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21.
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
22.
Alejandro Balbs Raquel Balbs Silvia Mayoral 《Mathematical and Computer Modelling》2007,45(11-12):1308-1318
The first Fundamental Theorem of Asset Pricing establishes the equivalence between the absence of arbitrage in financial markets and the existence of Equivalent Martingale Measures, if appropriate conditions hold. Since the theorem may fail when dealing with infinitely many trading dates, this paper draws on the A.A. Lyapunov Theorem in order to retrieve the equivalence for complete markets such that the Sharpe Ratio is adequately bounded. 相似文献
23.
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
24.
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
25.
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
26.
27.
The aim of this article is to give a new dynamical proof of the Ferrand–Obata theorem when the manifold is compact. This will give us a generalisation of this theorem to transversally conformal foliations ofcodimension greater than three and constant basic functions. 相似文献
28.
本文对几类B值小指标鞅空间建立了原子分解定理,利用原子分解讨论了它们之间的相互嵌入关系,其原子分解的存在性和它们之间的关系均与Banach空间的凸性和光滑性有密切联系. 相似文献
29.
30.
A phenanthridinium salt was prepared in four steps, including an intramolecular CH-arylation and a hydride abstraction reaction. Treatment with sterically demanding bases does not lead to the corresponding carbene, but rather to addition products: the planar-constrained geometry significantly enhances the electrophilicity over the acidity of C-aryl iminium salts. 相似文献