A New Approach to Output-Sensitive Construction of Voronoi Diagrams and Delaunay Triangulations

We describe a new algorithm for computing the Voronoi diagram of a set of \(n\) points in constant-dimensional Euclidean space. The running time of our algorithm is \(O(f \log n \log \varDelta )\) where \(f\) is the output complexity of the Voronoi diagram and \(\varDelta \) is the spread of the input, the ratio of largest to smallest pairwise distances. Despite the simplicity of the algorithm and its analysis, it improves on the state of the art for all inputs with polynomial spread and near-linear output size. The key idea is to first build the Voronoi diagram of a superset of the input points using ideas from Voronoi refinement mesh generation. Then, the extra points are removed in a straightforward way that allows the total work to be bounded in terms of the output complexity, yielding the output sensitive bound. The removal only involves local flips and is inspired by kinetic data structures.     

A Note on Heegaard Genus of Self-amalgamated 3-Manifold

Let M be a connected orientable compact irreducible 3-manifold. Suppose that αM consists of two homeomorphic surfaces F1 and F2, and both F1 and F2 are compressible in M. Suppose furthermore that g(M, F1) = g(M) + g(F1), where g(M, F1)is the Heegaard genus of M relative to F1. Let Mfbe the closed orientable 3-manifold obtained by identifying F1 and F2 using a homeomorphism f : F1 → F2. The authors show that if f is sufficiently complicated, then g(Mf) = g(M, αM) + 1.     

3-Manifold group and finite decomposition complexity

In this paper, we prove that the fundamental group of an orientable compact 3-manifold has finite decomposition complexity if Thurston's Hyperbolization Conjecture is true.     

L-拓扑空间中的半拟紧性

在L-拓扑空间中借助于半拟开L-集合和它们的不等式给出了半拟紧性的一个新定义,这里L是完备的DeMorgan代数。它也能够借助于半拟闭L-集和它们的不等式刻画。当L是完全分配的DeMorgan代数时,它的许多刻画被给出了。     

A New Approach to Arcs

Some properties of arcs in PG(2,q) are discussed via its cyclic model. A covering number of a set of points in PG(2,q) is the smallest number of lines needed to cover the set -, where the set of points of PG(2,q) is identified with Z . It is proved that the covering number of a conic is either 1 or greater than q/4. Hyperovals with covering number 2 are characterized for q even. Also, a possible method for constructing nonclassical hyperovals having small covering numbers is given.     

A New Approach to Analytic Multifunctions

We show how the theory of analytic multifunctions can be developed in an elementary and self-contained fashion, using the abstract notions of gauge and multigauge. This approach also yields new information about the metric properties of analytic multifunctions, leading to analogues of Schwarz's lemma and the Schwarz–Pick theorem.     

A New Approach to Numerical Integration

A novel method of estimating integrals is introduced using thetheory of measure and Lebesgue integration. It is shown thatmultiple integrals reduce to the evaluation of a one-dimensionalintegral of a measure function. Comparison of the method andvarious conventional techniques is carried out for several integrals.     

A New Approach to Polynomial Identities

Using the formal derivative idea, we give a generalization for the Cauchys Theorem relating to the factors of (x + y)ⁿ–xⁿ– yⁿ. We determine the polynomials A(n, a, b) and B(n, a, b) such that the polynomial

A New Approach to Hom-Left-Symmetric Bialgebras

Czechoslovak Mathematical Journal - The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In...     

A New Approach to Leibniz Bialgebras

A study of Leibniz bialgebras arising naturally through the double of Leibniz algebras analogue to the classical Drinfeld’s double is presented. A key ingredient of our work is the fact that the underline vector space of a Leibniz algebra becomes a Lie algebra and also a commutative associative algebra, when provided with appropriate new products. A special class of them, the coboundary Leibniz bialgebras, gives us the natural framework for studying the Yang-Baxter equation (YBE) in our context, inspired in the classical Yang-Baxter equation as well as in the associative Yang-Baxter equation. Results of the existence of coboundary Leibniz bialgebra on a symmetric Leibniz algebra under certain conditions are obtained. Some interesting examples of coboundary Leibniz bialgebras are also included. The final part of the paper is dedicated to coboundary Leibniz bialgebra structures on quadratic Leibniz algebras.     

一个积分等式的新证

通过傅立叶积分公式和筛选性质给出了关于积分等式∫ -∞ ^∞e^t^2/2dt=√2π的一种新证明方法．     

A New Approach to Stochastic Optimization

We derive general explicit solutions to the investment model without reliance on the existing duality or variational methods.     

A New Approach to Representations of 3-Lie Algebras and Abelian Extensions

In this paper, we introduce the notion of generalized representation of a 3-Lie algebra, by which we obtain a generalized semidirect product 3-Lie algebra. Moreover, we develop the corresponding cohomology theory. Various examples of generalized representations of 3-Lie algebras and computation of 2-cocycles of the new cohomology are provided. Also, we show that a split abelian extension of a 3-Lie algebra is isomorphic to a generalized semidirect product 3-Lie algebra. Furthermore, we describe general abelian extensions of 3-Lie algebras using Maurer-Cartan elements.     

求解一个整数方程的新解法

ni=1aixi =p是一个由实验数据问题抽象而出的整数方程求非负整数解的数学模型 .为了使该问题实现计算机求解的可能 ,本文首先将原问题转化为讨论一类整数规划最优解问题 .从对应松弛规划问题的目标函数值为 0的最优解出发 ,根据舍入凑整法原则 ,再次将问题转化为另一简化后的整数方程 ,这样大大缩小了解的范围 ,及进一步迅速降低了方程右端的 p值 ,使其在计算机上求解的运算量大大降低而能得以实现     

故障树计算的一种新方法

本文提出的顶事件发生概率的算法不借助割集，直接采用自顶向下的技术对故障树进行分割求解。该算法的时间和内存耗用与故障树的节点数目没有必然联系，而仅仅取决于故障树中不同的重复事件的个数。     

局部影响分析中的一种新二阶方法

本文通过考察一种新影响图的保形法曲率,给出一种新二阶局部影响分析方法,并通过实例验证了该方法的有效性.     

Asymptotic Singular Homology of a Complete Hyperbolic 3-Manifold of Finite Volume

Let V be a complete connected hyperbolic 3-manifold of finitevolume, with Liouville measure m, geodesic flow _t and Brownianmotion Z_t. Let be a smooth 1-form, closed in the cusps of V.Then the limit laws as t of under m and of are calculated, and seen to be Gaussian, and equal. The geodesic flow case isstudied via the Brownian case. 1991 Mathematics Subject Classification:60J65, 58F17, 51M10.     

Interval Exchange Map and Codimension One Measured Foliation on 3-Manifold

IntervalexchangemapwasfirstintroducedbyKeane[3].Itisprovedtobeusefulinthestudyofthemeasurepreservingflowsonthesurfaceandbilliardsonpolygons.LetX=[0,1),and2aninteger.Leta=(al,a2,'',am)beaprobabilityvector.DefineLetTbeapermutationofmelements.DefineWecanformthecorrespondingP:andThendefineforeachand.TmapseachilltervalXiisometricallyontothecorrespondingintervalX:(,).Tiscalledthe(a,T)intervalexchangemap.ItiseasytoseeifweidentifythetwoendpointsofX,anintervalexchangeInilpcanalsobeconsideredasa…     

A New Approach to Rearrangements of Maximal Operators

A general, albeit simple, approach to obtaining rearrangementinequalities of maximal operators is given. Being applied tospecific operators it leads not only to new proofs of well-knownrelations in a simpler and shorter way, but also to new, profitableresults. 2000 Mathematics Subject Classification 42B25.     

A New Approach to Optimization Under Monotonic Constraint

A new efficient branch and bound method is proposed for solving convex programs with an additional monotonic nonconvex constraint. Computational experiments demonstrated that this method is quite practical for solving rank k reverse convex programs with much higher values of k than previously considered in the literature and can be applied to a wider class of nonconvex problems.