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1.
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
2.
Emanuele Delucchi 《Journal of Algebraic Combinatorics》2007,26(4):477-494
Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice
(Proc. Internat. Sympos., 1971, pp. 101–115) and of its subposet of the G-symmetric partitions
which was recently introduced by Hultman (, 2006), together with the complex of G-symmetric phylogenetic trees
. Hultman shows that the complexes
and
are homotopy equivalent and Cohen–Macaulay, and determines the rank of their top homology.
An application of the theory of building sets and nested set complexes by Feichtner and Kozlov (Selecta Math. (N.S.)
10, 37–60, 2004) shows that in fact
is subdivided by the order complex of
. We introduce the complex of Dowling trees
and prove that it is subdivided by the order complex of
. Application of a theorem of Feichtner and Sturmfels (Port. Math. (N.S.)
62, 437–468, 2005) shows that, as a simplicial complex,
is in fact isomorphic to the Bergman complex of the associated Dowling geometry.
Topologically, we prove that
is obtained from
by successive coning over certain subcomplexes. It is well known that
is shellable, and of the same dimension as
. We explicitly and independently calculate how many homology spheres are added in passing from
to
. Comparison with work of Gottlieb and Wachs (Adv. Appl. Math.
24(4), 301–336, 2000) shows that
is intimely related to the representation theory of the top homology of
.
Research partially supported by the Swiss National Science Foundation, project PP002-106403/1. 相似文献
3.
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
4.
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
5.
X. M. Yang 《Journal of Optimization Theory and Applications》2009,140(3):537-542
In this paper, we study the minimization of a pseudoinvex function over an invex subset and provide several new and simple
characterizations of the solution set of pseudoinvex extremum problems. By means of the basic properties of pseudoinvex functions,
the solution set of a pseudoinvex program is characterized, for instance, by the equality
, for each feasible point x, where
is in the solution set. Our study improves naturally and extends some previously known results in Mangasarian (Oper. Res.
Lett. 7: 21–26, 1988) and Jeyakumar and Yang (J. Opt. Theory Appl. 87: 747–755, 1995).
This research was partially supported by National Natural Science Foundation of China Grants No. 10771228 and 10831009. 相似文献
6.
7.
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
8.
The aim of this paper is to give some representation formulas of Riesz and Poisson-Jensen type for super-solutions to a class
of hypoelliptic ultraparabolic operators on a homogeneous Lie group . Our results complete the ones obtained in Cinti (Math Scand 100:1–21, 2007). We also provide a suitable theory for -Green functions and for -Green potentials of Radon measures. The proofs mostly rely on the use of appropriate techniques relevant to the Potential
Theory for .
Investigation supported by University of Bologna. Funds for selected research topics. 相似文献
9.
Radoslav M. Dimitrić 《Acta Appl Math》2008,100(2):105-112
This paper generalizes a number of results obtained by Dimitrić in (Glas. Mat. 21(41):327–329, 1986; Proceedings of Hobart Conference on Rings, Modules and Radicals 1987, 204:41–50, Gordon and Breach, 1989) and Dimitrić and Goldsmith in (Glas. Mat. 23(43):241–246, 1988). The original papers were restricted to the category of Abelian groups and orthogonality was to the group of integers ℤ.
Here, we are in a general Abelian category with products and coproducts, with applications to module categories and further
to modules over PID’s. Another generalization is in replacing ℤ by an entire class of subobjects
of the underlying category. We examine properties of the torsion class
, Hom(T,C)=0} in relation to purity, direct summands and indecomposability as well as commutation with direct products, for example.
Of special interest are members of this class when
is a class of slender objects in the ground category; in this case, members of
are called ortho-slender objects. In a sense, ortho-slenderness represents complementary, if not dual, notion to slenderness.
相似文献
10.
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
11.
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
12.
Let B be a nilpotent matrix and suppose that its Jordan canonical form is determined by a partition λ. Then it is known that its
nilpotent commutator is an irreducible variety and that there is a unique partition μ such that the intersection of the orbit of nilpotent matrices corresponding to μ with is dense in . We prove that map given by is an idempotent map. This answers a question of Basili and Iarrobino [9] and gives a partial answer to a question of Panyushev [18]. In the proof, we use the fact that for a generic matrix the algebra generated by A and B is a Gorenstein algebra. Thus, a generic pair of commuting nilpotent matrices generates a Gorenstein algebra. We also describe
in terms of λ if has at most two parts. 相似文献
13.
Let be a finite-dimensional complex reductive Lie algebra and S() its symmetric algebra. The nilpotent bicone of is the subset of elements (x, y) of whose subspace generated by x and y is contained in the nilpotent cone. The nilpotent bicone is naturally endowed with a scheme structure, as nullvariety of
the augmentation ideal of the subalgebra of generated by the 2-order polarizations of invariants of . The main result of this paper is that the nilpotent bicone is a complete intersection of dimension , where and are the dimensions of Borel subalgebras and the rank of , respectively. This affirmatively answers a conjecture of Kraft and Wallach concerning the nullcone [KrW2]. In addition, we introduce and study in this paper the characteristic submodule of . The properties of the nilpotent bicone and the characteristic submodule are known to be very important for the understanding
of the commuting variety and its ideal of definition. The main difficulty encountered for this work is that the nilpotent
bicone is not reduced. To deal with this problem, we introduce an auxiliary reduced variety, the principal bicone. The nilpotent bicone, as well as the principal bicone, are linked to jet schemes. We study their dimensions using arguments
from motivic integration. Namely, we follow methods developed by Mustaţǎ in [Mu]. Finally, we give applications of our results to invariant theory. 相似文献
14.
Hendrik Hubrechts 《Foundations of Computational Mathematics》2008,8(1):137-169
Let E
Γ be a family of hyperelliptic curves defined by
, where
is defined over a small finite field of odd characteristic. Then with
in an extension degree n field over this small field, we present a deterministic algorithm for computing the zeta function of the curve
by using Dwork deformation in rigid cohomology. The time complexity of the algorithm is
and it needs
bits of memory. A slight adaptation requires only
space, but costs time
. An implementation of this last result turns out to be quite efficient for n big enough.
H. Hubrechts is a Research Assistant of the Research Foundation–Flanders (FWO–Vlaanderen). 相似文献
15.
J. Bagherian Ilia Ponomarenko A. Rahnamai Barghi 《Journal of Algebraic Combinatorics》2008,27(2):173-185
We introduce a concept of cyclotomic association scheme over a finite near-field
. It is proved that any isomorphism of two such nontrivial schemes is induced by a suitable element of the group AGL(V), where V is the linear space associated with
. A sufficient condition on a cyclotomic scheme
that guarantee the inclusion
where
is a finite field with
elements, is given.
I. Ponomarenko partially supported by RFFI, grants 03-01-00349, NSH-2251.2003.1. 相似文献
16.
Semyon Alesker 《Journal of Geometric Analysis》2008,18(3):651-686
A new class of plurisubharmonic functions on the octonionic plane
is introduced. An octonionic version of theorems of A.D. Aleksandrov (Vestnik Leningrad. Univ. Ser. Mat. Meh. Astr. 13(1):5–24,
1958) and Chern-Levine-Nirenberg (Global Analysis, pp. 119–139, 1969), and Błocki (Proc. Am. Math. Soc. 128(12):3595–3599, 2000) are proved. These results are used to construct new examples of continuous translation invariant valuations on convex subsets
of
. In particular, a new example of Spin(9)-invariant valuation on ℝ16 is given.
Partially supported by ISF grant 1369/04. 相似文献
17.
Let be the kernel of the natural map Out(Fn)→GLn(ℤ). We use combinatorial Morse theory to prove that has an Eilenberg–MacLane space which is (2n-4)-dimensional and that is not finitely generated (n≥3). In particular, this shows that the cohomological dimension of is equal to 2n-4 and recovers the result of Krstić–McCool that is not finitely presented. We also give a new proof of the fact, due to Magnus, that is finitely generated. 相似文献
18.
A new necessary and sufficient condition for the row
-property is given. By using this new condition and a special row rearrangement, we provide two global error bounds for the
extended vertical linear complementarity problem under the row
-property, which extend the error bounds given in Chen and Xiang (Math. Program. 106:513–525, 2006) and Mathias and Pang (Linear Algebra Appl. 132:123–136, 1990) for the P-matrix linear complementarity problem, respectively. We show that one of the new error bounds is sharper than
the other, and it can be computed easily for some special class of the row
-property block matrix. Numerical examples are given to illustrate the error bounds.
The work was in part supported by a Grant-in-Aid from Japan Society for the Promotion of Science, and the National Natural
Science Foundation of China (10671010). 相似文献
19.
B. T. Kien N. C. Wong J. C. Yao 《Journal of Optimization Theory and Applications》2007,135(3):515-530
We study the following generalized quasivariational inequality problem: given a closed convex set X in a normed space E with the dual E
*, a multifunction
and a multifunction Γ:X→2
X
, find a point
such that
,
. We prove some existence theorems in which Φ may be discontinuous, X may be unbounded, and Γ is not assumed to be Hausdorff lower semicontinuous.
The authors express their sincere gratitude to the referees for helpful suggestions and comments.
This research was partially supported by a grant from the National Science Council of Taiwan, ROC.
B.T. Kien was on leave from National University of Civil Engineering, Hanoi, Vietnam. 相似文献
20.
Luigi Santocanale 《Order》2007,24(3):155-179