Borromean Binding of Three or Four Bosons

We estimate the ratio $R=g_{3}/g_{2}$ of the critical coupling constants $g_{2}$ and $g_{3}$ which are required to achieve binding of 2 or 3 bosons, respectively, with a short-range interaction, and examine how this ratio depends on the shape of the potential. Simple monotonous potentials give $R\simeq 0.8$. A wide repulsive core pushes this ratio close to R=1. On the other hand, for an attractive well protected by an external repulsive barrier, the ratio approaches the rigorous lower bound $R=2/3$. We also present results for N=4 bosons, sketch the extension to $N>4$, and discuss various consequences.Comment: 12 pages, RevTeX, 5 Figures in tex include

How Can we Derive Consensus Among Various Rankings of Marketing Journals?

The identification of high quality journals often serves as a basis for the assessment of research contributions. In this context rankings have become an increasingly popular vehicle to decide upon incentives for researchers, promotions, tenure or even library budgets. These rankings are typically based on the judgments of peers or domain experts or scientometric methods (e.g., citation frequencies, acceptance rates). Depending on which (combination) of these ranking approaches is followed, the outcome leads to more or less diverging results. This paper addresses the issue on how to construct suitable aggregate (subsets) of these rankings. We present an optimization based consensus ranking approach and apply the proposed method to a subset of marketing-related journals from the Harzing Journal Quality List. Our results show that even though journals are not uniformly ranked it is possible to derive a consensus ranking with considerably high agreement among the individual rankings. In addition, we explore regional differences in consensus rankings.Series: Research Report Series / Department of Statistics and Mathematic

A Comparison of Standard Texturing and Mip-Mapping in a Real Time Application

Texture mapping is an efficient way to gain realism in computer generated pictures. However, if the texture is point sampled, aliasing occurs. MipMapping is a technique which pre-filters the texture several times to successively lower resolutions. The adequate texture-level is then chosen depending on the distance of the point in three-space from the image plane. This reduces aliasing but leads to higher computational complexity. Both approaches were implemented and compared in a real-time application, namely NotAScratch, a three-dimensional computer action game. 1 Introduction A major goal in developing a real-time application is achieving high realism in rendered images without compromising rendering speed too much. Textures [3] enhance the quality of images while entailing only a relatively small increase in computation. However, to avoid aliasing the texture has to be filtered, which can be quite computational complex when done at runtime. To speed up this process, the texture bes..

A Review of Two Simple Polygon Triangulation Algorithms

This paper describes two approaches to triangulate a simple polygon. Emphasis is on practical and easy to implement algorithms, especially the first algorithm is straightforward and intuitive but, however, quite efficient. Further, it does not require the sorting or the use of balanced tree structures. Its worst running time complexity is O(n 2 ), but for special classes of polygons it runs in linear time. The second approach requires some more sophisticated concepts of computational geometry but yields a better worst running time complexity of O(n log n). Both algorithms do not introduce new vertices and triangulate in a greedy fashion, that is they never remove edges once inserted. Further, they are designed to find an arbitrary triangulation and they do not optimize the result in any way. Keywords: computational geometry, polygon, triangulation, computational complexity, monotone polygon, trapezoidation 1 Introduction The problem of triangulating a polygon can be stated as: "giv..

Mastering Windows: Improving Reconstruction

Ideal reconstruction filters, for function or arbitrary derivative reconstruction, have to be bounded in order to be practicable since they are infinite in their spatial extent. This can be accomplished by multiplying them with windowing functions. In this paper we discuss and assess the quality of commonly used windows and show that most of them are unsatisfactory in terms of numerical accuracy. The best performing windows are Blackman, Kaiser and Gaussian win- ftheussl,helwig,[email protected] dows. The latter two are particularly useful since both have a parameter to control their shape, which, on the other hand, requires to find appropriate values for these parameters. We show how to derive optimal parameter values for Kaiser and Gaussian windows using a Taylor series expansion of the convolution sum. Optimal values for function and first derivative reconstruction for window widths of two, three, four and five are presented explicitly. Keywords: ideal reconstruction, wind..