A stochastic frontier approach to running performance

^** Email: e.sterken{at}eco.rug.nl Long-distance running performance depends on age of the runnerand race distance. In this paper we apply a stochastic frontierapproach to estimate optimal running performance across distancesfrom 5000 m up to and including the marathon. We present agecorrection factors for 5000, 10000 and 15000 m, half-marathonand marathon distances for women and men. Two conclusions emerge:(1) official age grading tables are too optimistic for olderrunners and (2) running performance–age curves differacross distances.     

Thue inequalities with a small number of primitive solutions

Several upper bounds are known for the numbers of primitive solutions (x; y) of the Thue equation (1) j F(x; y) j = m and the more general Thue inequality (3) 0 < j F(x; y) j m. A usual way to derive such an upper bound is to make a distinction between "small" and "large" solutions, according as max( j x j ; j y j ) is smaller or larger than an appropriate explicit constant Y depending on F and m; see e.g. [1], [11], [6] and [2]. As an improvement and generalization of some earlier results we give in Section 1 an upper bound of the form cn for the number of primitive solutions (x; y) of (3) with max( j x j ; j y j )Y0 , wherec 25 is a constant and n denotes the degree of the binary form F involved (cf. Theorem 1). It is important for applications that our lower bound Y0 for the large solutions is much smaller than those in [1], [11], [6] and [4], and is already close to the best possible in terms of m. ByusingTheorem1 we establish in Section 2 similar upper bounds for the total number of primitive solutions of (3), provided that the height or discriminant of F is suficiently large with respect to m (cf. Theorem 2 and its corollaries). These results assert in a quantitative form that, in a certain sense, almost all inequalities of the form (3) have only few primitive solutions. Theorem 2 and its consequences are considerable improvements of the results obtained in this direction in [3], [6], [13] and [4]. The proofs of Theorems 1 and 2 are given in Section 3. In the proofs we use among other things appropriate modifications and refenements of some arguments of [1] and [6].     

Probabilisticl p distances in location models

Modelling distances with thel _p norm is very widespread in site selecting location problems. This paper deals with the concept of a probabilisticp parameter which permits uncertainty in the directness of the routes that can be taken between a facility and demand points. This paper establishes the rather surprising result that the expected distances can themselves be closely approximated byl _p distances with appropriately chosenp parameters. This result is very useful when, as is often the case, expected distances are used in the optimization criterion.     

SPATIAL PATTERN INDUCED BY ASYMMETRIC COMPETITION: A MODELING APPROACH

ABSTRACT. The paper addresses the question: how does asymmetric competition for light affect the spatial pattern of trees? It is based on an individual-based spatially explicit model of forest dynamics, whose growth equations are derived from gap models. The model is calibrated on a stand of natural rainforest in French Guiana, where the tree pattern exhibits regularity at short distances (< 10 m) and clustering at medium distances (∼ 30 m). The model reproduces the regularity but not the clustering. As mortality and recruitment have been modeled so as to favor a random pattern, we conclude that regularity emerges from the asymmetric competition in the growth submodel. Also the scale at which regularity appears is linked to the range of interactions between trees.     

Isothermic Surfaces Generated via Bäcklund and Moutard Transformations: Boomeron and Zoomeron Connections

The asymptotic expansions for (1) the slow changes in particle number/energy density; namely, the kinetic equation, (2) frequency renormalization; and (3) the Nth‐order structure functions for wave turbulence systems are almost always nonuniform at either small or large length scales. The manifestation of this nonuniformity is fully nonlinear behavior either in the form of localized structures (coherent structures, shocks) or condensates (nonzero mean over large distances). The result is intermittent behavior dominated by large fluctuation events, anomolous scaling, and far from joint Gaussian statistics. Despite this unexpected surprise, and it is a surprise considering that wave turbulence has been the subject of continuous and intense investigation for several decades, wave turbulence still offers an advantage over systems that are nonlinear over all scales. The advantage is that the nature of the fully nonlinear behavior often can be identified, which gives us reasonable hope that wave turbulent systems may be treated as a two species gas of random wavetrains and randomly occurring coherent structures.     

环GR(4,2)上一类负循环码的Gray象

研究了GR(4,2)上长为2~s的负循环码的Gray象,证明了GR(4,2)上长为2~s的负循环码的Gray象是F_4上长为2~(s+2)指数为2的准循环码.通过计算GR(2~a,m)上长为2~s的负循环码的齐次距离,确定了GR(4,2)上长为2~s的负循环码的Gray象的汉明距离.     

Unit Distances and Diameters in Euclidean Spaces

We show that the maximum number of unit distances or of diameters in a set of n points in d-dimensional Euclidean space is attained only by specific types of Lenz constructions, for all d≥4 and n sufficiently large depending on d. As a corollary, we determine the exact maximum number of unit distances for all even d≥6 and the exact maximum number of diameters for all d≥4 and all n sufficiently large depending on d. This material is based upon work supported by the South African National Research Foundation.     

A decomposition algorithm for shortest paths in a network with many strongly connected components

Summary This paper presents an algorithm for finding all shortest distances in a network with a large number of strongly connected components. If the network hasN nodes the number of computations required by this algorithm is asymptotically 1/6N(N–1) (N–2) tripel operations.

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Zusammenfassung In der vorliegenden Arbeit wird ein Algorithmus zur Bestimmung der Längen aller kürzesten Wege in Netzwerken mit mehreren strengen Zusammenhangskomponenten entwickelt. Besitzt das NetzwerkN Knoten, so hat man bei diesem Algorithmus asymptotisch insgesamt 1/6N(N–1 (N–2) Additionen und ebenso viele Vergleiche durchzuführen.

     

Asymptotic expression for the correlation function of twisted fields in the two-dimensional Dirac model on a lattice

A determinant representation is obtained for the correlation function of twisted fields in the two-dimensional Dirac model on a lattice. These fields are determined by twisted boundary conditions for the Dirac fermions. The asymptotic expression is calculated for the correlation function at large distances (the vacuum expectation of the twisted field) at the critical point and in the scaling region. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2 pp. 329–346, Nember, 1999.     

Multi-Particle Correlation Functions in a Trapped Bose Gas

Multi-particle correlation functions at nonzero temperatures in a trapped Bose gas for D = 3, 2, 1 dimensions are considered. It is shown that, at relatively large distances, the multi-particle correlators are expressed in terms of one-particle ones. Bibliography: 13 titles.