The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the...The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.展开更多
In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with lin...In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.展开更多
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.展开更多
Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ） ＋ qnX^Bn-σ = 0, n ：0, 1, 2...wh...Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ） ＋ qnX^Bn-σ = 0, n ：0, 1, 2...which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10].展开更多
We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients are either linear or nonlinear but bounded by linear functions, has been...Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients are either linear or nonlinear but bounded by linear functions, has been investigated intensively. Recently, the stability of highly nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper, by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.展开更多
Let G be a locally compact Vilenkin gro up . We will establish the boundedness in Morrey spaces L p,λ (G) for a la rge class of sublinear operators and linear commutators.
In a viscous damping device under cyclic loading, after the piston reaches a peak stroke, the reserve movement that follows may sometimes experience a short period of delayed or significantly reduced device force outp...In a viscous damping device under cyclic loading, after the piston reaches a peak stroke, the reserve movement that follows may sometimes experience a short period of delayed or significantly reduced device force output. A similar delay or reduced device force output may also occur at the damper＇s initial stroke as it moves away from its neutral position. This phenomenon is referred to as the effect of ＂deadzone＂. The deadzone can cause a loss of energy dissipation capacity and less efficient vibration control. It is prominent in small amplitude vibrations. Although there are many potential causes of deadzone such as environmental factors, construction, material aging, and manufacture quality, in this paper, its general effect in linear and nonlinear viscous damping devices is analyzed. Based on classical dynamics and damping theory, a simple model is developed to capture the effect ofdeadzone in terms of the loss of energy dissipation capacity. The model provides several methods to estimate the loss of energy dissipation within the deadzone in linear and sublinear viscous fluid dampers. An empirical equation of loss of energy dissipation capacity versus deadzone size is formulated, and the equivalent reduction of effective damping in SDOF systems has been obtained. A laboratory experimental evaluation is carried out to verify the effect of deadzone and its numerical approximation. Based on the analysis, a modification is suggested to the corresponding formulas in FEMA 3 5 6 for calculation of equivalent damping if a deadzone is to be considered.展开更多
In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u...In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.展开更多
This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential w...This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential well V^-1(0).Combining this with other suitable assumptions on K and f,the existence of nontrivial solutions is obtained via variational methods.Furthermore,the concentration behavior of the nontrivial solution is also explored on the set V^-1(0)asλ→+∞as A—>H-oo as well.It is worth noting that the(PS)-condition can not be directly got as done in the literature,which makes the problem more complicated.To overcome this difficulty,we adopt different method.展开更多
It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the ...It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the operator -Δ in the space H 1 0(Ω).展开更多
In this paper,we study a class of sublinear Kirchhoff equations:-(a+b∫R_(N)|■u|^(2)dx)+△u+V(x)u=f(x,u)in R^(N),where a,b>0,V:R^(N)→R can be sign-changing,and f:R^(N)×R→R.Under some conditions on V and f,w...In this paper,we study a class of sublinear Kirchhoff equations:-(a+b∫R_(N)|■u|^(2)dx)+△u+V(x)u=f(x,u)in R^(N),where a,b>0,V:R^(N)→R can be sign-changing,and f:R^(N)×R→R.Under some conditions on V and f,we verify that the problem possesses at least one energy solution by using variational method.展开更多
The concept of upper variance under multiple probabilities is defined through a corresponding minimax optimization problem.This study proposes a simple algorithm to solve this optimization problem exactly.Additionally...The concept of upper variance under multiple probabilities is defined through a corresponding minimax optimization problem.This study proposes a simple algorithm to solve this optimization problem exactly.Additionally,we provide a probabilistic representation for a class of quadratic programming problems,demonstrating the practical application of our approach.展开更多
Sublinear expectation relaxes the linear property of classical expectation to subadditivity and positive homogeneity,which can be expressed as E(·)=sup_(θ∈θ) E_(θ)(·)for a certain set of linear expectati...Sublinear expectation relaxes the linear property of classical expectation to subadditivity and positive homogeneity,which can be expressed as E(·)=sup_(θ∈θ) E_(θ)(·)for a certain set of linear expectations{E_(θ):θ∈θ}.Such a framework can capture the uncertainty and facilitate a robust method of measuring risk loss reasonably.This study established a law of large numbers for m-dependent random vectors within the framework of sublinear expectation.Consequently,the corresponding explicit rate of convergence were derived.The results of this study can be considered as an extension of the Peng's law of large numbers[22].展开更多
The Shilkret integral or idempotent expectation is a sublinear functional which is very close to being a sublinear expectation since it satisfies all the required properties but its domain is not a linear space.In thi...The Shilkret integral or idempotent expectation is a sublinear functional which is very close to being a sublinear expectation since it satisfies all the required properties but its domain is not a linear space.In this paper,we prove that it admits a law of large numbers which is structurally similar to Peng's LLN for sublinear expectations although significant differences exist.As regards the central limit theorem,the situation is radically different as the Vn normalization can lead to a trivial limit and other normalizations are possible for variables with a finite second moment or even bounded.展开更多
In this paper,the authors firstly establish the weak laws of large numbers on the canonical space(R^(N),B(R^(N)))by traditional truncation method and Chebyshev’s inequality as in the classical probability theory.Then...In this paper,the authors firstly establish the weak laws of large numbers on the canonical space(R^(N),B(R^(N)))by traditional truncation method and Chebyshev’s inequality as in the classical probability theory.Then they extend them from the canonical space to the general sublinear expectation space.The necessary and sufficient conditions for Peng’s law of large numbers are obtained.展开更多
In this paper, the second order difference equation: △(rn△xn) + f(n, xn) = 0, n∈N(n0) (E) is considered. Some necessary and sufficient conditions for the oscillation of Eq.(E) are obtained.
In this paper, we study monotone properties of random and stochastic functional differential equations and their global dynamics. First, we show that random functional differential equations(RFDEs)generate the random ...In this paper, we study monotone properties of random and stochastic functional differential equations and their global dynamics. First, we show that random functional differential equations(RFDEs)generate the random dynamical system(RDS) if and only if all the solutions are globally defined, and establish the comparison theorem for RFDEs and the random Riesz representation theorem. These three results lead to the Borel measurability of coefficient functions in the Riesz representation of variational equations for quasimonotone RFDEs, which paves the way following the Smith line to establish eventual strong monotonicity for the RDS under cooperative and irreducible conditions. Then strong comparison principles, strong sublinearity theorems and the existence of random attractors for RFDEs are proved. Finally, criteria are presented for the existence of a unique random equilibrium and its global stability in the universe of all the tempered random closed sets of the positive cone. Applications to typical random or stochastic delay models in monotone dynamical systems,such as biochemical control circuits, cyclic gene models and Hopfield-type neural networks, are given.展开更多
In this paper some oscillation criteria are established for equation [q(t)y'] +a(t)f(y) = 0, where a(t) is not assumed to be non-negative and f(y) is nodecreasing in y, and yf(y) > 0 for y≠0, f(y) also satisf...In this paper some oscillation criteria are established for equation [q(t)y'] +a(t)f(y) = 0, where a(t) is not assumed to be non-negative and f(y) is nodecreasing in y, and yf(y) > 0 for y≠0, f(y) also satisfics a sublinear condition, q(t) is a positive function on [0, ). These results extend earlier oscillation theorems of Philos and Wong.展开更多
基金supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)Re-accompanying Funding Project of Academic Achievements of Jingdezhen Ceramic University(Grant Nos.215/20506277,215/20506341)。
文摘The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.
基金supported by the National Natural Science Foundation of China(12171106)the Guangxi Science and Technology Program(AD23023001)+4 种基金the Natural Science Foundation of Guangxi Province(2023GXNSFBA026029)the National Natural Science Foundation of China(12401403,12361063)the Research Project of Guangxi Minzu University(2022KJQD03)the Middle-aged and Young Teachers’Basic Ability Promotion Project of Guangxi Province(2023KY0168)the Xiangsihu Young Scholars Innovative Research Team of Guangxi Minzu University(2022GXUNXSHQN04).
文摘In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.
基金supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
基金revised September 27,2005.Research support by Natural Science Foundation of China(10271043)
文摘Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ） ＋ qnX^Bn-σ = 0, n ：0, 1, 2...which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10].
基金supported by the National Natural Science Foundation of China(11171262)the Specialized Research Fund for the Doctoral Program of Higher Education (200804860048)
文摘We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
基金Supported by the National Natural Science Foundation of China(71571001)
文摘Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients are either linear or nonlinear but bounded by linear functions, has been investigated intensively. Recently, the stability of highly nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper, by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.
文摘Let G be a locally compact Vilenkin gro up . We will establish the boundedness in Morrey spaces L p,λ (G) for a la rge class of sublinear operators and linear commutators.
文摘In a viscous damping device under cyclic loading, after the piston reaches a peak stroke, the reserve movement that follows may sometimes experience a short period of delayed or significantly reduced device force output. A similar delay or reduced device force output may also occur at the damper＇s initial stroke as it moves away from its neutral position. This phenomenon is referred to as the effect of ＂deadzone＂. The deadzone can cause a loss of energy dissipation capacity and less efficient vibration control. It is prominent in small amplitude vibrations. Although there are many potential causes of deadzone such as environmental factors, construction, material aging, and manufacture quality, in this paper, its general effect in linear and nonlinear viscous damping devices is analyzed. Based on classical dynamics and damping theory, a simple model is developed to capture the effect ofdeadzone in terms of the loss of energy dissipation capacity. The model provides several methods to estimate the loss of energy dissipation within the deadzone in linear and sublinear viscous fluid dampers. An empirical equation of loss of energy dissipation capacity versus deadzone size is formulated, and the equivalent reduction of effective damping in SDOF systems has been obtained. A laboratory experimental evaluation is carried out to verify the effect of deadzone and its numerical approximation. Based on the analysis, a modification is suggested to the corresponding formulas in FEMA 3 5 6 for calculation of equivalent damping if a deadzone is to be considered.
文摘In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.
基金Supported by the Youth Foundation of Shangqiu Institute of Technology(2018XKQ01)。
文摘This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential well V^-1(0).Combining this with other suitable assumptions on K and f,the existence of nontrivial solutions is obtained via variational methods.Furthermore,the concentration behavior of the nontrivial solution is also explored on the set V^-1(0)asλ→+∞as A—>H-oo as well.It is worth noting that the(PS)-condition can not be directly got as done in the literature,which makes the problem more complicated.To overcome this difficulty,we adopt different method.
基金This research is supported by NNSFC(1 9771 0 72 ) and ZNSF.And thanks to JNCASR in India Fortheir host when the firstauthor is
文摘It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the operator -Δ in the space H 1 0(Ω).
文摘In this paper,we study a class of sublinear Kirchhoff equations:-(a+b∫R_(N)|■u|^(2)dx)+△u+V(x)u=f(x,u)in R^(N),where a,b>0,V:R^(N)→R can be sign-changing,and f:R^(N)×R→R.Under some conditions on V and f,we verify that the problem possesses at least one energy solution by using variational method.
文摘The concept of upper variance under multiple probabilities is defined through a corresponding minimax optimization problem.This study proposes a simple algorithm to solve this optimization problem exactly.Additionally,we provide a probabilistic representation for a class of quadratic programming problems,demonstrating the practical application of our approach.
基金funded by the National Nature Science Foundation of China(Grant No.12001128)the GuangDong Basic and Applied Basic Research Foundation(Grant No.2022A1515011899).
文摘Sublinear expectation relaxes the linear property of classical expectation to subadditivity and positive homogeneity,which can be expressed as E(·)=sup_(θ∈θ) E_(θ)(·)for a certain set of linear expectations{E_(θ):θ∈θ}.Such a framework can capture the uncertainty and facilitate a robust method of measuring risk loss reasonably.This study established a law of large numbers for m-dependent random vectors within the framework of sublinear expectation.Consequently,the corresponding explicit rate of convergence were derived.The results of this study can be considered as an extension of the Peng's law of large numbers[22].
基金supported by Spanish project PID2022-139237NB-I00.
文摘The Shilkret integral or idempotent expectation is a sublinear functional which is very close to being a sublinear expectation since it satisfies all the required properties but its domain is not a linear space.In this paper,we prove that it admits a law of large numbers which is structurally similar to Peng's LLN for sublinear expectations although significant differences exist.As regards the central limit theorem,the situation is radically different as the Vn normalization can lead to a trivial limit and other normalizations are possible for variables with a finite second moment or even bounded.
基金supported by the National Natural Science Foundation of China(Nos.12326603,11601281,11501325)the National Key R&D Program of China(No.2018YFA0703900)+2 种基金the Natural Science Foundation of Shandong Province(No.ZR2021MA018)the Social Science Planning Project of Shandong Province(No.24CJJJ18)the Qilu Scholars Program of Shandong University。
文摘In this paper,the authors firstly establish the weak laws of large numbers on the canonical space(R^(N),B(R^(N)))by traditional truncation method and Chebyshev’s inequality as in the classical probability theory.Then they extend them from the canonical space to the general sublinear expectation space.The necessary and sufficient conditions for Peng’s law of large numbers are obtained.
文摘In this paper, the second order difference equation: △(rn△xn) + f(n, xn) = 0, n∈N(n0) (E) is considered. Some necessary and sufficient conditions for the oscillation of Eq.(E) are obtained.
基金supported by National Natural Science Foundation of China (Grant Nos.12171321, 11771295, 11371252 and 31770470)。
文摘In this paper, we study monotone properties of random and stochastic functional differential equations and their global dynamics. First, we show that random functional differential equations(RFDEs)generate the random dynamical system(RDS) if and only if all the solutions are globally defined, and establish the comparison theorem for RFDEs and the random Riesz representation theorem. These three results lead to the Borel measurability of coefficient functions in the Riesz representation of variational equations for quasimonotone RFDEs, which paves the way following the Smith line to establish eventual strong monotonicity for the RDS under cooperative and irreducible conditions. Then strong comparison principles, strong sublinearity theorems and the existence of random attractors for RFDEs are proved. Finally, criteria are presented for the existence of a unique random equilibrium and its global stability in the universe of all the tempered random closed sets of the positive cone. Applications to typical random or stochastic delay models in monotone dynamical systems,such as biochemical control circuits, cyclic gene models and Hopfield-type neural networks, are given.
文摘In this paper some oscillation criteria are established for equation [q(t)y'] +a(t)f(y) = 0, where a(t) is not assumed to be non-negative and f(y) is nodecreasing in y, and yf(y) > 0 for y≠0, f(y) also satisfics a sublinear condition, q(t) is a positive function on [0, ). These results extend earlier oscillation theorems of Philos and Wong.
