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1.
A novel method for the convex underestimation of univariate functions is presented in this paper. The method is based on a
piecewise application of the well-known αBB underestimator, which produces an overall underestimator that is piecewise convex. Subsequently, two algorithms are used
to identify the linear segments needed for the construction of its -continuous convex envelope, which is itself a valid convex underestimator of the original function. The resulting convex
underestimators are very tight, and their tightness benefits from finer partitioning of the initial domain. It is theoretically
proven that there is always some finite level of partitioning for which the method yields the convex envelope of the function
of interest. The method was applied on a set of univariate test functions previously presented in the literature, and the
results indicate that the method produces convex underestimators of high quality in terms of both lower bound and tightness
over the whole domain under consideration. 相似文献
2.
Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex
hyperbolic space with any specified value of the Hopf principal curvature α less than or equal to the corresponding value for the horosphere. We give a construction for all such hypersurfaces in terms
of Weierstrass-type data, and also obtain a classification of pseudo-Einstein hypersurfaces in .
相似文献
3.
In this article we extend Milnor’s fibration theorem to the case of functions of the form with f, g holomorphic, defined on a complex analytic (possibly singular) germ (X, 0). We further refine this fibration theorem by looking not only at the link of , but also at its multi-link structure, which is more subtle. We mostly focus on the case when X has complex dimension two. Our main result (Theorem 4.4) gives in this case the equivalence of the following three statements:
Moreover one has that if these conditions hold, then the Milnor-Lê fibration of is a fibration of the multilink . We also give a combinatorial criterium to decide whether or not the multilink is fibered. If the meromorphic germ f/g is semitame, then we show that the Milnor-Lê fibration given by is equivalent to the usual Milnor fibration given by . We finish this article by discussing several realization problems.
Research partially supported by CONACYT and DGAPA-UNAM, Mexico, and by CNRS and ECOS, France. 相似文献
(i) | The real analytic germ has 0 as an isolated critical value; |
(ii) | the multilink is fibered; and |
(iii) | if is a resolution of the holomorphic germ , then for each rupture vertex (j) of the decorated dual graph of π one has that the corresponding multiplicities of f, g satisfy: . |
4.
Let be a C
2 map and let Spec(Y) denote the set of eigenvalues of the derivative DY
p
, when p varies in . We begin proving that if, for some ϵ > 0, then the foliation with made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case
of Jelonek’s Jacobian Conjecture for polynomial maps of
The first author was supported by CNPq-Brazil Grant 306992/2003-5. The first and second author were supported by FAPESP-Brazil
Grant 03/03107-9. 相似文献
5.
Laguerre geometry of surfaces in is given in the book of Blaschke [Vorlesungen über Differentialgeometrie, Springer, Berlin Heidelberg New York (1929)], and has been studied by Musso and Nicolodi [Trans. Am. Math. soc. 348, 4321–4337 (1996); Abh. Math. Sem. Univ. Hamburg 69, 123–138 (1999); Int. J. Math. 11(7), 911–924 (2000)], Palmer [Remarks on a variation problem in Laguerre geometry. Rendiconti di Mathematica, Serie VII, Roma, vol. 19, pp. 281–293 (1999)] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in . For any umbilical free hypersurface with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invariant self-adjoint operator : TM → TM, and show that is a complete Laguerre invariant system for hypersurfaces in with n≥ 4. We calculate the Euler–Lagrange equation for the Laguerre volume functional of Laguerre metric by using Laguerre invariants. Using the Euclidean space , the semi-Euclidean space and the degenerate space we define three Laguerre space forms , and and define the Laguerre embeddings and , analogously to what happens in the Moebius geometry where we have Moebius space forms S
n
, and (spaces of constant curvature) and conformal embeddings and [cf. Liu et al. in Tohoku Math. J. 53, 553–569 (2001) and Wang in Manuscr. Math. 96, 517–534 (1998)]. Using these Laguerre embeddings we can unify the Laguerre geometry of hypersurfaces in , and . As an example we show that minimal surfaces in or are Laguerre minimal in .C. Wang Partially supported by RFDP and Chuang-Xin-Qun-Ti of NSFC. 相似文献
6.
Ioannis G. Akrotirianakis Christodoulos A. Floudas 《Journal of Global Optimization》2004,30(4):367-390
We present a new class of convex underestimators for arbitrarily nonconvex and twice continuously differentiable functions. The underestimators are derived by augmenting the original nonconvex function by a nonlinear relaxation function. The relaxation function is a separable convex function, that involves the sum of univariate parametric exponential functions. An efficient procedure that finds the appropriate values for those parameters is developed. This procedure uses interval arithmetic extensively in order to verify whether the new underestimator is convex. For arbitrarily nonconvex functions it is shown that these convex underestimators are tighter than those generated by the BB method. Computational studies complemented with geometrical interpretations demonstrate the potential benefits of the proposed improved convex underestimators. 相似文献
7.
P. Habegger 《Mathematische Annalen》2008,342(2):449-466
Let be an irreducible closed subvariety defined over . We bound the height of algebraic points on X that are in a certain sense close to the union of all algebraic subgroup of of dimension m < n/dim X. The bound we obtain is effective and will be expressed as a function of the height of X, the degree of X, and n. We then apply this bound to derive certain finiteness results if m is also strictly less than n − dim X. 相似文献
8.
Let G be a connected graph. For at distance 2, we define , and , if then . G is quasi-claw-free if it satisfies , and G is P
3-dominated() if it satisfies , for every pair (x, y) of vertices at distance 2. Certainly contains as a subclass. In this paper, we prove that the circumference of a 2-connected P
3-dominated graph G on n vertices is at least min or , moreover if then G is hamiltonian or , where is a class of 2-connected nonhamiltonian graphs. 相似文献
9.
We prove that several types of open Riemann surfaces, including the finitely connected planar domains, embed properly into
such that the values on any given discrete sequence can be arbitrarily prescribed.
Kutzschebauch supported by Schweizerische Nationalfonds grant 200021-107477/1. 相似文献
10.
Frédéric A. B. Edoukou 《Designs, Codes and Cryptography》2009,50(1):135-146
We study the functional codes of second order on a non-degenerate Hermitian variety as defined by G. Lachaud. We provide the best possible bounds for the number of points of quadratic sections of . We list the first five weights, describe the corresponding codewords and compute their number. The paper ends with two
conjectures. The first is about minimum distance of the functional codes of order h on a non-singular Hermitian variety . The second is about distribution of the codewords of first five weights of the functional codes of second order on a non-singular
Hermitian variety .
相似文献
11.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
12.
Given a hypersurface M of null scalar curvature in the unit sphere , n ≥ 4, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in as a normal graph over a truncated cone generated by M. Furthermore, this graph is 1-stable if the cone is strictly 1-stable. 相似文献
13.
Patrick Ingram 《Monatshefte für Mathematik》2009,339(1):69-89
A lower bound is obtained of the canonical height associated to the morphism evaluated at wandering points α. The lower bound is of the form Ch(c), for some constant C depending on the the number of primes of bad reduction for , and the degree of the number field .
The author was supported by a PDF grant from NSERC. 相似文献
14.
Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it
is proved that some designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs. And some
conditions are provided, under which a design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time. Some weak
minimum aberration designs are provided for illustrations and two nonisomorphic weak minimum aberration designs are constructed at the end of this paper. 相似文献
15.
We study permanence properties of the classes of stable and so-called -stable -algebras, respectively. More precisely, we show that a (X)-algebra A is stable if all its fibres are, provided that the underlying compact metrizable space X has finite covering dimension or that the Cuntz semigroup of A is almost unperforated (a condition which is automatically satisfied for -algebras absorbing the Jiang–Su algebra tensorially). Furthermore, we prove that if is a K
1-injective strongly self-absorbing -algebra, then A absorbs tensorially if and only if all its fibres do, again provided that X is finite-dimensional. This latter statement generalizes results of Blanchard and Kirchberg. We also show that the condition
on the dimension of X cannot be dropped. Along the way, we obtain a useful characterization of when a -algebra with weakly unperforated Cuntz semigroup is stable, which allows us to show that stability passes to extensions of
-absorbing -algebras.
Research supported by: Deutsche Forschungsgemeinschaft (through the SFB 478), by the EU-Network Quantum Spaces - Noncommutative
Geometry (Contract No. HPRN-CT-2002-00280), and by the Center for Advanced Studies in Mathematics at Ben-Gurion University 相似文献
16.
In this paper, we continue our investigation on “Extremal problems under dimension constraints” introduced [1]. The general problem we deal with in this paper can be formulated as follows. Let
be an affine plane of dimension k in
. Given
determine or estimate
.Here we consider and solve the problem in the special case where
is a hyperplane in
and the “forbidden set”
. The same problem is considered for the case, where
is a hyperplane passing through the origin, which surprisingly turns out to be more difficult. For this case we have only partial results.AMS Classification: 05C35, 05B30, 52C99 相似文献
17.
In this paper we present recent results concerning global aspects of and -actions on Stein surfaces. Our approach is based on a byproduct of techniques from Geometric Theory of Foliations (holonomy,
stability), Potential theory (parabolic Riemann surfaces, Riemann-Koebe Uniformization theorem) and Several Complex Variables
(Hartogs’ extension theorems, Theory of Stein spaces). Our main motivation comes from the original works of M. Suzuki and
Orlik-Wagreich. Some of their results are extended to a more general framework. In particular, we prove some linearization
theorems for holomorphic actions of and on normal Stein analytic spaces of dimension two. We also add a list of questions and open problems in the subject. The underlying
idea is to present the state of the art of this research field.
相似文献
18.
Boumediene Abdellaoui Veronica Felli Ireneo Peral 《Calculus of Variations and Partial Differential Equations》2009,34(1):97-137
We study the existence of different types of positive solutions to problem
where , , and is the critical Sobolev exponent. A careful analysis of the behavior of Palais-Smale sequences is performed to recover compactness
for some ranges of energy levels and to prove the existence of ground state solutions and mountain pass critical points of the associated functional on the Nehari manifold. A variational perturbative method is also used to study
the existence of a non trivial manifold of positive solutions which bifurcates from the manifold of solutions to the uncoupled
system corresponding to the unperturbed problem obtained for ν = 0.
B. Abdellaoui and I. Peral supported by projects MTM2007-65018, MEC and CCG06-UAM/ESP-0340, Spain. V. Felli supported by Italy
MIUR, national project Variational Methods and Nonlinear Differential Equations. 相似文献
19.
Claudemir Aniz 《Central European Journal of Mathematics》2008,6(4):497-503
Let K be a CW-complex of dimension 3 such that H
3(K;ℤ) = 0 and the orbit space of the 3-sphere with respect to the action of the quaternion group Q
8 determined by the inclusion Q
8 ⊆ . Given a point a ∈ , we show that there is no map f:K → which is strongly surjective, i.e., such that MR[f,a]=min{#(g
−1(a))|g ∈ [f]} ≠ 0.
相似文献
20.
In this paper we fix a set * of positive elements of the free group
(e. g. the set of finite words occurring in a Markov subshift) as well as n partial isometries on a Hilbert space H. Based on these we define a map S :
which we prove to be a partial representation of
on H under certain conditions studied by Matsumoto.*Supported by Capes. 相似文献