共查询到20条相似文献,搜索用时 31 毫秒
1.
《Numerical Functional Analysis & Optimization》2013,34(2):157-175
ABSTRACT We distinguish classes of operators T with fixed points on a real Hilbert space by comparing the distances of a point x and its image Tx to the (set of) fixed points of T; this leads to a ranking of those classes, based on a nonnegative parameter. That same parameter also lets us conclude about the sign of and an upper bound for a characteristic inner product result that arises in iterative processes to obtain a common fixed point of a set of operators. We use that parameter as the starting point for a geometrically-inclined study of specific iterative algorithms intended to find a common fixed point of operators belonging to such class. 相似文献
2.
J.-D. Boissonnat M. Sharir B. Tagansky M. Yvinec 《Discrete and Computational Geometry》1998,19(4):485-519
The paper bounds the combinatorial complexity of the Voronoi diagram of a set of points under certain polyhedral distance
functions. Specifically, if S is a set of n points in general position in R
d
, the maximum complexity of its Voronoi diagram under the L
∞
metric, and also under a simplicial distance function, are both shown to be . The upper bound for the case of the L
∞
metric follows from a new upper bound, also proved in this paper, on the maximum complexity of the union of n axis-parallel hypercubes in R
d
. This complexity is , for d ≥ 1 , and it improves to , for d ≥ 2 , if all the hypercubes have the same size. Under the L
1
metric, the maximum complexity of the Voronoi diagram of a set of n points in general position in R
3
is shown to be . We also show that the general position assumption is essential, and give examples where the complexity of the diagram increases
significantly when the points are in degenerate configurations. (This increase does not occur with an appropriate modification
of the diagram definition.) Finally, on-line algorithms are proposed for computing the Voronoi diagram of n points in R
d under a simplicial or L
∞
distance function. Their expected randomized complexities are for simplicial diagrams and for L
∞
-diagrams.
Received July 31, 1995, and in revised form September 9, 1997. 相似文献
3.
《Optimization》2012,61(10):1769-1796
ABSTRACTThe purpose of this paper is to introduce a new iterative method for solving a variational inequality over the set of common fixed points of a finite family of sequences of nearly non-expansive mappings in a real Hilbert space. And, using this result, we give some applications to the problem of finding a common fixed point of non-expansive mappings or non-expansive semigroups and the problem of finding a common null point of monotone operators. 相似文献
4.
Wiyada Kumam Konrawut Khammahawong Poom Kumam 《Numerical Functional Analysis & Optimization》2013,34(14):1644-1677
AbstractIn this paper, we introduce a new discontinuous operator and investigate the existence and uniqueness of fixed points for the operators in complete metric spaces. We also provide rate of convergence and data dependency of S-iterative scheme for a fixed point of the discontinuous operators in Banach spaces. Moreover, we prove the estimation Collage theorems and compare error estimate between data dependency and Collage theorems. Numerical examples are provided to support our results. 相似文献
5.
AbstractWe propose parallel algorithms for solving a class of variational inequalities over the set of common fixed points for a finite family of demicontractive mappings in real Hilbert spaces. Under some suitable conditions, we prove that the sequence generated by the proposed algorithms converges strongly to a solution of the problem. We apply the proposed algorithms to strongly monotone variational inequality problems with pseudomonotone equilibrium constraints by defining a quasi-nonexpansive and demi-closed mapping whose fixed point set coincides with the solution set of the equilibrium problem. 相似文献
6.
《复变函数与椭圆型方程》2012,57(1):69-81
We consider the generalization of linear fractional transformations of the plane to $ {\shadC}^n $ . Analogs of the one-variable theory are developed including fixed point sets and points of symmetry. The domains in $ {\shadC}^n $ that are images of the ball under these transformations are found. Finally, we see some examples where classical fixed point results follow from this theory in a natural way. 相似文献
7.
L. Devadoss 《Discrete and Computational Geometry》2008,29(1):61-75
Abstract. The real points of the Deligne—Knudsen—Mumford moduli space \overline \cal M
n
0
of marked points on the sphere have a natural tiling by associahedra. We extend this idea to construct an aspherical space
tiled by cyclohedra . We explore the structure of this space, coming from blow-ups of hyperplane arrangements, as well as discuss possibilities
of its role in knot theory and mathematical physics. 相似文献
8.
L. Devadoss 《Discrete and Computational Geometry》2003,29(1):61-75
Abstract. The real points of the Deligne—Knudsen—Mumford moduli space \overline \cal M
n
0
of marked points on the sphere have a natural tiling by associahedra. We extend this idea to construct an aspherical space
tiled by cyclohedra . We explore the structure of this space, coming from blow-ups of hyperplane arrangements, as well as discuss possibilities
of its role in knot theory and mathematical physics. 相似文献
9.
《Optimization》2012,61(5):1037-1072
ABSTRACTThe purpose of this paper is to investigate the problem of finding a common element of the set of zero points of the sum of two operators and the fixed point set of a quasi-nonexpansive mapping. We introduce modified forward-backward splitting methods based on the so-called inertial forward-backward splitting algorithm, Mann algorithm and viscosity method. We establish weak and strong convergence theorems for iterative sequences generated by these methods. Our results extend and improve some related results in the literature. 相似文献
10.
Bahram Sadeghi Bigham Marzieh Eskandari Maryam Tahmasbi 《Journal of computational science》2012,3(3):127-131
The polar diagram of a set of points in a plane and its extracted dual EDPD were recently introduced for static and dynamic cases. In this paper, the near-pole polar diagram NPPD for a set of points is presented. This new diagram can be considered as a generalization of the polar diagram and has applications in several communication systems and robotics problems. After reviewing the NPPD of points, we solve the problem for a set of line segments and simple polygons in optimal time Θ(n log n), where n is the number of line segments or polygon vertices. We introduce duality for the NPPD of points and identify some applications. 相似文献
11.
《复变函数与椭圆型方程》2012,57(1):83-94
This article studies the problem on the fixed points and hyper-order of differential polynomials generated by solutions of two type of second order differential equations. Because of the control of differential equation, we can obtain some precise estimates of their hyper-order and fixed points. 相似文献
12.
Greg Kuperberg 《Commentarii Mathematici Helvetici》1996,71(1):70-97
We prove that every 3-manifold possesses aC
1, volume-preserving flow with no fixed points and no closed trajectories. The main construction is a volume-preserving version
of the Schweitzer plug. We also prove that every 3-manifold possesses a volume-preserving,C
∞ flow with discrete closed trajectories and no fixed points (as well as a PL flow with the same geometry), which is needed
for the first result. The proof uses a Dehn-twisted Wilson-type plug which also preserves volume.
The author was supported by an NSF Postdoctoral Fellowship, grant #DMS-9107908. 相似文献
13.
Jaume Llibre 《Journal of Difference Equations and Applications》2013,19(3-4):417-422
Let M be a n -dimensional manifold with the same homology than the n -dimensional sphere. A C 1 map f : M M M is called transversal if for all m ] N the graph of f m intersects transversally the diagonal of M 2 M at each point ( x , x ) such that x is a fixed point of f m . We study the minimal set of periods of f by using the Lefschetz numbers for periodic points. In the particular case that n is even, we also study the set of periods for the transversal holomorphic self-maps of M . 相似文献
14.
The root system Σ of a complex semisimple Lie algebra is uniquely determined by its basis (also called a simple root system).
It is natural to ask whether all homomorphisms of root systems come from homomorphisms of their bases. Since the Dynkin diagram
of Σ is, in general, not large enough to contain the diagrams of all subsystems of Σ, the answer to this question is negative.
In this paper we introduce a canonical enlargement of a basis (called an enhanced basis) for which the stated question has
a positive answer. We use the name an enhanced Dynkin diagram for a diagram representing an enhanced basis. These diagrams
in combination with other new tools (mosets, core groups) allow us to obtain a transparent picture of the natural partial
order between Weyl orbits of subsystems in Σ. In this paper we consider only
ADE
root systems (i.e., systems represented by simply laced Dynkin diagrams). The general case will be the subject of the next publication. 相似文献
15.
Voronoi diagrams and arrangements 总被引:6,自引:0,他引:6
We propose a uniform and general framework for defining and dealing with Voronoi diagrams. In this framework a Voronoi diagram is a partition of a domainD induced by a finite number of real valued functions onD. Valuable insight can be gained when one considers how these real valued functions partitionD ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets inR
d
along with its order-k generalizations are intimately related to certain arrangements of hyperplanes. This fact can be used to obtain new Voronoi diagram algorithms. We also discuss how the formalism of arrangements can be used to solve certain intersection and union problems. 相似文献
16.
Marian Neamtu 《Transactions of the American Mathematical Society》2007,359(7):2993-3004
In the 1920s, B. N. Delaunay proved that the dual graph of the Voronoi diagram of a discrete set of points in a Euclidean space gives rise to a collection of simplices, whose circumspheres contain no points from this set in their interior. Such Delaunay simplices tessellate the convex hull of these points. An equivalent formulation of this property is that the characteristic functions of the Delaunay simplices form a partition of unity. In the paper this result is generalized to the so-called Delaunay configurations. These are defined by considering all simplices for which the interiors of their circumspheres contain a fixed number of points from the given set, in contrast to the Delaunay simplices, whose circumspheres are empty. It is proved that every family of Delaunay configurations generates a partition of unity, formed by the so-called simplex splines. These are compactly supported piecewise polynomial functions which are multivariate analogs of the well-known univariate B-splines. It is also shown that the linear span of the simplex splines contains all algebraic polynomials of degree not exceeding the degree of the splines.
17.
In this article, we study the Lotka–Volterra planar quadratic differential systems. We denote by LV systems all systems which can be brought to a Lotka–Volterra system by an affine transformation and time homotheties. All
these systems possess invariant straight lines. We classify the family of LV systems according to their geometric properties encoded in the configurations of invariant straight lines which these systems
possess. We obtain a total of 65 such configurations which are distinguished, roughly speaking, by the multiplicity of their
invariant lines and by the multiplicities of the singularities of the systems located on these lines. We determine an algebraic
subvariety of
\mathbbR12{\mathbb{R}^{12}} which contains all these systems and we find the bifurcation diagram of the configurations of LV systems within this algebraic subvariety, in terms of polynomial invariants with respect to the group action of affine transformations
and time homotheties. This geometric classification will serve as a basis for the full topological classification of LV systems. 相似文献
18.
L. D. Beklemishev 《Proceedings of the Steklov Institute of Mathematics》2011,274(1):25-33
We present a simplified proof of Japaridze’s arithmetical completeness theorem for the well-known polymodal provability logic
GLP. The simplification is achieved by employing a fragment J of GLP that enjoys a more convenient Kripke-style semantics than the logic considered in the papers by Ignatiev and Boolos. In particular,
this allows us to simplify the arithmetical fixed point construction and to bring it closer to the standard construction due
to Solovay. 相似文献
19.
Zhi-congLiu Bei-yeFeng 《应用数学学报(英文版)》2004,20(4):573-578
In this paper, we give a rigorous mathematical and complete parameter analysis for the rheodynamic model of cardiac and obtain the conditions and parameter region for global existence and uniqueness of limit cycle and the global bifurcation diagram of limit cycles. We also discuss the resonance phenomenons of the perturbed system. 相似文献
20.
《Journal of Mathematical Analysis and Applications》2005,308(1):79-91
We study the dynamical behavior of a discrete time dynamical system which can serve as a model of a learning process. We determine fixed points of this system and basins of attraction of attracting points. This system was studied by Fernanda Botelho and James J. Jamison in [A learning rule with generalized Hebbian synapses, J. Math. Anal. Appl. 273 (2002) 529-547] but authors used its continuous counterpart to describe basins of attraction. 相似文献