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1.
The aim of the present paper is to introduce a metric locally convex topology on the space
of δ-psh functions in the Cegrell class
. We prove that with this topology
is a non-separable and non-reflexive Fréchet space. At the same time, we extend the Monge–Ampère operator from the class
to
. 相似文献
2.
Simon M. Goberstein 《Algebra Universalis》2005,53(4):407-432
A partial automorphism of a semigroup S is any isomorphism between its subsemigroups, and the set all partial automorphisms of S with respect to composition is an inverse monoid called the partial automorphism monoid of S. Two semigroups are said to be
if their partial automorphism monoids are isomorphic. A class
of semigroups is called
if it contains every semigroup
to some semigroup from
Although the class of all inverse semigroups is not
we prove that the class of inverse semigroups, in which no maximal isolated subgroup is a direct product of an involution-free periodic group and the two-element cyclic group, is
It follows that the class of all combinatorial inverse semigroups (those with no nontrivial subgroups) is
A semigroup is called
if it is isomorphic or antiisomorphic to any semigroup that is
to it. We show that combinatorial inverse semigroups which are either shortly connected [5] or quasi-archimedean [10] are
To Ralph McKenzieReceived April 15, 2004; accepted in final form October 7, 2004. 相似文献
3.
Özden Koruoğlu Recep Sahin Sebahattin İkikardes 《Bulletin of the Brazilian Mathematical Society》2007,38(1):51-65
We consider the extended Hecke groups
generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups
. Then, we determine the abstract group structure of the commutator subgroups
, the even subgroup
, and the power subgroups
of the extended Hecke groups
. Also, finally, we give some relations between them. 相似文献
4.
For an l-graph
, the Turán number
is the maximum number of edges in an n-vertex l-graph
containing no copy of
. The limit
is known to exist [8]. The Ramsey–Turán density
is defined similarly to
except that we restrict to only those
with independence number o(n). A result of Erdős and Sós [3] states that
as long as for every edge E of
there is another edge E′of
for which |E∩E′|≥2. Therefore a natural question is whether there exists
for which
.
Another variant
proposed in [3] requires the stronger condition that every set of vertices of
of size at least εn (0<ε<1) has density bounded below by some threshold. By definition,
for every
. However, even
is not known for very many l-graphs
when l>2.
We prove the existence of a phenomenon similar to supersaturation for Turán problems for hypergraphs. As a consequence, we
construct, for each l≥3, infinitely many l-graphs
for which
.
We also prove that the 3-graph
with triples 12a, 12b, 12c, 13a, 13b, 13c, 23a, 23b, 23c, abc, satisfies
. The existence of a hypergraph
satisfying
was conjectured by Erdős and Sós [3], proved by Frankl and R?dl [6], and later by Sidorenko [14]. Our short proof is based
on different ideas and is simpler than these earlier proofs.
* Research supported in part by the National Science Foundation under grants DMS-9970325 and DMS-0400812, and an Alfred P.
Sloan Research Fellowship.
† Research supported in part by the National Science Foundation under grants DMS-0071261 and DMS-0300529. 相似文献
5.
If
is an initially hereditary family of finite subsets of positive integers (i.e., if
and G is initial segment of F then
) and M an infinite subset of positive integers then we define an ordinal index
. We prove that if
is a family of finite subsets of positive integers such that for every
the characteristic function χF is isolated point of the subspace
of { 0,1 }N with the product topology then
for every
infinite, where
is the set of all initial segments of the members of
and ω1 is the first uncountable ordinal. As a consequence of this result we prove that
is Ramsey, i.e., if
is a partition of
then there exists an infinite subset M of positive integers such that
where [M]< ω is the family of all finite subsets of M. 相似文献
6.
7.
If E is a separable symmetric sequence space with trivial Boyd indices and
is the corresponding ideal of compact operators, then there exists a C1-function fE, a self-adjoint element
and a densely defined closed symmetric derivation δ on
such that
, but
相似文献
8.
Alina Iacob 《Archiv der Mathematik》2005,85(4):335-344
We consider two pairs of complete hereditary cotorsion theories
on the category of left R-modules, such that
We prove that for any left R-modules M, N and for any n ≧ 1, the generalized Tate cohomology modules
can be computed either using a left
of M and a left
of M or using a right
a right
of N.
Received: 17 December 2004 相似文献
9.
M. Rovinsky 《Selecta Mathematica, New Series》2005,11(3-4):491-522
Let L be the function field of a projective space
over an algebraically closed field k of characteristic zero, and H be the group of projective transformations. An H-sheaf
on
is a collection of isomorphisms
for each g ∈ H satisfying the chain rule.
We construct, for any n > 1, a fully faithful functor from the category of finite-dimensional L-semilinear representations of H extendable to the semigroup End(L/k) to the category of coherent H-sheaves on
The paper is motivated by a study of admissible representations of the automorphism group G of an algebraically closed extension of k of countable transcendence degree undertaken in [4]. The semigroup End(L/k) is considered as a subquotient of G, hence the condition on extendability.
In the appendix it is shown that, if
is either H, or a bigger subgroup in the Cremona group (generated by H and a certain pair of involutions), then any semilinear
of degree one is an integral L-tensor power of
It is also shown that this bigger subgroup has no non-trivial representations of finite degree if n > 1. 相似文献
10.
A 1-factorization (or parallelism) of the complete graph with loops
is called polar if each 1-factor (parallel class) contains exactly one loop and for any three distinct vertices x1, x2, x3, if {x1} and {x2, x3} belong to a 1-factor then the same holds for any permutation of the set {1, 2, 3}. To a polar graph
there corresponds a polar involution set
, an idempotent totally symmetric quasigroup (P, *), a commutative, weak inverse property loop (P, + ) of exponent 3 and a Steiner triple system
.
We have:
satisfies the trapezium axiom
is self-distributive ⇔ (P, + ) is a Moufang loop
is an affine triple system; and:
satisfies the quadrangle axiom
is a group
is an affine space. 相似文献