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91.
William B. Johnson N. Lovasoa Randrianarivony 《Proceedings of the American Mathematical Society》2006,134(4):1045-1050
We show that a Banach space with a normalized symmetric basis behaving like that of () cannot coarsely embed into a Hilbert space.
92.
R. Sauer 《Geometric And Functional Analysis》2006,16(2):476-515
Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated
to a topological coupling. As an application we obtain that the cohomological dimension cdR over a commutative ring R satisfies the inequality
if Λ embeds uniformly into Γ and
holds. Another consequence of our results is that the Hirsch ranks of quasi-isometric solvable groups coincide. Further,
it is shown that the real cohomology rings of quasi-isometric nilpotent groups are isomorphic as graded rings. On the analytic
side, we apply the induction technique to Novikov-Shubin invariants of amenable groups, which can be seen as homological invariants,
and show their invariance under quasi-isometry.
Received: November 2004 Revision: April 2004 Accepted: April 2004 相似文献
93.
Let T
n
be the complete binary tree of height n considered as the Hasse-diagram of a poset with its root 1
n
as the maximum element. For a rooted tree T, define two functions counting the embeddings of T into T
n
as follows A(n;T)=|{S
T
n
: 1
n
∈S, S≅T}|, and B(n;T)=|{S
T
n
:1
n
∉S, S≅T}|. In this paper we investigate the asymptotic behavior of the ratio A(n;T)/B(n;T), and we show that lim
n→∞[A(n;T)/B(n;T)]=2ℓ;−1−1, for any tree T with ℓ leaves.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
94.
Vitalij A. Chatyrko Elzbieta Pol 《Proceedings of the American Mathematical Society》2000,128(4):1207-1213
In this note we construct a family of continuum many hereditarily strongly infinite-dimensional Cantor manifolds such that for every two spaces from this family, no open subset of one is embeddable into the other.
95.
It will be shown that a normed partially ordered vector space is linearly, norm, and order isomorphic to a subspace of a normed Riesz space if and only if its positive cone is closed and its norm p satisfies p(x)p(y) for all x and y with -yxy. A similar characterization of the subspaces of M-normed Riesz spaces is given. With aid of the first characterization, Krein's lemma on directedness of norm dual spaces can be directly derived from the result for normed Riesz spaces. Further properties of the norms ensuing from the characterization theorem are investigated. Also a generalization of the notion of Riesz norm is studied as an analogue of the r-norm from the theory of spaces of operators. Both classes of norms are used to extend results on spaces of operators between normed Riesz spaces to a setting with partially ordered vector spaces. Finally, a partial characterization of the subspaces of Riesz spaces with Riesz seminorms is given. 相似文献
96.
WeiJieFENG 《数学学报(英文版)》2004,20(6):983-988
In this paper, we obtain some existence results for a class of singular semilinear elliptic problems where we improve some earlier results of Zhijun Zhang. We show the existence of entire positive solutions without the monotonic condition imposed in Zhang‘s paper. The main point of our technique is to choose an approximating sequence and prove its convergence. The desired compactness can be obtained by the Sobolev embedding theorems. 相似文献
97.
In this paper, we classify the regular embeddings of arc-transitive simple graphs of order pq for any two primes p and q (not necessarily distinct) into orientable surfaces. Our classification is obtained by direct analysis of the structure of arc-regular subgroups (with cyclic vertex-stabilizers) of the automorphism groups of such graphs. This work is independent of the classification of primitive permutation groups of degree p or degree pq for p q and it is also independent of the classification of the arc-transitive graphs of order pq for p q. 相似文献
98.
David L. Fearnley 《Proceedings of the American Mathematical Society》1999,127(10):3095-3100
The author answers a question raised in the literature about twenty five years ago and raised again more recently in Open Problems in Topology, by G. M. Reed, concerning the conjecture that every Moore space with a -discrete -base can be densely embedded in a Moore space having the Baire property. Even though closely related results have made this conjecture seem likely to be true, the author shows that, surprisingly, the conjecture is false.
99.
We show that every sub-weak embedding of any singular (degenerate or not) orthogonal or unitary polar space of non-singular rank at least 3 in a projective space PG
,
a commutative field, is the projection of a full embedding in some subspace PG
of PG
, where PG
contains PG
and
is a subfield of
. The same result is proved in the symplectic case under the assumption that the field over which the polarity is defined is perfect if the characteristic is 2 and if each secant line of the embedded polar space contains exactly two points of . This completes the classification of all sub-weak embeddings of orthogonal, symplectic and unitary polar spaces (singular or not; degenerate or not) of non-singular rank at least 3 and defined over a commutative field
, where in the characteristic 2 case
is perfect if the polar space is symplectic and the degree of the embedding is 2. 相似文献
100.
Klaus Metsch 《Designs, Codes and Cryptography》1997,10(2):251-263
We show that every non-degenerate planar space with v points and planes can be embedded as a linear space into PG(3,q) for some prime power q provided that 1000( - v) v5/6; 相似文献