There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given...There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.展开更多
If n given control, points b_0,…b_(n-1)∈R^d are repeated periodically by b_(i+kn)=b_i, for all k∈Z. the uform limit of the Bernstein-Bezier polynomial curves of degree r with control points b_0,….b_ for r→∞ is a...If n given control, points b_0,…b_(n-1)∈R^d are repeated periodically by b_(i+kn)=b_i, for all k∈Z. the uform limit of the Bernstein-Bezier polynomial curves of degree r with control points b_0,….b_ for r→∞ is a Poisson curve(after a suitable reparametrization). This fact reveals some interesting self-simi- lar structures in case of regular n-gons in the plane.展开更多
The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （...The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （RVE） is selected to reflect the microstructures of the composite materials and the constituents are assumed to be elastic perfectly-plastic. Based on the homogenization theory and the static limit theorem, an optimization formulation to directly calculate the macroscopic strength domain of the RVE is obtained. The finite element modeling of the static limit analysis is formulated as a nonlinear mathematical programming and solved by the sequential quadratic programming method, where the temperature parameter method is used to construct the self-stress field. Secondly, Hill＇s yield criterion is adopted to connect the micromechanicai and macromechanical analyses. And the limit loads of composite structures are worked out on the macroscopic scale. Finally, some examples and comparisons are shown.展开更多
The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. ...The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. In this research work we study the dynamics of a bead sliding on a wire with a given specified shape. A long wire is bent into the shape of a curve with equation z = f (x) in a fixed vertical plane. We consider two cases, namely without friction and with friction, specifically for the cubic shape f (x) = x3−x . We derive the corresponding differential equation of motion representing the dynamics of the bead. We then study the resulting second order nonlinear ordinary differential equations, by performing simulations using MathCAD 14. Our main interest is to investigate the existence of periodic solutions for this dynamics in the neighbourhood of the critical points. Our results show clearly that periodic solutions do indeed exist for the frictionless case, as the phase portraits exhibit isolated limit cycles in the phase plane. For the case with friction, the phase portrait depicts a spiral sink, spiraling into the critical point.展开更多
In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the lin...In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.展开更多
基金Supported by the National Natural Science Foundation of china
文摘There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.
文摘If n given control, points b_0,…b_(n-1)∈R^d are repeated periodically by b_(i+kn)=b_i, for all k∈Z. the uform limit of the Bernstein-Bezier polynomial curves of degree r with control points b_0,….b_ for r→∞ is a Poisson curve(after a suitable reparametrization). This fact reveals some interesting self-simi- lar structures in case of regular n-gons in the plane.
基金supported by the National Natural Science Foundation of China (No.50809003)the National Foundation for Excellent Doctorial Dissertation of China (200025).
文摘The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （RVE） is selected to reflect the microstructures of the composite materials and the constituents are assumed to be elastic perfectly-plastic. Based on the homogenization theory and the static limit theorem, an optimization formulation to directly calculate the macroscopic strength domain of the RVE is obtained. The finite element modeling of the static limit analysis is formulated as a nonlinear mathematical programming and solved by the sequential quadratic programming method, where the temperature parameter method is used to construct the self-stress field. Secondly, Hill＇s yield criterion is adopted to connect the micromechanicai and macromechanical analyses. And the limit loads of composite structures are worked out on the macroscopic scale. Finally, some examples and comparisons are shown.
文摘The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. In this research work we study the dynamics of a bead sliding on a wire with a given specified shape. A long wire is bent into the shape of a curve with equation z = f (x) in a fixed vertical plane. We consider two cases, namely without friction and with friction, specifically for the cubic shape f (x) = x3−x . We derive the corresponding differential equation of motion representing the dynamics of the bead. We then study the resulting second order nonlinear ordinary differential equations, by performing simulations using MathCAD 14. Our main interest is to investigate the existence of periodic solutions for this dynamics in the neighbourhood of the critical points. Our results show clearly that periodic solutions do indeed exist for the frictionless case, as the phase portraits exhibit isolated limit cycles in the phase plane. For the case with friction, the phase portrait depicts a spiral sink, spiraling into the critical point.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61272069,61272114,61073026,61170031,and 61100076)
文摘In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.
