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 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 this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(x, t) = 0, which can be viewed as a gen...In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(x, t) = 0, which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann-Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear steepest-descent method to analyze the long-time asymptotics for the solution of the nonlocal m KdV equation. In contrast with the classical mKdV equation,we find some new and different results on long-time asymptotics for the nonlocal mKdV equation and some additional assumptions about the scattering data are made in our main results.展开更多
In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑...In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/｜n｜（log｜n｜dP（｜Sn/Vn｜≥ε√log log｜n｜） and ∑n（logn｜）b/｜n｜（log｜n｜）^d-1P（｜Sn/Vn｜≥ε√log n）,as ε↓0,is established.展开更多
In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomial...In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft ＆ Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior.展开更多
In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establi...In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.展开更多
In our recent work (Wang, Burgei, and Zhou, 2018) we studied the hearing loss injury among subjects in a crowd with a wide spectrum of heterogeneous individual injury susceptibility due to biovariability. The injury r...In our recent work (Wang, Burgei, and Zhou, 2018) we studied the hearing loss injury among subjects in a crowd with a wide spectrum of heterogeneous individual injury susceptibility due to biovariability. The injury risk of a crowd is defined as the average fraction of injured. We examined mathematically the injury risk of a crowd vs the number of acoustic impulses the crowd is exposed to, under the assumption that all impulses act independently in causing injury regardless of whether one is preceded by another. We concluded that the observed dose-response relation can be explained solely on the basis of biovariability in the form of heterogeneous susceptibility. We derived an analytical solution for the distribution density of injury susceptibility, as a power series expansion in terms of scaled log individual non-injury probability. While theoretically the power series converges for all argument values, in practical computations with IEEE double precision, at large argument values, the numerical accuracy of the power series summation is completely wiped out by the accumulation of round-off errors. In this study, we derive a general asymptotic approximation at large argument values, for the distribution density. The combination of the power series and the asymptotics provides a practical numerical tool for computing the distribution density. We then use this tool to verify numerically that the distribution obtained in our previous theoretical study is indeed a proper density. In addition, we will also develop a very efficient and accurate Pade approximation for the distribution density.展开更多
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 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 National Science Foundation of China under Grant Nos.11671095,51879045National Science Foundation of China under Grant No.11501365+1 种基金Shanghai Sailing Program supported by Science and Technology Commission of Shanghai Municipality under Grant No.15YF1408100Shanghai Youth Teacher Assistance Program No.ZZslg15056
文摘In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(x, t) = 0, which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann-Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear steepest-descent method to analyze the long-time asymptotics for the solution of the nonlocal m KdV equation. In contrast with the classical mKdV equation,we find some new and different results on long-time asymptotics for the nonlocal mKdV equation and some additional assumptions about the scattering data are made in our main results.
文摘In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/｜n｜（log｜n｜dP（｜Sn/Vn｜≥ε√log log｜n｜） and ∑n（logn｜）b/｜n｜（log｜n｜）^d-1P（｜Sn/Vn｜≥ε√log n）,as ε↓0,is established.
基金supported in part by the National Natural Science Foundation of China (10471154 and 10871212)
文摘In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft ＆ Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior.
基金supported by the Natural Science Foundation of China(10771017,10971015,10231030)Key Project to Ministry of Education of the People’s Republic of China(309007)
文摘In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.
文摘In our recent work (Wang, Burgei, and Zhou, 2018) we studied the hearing loss injury among subjects in a crowd with a wide spectrum of heterogeneous individual injury susceptibility due to biovariability. The injury risk of a crowd is defined as the average fraction of injured. We examined mathematically the injury risk of a crowd vs the number of acoustic impulses the crowd is exposed to, under the assumption that all impulses act independently in causing injury regardless of whether one is preceded by another. We concluded that the observed dose-response relation can be explained solely on the basis of biovariability in the form of heterogeneous susceptibility. We derived an analytical solution for the distribution density of injury susceptibility, as a power series expansion in terms of scaled log individual non-injury probability. While theoretically the power series converges for all argument values, in practical computations with IEEE double precision, at large argument values, the numerical accuracy of the power series summation is completely wiped out by the accumulation of round-off errors. In this study, we derive a general asymptotic approximation at large argument values, for the distribution density. The combination of the power series and the asymptotics provides a practical numerical tool for computing the distribution density. We then use this tool to verify numerically that the distribution obtained in our previous theoretical study is indeed a proper density. In addition, we will also develop a very efficient and accurate Pade approximation for the distribution density.
