共查询到20条相似文献,搜索用时 109 毫秒
1.
HANXI'AN HUANGXILI 《高校应用数学学报(英文版)》1998,13(4):445-450
For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments. 相似文献
2.
In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary. 相似文献
3.
In this paper,the Uzawa iteration algorithm is applied to the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind.Firstly, the multiplier in a convex set is introduced such that the variational inequality is equivalent to the variational identity.Moreover,the solution of the variational identity satisfies the saddle-point problem of the Lagrangian functional ?.Subsequently,the Uzawa algorithm is proposed to solve the solution of the saddle-point problem. We show the convergence of the algorithm and obtain the convergence rate.Finally,we give the numerical results to verify the feasibility of the Uzawa algorithm. 相似文献
4.
Ding-kang WANG~ Yan ZHANG Key Laboratory of Mathematics Mechanization Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2007,50(10):1441-1450
We present an algorithm to decompose a polynomial system into a finite set of normal ascending sets such that the set of the zeros of the polynomial system is the union of the sets of the regular zeros of the normal ascending sets.If the polynomial system is zero dimensional,the set of the zeros of the polynomials is the union of the sets of the zeros of the normal ascending sets. 相似文献
5.
求解一种带有微分方程约束的条件变分问题的多目标最优化方法 总被引:1,自引:0,他引:1
李乃成 《高等学校计算数学学报》2003,25(4):289-295
Aiming at the conditional variational problem with the bi-objective functionals and the differential equational constraint in the optimal design of the electrostatic lenses, the conditional variational problem is transformed into multi-objective optimization problem by means of the spline function and the integral transformation. For solving the transformed problem, the analytic representation formula of the optimal solution about the original problem is obtained with regard to the voltage distribution and the electron trajectory. It will provide a new effective method for the design of the electrostatic lenses. 相似文献
6.
《应用数学年刊》2019,(4)
Consider the n-dimensional incompressible Navier-Stokes equations ?/(?t)u-α△u +(u · ?)u + ?p = f(x, t), ? · u = 0, ? · f = 0,u(x, 0) = u0(x), ? · u0= 0.There exists a global weak solution under some assumptions on the initial function and the external force. It is well known that the global weak solutions become sufficiently small and smooth after a long time. Here are several very interesting questions about the global weak solutions of the Cauchy problems for the n-dimensional incompressible Navier-Stokes equations.· Can we establish better decay estimates with sharp rates not only for the global weak solutions but also for all order derivatives of the global weak solutions?· Can we accomplish the exact limits of all order derivatives of the global weak solutions in terms of the given information?· Can we use the global smooth solution of the linear heat equation, with the same initial function and the external force, to approximate the global weak solutions of the Navier-Stokes equations?· If we drop the nonlinear terms in the Navier-Stokes equations, will the exact limits reduce to the exact limits of the solutions of the linear heat equation?· Will the exact limits of the derivatives of the global weak solutions of the Navier-Stokes equations and the exact limits of the derivatives of the global smooth solution of the heat equation increase at the same rate as the order m of the derivative increases? In another word, will the ratio of the exact limits for the derivatives of the global weak solutions of the Navier-Stokes equations be the same as the ratio of the exact limits for the derivatives of the global smooth solutions for the linear heat equation?The positive solutions to these questions obtained in this paper will definitely help us to better understand the properties of the global weak solutions of the incompressible Navier-Stokes equations and hopefully to discover new special structures of the Navier-Stokes equations. 相似文献
7.
ZHOU Yulin YUAN Guangwei SHEN Longjun Laboratory of Computational Physics Center of Nonlinear Studies Institute of Applied Physics Computational Mathematics Beijing China 《中国科学A辑(英文版)》2004,47(3):453-472
A kind of the general finite difference schemes with intrinsic parallelism forthe boundary value problem of the quasilinear parabolic system is studied without assum-ing heuristically that the original boundary value problem has the unique smooth vectorsolution. By the method of a priori estimation of the discrete solutions of the nonlineardifference systems, and the interpolation formulas of the various norms of the discretefunctions and the fixed-point technique in finite dimensional Euclidean space, the exis-tence and uniqueness of the discrete vector solutions of the nonlinear difference systemwith intrinsic parallelism are proved. Moreover the unconditional stability of the generalfinite difference schemes with intrinsic parallelism is justified in the sense of the continu-ous dependence of the discrete vector solution of the difference schemes on the discretedata of the original problems in the discrete w_2~(2,1) norms. Finally the convergence of thediscrete vector solutions of the certain differe 相似文献
8.
Guang-wei YUAN Xu-deng HANG Zhi-qiang SHENG Laboratory of Computational Physics Institute of Applied Physics Computational Mathematics Beijing China 《中国科学A辑(英文版)》2007,50(2):253-275
In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism. 相似文献
9.
We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe fireworks is mathematically easy, this article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution by means of methods taken from the famous work by DiPerna & Lions about the Boltzmann equation. We also show both the regularity and the time-asymptotic behavior of solution to the Cauchy problem. 相似文献
10.
The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of the discrete functional analysis, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general difference schemes with intrinsic parallelism justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete initial data of the original problems in the discrete W_2~(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original semilinear parabolic problem is proved. 相似文献
11.
Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep
under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the
experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological
creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the
stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation
and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem
confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between
the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction
in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference
in their porosity.
Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.)
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000. 相似文献
12.
Peridynamics via finite element analysis 总被引:2,自引:0,他引:2
Peridynamics is a recently developed theory of solid mechanics that replaces the partial differential equations of the classical continuum theory with integral equations. Since the integral equations remain valid in the presence of discontinuities such as cracks, the method has the potential to model fracture and damage with great generality and without the complications of mathematical singularities that plague conventional continuum approaches. Although a discretized form of the peridynamic integral equations has been implemented in a meshless code called EMU, the objective of the present paper is to describe how the peridynamic model can also be implemented in a conventional finite element analysis (FEA) code using truss elements. Since FEA is arguably the most widely used tool for structural analysis, this implementation may hasten the verification of peridynamics and significantly broaden the range of problems that the practicing analyst might attempt. Also, the present work demonstrates that different subregions of a model can be solved with either the classical partial differential equations or the peridynamic equations in the same calculation thus combining the efficiency of FEA with the generality of peridynamics. Several example problems show the equivalency of the FEA and the meshless peridynamic approach as well as demonstrate the utility and robustness of the method for problems involving fracture, damage and penetration. 相似文献
13.
V. P. Stavrov V. V. Stavrov N. V. Pankova K. Friedrich 《Mechanics of Composite Materials》2000,36(2):155-162
The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final
composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned
fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions
formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned
fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity
of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the
internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective
permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation.
Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000. 相似文献
14.
Brian H. Gilding Mohammed Guedda 《Journal of Mathematical Analysis and Applications》2003,284(2):733-755
With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained. 相似文献
15.
Classical approaches to location problems are based on the minimization of the average distance (the median concept) or the minimization of the maximum distance (the center concept) to the service facilities. The median solution concept is primarily concerned with the spatial efficiency while the center concept is focused on the spatial equity. The k-centrum model unifies both the concepts by minimization of the sum of the k largest distances. In this paper we investigate a solution concept of the conditional median which is a generalization of the k-centrum concept taking into account the portion of demand related to the largest distances. Namely, for a specified portion (quantile) of demand we take into account the entire group of the corresponding largest distances and we minimize their average. It is shown that such an objective, similar to the standard minimax, may be modeled with a number of simple linear inequalities. Equitable properties of the solution concept are examined. 相似文献
16.
含有批处理机的三机流水作业加工总长问题在某些情形下的强NP困难性 总被引:2,自引:0,他引:2
本文研究含有批处理机的三台机器流水作业加工总长问题在某些情形下的计算复杂性。在批处理机上同时加工的工件组成一个工件批,一个工件批的所有工件同时开始、同时结束。当批处理机的容量有限时,我们证明了下列情形为强NP困难的:第一台机器是批处理机、其余两台机器是单机;第二台机器是单机、其余两台机器是批处理机;第三台机器是批处理机、其余两台机器是单机。 相似文献
17.
K. Petras 《Constructive Approximation》1998,14(2):231-245
We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain
complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented.
This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error
constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas
and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively
for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally
symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the
optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the
constant weight function and arguments outside the interval of integration.
September 7, 1995. Date revised: October 25, 1996. 相似文献
18.
Dynamical spin susceptibility is calculated for the t–J model in the superconducting phase using the memory function method in terms of the Hubbard operators. The self-consistent system of equations for the memory function is obtained within the mode-coupling approximation. Both itinerant hole excitations and localized spin fluctuations contribute to the memory function. Moreover, the itinerant contribution itself consists of two parts, i.e., the contribution of Bogoliubov quasiparticles and that of Cooper pairs. The spin dynamics is diffusive in the hydrodynamic limit, but the itinerant part does not contribute to the spin diffusion. In the high frequency region, spin–wave-like excitations continue to exist. We discuss our analytic results in the light of neutron scattering experiments performed on the cuprate superconductors. 相似文献
19.
The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning
precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be
able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening
of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are
highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete.
The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The
effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross
section are analyzed. A simple iterative design method for the shear debonding is finally proposed.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008. 相似文献
20.
基于VAR风险指标的投资组合模糊优化 总被引:6,自引:0,他引:6
在二目标有价证券选择基础上 ,引入目前流行的风险指标 VAR,以收益率与风险损失为目标 ,将模糊概念运用于有价证券组合选择 ,按投资者给定的期望目标及容差 ,讨论了 S型隶属函数模型 .通过 VAR的给定 ,将投资者所能承受的最大损失锁定 ,更好地反映出投资者对目标值的取值意图 .依据深圳股票市场9只股票收益率数据 ,采用进化规划进行优化计算 ,并验证模型的有效性 . 相似文献