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1.
H. Gröflin 《Combinatorica》1987,7(2):193-204
A class of integer polyhedra with totally dual integral (tdi) systems is proposed, which generalizes and unifies the “Switching
Paths Polyhedra” of Hoffman (introduced in his generalization of Max Flow-Min Cut) and such polyhedra as the convex hull of
(the incidence vectors of) all “path-closed sets” of an acyclic digraph, or the convex hull of all sets partitionable intok path-closed sets. As an application, new min-max theorems concerning the mentioned sets are given. A general lemma on when
a tdi system of inequalities is box tdi is also given and used. 相似文献
2.
In Machine Learning algorithms, one of the crucial issues is the representation of the data. As the given data source become
heterogeneous and the data are large-scale, multiple kernel methods help to classify “nonlinear data”. Nevertheless, the finite
combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, a novel method of “infinite”
kernel combinations is proposed with the help of infinite and semi-infinite programming regarding all elements in kernel space.
Looking at all infinitesimally fine convex combinations of the kernels from the infinite kernel set, the margin is maximized
subject to an infinite number of constraints with a compact index set and an additional (Riemann–Stieltjes) integral constraint
due to the combinations. After a parametrization in the space of probability measures, it becomes semi-infinite. We adapt
well-known numerical methods to our infinite kernel learning model and analyze the existence of solutions and convergence
for the given algorithms. We implement our new algorithm called “infinite” kernel learning (IKL) on heterogenous data sets
by using exchange method and conceptual reduction method, which are well known numerical techniques from solve semi-infinite
programming. The results show that our IKL approach improves the classifaction accuracy efficiently on heterogeneous data
compared to classical one-kernel approaches. 相似文献
3.
Sylvia Chiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,151(1):940-959
We study the pressureless gas equations, with piecewise constant initial data. In the immediate solution, δ-shocks and contact
vacuum states arise and even meet (interact) eventually. A solution beyond the “interaction” is constructed. It shows that
the δ-shock will continue with the velocity it attained instantaneously before the time of interaction, and similarly, the
contact vacuum state will move past the δ-shock with a velocity value prior to the interaction. We call this the “no-effect-from-interaction”
solution.
We prove that this solution satisfies a family of convex entropies (in the Lax’s sense). Next, we construct an infinitely
large family of weak solutions to the “interaction”. Suppose further that any of these solutions satisfy a convex entropy,
it is necessary and suffcient that these solutions reduce to only the “no-effect-from-interaction” solution. In [1], Bouchut
constructed another entropy satisfying solution. As with other previous papers, it is obvious that it will not be sufficient
that a “correct” solution satisfies a convex entropy, in a non-strictly hyperbolic conservation laws system. 相似文献
4.
Sylvia Chiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):940-959
We study the pressureless gas equations, with piecewise constant initial data. In the immediate solution, δ-shocks and contact
vacuum states arise and even meet (interact) eventually. A solution beyond the “interaction” is constructed. It shows that
the δ-shock will continue with the velocity it attained instantaneously before the time of interaction, and similarly, the
contact vacuum state will move past the δ-shock with a velocity value prior to the interaction. We call this the “no-effect-from-interaction”
solution.
We prove that this solution satisfies a family of convex entropies (in the Lax’s sense). Next, we construct an infinitely
large family of weak solutions to the “interaction”. Suppose further that any of these solutions satisfy a convex entropy,
it is necessary and suffcient that these solutions reduce to only the “no-effect-from-interaction” solution. In [1], Bouchut
constructed another entropy satisfying solution. As with other previous papers, it is obvious that it will not be sufficient
that a “correct” solution satisfies a convex entropy, in a non-strictly hyperbolic conservation laws system.
Research done in the University of Michigan-Ann Arbor, submission from Temasek Laboratories, National University of Singapore. 相似文献
5.
Benedikt Löwe 《Archive for Mathematical Logic》2001,40(8):651-664
We investigate Turing cones as sets of reals, and look at the relationship between Turing cones, measures, Baire category
and special sets of reals, using these methods to show that Martin's proof of Turing Determinacy (every determined Turing
closed set contains a Turing cone or is disjoint from one) does not work when you replace “determined” with “Blackwell determined”.
This answers a question of Tony Martin.
Received: 6 December 1999 / Revised version: 28 June 2000 Published online: 3 October 2001 相似文献
6.
Kalpana Dahiya Surjeet Kaur Suneja Vanita Verma 《Computational Optimization and Applications》2007,36(1):67-82
In this paper a minimization problem with convex objective function subject to a separable convex inequality constraint “≤”
and bounded variables (box constraints) is considered. We propose an iterative algorithm for solving this problem based on
line search and convergence of this algorithm is proved. At each iteration, a separable convex programming problem with the
same constraint set is solved using Karush-Kuhn-Tucker conditions. Convex minimization problems subject to linear equality/
linear inequality “≥” constraint and bounds on the variables are also considered. Numerical illustration is included in support
of theory. 相似文献
7.
G. Crombez 《Czechoslovak Mathematical Journal》2006,56(2):491-506
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in
a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor”
between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the
iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted.
In this paper we present a technique that may introduce interruption of the monotony for a sequential algorithm, but that
at the same time guarantees convergence of the constructed sequence to a point in the intersection of the sets. We compare
experimentally the behaviour concerning the speed of convergence of the new algorithm with that of an existing monotoneous
algorithm. 相似文献
8.
A class of biholomorphic mappings named “quasi-convex mapping” is introduced in the unit ball of a complex Banach space. It
is proved that this class of mappings is a proper subset of the class of starlike mappings and contains the class of convex
mappings properly, and it has the same growth and covering theorems as the convex mappings. Furthermore, when the Banach space
is confined to ℂn, the “quasi-convex mapping” is exactly the “quasi-convex mapping of type A” introduced by K. A. Roper and T. J. Suffridge. 相似文献
9.
Ulrich Brehm 《Discrete and Computational Geometry》1992,8(1):153-169
Let
be any finite set with no three points on a line. Then we construct explicitly families of bounded Borel sets which are not
uniquely determined by their X-ray images from the points inX. This result is in sharp contrast to the known uniqueness results for convex sets (Hammer's X-ray problem).
This research was partially supported by the Italian “Consiglio Nazionale delle Ricerche.” 相似文献
10.
We show that without using inaccessible cardinals it is possible to get models of “ZF+all sets of reals have the Baire property
+DC(ω1)” and “ZFC+all projective sets have the Baire property+the union of less than ω2 many meager sets is meager”, answering two well-known open questions of Woodin and Judah, respectively.
The authors would like to thank the Israel Academy of Sciences BSF for partial support.
The second author would like to thank the Landau Center for Mathematical Analysis, supported by the Minerva Foundation (Germany). 相似文献
11.
Aviad Heifetz 《International Journal of Game Theory》1999,28(3):435-442
Aumann (1989) argued that the natural partitions on the space of all maximally consistent sets of formulas in multi-player
S5 logic are necessarily “commonly known” by the players. We show, however, that there are many other sets of partitions on
this space that conform with the formulas that build the states – as many as there are subsets of the continuum! Thus, assuming
a set of partitions on this space is “common knowledge” is an informal but meaningful meta-assumption. 相似文献
12.
To minimize a convex function, we combine Moreau-Yosida regularizations, quasi-Newton matrices and bundling mechanisms. First
we develop conceptual forms using “reversal” quasi-Newton formulae and we state their global and local convergence. Then,
to produce implementable versions, we incorporate a bundle strategy together with a “curve-search”. No convergence results
are given for the implementable versions; however some numerical illustrations show their good behaviour even for large-scale
problems. 相似文献
13.
Lech Pasicki 《Czechoslovak Mathematical Journal》2011,61(2):383-388
The notion of a metric bead space was introduced in the preceding paper (L.Pasicki: Bead spaces and fixed point theorems,
Topology Appl., vol. 156 (2009), 1811–1816) and it was proved there that every bounded set in such a space (provided the space
is complete) has a unique central point. The bead spaces themselves can be considered in particular as natural extensions
of convex sets in uniformly convex spaces. It appears that normed bead spaces are identical with uniformly convex spaces.
On the other hand the “metric” approach leads to new elementary conditions equivalent to the uniform convexity. The initial
part of the paper contains the proof that discus spaces (they seem to have a richer structure) are identical with bead spaces. 相似文献
14.
Gy. Elekes 《Discrete and Computational Geometry》1994,12(1):439-449
We develop a technique suitable for determining the minimal area convex set that can cover certain prescribed regular polygons.
As a side effect we improve the well-known “circle-and-triangle” lower bound on the least area Universal Convex Cover (UCC).
Dedicated to the memory of Zs. Baranyai 相似文献
15.
C. Zălinescu 《Optimization Letters》2012,6(3):393-402
In their paper “Duality of linear conic problems” Shapiro and Nemirovski considered two possible properties (A) and (B) for
dual linear conic problems (P) and (D). The property (A) is “If either (P) or (D) is feasible, then there is no duality gap
between (P) and (D)”, while property (B) is “If both (P) and (D) are feasible, then there is no duality gap between (P) and
(D) and the optimal values val(P) and val(D) are finite”. They showed that (A) holds if and only if the cone K is polyhedral, and gave some partial results related to (B). Later Shapiro conjectured that (B) holds if and only if all
the nontrivial faces of the cone K are polyhedral. In this note we mainly prove that both the “if” and “only if” parts of this conjecture are not true by providing
examples of closed convex cone in
\mathbbR4{\mathbb{R}^{4}} for which the corresponding implications are not valid. Moreover, we give alternative proofs for the results related to (B)
established by Shapiro and Nemirovski. 相似文献
16.
T. E. Panov 《Proceedings of the Steklov Institute of Mathematics》2008,263(1):150-162
In the theory of algebraic group actions on affine varieties, the concept of a Kempf-Ness set is used to replace the categorical
quotient by the quotient with respect to a maximal compact subgroup. Using recent achievements of “toric topology,” we show
that an appropriate notion of a Kempf-Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate
subspace arrangement complements) arising in the Batyrev-Cox “geometric invariant theory” approach to toric varieties. We
proceed by studying the cohomology of these “toric” Kempf-Ness sets. In the case of projective nonsingular toric varieties
the Kempf-Ness sets can be described as complete intersections of real quadrics in a complex space.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 263, pp. 159–172. 相似文献
17.
Emanuel Milman 《Inventiones Mathematicae》2009,177(1):1-43
We show that for convex domains in Euclidean space, Cheeger’s isoperimetric inequality, spectral gap of the Neumann Laplacian,
exponential concentration of Lipschitz functions, and the a-priori weakest requirement that Lipschitz functions have arbitrarily slow uniform tail-decay, are all quantitatively equivalent (to within universal constants, independent of the dimension). This
substantially extends previous results of Maz’ya, Cheeger, Gromov–Milman, Buser and Ledoux. As an application, we conclude
a sharp quantitative stability result for the spectral gap of convex domains under convex perturbations which preserve volume
(up to constants) and under maps which are “on-average” Lipschitz. We also provide a new characterization (up to constants)
of the spectral gap of a convex domain, as one over the square of the average distance from the “worst” subset having half
the measure of the domain. In addition, we easily recover and extend many previously known lower bounds on the spectral gap
of convex domains, due to Payne–Weinberger, Li–Yau, Kannan–Lovász–Simonovits, Bobkov and Sodin. The proof involves estimates
on the diffusion semi-group following Bakry–Ledoux and a result from Riemannian Geometry on the concavity of the isoperimetric
profile. Our results extend to the more general setting of Riemannian manifolds with density which satisfy the CD(0,∞) curvature-dimension condition of Bakry-émery.
Supported by NSF under agreement #DMS-0635607. 相似文献
18.
Ivan Izmestiev 《Discrete and Computational Geometry》2008,40(4):561-585
We give a variational proof of the existence and uniqueness of a convex cap with the given metric on the boundary. The proof
uses the concavity of the total scalar curvature functional (also called Hilbert-Einstein functional) on the space of generalized
convex caps. As a by-product, we prove that generalized convex caps with the fixed metric on the boundary are globally rigid,
that is uniquely determined by their curvatures.
Research for this article was supported by the DFG Research Unit 565 “Polyhedral Surfaces”. 相似文献
19.
Laurent Stolovitch 《Publications Mathématiques de L'IHéS》2005,102(1):99-165
Let X be a germ of holomorphic vector field at the origin of Cn and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system.
The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first
integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets
in a neighborhood of the origin. These are biholomorphic to the intersection of a polydisc with an analytic set of the form
“resonant monomials = constants”. Such a biholomorphism conjugates the restriction of X to one of its invariant varieties
to the restriction of a linear diagonal vector field to a toric variety. Moreover, we show that the set of “frequencies” defining
the invariant sets is of positive measure. 相似文献
20.
Paola Magrone 《NoDEA : Nonlinear Differential Equations and Applications》2008,15(6):717-728
We prove the existence of a nontrivial solution for a quasilinear elliptic equation involving a nonlinearity having critical
growth and a convex principal part, which is not required to be strictly convex.
Supported by MURST, Project “Variational Methods and Nonlinear Differential Equations”. 相似文献