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51.
We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian
group of rank 3.
Both authors are supported by the NSF grants DMS-0308985 and DMS-0456185. Yaroslav Vorobets is supported by a Clay Research
Scholarship. 相似文献
52.
几种约束广义逆矩阵的有限算法 总被引:2,自引:0,他引:2
陈永林 《高等学校计算数学学报》1997,19(3):232-240
1引言与引理众所周知,关于非奇异方阵的正则逆的有限算法是由Faddeev大给在1949年之前提出的,这就是著名的Faddeev算法[1,P…334-336]。自从五十年代中期广义逆矩阵的研究复兴与发展以来,有不少学者提出了关于广义逆矩阵的有限算法。第一个给出关于广义逆矩 相似文献
53.
Philip T. Keenan 《Numerical Algorithms》1994,7(2):269-293
We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations. 相似文献
54.
This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear
dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency
trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional
in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge
symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold
fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried
out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching
the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade
to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons
discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely
indicates a new science paradigm in the economy and society domains beyond physics.
相似文献
55.
If M is an isoparametric hypersurface in a sphere S
n
with four distinct principal curvatures, then the principal curvatures κ1, . . . , κ4 can be ordered so that their multiplicities satisfy m
1 = m
2 and m
3 = m
4, and the cross-ratio r of the principal curvatures (the Lie curvature) equals −1. In this paper, we prove that if M is an irreducible connected proper Dupin hypersurface in R
n
(or S
n
) with four distinct principal curvatures with multiplicities m
1 = m
2 ≥ 1 and m
3 = m
4 = 1, and constant Lie curvature r = −1, then M is equivalent by Lie sphere transformation to an isoparametric hypersurface in a sphere. This result remains true if the
assumption of irreducibility is replaced by compactness and r is merely assumed to be constant.
相似文献
56.
Radu Miron 《Reports on Mathematical Physics》2004,54(2):131-147
The Randers spaces RFn were introduced by R. S. Ingarden. They are considered as Finsler spaces Fn = (M, α + β) equipped with the Cartan nonlinear connection. In the present paper we define and study what we call the Ingarden spaces, I Fn, as Finsler spaces I Fn = (M, α + β) equipped with the Lorentz nonlinear connection. The spaces R Fn and I Fn are completely different. For I Fn we discuss: the variational problem, Lorentz nonlinear connection, canonical N-metrical connection and its structure equations, the Cartan 1-form ω, the electromagnetic 2-form tF and the almost symplectic 2-form 0. The formula dω = F+θ is established. It has as a consequence the generalized Maxwell equations. Finally, the almost Hermitian model of I Fn is constructed. 相似文献
57.
Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis
for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also
apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible
dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our
algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.
相似文献
58.
59.
60.
M. D. Warren 《国际流体数值方法杂志》1983,3(3):217-225
This paper derives the convection–diffusion-reaction equation governing the reaction between the dissolved oxygen in sea-water and the steel walls of a pulsating crack. By the neglect of the diffusion term it is shown that an exact solution of the convection-reaction equation can be obtained. A numerical method for the solution of the complete convection–diffusion-reaction equation is derived by the use of finite differences. The numerical computation of the initial transient and the final periodic steady-state values is also discussed. 相似文献