Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Voronoi diagrams—a survey of a fundamental geometric data structure

Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

A planar subdivision is any partition of the plane into (possibly unbounded) polygonal regions. The subdivision search problem is the following: given a subdivision $S$ with $n$ line segments and a query point $p$, determine which region of $S$ contains $p$. We present a practical algorithm for subdivision search that achieves the same (optimal) worst case complexity bounds as the significantly more complex algorithm of Lipton and Tarjan, namely $O(\log n)$ search time with $O(n)$ storage. Our subdivision search structure can be constructed in linear time from the subdivision representation used in many applications.

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Optimal Search in Planar Subdivisions

This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of rational functions. On the other hand, some aspects where the transcendental case is analogous to the rational case are treated rather briefly here. For example, we introduce the different types of components of the Fatou set that occur in the iteration of rational functions but omit a detailed description of these types. Instead, we concentrate on the types of components that are special to transcendental functions (Baker domains and wandering domains).

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Iteration of meromorphic functions

This paper discusses the discrete analogue of the gradient of a function and shows how discrete gradients can be used in the numerical integration of ordinary differential equations (ODEs). Given a...

Geometric integration using discrete gradients

1 Basic Nevanlinna theory- 2 Unicity of functions of finite (lower) order- 3 Five-value, multiple value and uniqueness- 4 The four-value theorem- 5 Functions sharing three common values- 6 Three-value sets of meromorphic functions- 7 Functions sharing one or two values- 8 Functions sharing values with their derivatives- 9 Two functions whose derivatives share values- 10 Meromorphic functions sharing sets

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Uniqueness Theory of Meromorphic Functions

The main purpose of this paper is to prove difference and q-difference counterparts of the Clunie and Mohon’ko lemmas from the Nevanlinna theory of differential polynomials. We also give applications to the value distribution theory of meromorphic solutions of some complex difference equations.

Clunie theorems for difference and q-difference polynomials

Concerning the uniqueness and sharing values of meromorphic functions, many results about meromorphic functions that share more than or equal to two values have been ob- tained. In this paper, we shall study meromorphic functions that share only one value, and prove the following result: For n ≥ 11 and two meromorphic functions f(z) and g(z), if f n fand g n g ' share the same nonzero and finite value a with the same multiplicities, then f ≡ dg or g = c1e cz and f = c2e −cz , where d is an (n + 1)th root of unity, c, c1 and c2 being constants. As an application, we solve some non-linear differential equations.

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Uniqueness and value-sharing of meromorphic functions

On deficiencies of differential polynomials, II

We continue to studying value distribution of difference polynomials of meromorphic functions. In particular, we show that extending classical theorems of Tumura-Clunie type to difference polynomials needs additional assumptions.

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Chung-Chun Yang

Papers

Uniqueness Theory of Meromorphic Functions

Clunie theorems for difference and q-difference polynomials

Uniqueness and value-sharing of meromorphic functions

On deficiencies of differential polynomials, II

Value distribution of difference polynomials