共查询到20条相似文献,搜索用时 15 毫秒
1.
Joe Warren Scott Schaefer Anil N. Hirani Mathieu Desbrun 《Advances in Computational Mathematics》2007,27(3):319-338
In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates
over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located
on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation
in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric
coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review
the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how
these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide
a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally,
we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they
can be used to perform freeform deformations.
相似文献
2.
Mihai Cristea 《Complex Analysis and Operator Theory》2011,5(3):863-880
The paper continues the work of Royster (Duke Math J 19:447–457, 1952), Mocanu [Mathematica (Cluj) 22(1):77–83, 1980; Mathematica
(Cluj) 29:49–55, 1987], Cristea [Mathematica (Cluj) 36(2):137–144, 1994; Complex Var 42:333–345, 2000; Mathematica (Cluj)
43(1):23–34, 2001; Mathematica (Cluj), 2010, to appear; Teoria Topologica a Functiilor Analitice, Editura Universitatii Bucuresti,
Romania, 1999] of extending univalence criteria for complex mappings to C
1 mappings. We improve now the method of Loewner chains which is usually used in complex univalence theory for proving univalence
criteria or for proving quasiconformal extensions of holomorphic mappings f : B → C
n
to C
n
. The results are surprisingly strong. We show that the usual results from the theory, like Becker’s univalence criteria remain
true for C
1 mappings and since we use a stronger form of Loewner’s theory, we obtain results which are stronger even for holomorphic
mappings f : B → C
n
. In our main result (Theorem 4.1) we end the researches dedicated to quasiconformal extensions of K-quasiregular and holomorphic mappings f : B → C
n
to C
n
. We show that a C
1 quasiconformal map f : B → C
n
can be extended to a quasiconformal map F : C
n
→ C
n
, without any metric condition imposed to the map f. 相似文献
3.
Tianxiao He Leetsch C. Hsu Peter J. S. Shiue 《分析论及其应用》2005,21(4):359-369
We present a constructive generalization of Abel-Gontscharoff's series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given. 相似文献
4.
By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize
bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-regular Loewner spaces. Meanwhile the sufficient and necessary conditions for quasiconformal maps to become bi-Lipschitz
maps are also obtained. These results generalize Rohde’s theorem in ℝ
n
and improve Balogh’s corresponding results in Carnot groups.
This research is supported by China NSF (Grant No. 10271077) 相似文献
5.
Loewner’s Torus Inequality with Isosystolic Defect 总被引:1,自引:0,他引:1
We show that Bonnesen’s isoperimetric defect has a systolic analog for Loewner’s torus inequality. The isosystolic defect
is expressed in terms of the probabilistic variance of the conformal factor of the metric
G{\mathcal{G}}
with respect to the flat metric of unit area in the conformal class of
G{\mathcal{G}}
. 相似文献
6.
Xiang Fang 《Geometric And Functional Analysis》2006,16(2):367-402
This paper concerns Fredholm theory in several variables, and its applications to Hilbert spaces of analytic functions. One
feature is the introduction of ideas from commutative algebra to operator theory. Specifically, we introduce a method to calculate
the Fredholm index of a pair of commuting operators. To achieve this, we define and study the Hilbert space analogs of Samuel
multiplicities in commutative algebra. Then the theory is applied to the symmetric Fock space. In particular, our results
imply a satisfactory answer to Arveson’s program on developing a Fredholm theory for pure d-contractions when d = 2, including both the Fredholmness problem and the calculation of indices. We also show that Arveson’s curvature invariant
is in fact always equal to the Samuel multiplicity for an arbitrary pure d-contraction with finite defect rank. It follows that the curvature is a similarity invariant.
Received: October 2004 Revision: May 2005 Accepted: May 2005
Partially supported by National Science Foundation Grant DMS 0400509. 相似文献
7.
K. Gelashvili 《Journal of Mathematical Sciences》2011,177(3):373-382
The problem of existence of an optimal control is solved on the basis of Weierstrass’s classical theorem if the set of admissible
controls belongs to the class of piecewise continuous functions. In the process of describing admissible controls, the main
assumption is that the number of switchings (points of discontinuity) is uniformly bounded and not just finite, as in the
main problem of optimal control theory. On the one hand, this assumption does not restrict the spectrum of optimal control
applications. On the other hand, it fits the Weierstrass’s theorem owing to the convenience in characterizing the sequential
compactness. The formulation of Weierstrass’s theorem, which asserts the existence of continuous function extrema on sequentially
compact sets, is customary, and its proof complies with the traditional scheme, whereas the concepts (convergent sequences
and some others) are adapted to the peculiarity of optimal problems. 相似文献
8.
V. I. Maksimov 《Proceedings of the Steklov Institute of Mathematics》2010,271(1):138-148
We consider the problem of tracking a reference solution of a dynamical system described by a pair of distributed differential
equations, the phase field equations. To solve this problem, we propose an algorithm based on Yu.S. Osipov’s theory of dynamic
inversion and on N.N. Krasovskii’s extremal shift method developed in the theory of positional differential games. 相似文献
9.
In this paper, we investigate a third-order linear differential equation with three additional conditions. We find a solution
to this problem and give a formula and an existence condition for Green’s function. We compare two Green’s functions for two
such problems with different additional conditions: nonlocal and classical boundary conditions. Formula applications are shown
by examples. 相似文献
10.
We consider the interpolation Nevanlinna-Pick problem with infinitely many interpolation nodes in the class S[a, b] and rational matrix functions associated with this problem and orthogonal on the segment [a, b]. We obtain a criterion of complete indeterminacy of the Nevanlinna-Pick problem in terms of orthogonal rational matrix functions.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 6, pp. 764–770, June, 2007. 相似文献
11.
In bilevel optimization problems there are two decision makers, the leader and the follower, who act in a hierarchy. Each
decision maker has his own objective function, but there are common constraints. This paper deals with bilevel assignment
problems where each decision maker controls a subset of edges and each edge has a leader’s and a follower’s weight. The edges
selected by the leader and by the follower need to form a perfect matching. The task is to determine which edges the leader
should choose such that his objective value which depends on the follower’s optimal reaction is maximized. We consider sum-
and bottleneck objective functions for the leader and follower. Moreover, if not all optimal reactions of the follower lead
to the same leader’s objective value, then the follower either chooses an optimal reaction which is best (optimistic rule)
or worst (pessimistic rule) for the leader. We show that all the variants arising if the leader’s and follower’s objective
functions are sum or bottleneck functions are NP-hard if the pessimistic rule is applied. In case of the optimistic rule the problem is shown to be NP-hard if at least one of the decision makers has a sum objective function. 相似文献
12.
Discrete convex analysis 总被引:6,自引:0,他引:6
Kazuo Murota 《Mathematical Programming》1998,83(1-3):313-371
A theory of “discrete convex analysis” is developed for integer-valued functions defined on integer lattice points. The theory
parallels the ordinary convex analysis, covering discrete analogues of the fundamental concepts such as conjugacy, subgradients,
the Fenchel min-max duality, separation theorems and the Lagrange duality framework for convex/nonconvex optimization. The
technical development is based on matroid-theoretic concepts, in particular, submodular functions and exchange axioms. Sections
1–4 extend the conjugacy relationship between submodularity and exchange ability, deepening our understanding of the relationship
between convexity and submodularity investigated in the eighties by A. Frank, S. Fujishige, L. Lovász and others. Sections
5 and 6 establish duality theorems for M- and L-convex functions, namely, the Fenchel min-max duality and separation theorems.
These are the generalizations of the discrete separation theorem for submodular functions due to A. Frank and the optimality
criteria for the submodular flow problem due to M. Iri-N. Tomizawa, S. Fujishige, and A. Frank. A novel Lagrange duality framework
is also developed in integer programming. We follow Rockafellar’s conjugate duality approach to convex/nonconvex programs
in nonlinear optimization, while technically relying on the fundamental theorems of matroid-theoretic nature. 相似文献
13.
L. L. Maksimova 《Siberian Mathematical Journal》2010,51(3):479-490
Analogs of Robinson’s theorem on joint consistency are found which are equivalent to the weak interpolation property (WIP)
in extensions of Johansson’s minimal logic J. Although all propositional superintuitionistic logics possess this property,
there are J-logics without WIP. It is proved that the problem of the validity of WIP in J-logics can be reduced to the same
problem over the logic Gl obtained from J by adding the tertium non datur. Some algebraic criteria for validity of WIP over
J and Gl are found. 相似文献
14.
Michael Kunzinger 《Monatshefte für Mathematik》2002,137(1):31-49
Based on Colombeau’s theory of algebras of generalized functions we introduce the concepts of generalized functions taking
values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic properties,
in particular with respect to some new point value concepts for generalized functions and indicate applications of the resulting
theory in general relativity.
Received February 13, 2002 相似文献
15.
Within the framework of the multiple Nevanlinna–Pick matrix interpolation and its related matrix moment problem, we study the rank of block moment matrices of various kinds, generalized block Pick matrices and generalized block Loewner matrices, as well as their Potapov modifications, generated by Nevanlinna matrix functions, and derive statements either on rank (or inertia) invariance in different senses or on rank variation of such types of block matrices (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
Aurelian Bejancu 《Constructive Approximation》2011,34(2):237-256
Duchon’s method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain
integral functional. For transfinite interpolation, i.e., interpolation of continuous data prescribed on curves or hypersurfaces,
Kounchev has developed the method of polysplines, which are piecewise polyharmonic functions of fixed smoothness across the
given hypersurfaces and satisfy some boundary conditions. Recently, Bejancu has introduced boundary conditions of Beppo–Levi
type to construct a semicardinal model for polyspline interpolation to data on an infinite set of parallel hyperplanes. The
present paper proves that, for periodic data on a finite set of parallel hyperplanes, the polyspline interpolant satisfying
Beppo–Levi boundary conditions is in fact a thin plate spline, i.e., it minimizes a Duchon type functional. The construction
and variational characterization of the Beppo–Levi polysplines are based on the analysis of a new class of univariate exponential
ℒ-splines satisfying adjoint natural end conditions. 相似文献
17.
This paper presents a bilevel fuzzy principal-agent model for optimal nonlinear taxation problems with asymmetric information,
in which the government and the monopolist are the principals, the consumer is their agent. Since the assessment of the government
and the monopolist about the consumer’s taste is subjective, therefore, it is reasonable to characterize this assessment as
a fuzzy variable. What’s more, a bilevel fuzzy optimal nonlinear taxation model is developed with the purpose of maximizing
the expected social welfare and the monopolist’s expected welfare under the incentive feasible mechanism. The equivalent model
for the bilevel fuzzy optimal nonlinear taxation model is presented and Pontryagin maximum principle is adopted to obtain
the necessary conditions of the solutions for the fuzzy optimal nonlinear taxation problems. Finally, one numerical example
is given to illustrate the effectiveness of the proposed model, the results demonstrate that the consumer’s purchased quantity
not only relates with the consumer’s taste, but also depends on the structure of the social welfare. 相似文献
18.
Masao Ishikawa 《The Ramanujan Journal》2008,16(2):211-234
In the open problem session of the FPSAC’03, R.P. Stanley gave an open problem about a certain sum of the Schur functions.
The purpose of this paper is to give a proof of this open problem. The proof consists of three steps. At the first step we
express the sum by a Pfaffian as an application of our minor summation formula (Ishikawa and Wakayama in Linear Multilinear
Algebra 39:285–305, 1995). In the second step we prove a Pfaffian analogue of a Cauchy type identity which generalizes Sundquist’s
Pfaffian identities (J. Algebr. Comb. 5:135–148, 1996). Then we give a proof of Stanley’s open problem in Sect. 4. At the end of this paper we present certain corollaries obtained
from this identity involving the Big Schur functions and some polynomials arising from the Macdonald polynomials, which generalize
Stanley’s open problem.
相似文献
19.
We investigate the problem of interpolation of functions of two real variables by two-dimensional continued fractions.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 6, pp. 842–851, June, 2006. 相似文献
20.
In this paper we propose a class of new large-update primal-dual interior-point algorithms for P
*(κ) nonlinear complementarity problem (NCP), which are based on a class of kernel functions investigated by Bai et al. in their
recent work for linear optimization (LO). The arguments for the algorithms are followed as Peng et al.’s for P
*(κ) complementarity problem based on the self-regular functions [Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm
for Primal-Dual Interior-Point Algorithms, Princeton University Press, Princeton, 2002]. It is worth mentioning that since
this class of kernel functions includes a class of non-self-regular functions as special case, so our algorithms are different
from Peng et al.’s and the corresponding analysis is simpler than theirs. The ultimate goal of the paper is to show that the
algorithms based on these functions have favorable polynomial complexity. 相似文献