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1.
2.
Let be a commutative Noetherian local ring and let be an ideal of R. We give some inequalities between the Bass numbers of an R–module and those of its local cohomology modules with respect to . As an application of these inequalities, we recover results of Delfino-Marley and Kawasaki by showing that for a minimax
R-module M and for any non-negative integer i, the Bass numbers of the ith local cohomology module are finite if one of the following holds:
S. Yassemi was supported by a grant from IPM No. 85130214. 相似文献
(a) | , |
(b) | is a principal ideal. |
3.
For a smooth curve C it is known that a very ample line bundle on C is normally generated if Cliff() < Cliff(C) and there exist extremal line bundles (:non-normally generated very ample line bundle with Cliff() = Cliff(C)) with . However it has been unknown whether there exists an extremal line bundle with . In this paper, we prove that for any positive integers (g, c) with g = 2c + 5 and (mod 2) there exists a smooth curve of genus g and Clifford index c carrying an extremal line bundle with . In fact, a smooth quadric hypersurface section C of a general projective K3 surface always has an extremal line bundle with . More generally, if C has a line bundle computing the Clifford index c of C with , then C has such an extremal line bundle .
For all authors, this work was supported by Korea Research Foundation Grant funded by Korea Government (MOEHRD, Basic Reasearch
Promotion Fund)(KRF-2005-070-C00005). 相似文献
4.
A. Gerlo 《Applied Categorical Structures》2008,16(4):479-493
In a topological construct endowed with a proper -factorization system and a concrete functor , we study -compactness and -Hausdorff separation, where is a class of “closed morphisms” in the sense of Clementino et al. (A functional approach to general topology. In: Categorical
Foundations. Encyclopedia of Mathematics and Its Applications, vol. 97, pp. 103–163. Cambridge University Press, Cambridge,
2004), determined by Λ. In particular, we point out under which conditions on Λ, the notion of -compactness of an object of coincides with 0-compactness of the image in Prap. Our results will be illustrated by some examples: except for some well-known ones, like b-compactness of a topological space, we also capture some compactness notions that were not considered before in the literature.
In particular, we obtain a generalization of b-compactness to the setting of approach spaces. This notion is shown to play an important role in the study of uniformizability.
The author is research assistant at the Fund of Scientific Research Vlaanderen (FWO). 相似文献
5.
In the study of the asymptotic behaviour of solutions of differential-difference equations the
-spectrum has been useful, where
and
implies Fourier transform
, with
given
, φ∈L
∞(ℝ,X), X a Banach space,
(half)line. Here we study
and related concepts, give relations between them, especially
weak Laplace half-line spectrum of φ, and thus ⊂ classical Beurling spectrum = Carleman spectrum =
; also
= Beurling spectrum of “φ modulo
” (Chill-Fasangova). If
satisfies a Loomis type condition (L
U
), then
countable and
uniformly continuous ∈U are shown to imply
; here (L
U
) usually means
, indefinite integral Pf of f in U imply Pf in
(the Bohl-Bohr theorem for
= almost periodic functions, U=bounded functions). This spectral characterization and other results are extended to unbounded functions via mean classes
, ℳ
m
U ((2.1) below) and even to distributions, generalizing various recent results for uniformly continuous bounded φ. Furthermore for solutions of convolution systems S*φ=b with
in some
we show
. With these above results, one gets generalizations of earlier results on the asymptotic behaviour of solutions of neutral
integro-differential-difference systems. Also many examples and special cases are discussed. 相似文献
6.
Jeroen Demeyer 《Inventiones Mathematicae》2007,170(3):655-670
We construct a Diophantine interpretation of over . Using this together with a previous result that every recursively enumerable (r.e.) relation over is Diophantine over , we will prove that every r.e. relation over is Diophantine over . We will also look at recursive infinite base fields , algebraic over . It turns out that the Diophantine relations over are exactly the relations which are r.e. for every recursive presentation. 相似文献
7.
Hideo Mitsuhashi 《Algebras and Representation Theory》2006,9(3):309-322
In this paper, we establish Schur–Weyl reciprocity between the quantum general super Lie algebra and the Iwahori–Hecke algebra . We introduce the sign -permutation representation of on the tensor space of dimensional -graded -vector space . This action commutes with that of derived from the vector representation on . Those two subalgebras of satisfy Schur–Weyl reciprocity. As special cases, we obtain the super case (), and the quantum case (). Hence this result includes both the super case and the quantum case, and unifies those two important cases.Presented by A. Verschoren. 相似文献
8.
Let be a field and q be a nonzero element of that is not a root of unity. We give a criterion for 〈0〉 to be a primitive ideal of the algebra of quantum matrices. Next, we describe all height one primes of ; these two problems are actually interlinked since it turns out that 〈0〉 is a primitive ideal of whenever has only finitely many height one primes. Finally, we compute the automorphism group of in the case where m ≠ n. In order to do this, we first study the action of this group on the prime spectrum of . Then, by using the preferred basis of and PBW bases, we prove that the automorphism group of is isomorphic to the torus when m ≠ n and (m,n) ≠ (1, 3),(3, 1).
This research was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme
and by Leverhulme Research Interchange Grant F/00158/X. 相似文献
9.
Dmitri I. Panyushev 《Transformation Groups》2009,14(2):463-482
Let be an algebraic Lie algebra and a (generalised) Takiff algebra. Any finite-order automorphism θ of induces an automorphism of of the same order, denoted . We study invariant-theoretic properties of representations of the fixed point subalgebra of on other eigenspaces of in . We use the observation that, for special values of m, the fixed point subalgebra, , turns out to be a contraction of a certain Lie algebra associated with and θ.
To my teacher
Supported in part by R.F.B.R. grant 06-01-72550. 相似文献
10.
Christopher Kennedy 《Algebras and Representation Theory》2006,9(5):525-537
Deep matrix algebras based on a set over a ring are introduced and studied by McCrimmon when has infinite cardinality. Here, we construct a new -module that is faithful for of any cardinality. For a field of arbitrary characteristic and , is studied in depth. The algebra is shown to possess a unique proper non-zero ideal, isomorphic to . This leads to a new and interesting simple algebra, , the quotient of by its unique ideal. Both and the quotient algebra are shown to have centers isomorphic to . Via the new faithful representation, all automorphisms of are shown to be inner in the sense of Definition 18.Presented by D. Passman. 相似文献
11.
In [2] the subconstruct of sober approach spaces was introduced and it was shown to be a reflective subconstruct of the category of approach spaces. The main result of this paper states that moreover is firmly -reflective in for the class of epimorphic embeddings. ‘Firm -reflective’ is a notion introduced in [3] by G.C.L. Brümmer and E. Giuli and is inspired by the exemplary behaviour of the usual completion in the category of Hausdorff uniform spaces with uniformly continuous maps. It means that is -reflective in and that the reflector is such that belongs to if and only if is an isomorphism. Firm -reflectiveness implies uniqueness of completion in the sense that whenever is a map with and sober, the associated is an isomorphism. Our result generalizes the fact that in the category the subconstruct of sober topological spaces is firmly reflective for the class of b-dense embeddings in . Also firmness in some other subconstructs of will be easily obtained.A. Gerlo and C. Van Olmen are research assistants at the Fund of Scientific Research Vlaanderen (FWO). E. Vandersmissen is a research assistant supported by the FWO-grant G.0244.05. 相似文献
12.
13.
T. Skrypnyk 《Acta Appl Math》2007,99(3):261-282
We construct a family of special quasigraded Lie algebras
of functions of one complex variables with values in finite-dimensional Lie algebra
, labeled by the special 2-cocycles F on
. The main property of the constructed Lie algebras
is that they admit Kostant-Adler-Symes scheme. Using them we obtain new integrable finite-dimensional Hamiltonian systems
and new hierarchies of soliton equations. 相似文献
14.
In this paper we develop a robust uncertainty principle for
finite signals in
which states that, for nearly all choices
such that
there is no signal
supported on
whose discrete Fourier transform
is supported on
In fact, we can make the above uncertainty principle quantitative in the sense that if
is supported on
then only a small percentage of the energy (less than half, say) of
is concentrated on
As an application of this robust uncertainty principle (QRUP), we consider the problem of decomposing a signal into a sparse
superposition of spikes and complex sinusoids
We show that if a generic signal
has a decomposition
using spike and frequency locations in
and
respectively, and obeying
then
is the unique sparsest possible decomposition (all other decompositions have more nonzero terms). In addition, if
then the sparsest
can be found by solving a convex optimization problem. Underlying our results is a new probabilistic approach which insists
on finding the correct uncertainty relation, or the optimally sparse solution for nearly all subsets but not necessarily all
of them, and allows us to considerably sharpen previously known results [9], [10]. In fact, we show that the fraction of sets
for which the above properties do not hold can be upper bounded by quantities like
for large values of
The QRUP (and the application to finding sparse representations) can be extended to general pairs of orthogonal bases
For nearly all choices
obeying
where
there is no signal
such that
is supported on
and
is supported on
where
is the mutual coherence between
and
An erratum to this article is available at . 相似文献
15.
Martin Kassabov 《Inventiones Mathematicae》2007,170(2):327-354
We construct explicit generating sets S
n
and of the alternating and the symmetric groups, which turn the Cayley graphs and into a family of bounded degree expanders for all n. 相似文献
16.
If a nonzero linear functional has finite, countable, or bounded range when restricted to an irreducible semigroup
of complex matrices, it is shown that
itself has the same property. Similar results are proven under the hypothesis that a nontrivial ideal of
is finite, countable, or bounded. 相似文献
17.
The digitisation
of a real disc
having radius
and centre
consists of all integer points inside
, i.e.,
In this paper we show that there are
different (up to translations) digitisations of discs having radius
. More formally,
The result is of interest in the area of digital image processing because it describes how large the impact of the object
position can be on its digitisation. 相似文献
18.
Jonatan Lenells 《Arkiv f?r Matematik》2007,45(2):297-325
The topological group of diffeomorphisms of the unit circle of Sobolev class H
k
, for k large enough, is a Banach manifold modeled on the Hilbert space . In this paper we show that the H
1 right-invariant metric obtained by right-translation of the H
1 inner product on defines a smooth Riemannian metric on , and we explicitly construct a compatible smooth affine connection. Once this framework has been established results from
the general theory of affine connections on Banach manifolds can be applied to study the exponential map, geodesic flow, parallel
translation, curvature etc. The diffeomorphism group of the circle provides the natural geometric setting for the Camassa–Holm
equation – a nonlinear wave equation that has attracted much attention in recent years – and in this context it has been remarked
in various papers how to construct a smooth Riemannian structure compatible with the H
1 right-invariant metric. We give a self-contained presentation that can serve as a detailed mathematical foundation for the
future study of geometric aspects of the Camassa–Holm equation. 相似文献
19.
Dusa McDuff 《Geometriae Dedicata》2008,132(1):1-29
We study the relation between the symplectomorphism group Symp M of a closed connected symplectic manifold M and the symplectomorphism and diffeomorphism groups Symp and Diff of its one point blow up . There are three main arguments. The first shows that for any oriented M the natural map from to is often injective. The second argument applies when M is simply connected and detects nontrivial elements in the homotopy group that persist into the space of self-homotopy equivalences of . Since it uses purely homological arguments, it applies to c-symplectic manifolds (M, a), that is, to manifolds of dimension 2n that support a class such that . The third argument uses the symplectic structure on M and detects nontrivial elements in the (higher) homology of BSymp, M using characteristic classes defined by parametric Gromov–Witten invariants. Some results about many point blow ups are also
obtained. For example we show that if M is the four-torus with k-fold blow up (where k > 0) then is not generated by the groups as ranges over the set of all symplectic forms on .
Partially supported by NSF grants DMS 0305939 and 0604769. 相似文献
20.
Enkelejd Hashorva 《Extremes》2007,10(4):175-206
Let be an elliptical random vector with a non-singular square matrix and a spherical random vector in , and let be a sequence of vectors in such that . We assume in this paper that the associated random radius R
k
=(S
1 + S
2 +...+S
k
)1/2 is almost surely positive, and it has distribution function in the Gumbel max-domain of attraction. Relying on extreme value
theory we obtain an exact asymptotic expansion of the tail probability for converging as to a boundary point. Further we discuss density convergence under a suitable transformation. We apply our results to obtain
an asymptotic approximation of the distribution of partial excess above a high threshold, and to derive a conditional limiting
result. Further, we investigate the asymptotic behaviour of concomitants of order statistics, and the tail asymptotics of
associated random radius for subvectors of .
相似文献