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
We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit ball inℝ3 with one-speed velocity.The model consists of a steady kinetic equation satisfied by the specific intensity of...We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit ball inℝ3 with one-speed velocity.The model consists of a steady kinetic equation satisfied by the specific intensity of radiation coupled with a nonhomogeneous elliptic equation satisfied by the material temperature.For the O(ϵ)boundary data of the intensity of the radiation and the suitable small boundary data of the temperature,we prove the existence,uniqueness and the nonequilibrium diffusion limit of solutions to the boundary value problem for the coupled model.展开更多
Covert communication guarantees the security of wireless communications via hiding the existence of the transmission.This paper focuses on the first and second order asymptotics of covert communication in the AWGN cha...Covert communication guarantees the security of wireless communications via hiding the existence of the transmission.This paper focuses on the first and second order asymptotics of covert communication in the AWGN channels.The covertness is measured by the total variation distance between the channel output distributions induced with and without the transmission.We provide the exact expressions of the maximum amount of information that can be transmitted with the maximum error probability and the total variation less than any small numbers.The energy detection and the random coding are employed to prove our results.We further compare our results with those under relative entropy.The results show how many additional amounts of information can be transmitted covertly when changing the covertness constraint to total variation.展开更多
Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n...Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n|≥εn^1p ),_~n≥1 1nP(|S_n|≥εn^1p ) and _~n≥1 (log n)δnP(|S_n|≥εnlogn) as ε0 are established.展开更多
Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers s...Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.展开更多
In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
In this 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
In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface...In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.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
This paper examines whether the parametric regression model is correctly specified for both source and target data and whether the regression pattern in the source domain aligns with that of the target domain.This eva...This paper examines whether the parametric regression model is correctly specified for both source and target data and whether the regression pattern in the source domain aligns with that of the target domain.This evaluation is a critical prerequisite for applying model-based transfer learning methods under covariate shift assumptions.Traditional regression model checks and twosample regression tests are insufficient to address this issue.To overcome these limitations,the authors propose a novel adaptive-to-regression test statistic that is asymptotically distribution-free.Under the null hypothesis,the test follows a chi-square weak limit,preserving the significance level and enabling critical value determination without resampling techniques.Additionally,the authors systematically analyze the test's power performance,highlighting its sensitivity to different sub-local alternatives that deviate from the null hypothesis.Numerical studies,including simulations,assess finite-sample performance,and a real-world data example is provided for illustration.展开更多
Model checking evaluates whether a statistical model faithfully captures the underlying data-generating process.Classical tests—such as local-smoothing and empirical-process methods—break down in high dimensions.Mor...Model checking evaluates whether a statistical model faithfully captures the underlying data-generating process.Classical tests—such as local-smoothing and empirical-process methods—break down in high dimensions.More recent approaches use predictiveness comparisons with flexible machine-learning model fitting procedures to yield algorithm-agnostic tests,yet they require large labeled samples.The authors introduce a prediction-powered,semi-supervised framework that:1)Imputes responses for unlabeled data via a pretrained model;2)Corrects imputation bias with a rectifier calibrated on labeled data;3)Adaptively balances these components through a data-driven power-tuning parameter.Building on algorithm-agnostic out-of-sample predictiveness comparisons,the proposed method integrates unlabeled information to enhance power.Theoretical analyses and numerical results demonstrate that the proposed test controls Type I error and substantially improves power over fully supervised counterparts,even under imputation-model misspecification.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
This paper presents a simplified design tool based on semi-analytical formulations to investigate the dynamic response of an immersed composite cylinder subjected to a far-field underwater explosion.The cylinder is si...This paper presents a simplified design tool based on semi-analytical formulations to investigate the dynamic response of an immersed composite cylinder subjected to a far-field underwater explosion.The cylinder is simply supported,fully submerged and filled with air inside.A classical shell theory using a Double Fourier series solution combined with the first-order Doubly Asymptotic Approximation(DAA1)formulation is adapted to model the fluid-structure interaction.An explicit non-standard finite difference scheme is applied to solve the coupled differential equations in time domain.The validity of DAA1 model is established by comparing the LS-DYNA/USA finite element results with existing experimental data from the literature.Then the proposed semi-analytical solutions are compared to the LS-DYNA/USA results,showing good correlation with a discrepancy of 7%for peak deflections and±9%for maximum stresses at the stand-off point for cylinders with relatively small length over radius ratios.Parametric studies examining the effect of different loading conditions,areal masses,and material configurations reveal that a large charge mass located far from the composite panel turns out to be more damaging than a small mass located nearby due to a broader pressure-time profile.Finally,the proposed model demonstrates a significant reduction in computation time,being approximately 30 times faster than its numerical counterpart,LS-DYNA/USA,making it a valuable tool for the preliminary design stages.展开更多
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.
基金Zhang’s research was supported by the NSFC(12271423,12071044)the Fundamental Research Funds for the Central Universities(xzy012022005)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSY026).
文摘We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit ball inℝ3 with one-speed velocity.The model consists of a steady kinetic equation satisfied by the specific intensity of radiation coupled with a nonhomogeneous elliptic equation satisfied by the material temperature.For the O(ϵ)boundary data of the intensity of the radiation and the suitable small boundary data of the temperature,we prove the existence,uniqueness and the nonequilibrium diffusion limit of solutions to the boundary value problem for the coupled model.
基金supported in part by the Natural Science Foundation of Xinjiang Uygur Autonomous Region under Grant 2022D01B184the National Natural Science Foundation of China under Grant 62301117,62131005.
文摘Covert communication guarantees the security of wireless communications via hiding the existence of the transmission.This paper focuses on the first and second order asymptotics of covert communication in the AWGN channels.The covertness is measured by the total variation distance between the channel output distributions induced with and without the transmission.We provide the exact expressions of the maximum amount of information that can be transmitted with the maximum error probability and the total variation less than any small numbers.The energy detection and the random coding are employed to prove our results.We further compare our results with those under relative entropy.The results show how many additional amounts of information can be transmitted covertly when changing the covertness constraint to total variation.
文摘Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n|≥εn^1p ),_~n≥1 1nP(|S_n|≥εn^1p ) and _~n≥1 (log n)δnP(|S_n|≥εnlogn) as ε0 are established.
基金National Natural Science Foundation of China(10571073).
文摘Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金Supported by the National Natural Science Foundation of China(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.
文摘In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.
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.
基金supported by the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science(East China Normal University),Ministry of Educationsupported by the National Natural Scientific Foundation of China under Grant No.NSFC12131006the Scientific and Technological Innovation Project of China Academy of Chinese Medical Science under Grant No.CI2023C063YLL。
文摘This paper examines whether the parametric regression model is correctly specified for both source and target data and whether the regression pattern in the source domain aligns with that of the target domain.This evaluation is a critical prerequisite for applying model-based transfer learning methods under covariate shift assumptions.Traditional regression model checks and twosample regression tests are insufficient to address this issue.To overcome these limitations,the authors propose a novel adaptive-to-regression test statistic that is asymptotically distribution-free.Under the null hypothesis,the test follows a chi-square weak limit,preserving the significance level and enabling critical value determination without resampling techniques.Additionally,the authors systematically analyze the test's power performance,highlighting its sensitivity to different sub-local alternatives that deviate from the null hypothesis.Numerical studies,including simulations,assess finite-sample performance,and a real-world data example is provided for illustration.
基金supported by the National Key R&D Program of China under Grant Nos.2022YFA1003800 and 2022YFA1003703the National Natural Science Foundation of China under Grant Nos.12531011,12231011 and 12471255+3 种基金the Natural Science Foundation of Shanghai under Grant No.23ZR1419400the Fundamental Research Funds for the Central Universities under Grant No.63253110supported by China Postdoctoral Science Foundation General Funding Program under Grant No.2025M7730792025 Annual Planning Project of the Commerce Statistical Society of China under Grant No.2025STY115。
文摘Model checking evaluates whether a statistical model faithfully captures the underlying data-generating process.Classical tests—such as local-smoothing and empirical-process methods—break down in high dimensions.More recent approaches use predictiveness comparisons with flexible machine-learning model fitting procedures to yield algorithm-agnostic tests,yet they require large labeled samples.The authors introduce a prediction-powered,semi-supervised framework that:1)Imputes responses for unlabeled data via a pretrained model;2)Corrects imputation bias with a rectifier calibrated on labeled data;3)Adaptively balances these components through a data-driven power-tuning parameter.Building on algorithm-agnostic out-of-sample predictiveness comparisons,the proposed method integrates unlabeled information to enhance power.Theoretical analyses and numerical results demonstrate that the proposed test controls Type I error and substantially improves power over fully supervised counterparts,even under imputation-model misspecification.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
基金supported by French Defense Innovation Agency(AID-DGA)(Grant No.ANR-21-ASM2-0002-02)in the framework of the Astrid Maturation SUCCESS+project,a collaborative French research project.
文摘This paper presents a simplified design tool based on semi-analytical formulations to investigate the dynamic response of an immersed composite cylinder subjected to a far-field underwater explosion.The cylinder is simply supported,fully submerged and filled with air inside.A classical shell theory using a Double Fourier series solution combined with the first-order Doubly Asymptotic Approximation(DAA1)formulation is adapted to model the fluid-structure interaction.An explicit non-standard finite difference scheme is applied to solve the coupled differential equations in time domain.The validity of DAA1 model is established by comparing the LS-DYNA/USA finite element results with existing experimental data from the literature.Then the proposed semi-analytical solutions are compared to the LS-DYNA/USA results,showing good correlation with a discrepancy of 7%for peak deflections and±9%for maximum stresses at the stand-off point for cylinders with relatively small length over radius ratios.Parametric studies examining the effect of different loading conditions,areal masses,and material configurations reveal that a large charge mass located far from the composite panel turns out to be more damaging than a small mass located nearby due to a broader pressure-time profile.Finally,the proposed model demonstrates a significant reduction in computation time,being approximately 30 times faster than its numerical counterpart,LS-DYNA/USA,making it a valuable tool for the preliminary design stages.
