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41.
In this article we make a full study of the class of non-degenerate real planar quadratic differential systems having all
points at infinity (in the Poincaré compactification) as singularities. We prove that all such systems have invariant affine
lines of total multiplicity 3, give all their configurations of invariant lines and show that all these systems are integrable
via the method of Darboux having cubic polynomials as inverse integrating factors. After constructing the topologically distinct
phase portraits in this class we give invariant necessary and sufficient conditions in terms of the 12 coefficients of the
systems for the realization of each one of them and give representatives of the orbits under the action of the affine group
and time rescaling. We construct the moduli space of this class for this action and give the corresponding bifurcation diagram.
Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday 相似文献
42.
43.
A VIP system is a polynomial-type generalization of the notion of an IP system, i.e., a set of finite sums. We extend the notion of VIP system to commutative partial semigroups and obtain an analogue of Furstenberg's central sets theorem for these systems which extends the polynomial Hales–Jewett Theorem of Bergelson and Leibman. Several Ramsey theoretic consequences, including the central sets theorem itself, are then derived from these results. 相似文献
44.
Enrico Leuzinger 《Differential Geometry and its Applications》2004,20(3):141-318
The results in this paper are based on a previously constructed exhaustion of a locally symmetric space V=ΓX by Riemannian polyhedra, i.e., compact submanifolds with corners: V=s0V(s). We show that the interior of every polyhedron V(s) is homeomorphic to V. The universal covering space X(s) of V(s) is quasi-isometric to the discrete group Γ. It can be written as the complement of a Γ-invariant union of horoballs in X (which in general have intersections giving rise to the corners). This yields exponential isoperimetric inequalities for Γπ1(V(s)). We also discuss the relation of this compactification of V with the Borel–Serre compactification. 相似文献
45.
Wojciech Chojnacki 《Letters in Mathematical Physics》1991,22(1):7-10
We prove that every eigenvalue of a Schrödinger operator with an almost periodic potential acting in the space of all square Haar-integrable functions on the Bohr compactification of has multiplicity not greater than 2. 相似文献
46.
S. K. Acharyya K. C. Chattopadhyay D. P. Ghosh 《Proceedings of the American Mathematical Society》1997,125(2):611-615
Let be a Tychonoff space and a subalgebra of containing . Suppose that is the set of all functions in with compact support. Kohls has shown that is precisely the intersection of all the free ideals in or in . In this paper we have proved the validity of this result for the algebra . Gillman and Jerison have proved that for a realcompact space , is the intersection of all the free maximal ideals in . In this paper we have proved that this result does not hold for the algebra , in general. However we have furnished a characterisation of the elements that belong to all the free maximal ideals in . The paper terminates by showing that for any realcompact space , there exists in some sense a minimal algebra for which becomes -compact. This answers a question raised by Redlin and Watson in 1987. But it is still unsettled whether such a minimal algebra exists with respect to set inclusion.
47.
Consider a manifold with boundary, and such that the interior is equipped with a pseudo-Riemannian metric. We prove that, under mild asymptotic non-vanishing conditions on the scalar curvature, if the Levi-Civita connection of the interior does not extend to the boundary (because for example the interior is complete) whereas its projective structure does, then the metric is projectively compact of order 2; this order is a measure of volume growth towards infinity. This implies a host of results including that the metric satisfies asymptotic Einstein conditions, and induces a canonical conformal structure on the boundary. Underpinning this work is a new interpretation of scalar curvature in terms of projective geometry. This enables us to show that if the projective structure of a metric extends to the boundary then its scalar curvature also naturally and smoothly extends. 相似文献
48.
Themba Dube 《Topology and its Applications》2010,157(14):2159-2331
Given a completely regular frame L, let, as usual, βL, λL and υL denote, respectively, the Stone-?ech compactification, the universal Lindelöfication and the Hewitt realcompactification of L. Let γ denote any of the functors β, λ or υ. It is well known that any frame homomorphism h:L→M has a unique “lift” to a frame homomorphism hγ:γL→γM such that σM⋅hγ=h⋅σL, where the σ-maps are effected by join. We find a condition on h such that if h satisfies it, then h is open iff its lift hγ is open. Furthermore, the same condition ensures that hγ is nearly open iff h is nearly open. This latter result is, in fact, a special case of a more general phenomenon. In the last part of the paper we investigate when hυ is surjective. The instances when hβ or hλ is surjective are known. It turns out that the surjectivity of the lifted map hυ:υL→υM captures Blair's notion of υ-embedding in the sense that a subspace S of a Tychonoff space X is υ-embedded iff the lifted map υ(Oi):υ(OX)→υ(OS) is surjective, where i:S→X is the subspace embedding. 相似文献
49.
50.
We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that a topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other hand, we construct a (consistent) example of a pseudocompact (countably compact) Tychonoff semigroup containing a copy of C(p,q). 相似文献