共查询到20条相似文献,搜索用时 31 毫秒
1.
P. Cubiotti 《Journal of Optimization Theory and Applications》1997,92(3):457-475
In this paper, we deal with the following problem: given a real normed space E with topological dual E*, a closed convex set XE, two multifunctions :X2X and
, find
such that
We extend to the above problem a result established by Ricceri for the case (x)X, where in particular the multifunction is required only to satisfy the following very general assumption: each set (x) is nonempty, convex, and weakly-star compact, and for each yX–:X the set
is compactly closed. Our result also gives a partial affirmative answer to a conjecture raised by Ricceri himself. 相似文献
2.
We consider the following implicit quasi-variational inequality problem: given two topological vector spaces E and F, two nonempty sets X
E and C
F, two multifunctions Γ : X → 2
X
and Ф : X → 2
C
, and a single-valued map ψ :
, find a pair
such that
,
Ф
and
for all
. We prove an existence theorem in the setting of Banach spaces where no continuity or monotonicity assumption is required
on the multifunction Ф. Our result extends to non-compact and infinite-dimensional setting a previous results of the authors
(Theorem 3.2 of Cubbiotti and Yao [15] Math. Methods Oper. Res. 46, 213–228 (1997)). It also extends to the above problem a recent existence result established for the explicit case (C = E
* and
). 相似文献
3.
We consider the following generalized quasivariational inequality problem: given a real Banach space E with topological dual E* and given two multifunctions G:X2
X
and F:X2
E
*, find
such that
We prove an existence theorem where F is not assumed to have any continuity or monotonicity property. Making use of a different technical construction, our result improves some aspects of a recent existence result (Theorem 3.1 of Ref. 1). In particular, the coercivity assumption of this latter result is weakened meaningfully. 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.
Given a set of points
and ε>0, we propose and analyze an algorithm for the problem of computing a (1+ε)-approximation to the minimum-volume axis-aligned ellipsoid enclosing
. We establish that our algorithm is polynomial for fixed ε. In addition, the algorithm returns a small core set
, whose size is independent of the number of points m, with the property that the minimum-volume axis-aligned ellipsoid enclosing
is a good approximation of the minimum-volume axis-aligned ellipsoid enclosing
. Our computational results indicate that the algorithm exhibits significantly better performance than the theoretical worst-case
complexity estimate.
This work was supported in part by the National Science Foundation through CAREER Grants CCF-0643593 and DMI-0237415. 相似文献
7.
In this paper, we study a class of vector minimization problems on a complete metric space X which is identified with the corresponding complete metric space of objective functions
. We do not impose any compactness assumption on X. We show that, for most (in the sense of Baire category) functions
, the corresponding vector optimization problem has a solution. 相似文献
8.
P. Cubiotti 《Journal of Optimization Theory and Applications》1997,92(3):477-495
Given a nonempty set
and two multifunctions
, we consider the following generalized quasi-variational inequality problem associated with X, : Find
such that
. We prove several existence results in which the multifunction is not supposed to have any continuity property. Among others, we extend the results obtained in Ref. 1 for the case (x(X. 相似文献
9.
Biagio Ricceri 《Journal of Global Optimization》2008,40(1-3):389-397
In this paper, it is proved a very general well-posedness result for a class of constrained minimization problems of which
the following is a particular case: Let X be a Hausdorff topological space and let be two non-constant functions such that, for each , the function has sequentially compact sub-level sets and admits a unique global minimum in X. Then, for each , the restriction of J to has a unique global minimum, say , toward which every minimizing sequence converges. Moreover, the functions and are continuous in . 相似文献
10.
Let M be a smooth manifold endowed with a symmetric connection . There are two important ways of lift the connection of M to the frame bundle BM, the canonical lift and the horizontal lift . The aim of this work is determine the -martingales and the -martingales on BM. Our results allow to establish new characterizations of harmonic maps from Riemannian manifolds to frame bundles.
The research of P. Catuogno is supported in part by FAPESP 01/13158-4 and S. Stelmastchuk is fully supported by FAPESP 02/12154-8. 相似文献
11.
B. Heidergott F. J. Vázquez-Abad 《Journal of Optimization Theory and Applications》2008,136(2):187-209
This paper addresses the problem of sensitivity analysis for finite-horizon performance measures of general Markov chains.
We derive closed-form expressions and associated unbiased gradient estimators for the derivatives of finite products of Markov
kernels by measure-valued differentiation (MVD). In the MVD setting, the derivatives of Markov kernels, called
-derivatives, are defined with respect to a class of performance functions
such that, for any performance measure
, the derivative of the integral of g with respect to the one-step transition probability of the Markov chain exists. The MVD approach (i) yields results that
can be applied to performance functions out of a predefined class, (ii) allows for a product rule of differentiation, that
is, analyzing the derivative of the transition kernel immediately yields finite-horizon results, (iii) provides an operator
language approach to the differentiation of Markov chains and (iv) clearly identifies the trade-off between the generality
of the performance classes that can be analyzed and the generality of the classes of measures (Markov kernels). The
-derivative of a measure can be interpreted in terms of various (unbiased) gradient estimators and the product rule for
-differentiation yields a product-rule for various gradient estimators.
Part of this work was done while the first author was with EURANDOM, Eindhoven, Netherlands, where he was supported by Deutsche
Forschungsgemeinschaft under Grant He3139/1-1. The work of the second author was partially supported by NSERC and FCAR grants
of the Government of Canada and Québec. 相似文献
12.
Tomoyuki Arakawa 《Inventiones Mathematicae》2007,169(2):219-320
We study the representation theory of the -algebra associated with a simple Lie algebra at level k. We show that the “-” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any
level k∈ℂ. Moreover, we show that the character of each irreducible highest weight representation of is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra of . As a consequence we complete (for the “-” reduction) the proof of the conjecture of E. Frenkel, V. Kac and M. Wakimoto on
the existence and the construction of the modular invariant representations of -algebras.
Mathematics Subject Classification (1991) 17B68, 81R10 相似文献
13.
Sophie Chemla 《Transformation Groups》2008,13(1):91-123
In this paper, X will denote a manifold. In a very famous paper, Kontsevich [Ko] showed that the differential graded Lie algebra (DGLA) of polydifferential
operators on X is formal. Calaque [C1] extended this theorem to any Lie algebroid. More precisely, given any Lie algebroid E over X, he defined the DGLA of E-polydifferential operators, and showed that it is formal. Denote by the DGLA of E-polyvector fields. Considering M, a module over E, we define the-module of E-polyvector fields with values in M. Similarly, we define the-module of E-polydifferential operators with values in M,. We show that there is a quasi-isomorphism of L
∞-modules over from to . Our result extends Calaque’s (and Kontsevich’s) result. 相似文献
14.
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
15.
Kerstin Hesse 《Advances in Computational Mathematics》2009,30(1):37-59
This paper investigates the s-energy of (finite and infinite) well separated sequences of spherical designs on the unit sphere S
2. A spherical n-design is a point set on S
2 that gives rise to an equal weight cubature rule which is exact for all spherical polynomials of degree ≤n. The s-energy E
s
(X) of a point set of m distinct points is the sum of the potential for all pairs of distinct points . A sequence Ξ = {X
m
} of point sets X
m
⊂S
2, where X
m
has the cardinality card(X
m
)=m, is well separated if for each pair of distinct points , where the constant λ is independent of m and X
m
. For all s>0, we derive upper bounds in terms of orders of n and m(n) of the s-energy E
s
(X
m(n)) for well separated sequences Ξ = {X
m(n)} of spherical n-designs X
m(n) with card(X
m(n))=m(n).
相似文献
16.
Euisung Park 《Mathematische Zeitschrift》2007,256(3):685-697
In this article we study nondegenerate projective curves of degree d which are not arithmetically Cohen-Macaulay. Note that for a rational normal curve and a point . Our main result is about the relation between the geometric properties of X and the position of P with respect to . We show that the graded Betti numbers of X are uniquely determined by the rank of P with respect to . In particular, X satisfies property N
2,p
if and only if . Therefore property N
2,p
of X is controlled by and conversely can be read off from the minimal free resolution of X. This result provides a non-linearly normal example for which the converse to Theorem 1.1 in (Eisenbud et al., Compositio
Math 141:1460–1478, 2005) holds. Also our result implies that for nondegenerate projective curves of degree d which are not arithmetically Cohen–Macaulay, there are exactly distinct Betti tables. 相似文献
17.
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
18.
19.
Masanori Katsurada 《The Ramanujan Journal》2007,14(2):249-275
Let Q(u,v)=|u+vz|2 be a positive-definite quadratic form with a complex parameter z=x+iy in the upper-half plane. The Epstein zeta-function attached to Q is initially defined by
for Re s>1, where the term with m=n=0 is to be omitted. We deduce complete asymptotic expansions of
as y→+∞ (Theorem 1 in Sect. 2), and of its weighted mean value (with respect to y) in the form of a Laplace-Mellin transform of
(Theorem 2 in Sect. 2). Prior to the proofs of these asymptotic expansions, the meromorphic continuation of
over the whole s-plane is prepared by means of Mellin-Barnes integral transformations (Proposition 1 in Sect. 3). This procedure, differs
slightly from other previously known methods of the analytic continuation, gives a new alternative proof of the Fourier expansion
of
(Proposition 2 in Sect. 3). The use of Mellin-Barnes type of integral formulae is crucial in all aspects of the proofs; several
transformation properties of hypergeometric functions are especially applied with manipulation of these integrals.
Research supported in part by Grant-in-Aid for Scientific Research (No. 13640041), the Ministry of Education, Culture, Sports,
Science and Technology of Japan. 相似文献
20.
Carlos Castaño-Bernard 《The Ramanujan Journal》2008,17(1):107-121
Certain identities of Ramanujan may be succinctly expressed in terms of the rational function
on the modular curve X
0(N), where
and f
χ
is a certain modular unit on the Nebentypus cover X
χ
(N) introduced by Ogg and Ligozat for prime
and w
N
is the Fricke involution. These correspond to levels N=5,13, where the genus g
N
of X
0(N) is zero. In this paper we study slightly more general kind of relations for each
such that X
0(N) has genus g
N
=1,2, and also for each
such that the Atkin–Lehner quotient X
0+(N) has genus g
N
+=1,2. Finally we study the normal closure of the field of definition of the zeros of the latter.
相似文献