Very recently, we have found that the method used in our recent paper （appeared in 2005） could be extended to obtain two general series-transformation formulas for formal power series defined over the complex number...Very recently, we have found that the method used in our recent paper （appeared in 2005） could be extended to obtain two general series-transformation formulas for formal power series defined over the complex number field. As usual, △, △k, D, and Dk denote, respectively, the difference and differential operators with △f（t） = f（t ＋ 1） - f（t）, Dr（t） = （d/dr）f （t） and △^0 = D0 = 1 （the identity operator）. What we have obtained are the following two general transformation formulas （formal expansion formulas） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=0△^kf（0）φ^（k）（0）t^k/k! （1） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=01/k!f（0）φ^（k）（0）t^k/k! （2）展开更多
This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, suf...This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established展开更多
Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed bas...Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed based on the multiresolution design strategy(MRDS)and the additive hyperelasticity technique(AHT),taking into account the geometric nonlinearity and material nonlinearity.The MR-NTO strategy is established in the framework of the solid isotropic material with penalization(SIMP)method,while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity.The coarse analysis grid is employed for finite element(FE)calculation,and the fine material grid is applied to describe the material configuration.To alleviate the convergence problem and reduce sensitivity calculation complexity,the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation.A strategy for redistributing strain energy is proposed during the sensitivity analysis,i.e.,transforming the strain energy of the analysis element into that of the material element,including Neo-Hooken and second-order Yeoh material.Numerical examples highlight three distinct advantages of the proposed method,i.e.,it can(1)significantly improve the computational efficiency,(2)make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem,especially for 3D problems,(3)successfully cope with high-resolution 3D complex NTO problems on a personal computer.展开更多
In the PnP problem,the imaging devices follow the perspective rule and the imaging rays pass through a common point. However,there are many new imaging devices being developed for robot navigation or other fields with...In the PnP problem,the imaging devices follow the perspective rule and the imaging rays pass through a common point. However,there are many new imaging devices being developed for robot navigation or other fields with the advance in imaging technologies for machine vision. These devise are not necessarily being designed to follow the perspective rule in order to satisfy some design criterion and,thus, the imaging rays may not pass through a common point.Such generalized imaging devices may not be perspective and, therefore, their poses cannot be estimated with traditional perspective technique.Using the Wu-Ritt＇s zero decomposition method,the main component for the nonperspective-three-point problem is given. We prove that there are at most eight solutions in the general case and give the solution classification for the NP3P problem.展开更多
Abstract The authors consider one specific kind of heat transfer problems in a threedimensional layered domain, with nonlinear Stefan-Boltzmann conditions on the boundaries as well as on the interfaces. To determine t...Abstract The authors consider one specific kind of heat transfer problems in a threedimensional layered domain, with nonlinear Stefan-Boltzmann conditions on the boundaries as well as on the interfaces. To determine the unknown part of the boundary （or corrosion） by the Cauchy data on the reachable part is an important inverse problem in engineering. The mathematical model of this problem is introduced, the well-posedness of the forward problems and the uniqueness of the inverse problems are obtained.展开更多
In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified. Starting from the three-dimensional nonlinear Signorini problem, by an asymptotic approach the convergence of ...In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified. Starting from the three-dimensional nonlinear Signorini problem, by an asymptotic approach the convergence of the displacement field as the thickness of the plate goes to zero is studied. It is shown that the transverse mechanical displacement field decouples from the in-plane components and solves an obstacle problem.展开更多
A closed orientable Haken 3-manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation.Heegaard distanc...A closed orientable Haken 3-manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation.Heegaard distance introduced by Hempel is a useful index in studying Heegaard splitting. This paper studies the stabilization problem for the bilateral self-amalgamation, and proves that if the distance of bilateral selfamalgamation of a Heegaard splitting is at least 9, then it is unstabilized, weakly reducible and irreducible.展开更多
基金the Natural Science Foundation of Gansu Province of China
文摘Very recently, we have found that the method used in our recent paper （appeared in 2005） could be extended to obtain two general series-transformation formulas for formal power series defined over the complex number field. As usual, △, △k, D, and Dk denote, respectively, the difference and differential operators with △f（t） = f（t ＋ 1） - f（t）, Dr（t） = （d/dr）f （t） and △^0 = D0 = 1 （the identity operator）. What we have obtained are the following two general transformation formulas （formal expansion formulas） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=0△^kf（0）φ^（k）（0）t^k/k! （1） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=01/k!f（0）φ^（k）（0）t^k/k! （2）
基金the Tutorial Scientific Research Program Foundation of Education Department of Gansu Province (Nos. 0710-040810-03)
文摘This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established
基金supported by the National Natural Science Foundation of China(Grant Nos.11902085 and 11832009)the Science and Technology Association Young Scientific and Technological Talents Support Project of Guangzhou City(Grant No.SKX20210304)the Natural Science Foundation of Guangdong Province(Grant No.2021Al515010320).
文摘Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed based on the multiresolution design strategy(MRDS)and the additive hyperelasticity technique(AHT),taking into account the geometric nonlinearity and material nonlinearity.The MR-NTO strategy is established in the framework of the solid isotropic material with penalization(SIMP)method,while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity.The coarse analysis grid is employed for finite element(FE)calculation,and the fine material grid is applied to describe the material configuration.To alleviate the convergence problem and reduce sensitivity calculation complexity,the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation.A strategy for redistributing strain energy is proposed during the sensitivity analysis,i.e.,transforming the strain energy of the analysis element into that of the material element,including Neo-Hooken and second-order Yeoh material.Numerical examples highlight three distinct advantages of the proposed method,i.e.,it can(1)significantly improve the computational efficiency,(2)make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem,especially for 3D problems,(3)successfully cope with high-resolution 3D complex NTO problems on a personal computer.
基金This project was partially supported by Shuxue Tianyuan Foundation(No.10526031).
文摘In the PnP problem,the imaging devices follow the perspective rule and the imaging rays pass through a common point. However,there are many new imaging devices being developed for robot navigation or other fields with the advance in imaging technologies for machine vision. These devise are not necessarily being designed to follow the perspective rule in order to satisfy some design criterion and,thus, the imaging rays may not pass through a common point.Such generalized imaging devices may not be perspective and, therefore, their poses cannot be estimated with traditional perspective technique.Using the Wu-Ritt＇s zero decomposition method,the main component for the nonperspective-three-point problem is given. We prove that there are at most eight solutions in the general case and give the solution classification for the NP3P problem.
基金supported by the Shanghai Natural Science Foundation of China (No.07JC14001)the Doctoral Program Foundation of the Ministry of Education of China+2 种基金the Tianyuan Fund for Mathematics (No.10826105)the National Basic Research Program (No.2005CB321701)the 111 Project (No.B08018)
文摘Abstract The authors consider one specific kind of heat transfer problems in a threedimensional layered domain, with nonlinear Stefan-Boltzmann conditions on the boundaries as well as on the interfaces. To determine the unknown part of the boundary （or corrosion） by the Cauchy data on the reachable part is an important inverse problem in engineering. The mathematical model of this problem is introduced, the well-posedness of the forward problems and the uniqueness of the inverse problems are obtained.
基金Project supported by the Innovation Program of Shanghai Municipal Education Commission(No.11YZ80)the Program of Shanghai Normal University(No.SK201301)
文摘In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified. Starting from the three-dimensional nonlinear Signorini problem, by an asymptotic approach the convergence of the displacement field as the thickness of the plate goes to zero is studied. It is shown that the transverse mechanical displacement field decouples from the in-plane components and solves an obstacle problem.
基金supported by National Natural Science Foundation of China(Grant Nos.11271058 and 11371076)the Fundamental Research Funds for the Central Universities(Grant No.DUT14ZD208)
文摘A closed orientable Haken 3-manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation.Heegaard distance introduced by Hempel is a useful index in studying Heegaard splitting. This paper studies the stabilization problem for the bilateral self-amalgamation, and proves that if the distance of bilateral selfamalgamation of a Heegaard splitting is at least 9, then it is unstabilized, weakly reducible and irreducible.
