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81.
82.
Martin Raussen 《Applied Categorical Structures》2007,15(4):355-386
Directed spaces are the objects of study within directed algebraic topology. They are characterised by spaces of directed
paths associated to a source and a target, both elements of an underlying topological space. The algebraic topology of these
path spaces and their connections are studied from a categorical perspective. In particular, we study the preorder category
associated to a directed space and various “quotient” categories arising from algebraic topological functors. Furthermore,
we propose and study a new notion of directed homotopy equivalence between directed spaces.
相似文献
83.
Sergio Benenti 《Acta Appl Math》2005,87(1-3):33-91
A general analysis of special classes of symmetric two-tensor on Riemannian manifolds is provided. These tensors arise in connection with special topics in differential geometry and analytical mechanics: geodesic equivalence and separation of variables. It is shown that they play an important role in the theory of correspondent (or equivalent) dynamical systems of Levi-Civita. By applying some new developments of this theory, it is shown that the recent notions of cofactor and cofactor-pair systems arise in a natural way, as non-Lagrangian systems having a Lagrangian equivalent. This circumstance extends the Hamiltonian methods, including the separation of variables of the Hamilton–Jacobi equation, to a special class of nonconservative systems. In this extension the case of indefinite metrics, may occur. Hence, it is shown that also pseudo-Riemannian geometry plays an important role also in classical mechanics.Research sponsored by the Dept. of Mathematics, University of Turin, and by INDAM-GNFM. 相似文献
84.
F. Fang 《Commentarii Mathematici Helvetici》1997,72(3):466-480
Let X
n
(d) and X
n
(d') be two n-dimensional complete intersections with the same total degree d. In this paper we prove that, if n is even and d has no prime factors less than , then X
n
(d) and X
n
(d') are homotopy equivalent if and only if they have the same Euler characteristics and signatures. This confirms a conjecture
of Libgober and Wood [16]. Furthermore, we prove that, if d has no prime factors less than , then X
n
(d) and X
n
(d') are homeomorphic if and only if their Pontryagin classes and Euler characteristics agree.
Received: September 6, 1996 相似文献
85.
设P(G,λ)是图G关于变量λ的色多项式,P(G,λ)=P(H,λ),称G和H色等价,由连接两个顶点的S条内部不交的路组成的图叫S-桥图。本讨论了5-桥图F(2,a,a,b,c)(c≥b≥a 1,a≥2)的色性,完整刻画了这类图的色等价图。 相似文献
86.
We describe the problem of the equivalence of ensembles at the level of states for classical lattice systems. We discuss circumstances where the vanishing of the specific information gain of a sequence of microcanonical measures with respect to a sequence of grand canonical measures implies the equivalence of ensembles. We give a simple derivation of a criterion for the vanishing of the specific information gain in terms of thermodynamic functions. The proof uses ideas from the theory of large deviations but is self-contained. We show how the criterion works in a simple model of a paramagnet and in the Ising model of a ferromagnet in any dimension but fails in the case of the Curie-Weiss mean-field model. 相似文献
87.
B. Z. Shavarovskii 《Mathematical Notes》1998,64(5):663-673
The structure of polynomial matrices in connection with their reducibility by semiscalar-equivalent transformations and similarity
transformations to simpler forms is considered. In particular, the canonical form of polynomial matrices without multiple
characteristic roots with respect to the above transformations is indicated. This allows one to establish a canonical form
with respect to similarity for a certain type of finite collections of numerical matrices.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 769–782, November, 1998. 相似文献
88.
Ron Tzur 《The Journal of Mathematical Behavior》2004,23(1):93-114
Within a constructivist perspective, I conducted a teaching experiment with two fourth graders to study how a teacher and students can jointly produce the reversible fraction conception. Ongoing and retrospective analysis of the data revealed the non-trivial process by which students can abstract multiplicative reasoning about fractions. The study articulates a conception in a developmental sequence of iteration-based fraction conceptions and the teacher’s role in fostering such a conception in students. 相似文献
89.
We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K
0-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify the semiclassical limit of bimodule deformations as contravariant connections and study the associated deformation quantization problem. Our main focus is on formal deformation quantization of Poisson manifolds by star products. 相似文献
90.
LetE andF be two Borel sets of the countable productZ of the two point space {0,1}. Assume thatE andF are invariant sets for the odometer transformationR and thatE andF are of measure zero with respect to the unique finiteR-invariant measure onZ. We show thatE andF areR-orbit equivalent in a strict sense. 相似文献