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91.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
92.
A recent analysis of the experimental data on some physical phenomena ruled by the four fundamental interactions (electromagnetic, weak, strong and gravitational) seems to show the possibility of describing such interactions in terms of a deformation of the usual Minkowski spacetime, with a metric whose coefficients do depend on the energy of the process considered. In this paper, we show that such results can be accounted for in terms of a Kaluza-Klein-like scheme, based on a five-dimensional Riemannian space in which energy plays the role of the fifth dimension. The corresponding five-dimensional Einstein equations in vacuum are solved in some cases of physical relevance and it is shown that all the phenomenological metrics describing the four fundamental forces are recovered as special cases of the classes of solutions found. Possible developments of the formalism are also briefly outlined. 相似文献
93.
本文从 H_O_2的电极反应的氧化反应和还原反应半反应入手,结合热办学原理和偶合反应原理,运用自由能变与电极电势的关系从理论上解释了 H_2O_2在酸碱性介质中氧化还原性存在极大差异的原因. 相似文献
94.
95.
We discuss boosts in a deformed Minkowski space, i.e., a four-dimensional spacetime with metric coefficients depending on nonmetric coordinates (in particular on the energy). The general form of a boost in an arbitrary direction is derived in the case of space anisotropy. Two maximal trivector velocities are mathematically possible, an isotropic and an anisotropic one. However, only the anisotropic velocity has physical meaning, being invariant indeed under deformed boosts. 相似文献
96.
在分析自来水的潜在危害、家用净水器及长期饮用纯净水的不足的基础上 ,提出了分质分区供水的构想 ,探讨了分质供水、分区供水的技术保障 ,并进行了分质分区供水的经济效益分析。 相似文献
97.
By using hyperbolic virtual unit of Clifford algebra, the concept of n-dimensional space-time unit spheres is introduced. It is used as n-dimensional Minkowski space-time and Lorentz transformation. 相似文献
98.
Clifford algebraic geometry corresponds to Minkowski space. Using the discrete structure of Minkowski space, we can abstract
a class n-dimensional hyperbolic Hilbert phase space. To discussing the causality of physical event in Minkowski space, we
can obtain the geometrical interpretation of uncertainty relation. 相似文献
99.
K. Pichard 《Set-Valued Analysis》2003,11(2):111-132
We introduce a new operation for the difference of two sets A and C of R
n
depending on a parameter . This new operation may yield as special cases the classical difference and the Minkowski difference, if the sets A and C are closed, convex sets, if int(C) is nonempty, and if A or C bounded. Continuity properties with respect to both the operands and the parameter of this operation are studied. Lipschitz properties of the Minkowski difference between two sets of a normed vector space are proved in the bounded case as well as in the unbounded case without condition on the dimension of the space. 相似文献
100.
采用扩阶方法(使响应系统和驱动系统的维数相同),把不同阶数混沌系统的广义同步问题转化为相同阶数混沌系统之间的广义同步,基于Lyapunov稳定性定理和自适应控制方法(用于相同阶数混沌系统的同步),给出了自适应控制器和参数自适应律,进而实现了不同阶数混沌系统的广义同步.将该方法应用于参数未知的超Lü,Lorenz,广义Lorenz和Liu等系统之间的广义混沌同步,理论证明了该方法可以使这些系统达到渐近广义同步,并且可以辨识驱动系统和响应系统的所有参数,数值模拟进一步证明了该方法的有效性. 相似文献