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1.
In this paper we consider the problem
where B is a ball in R
n
. For a small d>0, we show the uniqueness (up to rotation) of the one-bubbling solution which concentrates at a point of the boundary.
Received: 12 December 2001 / Published online: 10 February 2003
RID="⋆"
ID="⋆" Supported by M.U.R.S.T., project: ``Variational methods and nonlinear differential equations'
RID="⋆⋆"
ID="⋆⋆" Partial supported by National Center for Theoretical Sciences of NSC, Taiwan
Mathematics Subject Classification (2000): 35J60 相似文献
2.
On polynomial collocation for second kind integral equations with fixed singularities of Mellin type
Summary. We consider a polynomial collocation for the numerical solution of a second kind integral equation with an integral kernel
of Mellin convolution type. Using a stability result by Junghanns and one of the authors, we prove that the error of the approximate
solution is less than a logarithmic factor times the best approximation and, using the asymptotics of the solution, we derive
the rates of convergence. Finally, we describe an algorithm to compute the stiffness matrix based on simple Gau? quadratures
and an alternative algorithm based on a recursion in the spirit of Monegato and Palamara Orsi. All together an almost best
approximation to the solution of the integral equation can be computed with 𝒪(n
2[log n]2) resp. 𝒪(n
2) operations, where n is the dimension of the polynomial trial space.
Received February 18, 2002 / Revised version received May 15, 2002 / Published online October 29, 2002
RID="⋆"
ID="⋆" Correspondence to: A. Rathsfeld
Mathematics Subject Classification (1991): 65R20 相似文献
3.
In this paper we show that the so-called commutative class of primal-dual interior point algorithms which were designed by
Monteiro and Zhang for semidefinite programming extends word-for-word to optimization problems over all symmetric cones. The
machinery of Euclidean Jordan algebras is used to carry out this extension. Unlike some non-commutative algorithms such as
the XS+SX method, this class of extensions does not use concepts outside of the Euclidean Jordan algebras. In particular no assumption
is made about representability of the underlying Jordan algebra. As a special case, we prove polynomial iteration complexities
for variants of the short-, semi-long-, and long-step path-following algorithms using the Nesterov-Todd, XS, or SX directions.
Received: April 2000 / Accepted: May 2002
Published online: March 28, 2003
RID="⋆"
ID="⋆" Part of this research was conducted when the first author was a postdoctoral associate at Center for Computational
Optimization at Columbia University.
RID="⋆⋆"
ID="⋆⋆" Research supported in part by the U.S. National Science Foundation grant CCR-9901991 and Office of Naval Research
contract number N00014-96-1-0704. 相似文献
4.
For a fixed q ℕ and a given Σ1 definition φ(d,x), where d is a parameter, we construct a model M of 1 Δ0 + ? exp and a non standard d M such that in M either φ has no witness smaller than d or phgr; is equivalent to a formula ϕ(d,x) having no more than q alternations of blocks of quantifiers.
Received: 29 September 1998 / Revised version: 7 November 2001 Published online: 10 October 2002
RID="⋆"
ID="⋆" Research supported in part by The State Committee for Scientific Research (Poland), KBN, grant number 2 PO3A 018 13.
RID="⋆"
ID="⋆" Research supported in part by The State Committee for Scientific Research (Poland), KBN, grant number 2 PO3A 018 13. 相似文献
5.
The maximal Seshadri number μ(L) of an ample line bundle L on a smooth projective variety X measures the local positivity of the line bundle L at a general point of X. By refining the method of Ein-Küchle-Lazarsfeld, lower bounds on μ(L) are obtained in terms of L
n
, n=dim(X), for a class of varieties. The main idea is to show that if a certain lower bound is violated, there exists a non-trivial
foliation on the variety whose leaves are covered by special curves. In a number of examples, one can show that such foliations
must be trivial and obtain lower bounds for μ(L). The examples include the hyperplane line bundle on a smooth surface in ℙ3 and ample line bundles on smooth threefolds of Picard number 1.
Received: 29 June 2001 / Published online: 16 October 2002
RID="⋆"
ID="⋆" Supported by Grant No. 98-0701-01-5-L from the KOSEF.
RID="⋆⋆"
ID="⋆⋆" Supported by Grant No. KRF-2001-041-D00025 from the KRF. 相似文献
6.
We consider Finsler spaces with a Randers metric F=α+β, on the three dimensional real vector space, where α is the Euclidean metric and β=bdx
3
is a 1-form with norm b,0≤b<1. By using the notion of mean curvature for immersions in Finsler spaces introduced by Z. Shen, we get the ordinary differential
equation that characterizes the minimal surfaces of rotation around the x
3
axis. We prove that for every b,0≤b<1, there exists, up to homothety, a unique forward complete minimal surface of rotation. The surface is embedded, symmetric
with respect to a plane perpendicular to the rotation axis and it is generated by a concave plane curve. Moreover, for every
there are non complete minimal surfaces of rotation, which include explicit minimal cones.
Received: 30 November 2001 / Published online: 10 February 2003
RID="⋆"
ID="⋆" Partially supported by CAPES
RID="⋆⋆"
ID="⋆⋆" Partially supported by CNPq and PROCAD. 相似文献
7.
The authors of this paper recently introduced a transformation [4] that converts a class of semidefinite programs (SDPs)
into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation enables the application
of nonlinear optimization techniques to the solution of certain SDPs that are too large for conventional interior-point methods
to handle efficiently. Based on the transformation, we proposed a globally convergent, first-order (i.e., gradient-based)
log-barrier algorithm for solving a class of linear SDPs. In this paper, we discuss an efficient implementation of the proposed
algorithm and report computational results on semidefinite relaxations of three types of combinatorial optimization problems.
Our results demonstrate that the proposed algorithm is indeed capable of solving large-scale SDPs and is particularly effective
for problems with a large number of constraints.
Received: June 22, 2001 / Accepted: January 20, 2002 Published online: December 9, 2002
RID="†"
ID="†"Computational results reported in this paper were obtained on an SGI Origin2000 computer at Rice University acquired
in part with support from NSF Grant DMS-9872009.
RID="⋆"
ID="⋆"This author was supported in part by NSF Grants CCR-9902010, INT-9910084 and CCR-0203426
RID="⋆⋆"
ID="⋆⋆"This author was supported in part by NSF Grants CCR-9902010, INT-9910084 and CCR-0203113
RID="⋆⋆⋆"
ID="⋆⋆⋆"This author was supported in part by DOE Grant DE-FG03-97ER25331, DOE/LANL Contract 03891-99-23 and NSF Grant DMS-9973339.
Key Words. semidefinite program – semidefinite relaxation – nonlinear programming – interior-point methods – limited memory quasi-Newton
methods.
Mathematics Subject Classification (1991): 90C06, 90C27, 90C30. 相似文献
8.
Let Γ be the fundamental group of the complement of a K(Γ, 1) hyperplane arrangement (such as Artin's pure braid group) or more generally a homologically toroidal group as defined below.
The triviality of bundles arising from orthogonal representations of Γ is characterized completely as follows. An orthogonal
representation gives rise to a trivial bundle if and only if the representation factors through the spinor groups. Furthermore,
the subgroup of elements in the complex K-theory of BΓ which arises from complex unitary representations of Γ is shown to be trivial. In the case of real K-theory, the subgroup of elements which arises from real orthogonal representations of Γ is an elementary abelian 2-group,
which is characterized completely in terms of the first two Stiefel-Whitney classes of the representation.
In addition, quadratic relations in the cohomology algebra of the pure braid groups which correspond precisely to the Jacobi
identity for certain choices of Poisson algebras are shown to give the existence of certain homomorphisms from the pure braid
group to generalized Heisenberg groups. These cohomology relations correspond to non-trivial Spin representations of the pure
braid groups which give rise to trivial bundles.
Received: 6 February 2002 / Revised version: 19 September 2002 /
Published online: 8 April 2003
RID="⋆"
ID="⋆" Partially supported by the NSF
RID="⋆⋆"
ID="⋆⋆" Partially supported by grant LEQSF(1999-02)-RD-A-01 from the Louisiana Board of Regents, and by grant MDA904-00-1-0038
from the National Security Agency
RID="⋆"
ID="⋆" Partially supported by the NSF
Mathematics Subject Classification (2000): 20F36, 32S22, 55N15, 55R50 相似文献
9.
We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a ℂ*-action. For varieties with an isolated singularity, covered by a family of rational curves with a general member not passing
through the singular point, we show that this singularity is rational. In particular, this provides an explanation of classical
results due to H. A. Schwartz and G. H. Halphen on polynomial solutions of the generalized Fermat equation.
Received: 7 May 2002 /
Published online: 16 May 2003
Mathematics Subject Classification (2000): 14J17, 14L30, 13H10 相似文献
10.
Given the integer polyhedronP
t
:= conv{x ∈ℤ
n
:Ax⩽b}, whereA ∈ℤ
m × n
andb ∈ℤ
m
, aChvátal-Gomory (CG)cut is a valid inequality forP
1 of the type λτAx⩽⌊λτb⌋ for some λ∈ℝ
+
m
such that λτA∈ℤ
n
. In this paper we study {0, 1/2}-CG cuts, arising for λ∈{0, 1/2}
m
. We show that the associated separation problem, {0, 1/2}-SEP, is equivalent to finding a minimum-weight member of a binary
clutter. This implies that {0, 1/2}-SEP is NP-complete in the general case, but polynomially solvable whenA is related to the edge-path incidence matrix of a tree. We show that {0, 1/2}-SEP can be solved in polynomial time for a
convenient relaxation of the systemAx<-b. This leads to an efficient separation algorithm for a subclass of {0, 1/2}-CG cuts, which often contains wide families of
strong inequalities forP
1. Applications to the clique partitioning, asymmetric traveling salesman, plant location, acyclic subgraph and linear ordering
polytopes are briefly discussed. 相似文献
11.
Parviz Sahandi 《Ricerche di matematica》2009,58(2):219-242
Given a stable semistar operation of finite type ⋆ on an integral domain D, we show that it is possible to define in a canonical way a stable semistar operation of finite type ⋆[X] on the polynomial ring D[X], such that, if n := ⋆-dim(D), then n+1 ≤ ⋆[X]-dim(D[X]) ≤ 2n+1. We also establish that if D is a ⋆-Noetherian domain or is a Prüfer ⋆-multiplication domain, then ⋆[X]-dim(D[X]) = ⋆- dim(D)+1. Moreover we define the semistar valuative dimension of the domain D, denoted by ⋆-dim
v
(D), to be the maximal rank of the ⋆-valuation overrings of D. We show that ⋆-dim
v
(D) = n if and only if ⋆[X
1, . . . , X
n
]-dim(D[X
1, . . . , X
n
]) = 2n, and that if ⋆-dim
v
(D) < ∞ then ⋆[X]-dim
v
(D[X]) = ⋆-dim
v
(D) + 1. In general ⋆-dim(D) ≤ ⋆-dim
v
(D) and equality holds if D is a ⋆-Noetherian domain or is a Prüfer ⋆-multiplication domain. We define the ⋆-Jaffard domains as domains D such that ⋆-dim(D) < ∞ and ⋆-dim(D) = ⋆-dim
v
(D). As an application, ⋆-quasi-Prüfer domains are characterized as domains D such that each (⋆, ⋆′)-linked overring T of D, is a ⋆′-Jaffard domain, where ⋆′ is a stable semistar operation of finite type on T. As a consequence of this result we obtain that a Krull domain D, must be a w
D
-Jaffard domain. 相似文献
12.
Given an integer polyhedron
, an integer point
, and a point
, the primal separation problem is the problem of finding a linear inequality which is valid for P
I
, violated by x
*, and satisfied at equality by
. The primal separation problem plays a key role in the primal approach to integer programming. In this paper we examine the complexity of primal separation for several well-known classes of inequalities for various important combinatorial optimization problems, including the knapsack, stable set and travelling salesman problems.Received: November 2002, Revised: March 2003, 相似文献
13.
A stable set in a graph G is a set of pairwise nonadjacent vertices. The problem of finding a maximum weight stable set is one of the most basic ℕℙ-hard
problems. An important approach to this problem is to formulate it as the problem of optimizing a linear function over the
convex hull STAB(G) of incidence vectors of stable sets. Since it is impossible (unless ℕℙ=coℕℙ) to obtain a “concise” characterization of STAB(G) as the solution set of a system of linear inequalities, it is a more realistic goal to find large classes of valid inequalities
with the property that the corresponding separation problem (given a point x
*, find, if possible, an inequality in the class that x
* violates) is efficiently solvable.?Some known large classes of separable inequalities are the trivial, edge, cycle and wheel
inequalities. In this paper, we give a polynomial time separation algorithm for the (t)-antiweb inequalities of Trotter. We then introduce an even larger class (in fact, a sequence of classes) of valid inequalities,
called (t)-antiweb-s-wheel inequalities. This class is a common generalization of the (t)-antiweb inequalities and the wheel inequalities. We also give efficient separation algorithms for them.
Received: June 2000 / Accepted: August 2001?Published online February 14, 2002 相似文献
14.
We study the local operator space structure of nuclear C
*
-algebras. It is shown that a C
*
-algebra is nuclear if and only if it is an 𝒪ℒ∞,λ space for some (and actually for every) λ>6. The 𝒪ℒ∞ constant λ provides an interesting invariant
for nuclear C
*
-algebras. Indeed, if 𝒜 is a nuclear C
*
-algebra, then we have 1≤𝒪ℒ∞(𝒜)≤6, and if 𝒜 is a unital nuclear C
*
-algebra with , we show that 𝒜 must be stably finite. We also investigate the connection between the rigid 𝒪ℒ∞,1+ structure and the rigid complete order 𝒪ℒ∞,1+ structure on C
*
-algebras, where the latter structure has been studied by Blackadar and Kirchberg in their characterization of strong NF C
*
-algebras. Another main result of this paper is to show that these two local structrues are actually equivalent on unital
nuclear C
*
-algebras. We obtain this by showing that if a unital (nuclear) C
*
-algebra is a rigid 𝒪ℒ∞,1+ space, then it is inner quasi-diagonal, and thus is a strong NF algebra. It is also shown that if a unital (nuclear) C
*
-algebra is an 𝒪ℒ∞,1+ space, then it is quasi-diagonal, and thus is an NF algebra.
Received: 26 June 2001 / Revised version: 7 May 2002 / Published online: 10 February 2003
Mathematics Subject Classification (2000): 46L07, 46L05, 47L25
Junge and Ruan were partially supported by the National Science Foundation. Ozawa was supported by the Japanese Society for
Promotion of Science. 相似文献
15.
Imre Patyi 《Mathematische Annalen》2003,326(3):443-458
Let X be one of the Banach spaces c
0
, ℓ
p
, 1≤p<∞; Ω⊂X pseudoconvex open, a holomorphic Banach vector bundle with a Banach Lie group G
*
for structure group. We show that a suitable Runge-type approximation hypothesis on X, G
*
(which we also prove for G
*
a solvable Lie group) implies the vanishing of the sheaf cohomology groups H
q
(Ω, 𝒪
E
), q≥1, with coefficients in the sheaf of germs of holomorphic sections of E. Further, letting 𝒪Γ (𝒞Γ) be the sheaf of germs of holomorphic (continuous) sections of a Banach Lie group bundle Γ→Ω with Banach Lie groups G, G
*
for fiber group and structure group, we show that a suitable Runge-type approximation hypothesis on X, G, G
*
(which we prove again for G, G
*
solvable Lie groups) implies the injectivity (and for X=ℓ1 also the surjectivity) of the Grauert–Oka map H
1
(Ω, 𝒪Γ)→H
1
(Ω, 𝒞Γ) of multiplicative cohomology sets.
Received: 1 March 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 32L20, 32L05, 46G20
RID="*"
ID="*" Kedves Laci Móhan kisfiamnak.
RID="*"
ID="*" To my dear little Son 相似文献
16.
In this paper, we analyze a unique continuation problem for the linearized Benjamin-Bona-Mahony equation with space-dependent
potential in a bounded interval with Dirichlet boundary conditions. The underlying Cauchy problem is a characteristic one.
We prove two unique continuation results by means of spectral analysis and the (generalized) eigenvector expansion of the
solution, instead of the usual Holmgren-type method or Carleman-type estimates. It is found that the unique continuation property
depends very strongly on the nature of the potential and, in particular, on its zero set, and not only on its boundedness
or integrability properties.
Received: 6 December 2001 / Revised version: 13 June 2002 / Published online: 10 February 2003
RID="⋆"
ID="⋆" Supported by a Postdoctoral Fellowship of the Spanish Education and Culture Ministry, the Foundation for the Author
of National Excellent Doctoral Dissertation of P.R. China (Project No: 200119), and the NSF of China under Grant 19901024
RID="⋆⋆"
ID="⋆⋆" Supported by grant PB96-0663 of the DGES (Spain) and the EU TMR Project "Homogenization and Multiple Scales".
Mathematics Subject Classification (2000): 35B60, 47A70, 47B07 相似文献
17.
John S. Caughman 《Graphs and Combinatorics》1998,14(4):321-343
Let Y=(X,{R
i
}0≤i≤D) denote a symmetric association scheme with D≥3, and assume Y is not an ordinary cycle. Suppose Y is bipartite P-polynomial with respect to the given ordering A
0, A
1,…, A
D
of the associate matrices, and Q-polynomial with respect to the ordering E
0, E
1,…,E
D
of the primitive idempotents. Then the eigenvalues and dual eigenvalues satisfy exactly one of (i)–(iv).
(i)
(ii) D is even, and
(iii) θ*
0>θ0, and
(iv) θ*
0>θ0, D is odd, and
Received: February 13, 1996 / Revised: October 16, 1996 相似文献
18.
Fedor V. Fomin 《Graphs and Combinatorics》2003,19(1):91-99
We prove that for every 2-connected planar graph the pathwidth of its geometric dual is less than the pathwidth of its line
graph. This implies that pathwidth(H)≤ pathwidth(H
*)+1 for every planar triangulation H and leads us to a conjecture that pathwidth(G)≤pathwidth(G
*)+1 for every 2-connected graph G.
Received: May 8, 2001 Final version received: March 26, 2002
RID="*"
ID="*" I acknowledge support by EC contract IST-1999-14186, Project ALCOM-FT (Algorithms and Complexity - Future Technologies)
and support by the RFBR grant N01-01-00235.
Acknowledgments. I am grateful to Petr Golovach, Roland Opfer and anonymous referee for their useful comments and suggestions. 相似文献
19.
Zeng Fanping 《数学学报(英文版)》1998,14(4):457-462
LetP andAC be two primary sequences with min{P, AC}≥RLR
∞,ρ(P) and ρ(AC) be the eigenvalues ofP andAC, respectively. Letf∈C
0
(I, I) be a unimodal expanding map with expanding constant λ and m be a nonegative integer. It is proved thatf has the kneading sequenceK(f)≥(RC)
*m
*P if λ≥(ρ(P))1/2m, andK(f)>(RC)
*m*AC*E for any shift maximal sequenceE if λ>(ρ(AC))1/2m. The value of (ρ(P))1/2m or (ρ(AC))1/2m is the best possible in the sense that the related conclusion may not be true if it is replaced by any smaller one.
Project supported by the National Natural Science Foundation of China 相似文献
20.
Summary. Impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current
flows and voltages on its surface. In its most general form impedance tomography is quite ill-posed, but when additional a-priori
information is admitted the situation changes dramatically. In this paper we consider the case where the goal is to find a
number of small objects (inhomogeneities) inside an otherwise known conductor. Taking advantage of the smallness of the inhomogeneities,
we can use asymptotic analysis to design a direct (i.e., non-iterative) reconstruction algorithm for the determination of
their locations. The viability of this direct approach is documented by numerical examples.
Received May 28, 2001 / Revised version received March 15, 2002 / Published online July 18, 2002
RID="⋆"
ID="⋆" Supported by the Deutsche Forschungsgemeinschaft (DFG) under grant HA 2121/2-3
RID="⋆⋆"
ID="⋆⋆" Supported by the National Science Foundation under grant DMS-0072556
Mathematics Subject Classification (2000): 65N21, 35R30, 35C20 相似文献