Henri Poincare's intuitive concept of the linear continuum was described by his famous remark which was noted by Bertrand Russell, and in which the notion of 'intimate bond' first appeared. This semi-expos...Henri Poincare's intuitive concept of the linear continuum was described by his famous remark which was noted by Bertrand Russell, and in which the notion of 'intimate bond' first appeared. This semi-expository paper gives an exposition of Poincare's remark, and also aims at a formulation of the intimate bond with the aid of introducing a kind of 'leap structure' into Robinson's *R as a supplemental construction. As a result, we obtain a kind of hyperstandard model that may be called 'Poincare continuum'.展开更多
In this paper,with Poincare's formalism,and an indirect method,the canonical forms of the generalized equations of motion due to Nielsen and Cenov of a holonomic dynamical system in the velocity-phase space and th...In this paper,with Poincare's formalism,and an indirect method,the canonical forms of the generalized equations of motion due to Nielsen and Cenov of a holonomic dynamical system in the velocity-phase space and the acenleration-phase space are obtained in terms of the Poincare parameters.展开更多
In this paper, the author extends Ren's results in plane to the case of R2n,i.e., estimates the kinematic measure of a convex domain D1 with boundary Σ1 moving to another domain D0 with boundary Σ0 under the iso...In this paper, the author extends Ren's results in plane to the case of R2n,i.e., estimates the kinematic measure of a convex domain D1 with boundary Σ1 moving to another domain D0 with boundary Σ0 under the isometry group G in R2n. A sufficient condition for D0 contain D1 by using kinematic foundamatal formula and Poincare's formula in Rn is obtained.展开更多
By discussing the relation between the method of Poincare's transformation and the method of Bendixsion's transformation which are used to analyse the behavior of singular points at infinity, a formula for ind...By discussing the relation between the method of Poincare's transformation and the method of Bendixsion's transformation which are used to analyse the behavior of singular points at infinity, a formula for index of a singular point of polynomial differential system in the plane is deduced. It is convenient to use the formula in this paper to calculate the index of a singular point with higher order.展开更多
In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type.An explicit L2 norm estimate for the gradient of the solution of this problem is est...In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type.An explicit L2 norm estimate for the gradient of the solution of this problem is established.This leads to an explicit bound of the H1 norm of this solution.Note that the obtained upper-bound is not optimal.展开更多
文摘Henri Poincare's intuitive concept of the linear continuum was described by his famous remark which was noted by Bertrand Russell, and in which the notion of 'intimate bond' first appeared. This semi-expository paper gives an exposition of Poincare's remark, and also aims at a formulation of the intimate bond with the aid of introducing a kind of 'leap structure' into Robinson's *R as a supplemental construction. As a result, we obtain a kind of hyperstandard model that may be called 'Poincare continuum'.
基金This paper was presented at the International Congress of Mathematicians(ICM),21—29 August,1990,Kyoto University,Japan.
文摘In this paper,with Poincare's formalism,and an indirect method,the canonical forms of the generalized equations of motion due to Nielsen and Cenov of a holonomic dynamical system in the velocity-phase space and the acenleration-phase space are obtained in terms of the Poincare parameters.
文摘In this paper, the author extends Ren's results in plane to the case of R2n,i.e., estimates the kinematic measure of a convex domain D1 with boundary Σ1 moving to another domain D0 with boundary Σ0 under the isometry group G in R2n. A sufficient condition for D0 contain D1 by using kinematic foundamatal formula and Poincare's formula in Rn is obtained.
文摘By discussing the relation between the method of Poincare's transformation and the method of Bendixsion's transformation which are used to analyse the behavior of singular points at infinity, a formula for index of a singular point of polynomial differential system in the plane is deduced. It is convenient to use the formula in this paper to calculate the index of a singular point with higher order.
文摘In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type.An explicit L2 norm estimate for the gradient of the solution of this problem is established.This leads to an explicit bound of the H1 norm of this solution.Note that the obtained upper-bound is not optimal.
