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31.
Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m-manifolds to the bundle functor K
A
of Weil contact elements and the subalgebra of fixed elements SA of the Weil algebra A is determined and the bijection between all natural affinors on K
A
and SA is deduced. Furthermore, the rigidity of the functor K
A
is proved. Requisite results about the structure of SA are obtained by a purely algebraic approach, namely the existence of nontrivial SA is discussed. 相似文献
32.
A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
33.
We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature. 相似文献
34.
In Leitmann (Ref. 1), a coordinate transformation method was introduced to obtain global solutions for free problems in the calculus of variations. This direct method was extended and broadened in Carlson (Ref. 2) and later in Leitmann (Ref. 3). The applicability of the original work of Leitmann (Ref. 1) was further developed in Dockner and Leitmann (Ref. 4) to include the class of open-loop dynamic games. In the present work, we improve the results of Ref. 4 in two directions. First, we enlarge the class of open-loop dynamic games to permit coupling among the dynamic equations via the states of the players; second, we incorporate the modifications given in Refs. 2 and 3. Our results greatly increase the applicability of this method. An example arising from the harvesting of a renewable resource is presented to illustrate the utility of our results. 相似文献
35.
M. Markl 《Czechoslovak Mathematical Journal》2007,57(1):473-503
The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology
of various types of algebras. It contains a lot of very surprising partial results and examples. 相似文献
36.
本文推导了两种非标准色传感器在测色时引入的误差公式,并对其进行分析。最后通过计算8个样品的颜色对分析结果给于验证。 相似文献
37.
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40.
Alternatives based on polynomial expansions of gaussian basis set exponents are introduced and evaluated. The formulas presented here outperform methods based upon the even-tempered formula or combinations of it. They closely match the performance of other methods based upon larger polynomial expansions of the logarithm of the exponents using the same or one less parameter per orbital angular symmetry. 相似文献