共查询到20条相似文献,搜索用时 0 毫秒
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Marilyn Breen 《Israel Journal of Mathematics》1976,24(3-4):211-216
LetS be a closedm-convex subset of the plane,m≧2,Q the set of points of local nonconvexity ofS, with convQ ⊆S. If there is some pointp in [(bdryS) ∩ (kerS)] ∼Q, thenS is a union ofm−1 closed convex sets. The result is best possible for everym. 相似文献
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Heiko Ewert 《Proceedings of the American Mathematical Society》1998,126(8):2443-2452
A submanifold in a symmetric space is called equifocal if it has a globally flat abelian normal bundle and its focal data is invariant under normal parallel transportation. This is a generalization of the notion of isoparametric submanifolds in Euclidean spaces. To each equifocal submanifold, we can associate a Coxeter group, which is determined by the focal data at one point. In this paper we prove that an equifocal submanifold in a simply connected compact symmetric space is a non-trivial product of two such submanifolds if and only if its associated Coxeter group is decomposable. As a consequence, we get a similar splitting result for hyperpolar group actions on compact symmetric spaces. These results are an application of a splitting theorem for isoparametric submanifolds in Hilbert spaces by Heintze and Liu.
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Let D ⊂ ℜ2 be simply connected. A subset K ⊂ D is relatively convex if a, b ∈ K, [a, b] ⊂ D implies [a, b] ⊂ K. We establish the following version of Helly’s Topological Theorem: If
is a family of (at least 3) compact, polygonally connected and relatively convex subsets of D, then
, provided each three members of
meet.
We also prove other results related to the combinatorial metric ρK(a, b) (= smallest number of edges of a polygonal path from a to b in K). 相似文献
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A. O. Prishlyak 《Ukrainian Mathematical Journal》1994,46(12):1907-1913
A theorem on the existence of the unique minimal topologic handle decomposition of differentiable simply connected five-dimensional manifolds is proved. For a decomposition of this sort, the number of handles of each index is given.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 12, pp. 1714–1720, December, 1994.This research was partially supported by the International Scientific Foundation, grant No. V6F000. 相似文献
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Marilyn Breen 《Discrete Mathematics》1982,41(2):131-138
A set S in is said to be χ-convex if and only if S does not contain a visually independent subset having cardinality χ. It is natural to ask when an χ-convex set may be expressed as a countable union of convex sets. Here it is proved that if S is a closed χ-convex set in the plane and has at most finitely many bounded components, then S is a countable union of convex sets. A parallel result holds in when S is a closed χ-convex set which contains all triangular regions whose relative boundaries are in S. However, the result fails for arbitrary χ-convex sets, even in the plane. 相似文献
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Daniel Neuenschwander 《Journal of Theoretical Probability》1995,8(1):165-174
A limit theorem due to J. Kuelbs and M. Ledoux, valid for dilatation-stable laws on type 2-Banach spaces, is carried over to stable laws on simply connected step 2-nilpotent Lie groupsG. We show that for products of i.i.d. random variables in the of attraction of a nondegenerate semigroup onG, where is a one-parameter automorphism group acting contracting onG, a certain intermediate trimming procedure, together with a suitable norming, always yields a nondegenerate centered Gaussian limit. 相似文献
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We discuss a problem to reconstruct the measurable sets in the plane from their fixed finite projections. In the main theorem, we construct an example of connected and simply connected polygons which are not uniquely reconstructed by their fixed finite projections. We also make a comparison between our main theorem and the known results on this problem. 相似文献
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Rolf Kultze 《manuscripta mathematica》1990,69(1):31-42
LetX be a connected, locally finite spectrum and letk(n) (n>-1) denote the (−1)-connected cover of then-th MoravaK-Theory associated to the primep.k(n) is aBP-module spectrum with π*(k(n)) ≅ ℤ
p
[υ
n
] where |v
n
| = 2(p
n
-1). We prove the following splitting theorem: Thek(n)
*-torsion ofk(n)
* (X) is already annihilated byv
n
e
(e≥1) if and only ifk(n)ΛX is homotopy equivalent to a wedge of spectrak(n) and
r
k(n) (0≤r≤e-1) where
r
k(n) denotes ther-th Postnikov factor ofk(n). Moreover we investigate splitting conditions for
r
k(n)ΛX. 相似文献
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Antonia Chinnì 《Rendiconti del Circolo Matematico di Palermo》1921,45(1):5-8
In this paper we give a complete answer to a question which naturally arises in comparing classical results of F. E. Browder and K. Fan on sets with convex sections with a recent result of B. Ricceri on sets with connected sections. 相似文献
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Imme van den Berg 《Annals of Pure and Applied Logic》2010,161(7):851-865
Neutrices are convex additive subgroups of the nonstandard space Rk, most of them are external sets. Because of the convexity and the invariance under some translations and multiplications, external neutrices are models for orders of magnitude. One dimensional neutrices have been applied to asymptotics, singular perturbations, and statistics. This paper shows that in Rk, with standard k, every neutrix is the direct sum of k neutrices of R. These components may be chosen to be orthogonal. 相似文献
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I. Lizasoain 《数学学报(英文版)》2010,26(3):405-418
Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups (G-groups). In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible. 相似文献
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Fernando Bombal Ignacio Villanueva 《Journal of Mathematical Analysis and Applications》2007,336(2):1316-1323
We prove that every countably additive polymeasure can be decomposed in a unique way as the sum of a “discrete” polymeasure plus a “continuous” polymeasure. This generalizes a previous result of Saeki. 相似文献
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Dr. J. D. Maitland Wright 《Mathematische Zeitschrift》1970,115(5):387-391
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Let A be a representation-finite simply connected algebra, and TAbe an arbitrary tilting module (in the sense of Happei and Ringel). We show that B = End TA satisfies the separation condition of Bautista, Larrion and Salmeron. This implies that B is also simply connected. 相似文献
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Klaus Bongartz 《manuscripta mathematica》1984,46(1-3):117-136
It is well-known that simply connected algebras are uniquely determined by a graded tree.Reversely,each graded tree gives rise to a not necessarily representation-finite algebra. We call an algebra critical provided it is not representation-finite, but any proper convex full subalgebra is.All critical algebras arising from graded trees are classified. 相似文献
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M. Laczkovich 《Proceedings of the American Mathematical Society》2002,130(10):3085-3089
We prove that if is a perfect Polish space and is a partition with universally measurable pieces, then there is Cantor set with for some
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In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed Herman map is developed. It's shown that every Herman map can be decomposed along a stable multicurve into finitely many Siegel maps and Thurston maps, such that the combinations and rational realizations of these resulting maps essentially dominate the original one. This result is motivated by a non-expanding version of McMullen's problem, and Thurston's theory on characterization of rational maps. It enables us to prove a Thurston-type theorem for rational maps with Herman rings. 相似文献