Applying the integral a priori estimates method, the existence and uniqueness ofthe global solution for the dissipative Hasegawa-Mima equation with initial periodic bound-ary condition was proved.
A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two a...A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.展开更多
This paper considers the scalar differential delay equation x（t） -μ x（t）-f（x（t-τ））, where f（x） is a decreasing continuous function. By proving that all solutions will beultimately in some interval, we give...This paper considers the scalar differential delay equation x（t） -μ x（t）-f（x（t-τ））, where f（x） is a decreasing continuous function. By proving that all solutions will beultimately in some interval, we give tile conditions under which the unique equilibrium pointof the differential delay equation is globally attractive.展开更多
In this paper, the authors propose a class of Dai-Yuan （abbr. DY） conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their ite...In this paper, the authors propose a class of Dai-Yuan （abbr. DY） conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is xk＋1 = xk ＋ αk（sk ＋ ωk）, where the main direction sk is obtained by DY conjugate gradient method, ωk is perturbation term, and stepsize αk is determined by linesearch which does not tend to zero in the limit necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported.展开更多
We study the blow-up and/or global existence of the following p-Laplacian evolution equation with variable source power where Ω is either a bounded domain or the whole space RN and q（x） is a positive and continuous...We study the blow-up and/or global existence of the following p-Laplacian evolution equation with variable source power where Ω is either a bounded domain or the whole space RN and q（x） is a positive and continuous function defined in with 0 〈 q- infq（x） = q（x） 〈 ∞supq（x） = q＋ 〈 ∞. It is demonstrated that the equation with variable source power has much richer dynamics with interesting phenomena which depends on the interplay of q（x） and the structure of spatial domain Ω, compared with the case of constant source power. For the case that is a bounded domain, the exponent p - 1 plays a crucial role. If q＋ 〉 p - 1, there exist blow-up solutions, while if q＋ p - 1, all the solutions are global. If q-〉 p - 1, there exist global solutions, while for given q- 〈 p - 1 〈 q＋, there exist some function q（x） and such that all nontrivial solutions will blow up, which is called the Fujita phenomenon. For the case Ω = RN the Fujita phenomenon occurs if 1 q＋ q＋ ≤p--1＋p/N, while if q_ 〉 p -- 1 ＋p/N there exist global solutions.展开更多
Let X={X(t),t 0} be a process with independent increments (PII)such that E=0, D X(t)E 2<∞, lim t→∞D X(t)t=1, and there exists a majoring measure G for the jump △X of X . Under these assu...Let X={X(t),t 0} be a process with independent increments (PII)such that E=0, D X(t)E 2<∞, lim t→∞D X(t)t=1, and there exists a majoring measure G for the jump △X of X . Under these assumptions, using rather a direct method, a Strassen's law of the iterated logarithm (Strassen LIL) is established. As some special cases,the Strassen LIL for homogeneous PII and for partial sum process of i.i.d.random variables are comprised.展开更多
In this paper, a trust region method for equality constrained optimizationbased on nondifferentiable exact penalty is proposed. In this algorithm, the trail step ischaracterized by computation of its normal component ...In this paper, a trust region method for equality constrained optimizationbased on nondifferentiable exact penalty is proposed. In this algorithm, the trail step ischaracterized by computation of its normal component being separated from computation of itstangential component, i.e., only the tangential component of the trail step is constrained by trustradius while the normal component and trail step itself have no constraints. The other maincharacteristic of the algorithm is the decision of trust region radius. Here, the decision of trustregion radius uses the information of the gradient of objective function and reduced Hessian.However, Maratos effect will occur when we use the nondifferentiable exact penalty function as themerit function. In order to obtain the superlinear convergence of the algorithm, we use the twiceorder correction technique. Because of the speciality of the adaptive trust region method, we usetwice order correction when p = 0 (the definition is as in Section 2) and this is different from thetraditional trust region methods for equality constrained optimization. So the computation of thealgorithm in this paper is reduced. What is more, we can prove that the algorithm is globally andsuperlinearly convergent.展开更多
The electronic structure and possible electronic orders in monolayer NbF4 are investigated by density functional theory and functional renormalization group.Because of the niobium-centered octahedra,the energy band ne...The electronic structure and possible electronic orders in monolayer NbF4 are investigated by density functional theory and functional renormalization group.Because of the niobium-centered octahedra,the energy band near the Fermi level is found to derive from the 4 dxyorbital,well separated from the other bands.Local Coulomb interaction drives the undoped system into an antiferromagnetic insulator.Upon suitable electron/hole doping,the system is found to develop dx2à-y2 wave superconductivity with sizable transition temperature.Therefore,the monolayer NbF4 may be an exciting 4d1 analogue of cuprates,providing a new two-dimensional platform for high-Tc superconductivity.展开更多
基金Supported by the Natural Science Foundation of Henan Educational Committee(2003110005)Supported by the Natural Science Foundation of Henan University(XK02069)
文摘Applying the integral a priori estimates method, the existence and uniqueness ofthe global solution for the dissipative Hasegawa-Mima equation with initial periodic bound-ary condition was proved.
基金Supported by the National Science Foundation of China(10171118)Supported by the Science Foundation of University of Science and Technology of Henan(2003ZY06)
文摘A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.
文摘This paper considers the scalar differential delay equation x（t） -μ x（t）-f（x（t-τ））, where f（x） is a decreasing continuous function. By proving that all solutions will beultimately in some interval, we give tile conditions under which the unique equilibrium pointof the differential delay equation is globally attractive.
基金The work is supported by the National Natural Science Foundation of China under Grant No.10571106.
文摘In this paper, the authors propose a class of Dai-Yuan （abbr. DY） conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is xk＋1 = xk ＋ αk（sk ＋ ωk）, where the main direction sk is obtained by DY conjugate gradient method, ωk is perturbation term, and stepsize αk is determined by linesearch which does not tend to zero in the limit necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported.
基金supported by Shanxi Bairen Plan of China and Ng-Jhit-Cheong Foundation
文摘We study the blow-up and/or global existence of the following p-Laplacian evolution equation with variable source power where Ω is either a bounded domain or the whole space RN and q（x） is a positive and continuous function defined in with 0 〈 q- infq（x） = q（x） 〈 ∞supq（x） = q＋ 〈 ∞. It is demonstrated that the equation with variable source power has much richer dynamics with interesting phenomena which depends on the interplay of q（x） and the structure of spatial domain Ω, compared with the case of constant source power. For the case that is a bounded domain, the exponent p - 1 plays a crucial role. If q＋ 〉 p - 1, there exist blow-up solutions, while if q＋ p - 1, all the solutions are global. If q-〉 p - 1, there exist global solutions, while for given q- 〈 p - 1 〈 q＋, there exist some function q（x） and such that all nontrivial solutions will blow up, which is called the Fujita phenomenon. For the case Ω = RN the Fujita phenomenon occurs if 1 q＋ q＋ ≤p--1＋p/N, while if q_ 〉 p -- 1 ＋p/N there exist global solutions.
文摘Let X={X(t),t 0} be a process with independent increments (PII)such that E=0, D X(t)E 2<∞, lim t→∞D X(t)t=1, and there exists a majoring measure G for the jump △X of X . Under these assumptions, using rather a direct method, a Strassen's law of the iterated logarithm (Strassen LIL) is established. As some special cases,the Strassen LIL for homogeneous PII and for partial sum process of i.i.d.random variables are comprised.
基金This research is supported in part by the National Natural Science Foundation of China(Grant No. 39830070,10171055)and China Postdoctoral Science Foundation
文摘In this paper, a trust region method for equality constrained optimizationbased on nondifferentiable exact penalty is proposed. In this algorithm, the trail step ischaracterized by computation of its normal component being separated from computation of itstangential component, i.e., only the tangential component of the trail step is constrained by trustradius while the normal component and trail step itself have no constraints. The other maincharacteristic of the algorithm is the decision of trust region radius. Here, the decision of trustregion radius uses the information of the gradient of objective function and reduced Hessian.However, Maratos effect will occur when we use the nondifferentiable exact penalty function as themerit function. In order to obtain the superlinear convergence of the algorithm, we use the twiceorder correction technique. Because of the speciality of the adaptive trust region method, we usetwice order correction when p = 0 (the definition is as in Section 2) and this is different from thetraditional trust region methods for equality constrained optimization. So the computation of thealgorithm in this paper is reduced. What is more, we can prove that the algorithm is globally andsuperlinearly convergent.
基金the National Key Research and Development Program of China(2016YFA0300401)the National Natural Science Foundation of China(11604303,11604168 and 11574134)+1 种基金the Texas Center for Superconductivity at the University of Houston and the Robert A.Welch Foundation(E-1146)the support from China Scholarship Council(201909440001)。
文摘The electronic structure and possible electronic orders in monolayer NbF4 are investigated by density functional theory and functional renormalization group.Because of the niobium-centered octahedra,the energy band near the Fermi level is found to derive from the 4 dxyorbital,well separated from the other bands.Local Coulomb interaction drives the undoped system into an antiferromagnetic insulator.Upon suitable electron/hole doping,the system is found to develop dx2à-y2 wave superconductivity with sizable transition temperature.Therefore,the monolayer NbF4 may be an exciting 4d1 analogue of cuprates,providing a new two-dimensional platform for high-Tc superconductivity.
