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131.
The closed model category of exterior spaces, that contains the proper category, is a useful tool for the study of non compact
spaces and manifolds. The notion of exterior weak ℕ-S-equivalences is given by exterior maps which induce isomorphisms on the k-th ℕ-exterior homotopy groups for k ∈ S, where S is a set of non negative integers. The category of exterior spaces with a base ray localized by exterior weak ℕ-S-equivalences is called the category of exterior ℕ-S-types. The existence of closed model structures in the category of exterior spaces permits to establish equivalences between
homotopy categories obtained by dividing by exterior homotopy relations, and categories of fractions (localized categories)
given by the inversion of classes of week equivalences. The family of neighbourhoods ‘at infinity’ of an exterior space can
be interpreted as a global prospace and under the condition of first countable at infinity we can consider a global tower
instead of a prospace. The objective of this paper is to use localized categories to find the connection between S-types of exterior spaces and S-types of global towers of spaces. The main result of this paper establishes an equivalence between the category of S-types of rayed first countable exterior spaces and the category of S-types of global towers of pointed spaces. As a consequence of this result, categories of global towers of algebraic models
localized up to weak equivalences can be used to give some algebraic models of S-types.
The authors acknowledge the financial support given by the projects FOMENTA 2007/03 and MTM2007-65431. 相似文献
132.
Gabriela Jeronimo Guillermo Matera Pablo Solernó Ariel Waissbein 《Foundations of Computational Mathematics》2009,9(1):1-50
We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems. Our algorithm combines a symbolic
homotopy procedure, based on a flat deformation of a certain morphism of affine varieties, with the polyhedral deformation
of Huber and Sturmfels. The complexity of our algorithm is cubic in the size of the combinatorial structure of the input system.
This size is mainly represented by the cardinality and mixed volume of Newton polytopes of the input polynomials and an arithmetic
analogue of the mixed volume associated to the deformations under consideration.
Research was partially supported by the following grants: UBACyT X112 (2004–2007), UBACyT X847 (2006–2009), PIP CONICET 2461,
PIP CONICET 5852/05, ANPCyT PICT 2005 17-33018, UNGS 30/3005, MTM2004-01167 (2004–2007), MTM2007-62799 and CIC 2007–2008. 相似文献
133.
分析了壁面具有不同渗透的涨缩管道内微极性流体的流动.对于壁面的胀缩,考虑常系数和时间函数的膨胀率两种情况.对于第1种情况,应用同伦分析方法得到该问题的速度和微旋转角度的表达式.并且画图分析了各个不同参数,特别是膨胀系数和不同的渗透率对流体的动力特征的影响.可以得到第1个重要的结论:壁面的膨胀率和不同的渗透对流体的动力特征有重要的影响.根据Xu的模型,考虑了第2种也是更具有一般性的情况,假设壁面的膨胀率随时间的变化而变化.在这样的假设下,控制方程被转化成非线性偏微分方程,并且同样也可以应用HAM方法进行求解.应用代数和指数的模型来描述膨胀率从初始状态到最终状态的演变过程.然而,结果表明包含有时间的解很快地趋向于稳态的解.这样可以得到第2个重要的结论,时间在壁面的膨胀收缩中扮演着次要的角色,可以忽略不计. 相似文献
134.
Ga&scaron per Jaklič Jernej Kozak Marjeta Krajnc Vito Vitrih & Emil Žagar 《高等学校计算数学学报(英文版)》2014,7(3):374-398
In this paper, the $G^2$ interpolation by Pythagorean-hodograph (PH) quintic curves in $\mathbb{R}^d$, $d ≥2$, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension $d$, they supply a $G^2$ quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as unknowns. Although several solutions might exist, the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case. The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method. Numerical examples confirm the efficiency of the proposed method. 相似文献
135.
Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong. 相似文献
136.
The unsteady,laminar,incompressible,and two-dimensional flow of a micropolar fluid between two orthogonally moving porous coaxial disks is considered.The extension of von Karman’s similarity transformations is used to reduce the governing partial differential equations(PDEs) to a set of non-linear coupled ordinary differential equations(ODEs) in the dimensionless form.The analytical solutions are obtained by employing the homotopy analysis method(HAM).The effects of various physical parameters such as the expansion ratio and the permeability Reynolds number on the velocity fields are discussed in detail. 相似文献
137.
Impact of Linear Operator on the Convergence of HAM Solution: A Modified Operator Approach
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S. T. Hussain S. Nadeem & M. Qasim 《advances in applied mathematics and mechanics.》2016,8(3):499-516
The linear operator plays an important role in the computational process of
Homotopy Analysis Method (HAM). In HAM frame any kind of linear operator can
be chosen to develop a solution. Hence, it is easy to introduce the modified/physical
parameter dependent linear operators. The effective use of these operators has been
judged through solving fluid flow problems. Modification in linear operators affects
the solution and improves the computational efficiency of HAM for larger values of
parameters. The convergence rate of the solution is rapid and several times higher
resulting in less computational time. 相似文献
138.
A. Allahverdizadeh R. Oftadeh M. J. Mahjoob M. It. Naei 《Acta Mechanica Solida Sinica》2014,27(2):210-220
In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman's dynamic equations. Functionaily Graded Material (FGM) properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing's equation. The homotopy perturbation solution of generated Duffing's equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green's function and Schauder's fixed point theorem. 相似文献
139.
140.
In this paper, we propose new technique for solving stiff system of ordinary differential equations. This algorithm is based on Laplace transform and homotopy perturbation methods. The new technique is applied to solving two mathematical models of stiff problem. We show that the present approach is relatively easy, efficient and highly accurate. 相似文献