averaging can be effectively applied to distributed data by combining information from all machines.For linear models,the model averaging approach has been developed in the context of distributed data.However,further investigation is needed for more complex models.In this paper,the authors propose a distributed optimal model averaging approach based on multivariate additive models,which approximates unknown functions using B-splines allowing each machine to have a different smoothing degree.To utilize the information from the covariance matrix of dependent errors in multivariate multiple regressions,the authors use the Mahalanobis distance to construct a Mallows-type weight choice criterion.The criterion can be computed by transmitting information between the local machines and the center machine in two steps.The authors demonstrate the asymptotic optimality of the proposed model averaging estimator when the covariates are subject to uncertainty,and obtain the convergence rate of the weight vector to the theoretically optimal weights.The results remain novel even for additive models with a single response variable.The numerical examples show that the proposed method yields good performance.展开更多
In this paper we investigates the problem of inequalities on Riemannian manifolds with nonnegative Ricci curvature.By employing the method of Jia-Wang-Xia-Zhang,two types of results on geometric inequalities are obtai...In this paper we investigates the problem of inequalities on Riemannian manifolds with nonnegative Ricci curvature.By employing the method of Jia-Wang-Xia-Zhang,two types of results on geometric inequalities are obtained,generalizing the results of Jia-Wang-Xia-Zhang.展开更多
Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algeb...Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.展开更多
Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic...Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by c(n),a constant depending only on n,and we will survey partial results(up to date)on the c(n)-cyclic conjecture.展开更多
We investigate the alpha helical protein structure characterized by fourth-order interspine coupling,focusing on a three-coupled fourth-order nonlinear Schr??dinger system.We introduce a generalized Darboux transforma...We investigate the alpha helical protein structure characterized by fourth-order interspine coupling,focusing on a three-coupled fourth-order nonlinear Schr??dinger system.We introduce a generalized Darboux transformation,departing from the classical Darboux transformation.Based on this,we construct the two-and three-degenerate soliton solutions and four-degenerate asymptotic soliton solutions.Based on the asymptotic analysis,we find that the amplitudes of interacting solitons are retained upon the interactions.Elastic interactions between two degenerate solitons exhibiting four curve-type asymptotic solitons are depicted.When the lattice parameterβchanges,the velocities of the two degenerate solitons also change.Elastic interaction among three degenerate solitons comprising four curve-type asymptotic solitons and two line-type solitons is presented.Interaction among one soliton and two degenerate solitons with different velocities is shown.Elastic interaction among four degenerate solitons comprising eight curve-type asymptotic solitons is also presented.Interaction among two two-degenerate solitons with two spectral parameters is shown.The relative distance between two asymptotic solitons exhibits logarithmic growth with|t|,where t represents the retarded time.Acceleration of soliton separation decays exponentially with relative distance,and eventually approaches zero.Phase shifts depend on t.展开更多
In mixture experiments,the observed response is determined by the relative proportions of the components,consequently rendering the experimental region a simplex.This paper focuses primarily on the optimal designs of ...In mixture experiments,the observed response is determined by the relative proportions of the components,consequently rendering the experimental region a simplex.This paper focuses primarily on the optimal designs of mixture experiments that involve process variables.Prior research has extensively delved into optimal orthogonal block designs for some classic mixture models with process variables.Based on the framework of general blending models,this paper proposes a class of symmetric linear mixture models,which can be regarded as a generalization of many existing ones.Under the orthogonal blocking conditions,orthogonal block designs are devised through Latin squares in the presence of process variables.TheD-,A-,and E-optimality criteria are utilized to obtain optimal designs at the boundary of the simplex in the case of 3 components.As the values of the exponents change,numerically derived optimal design points are presented to illustrate the pattern of their variations,and to verify the consistency of the results with previous research on some specific symmetric general blending models.展开更多
Shor's algorithm outperforms its classical counterpart in efficient prime factorization.We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm,showing that the coheren...Shor's algorithm outperforms its classical counterpart in efficient prime factorization.We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm,showing that the coherence in each step relies on the dimension of register or the order,and discuss the relations between geometric coherence and geometric entanglement.We investigate how unitary operators induce variations in coherence and entanglement,and analyze the variations of coherence and entanglement within the entire algorithm,demonstrating that the overall effect of Shor's algorithm tends to deplete coherence and produce entanglement.Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms.展开更多
基金Project supported by the National Key Research and Development Program of China(Grant No.2020YFC2200100)the CAS's Strategic Pioneer Program on Space Science(Grant No.XDA1502110201)。
文摘Tilt-to-length(TTL)coupling noise is a critical issue in space-based gravitational wave detection due to its complex dependence on multiple interacting factors,which complicates the identification of dominant parameters.To address this challenge,we develop a simulation model of the Taiji scientific interferometer,generating noise datasets under multiparameter conditions.Given the uniqueness of the telescope as well as the convergence behavior of the algorithm,the analysis is structured hierarchically:(i)the telescope level and(ii)the optical bench level.A hierarchical framework combining XGBoost and SHapley Additive exPlanations(SHAP)values is employed to model the intricate relationships between parameters and TTL coupling noise,supplemented by sensitivity analysis.Our results identify pointing jitter and telescope radius as the dominant parameters at the telescope level,while the angles of the plane mirrors and beam splitters are most influential at the optical bench level.The parameter space is reduced from 86 dimensions to 14 dimensions without sacrificing model accuracy.This approach offers actionable insights for optimizing the Taiji interferometer design.
文摘This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
文摘In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
基金supported by Xinjiang Normal University Outstanding Young Teacher Research Launch Fund Project(Grant No.XJNU202116)。
文摘We study a finite number of independent random walks with subexponentially distributed increments and negative drifts.We extend the one-dimensional results to finite and fully general stopping times.Assuming that the distribution of the lengths of these intervals is relatively light compared to the distribution of the increments of the random walks,we derive the asymptotic tail distribution of the partial maximum sum over the random time interval.
文摘Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.
基金Supported by the National Natural Science Foundation of China(12261018)Universities Key Laboratory of Mathematical Modeling and Data Mining in Guizhou Province(2023013)。
文摘In this paper,we establish and study a single-species logistic model with impulsive age-selective harvesting.First,we prove the ultimate boundedness of the solutions of the system.Then,we obtain conditions for the asymptotic stability of the trivial solution and the positive periodic solution.Finally,numerical simulations are presented to validate our results.Our results show that age-selective harvesting is more conducive to sustainable population survival than non-age-selective harvesting.
基金Supported by NSFC (No.12401024)the Scientific Research Innovation Project of Lingnan Normal University (Nos.LT2401,LT2410)。
文摘Let T_(n) and S_(n) be the full transformation semigroup and the symmetric group on X_(n)={1,2,...,n},respectively.Let G be a transitiveimprimitive subgroupof S_(n) with nontrivial blocksΔand letαbe a transformation in T_(n)\S_(n).The kernel ofαis the partition of X_(n) induced by the equivalence relation{(x,y)|xα=yα};the kernel type ofαis the partition of n given by the sizes of the parts of the kernel.A transformation semigroup is called synchronizing if it contains a constant map.Then a group G synchronizes a transformationαif the semigroup(G,α)contains a constant map.In this paper,we study a transitive imprimitive permutation group G together with a non-invertible transformationαthat generate a synchronizing semigroup.We mainly discuss 7 cases where G synchronizes a special transformationαwith each kernel class A_(i)(A_(1)j)satisfying|A_(i)∩Δ|=1(|A_(1)j∩Δ|=1)for all blocksΔofG,that is,the kernel type ofαis(|A_(1)|,1,...,1),(|A_(1)1|,...,|A_(1m)|,|A_(2)|,...,|Ar|),or(|A_(1)|,...,|A_(t)|,1,...,1),or the rank is 2,3,4,or n-2.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金supported by the Iran National Science Foundation(INSF)the University of Birjand under grant number 4034771.
文摘Groundwater modeling remains challenging due to heterogeneity and complexity of aquifer systems,necessitating endeavors to quantify Groundwater Levels(GWL)dynamics to inform policymakers and hydrogeologists.This study introduces a novel Fuzzy Nonlinear Additive Regression(FNAR)model to predict monthly GWL in an unconfined aquifer in eastern Iran,using a 19-year(1998–2017)dataset from 11 piezometric wells.Under three distinct scenarios with progressively increasing input complexity,the study utilized readily available climate data,including Precipitation(Prc),Temperature(Tave),Relative Humidity(RH),and Evapotranspiration(ETo).The dataset was split into training(70%)and validation(30%)subsets.Results showed that among three input scenarios,Scenario 3(Sc3,incorporating all four variables)achieved the best predictive performance,with RMSE ranging from 0.305 m to 0.768 m,MAE from 0.203 m to 0.522 m,NSE from 0.661 to 0.980,and PBIAS from 0.771%to 0.981%,indicating low bias and high reliability.However,Sc2(excluding ETo)with RMSE ranging from 0.4226 m to 0.9909 m,MAE from 0.3418 m to 0.8173 m,NSE from 0.2831 to 0.9674,and PBIAS from−0.598%to 0.968%across different months offers practical advantages in data-scarce settings.The FNAR model outperforms conventional Fuzzy Least Squares Regression(FLSR)and holds promise for GWL forecasting in data-scarce regions where physical or numerical models are impractical.Future research should focus on integrating FNAR with deep learning algorithms and real-time data assimilation expanding applications across diverse hydrogeological settings.
基金supported by the Innovation Foundation of the School of Mathematical Sciences in Hebei Normal University in 2025(ycxzzbs202503)the NSF of Hebei Province(A2023205006,A2022208007,A2023205045,A2024208005)+2 种基金the Hebei Research Center of the Basic Discipline Pure Mathematics,the Key Development Foundation of Hebei Normal University(L2024ZD08)the NSFC(12431005)the Funding Project of Central Guidance for Local Scientific and Technological Development(246Z7608G).
文摘In this paper,Schwarz-type lemmas for different classes of quaternion functions are obtained.Firstly,some properties of symmetric points are given.Secondly,the Schwarz-type lemma and the Schwarz-Pick-type theorem for quaternion regular functions are obtained.Finally,the Schwarz-type lemma for quaternion k-regular functions is derived.
基金Supported by the National Natural Science Foundation of China(Grant No.12371110).
文摘This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural conditions on f,using the Crandall-Rabinowitz bifurcation theorem,we obtain a bifurcation curve emanating from(k,0).Furthermore,we also analyze the local structure of bifurcation curves and stability of solutions on them.Specifically,our results indicate the bifurcation is critical for each k and is subcritical(supercritical)if f'''(0)>0(f'''(0)<0).
基金supported by the NNSF of China(Grant No.12471427)the Fundamental Research Funds for the Central Universities(Grant No.4303088)。
文摘In this paper,we investigate the convex roof measures of quantum coherence,with a focus on their superadditive properties.We propose sufficient conditions and establish a framework for coherence superadditivity in tripartite and multipartite systems.Through theoretical derivation,the relevant theorems are given.These results not only expand our understanding of the superadditivity of pure and mixed states but also characterize the conditions under which the superadditivity relations reach equality.Finally,the proposed methods and conclusions are verified through representative examples,providing new theoretical insights into the distribution of quantum coherence in multipartite systems.
基金supported by Youth Academic Innocation Team Construction project of Capital University of Economics and Business under Grant No.QNTD202303supported by the Beijing Outstanding Young Scientist Program under Grant No.JWZQ20240101027the National Natural Science Foundation of China under Grant Nos.12031016,12531012 and 12426308。
文摘In the era of massive data,the study of distributed data is a significant topic.Model averaging can be effectively applied to distributed data by combining information from all machines.For linear models,the model averaging approach has been developed in the context of distributed data.However,further investigation is needed for more complex models.In this paper,the authors propose a distributed optimal model averaging approach based on multivariate additive models,which approximates unknown functions using B-splines allowing each machine to have a different smoothing degree.To utilize the information from the covariance matrix of dependent errors in multivariate multiple regressions,the authors use the Mahalanobis distance to construct a Mallows-type weight choice criterion.The criterion can be computed by transmitting information between the local machines and the center machine in two steps.The authors demonstrate the asymptotic optimality of the proposed model averaging estimator when the covariates are subject to uncertainty,and obtain the convergence rate of the weight vector to the theoretically optimal weights.The results remain novel even for additive models with a single response variable.The numerical examples show that the proposed method yields good performance.
文摘In this paper we investigates the problem of inequalities on Riemannian manifolds with nonnegative Ricci curvature.By employing the method of Jia-Wang-Xia-Zhang,two types of results on geometric inequalities are obtained,generalizing the results of Jia-Wang-Xia-Zhang.
基金Supported by the Science and Technology Program of Guizhou Province(Grant No.QKHJC QN[2025]362)the National Natural Science Foundation of China(Grant No.12361005).
文摘Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.
文摘Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by c(n),a constant depending only on n,and we will survey partial results(up to date)on the c(n)-cyclic conjecture.
基金supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2025QC30)。
文摘We investigate the alpha helical protein structure characterized by fourth-order interspine coupling,focusing on a three-coupled fourth-order nonlinear Schr??dinger system.We introduce a generalized Darboux transformation,departing from the classical Darboux transformation.Based on this,we construct the two-and three-degenerate soliton solutions and four-degenerate asymptotic soliton solutions.Based on the asymptotic analysis,we find that the amplitudes of interacting solitons are retained upon the interactions.Elastic interactions between two degenerate solitons exhibiting four curve-type asymptotic solitons are depicted.When the lattice parameterβchanges,the velocities of the two degenerate solitons also change.Elastic interaction among three degenerate solitons comprising four curve-type asymptotic solitons and two line-type solitons is presented.Interaction among one soliton and two degenerate solitons with different velocities is shown.Elastic interaction among four degenerate solitons comprising eight curve-type asymptotic solitons is also presented.Interaction among two two-degenerate solitons with two spectral parameters is shown.The relative distance between two asymptotic solitons exhibits logarithmic growth with|t|,where t represents the retarded time.Acceleration of soliton separation decays exponentially with relative distance,and eventually approaches zero.Phase shifts depend on t.
基金supported by the National Natural Science Foundation of China[grant numbers 12071329,12471246].
文摘In mixture experiments,the observed response is determined by the relative proportions of the components,consequently rendering the experimental region a simplex.This paper focuses primarily on the optimal designs of mixture experiments that involve process variables.Prior research has extensively delved into optimal orthogonal block designs for some classic mixture models with process variables.Based on the framework of general blending models,this paper proposes a class of symmetric linear mixture models,which can be regarded as a generalization of many existing ones.Under the orthogonal blocking conditions,orthogonal block designs are devised through Latin squares in the presence of process variables.TheD-,A-,and E-optimality criteria are utilized to obtain optimal designs at the boundary of the simplex in the case of 3 components.As the values of the exponents change,numerically derived optimal design points are presented to illustrate the pattern of their variations,and to verify the consistency of the results with previous research on some specific symmetric general blending models.
基金supported by National Natural Science Foundation of China(Grant Nos.12161056,12075159,12171044)Natural Science Foundation of Jiangxi Province(Grant No.20232ACB211003)+1 种基金Beijing Natural Science Foundation(Grant No.Z190005)the specific research fund of the Innovation Platform for Academicians of Hainan Province。
文摘Shor's algorithm outperforms its classical counterpart in efficient prime factorization.We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm,showing that the coherence in each step relies on the dimension of register or the order,and discuss the relations between geometric coherence and geometric entanglement.We investigate how unitary operators induce variations in coherence and entanglement,and analyze the variations of coherence and entanglement within the entire algorithm,demonstrating that the overall effect of Shor's algorithm tends to deplete coherence and produce entanglement.Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms.
