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排序方式: 共有337条查询结果,搜索用时 15 毫秒
31.
Michael R. Kelly 《Topology and its Applications》2011,158(16):2210-2215
A fixed point detection theorem for a family of maps defined on the once punctured torus is proved. As a consequence, we produce an example of a homotopy class [f] of self-maps on the once punctured torus that illustrates the following: (i) there is a map in the homotopy class that has no fixed points, and (ii) if the image of f lies in a 1-complex that embeds as a homotopy equivalence, then f must have a fixed point. 相似文献
32.
Takefumi Nosaka 《Topology and its Applications》2011,158(8):996-1011
For a quandle X, the quandle space BX is defined, modifying the rack space of Fenn, Rourke and Sanderson (1995) [13], and the quandle homotopy invariant of links is defined in Z[π2(BX)], modifying the rack homotopy invariant of Fenn, Rourke and Sanderson (1995) [13]. It is known that the cocycle invariants introduced in Carter et al. (2005) [3], Carter et al. (2003) [5], Carter et al. (2001) [6] can be derived from the quandle homotopy invariant.In this paper, we show that, for a finite quandle X, π2(BX) is finitely generated, and that, for a connected finite quandle X, π2(BX) is finite. It follows that the space spanned by cocycle invariants for a finite quandle is finitely generated. Further, we calculate π2(BX) for some concrete quandles. From the calculation, all cocycle invariants for those quandles are concretely presented. Moreover, we show formulas of the quandle homotopy invariant for connected sum of knots and for the mirror image of links. 相似文献
33.
This article combines the application of a global analysis approach and the more classical continuation, bifurcation and stability analysis approach of a cyclic symmetric system. A solid disc with four blades, linearly coupled, but with an intrinsic non-linear cubic stiffness is at stake. Dynamic equations are turned into a set of non-linear algebraic equations using the harmonic balance method. Then periodic solutions are sought using a recursive application of a global analysis method for various pulsation values. This exhibits disconnected branches in both the free undamped case (non-linear normal modes, NNMs) and in a forced case which shows the link between NNMs and forced response. For each case, a full bifurcation diagram is provided and commented using tools devoted to continuation, bifurcation and stability analysis. 相似文献
34.
WANG Zhen ZOU Li ZHANG Hong-Qing 《理论物理通讯》2008,49(6):1373-1378
In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows that homotopy analysis method is effective and validity in solving hybrid nonlinear problems, including solitary solution of difference-differential equation. 相似文献
35.
The number of trials that is required by an algorithm to produce a given fraction of the problem solutions with a specified level of confidence is analyzed. The analysis indicates that the number of trials required to find a large fraction of the solutions rapidly decreases as the number of solutions obtained on each trial by an algorithm increases. In applications where multiple solutions are sought, this decrease in the number of trials could potentially offset the additional computational cost of algorithms that produce multiple solutions on a single trial. The analysis framework presented is used to compare the efficiency of a homotopy algorithm to that of a Newton method by measuring both the number of trials and the number of calculations required to obtain a specified fraction of the solutions. 相似文献
36.
Schematization of networks 总被引:2,自引:0,他引:2
We study the problem of computing schematized versions of network maps, like railroad or highway maps. Every path of the schematized map has two or three links with restricted orientations, and the schematized map must be topologically equivalent to the input map. Our approach can handle several types of schematizations, and certain additional constraints can be added, such as a minimum vertical distance between two paths. Our algorithm runs in O(nlogn) time, and experimental results showing the quality of the output are given. 相似文献
37.
This paper studies the effects of a circular magnetic field on the flow of a conducting fluid about a porous rotating disk. Using modern quasi-Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magnetic field strengths, suction and injection velocities and Alfven and disk speeds. Results are presented graphically in terms of three non-dimensional parameters. There is excellent agreement with previous work and asymptotic formulae. 相似文献
38.
Michael J. Todd 《Mathematical Programming》1982,24(1):216-224
We show that piecewise-linear homotopy algorithms may take a number of steps that grows exponentially with the dimension when solving a system of linear equations whose solution lies close to the starting point. Our examples are based on an example of Murty exhibiting exponential growth for Lemke's algorithm for the linear complementarity problem.This research was supported in part by NSF grant ECS-7921279 and by a Guggenheim Fellowship. 相似文献
39.
Homotopy continuation methods can be applied to compute all finite solutions to a given polynomial system. Computations will be performed more efficiently if the symmetric structure of the system can be exploited. This paper presents the construction of a symmetric homotopy. Using this homotopy, only the paths according to the generating solutions have to be traced during continuation. 相似文献
40.
Lin Junmin 《数学年刊B辑(英文版)》1998,19(2):153-156
§1.IntroductionLetM3beacomplete,noncompactRiemannianmanifold,andRicciMbeitsRicicurvature.SchoenYau[1]provedthefolowingTheor... 相似文献