Let S be a polynomial of degree 2n + 2, that is, positive on the real axis, and let w = 1/S on (−∞,∞). We present an explicit formula for the nth orthogonal polynomial and related quantities for the weight w. This is an analogue for the real line of the classical Bernstein-Szegő formula for (−1, 1). 1. The result The Bernstein-Szegő formula provides an explicit formula for orthogonal polynomial...

The cabbage beetle, Colaphellus bowringi Baly (Coleoptera: Chrysomelidae), a serious pest of crucifers in China, undergoes summer or winter diapause in the soil as an adult. In the present study, the incidence of diapause were measured in reciprocal crosses between a high-diapause strain (HD strain) and a laboratory-selected nondiapausing strain (ND strain) under different photoperiods and temp...

It takes longer to accomplish difficult tasks than easy ones. In the context of motor behaviour, Fitts' famous law states that the time needed to successfully execute an aiming movement increases linearly with task difficulty. While Fitts' explicit formulation has met criticism, the relation between task difficulty and movement time is invariantly portrayed as continuous. Here, we demonstrate t...

The reciprocal class of a Markov path measure is the set of all mixtures of its bridges. We give characterizations of the reciprocal class of a continuous-time Markov random walk on a graph. Our main result is in terms of some reciprocal characteristics whose expression only depends on the jump intensity. We also characterize the reciprocal class by means of Taylor expansions in small time of s...

PURPOSE The aim of this longitudinal three-wave study was to examine (i) reciprocal associations among job demands, work-related perseverative cognition (PC), and sleep quality; (ii) PC as a mediator in-between job demands and sleep quality; and (iii) continuous high job demands in relation to sleep quality and work-related PC over time. METHOD A representative sample of the Swedish working p...

Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of a continuous time random walk with values in a countable Abelian group, compute explicitly its reciprocal characteristics and present an integral characterization of it. Our main tool is a new iterated version of the celebrated Mecke’s formula fro...

INTRODUCTION The aim of this study was to evaluate the resistance to flexural fatigue of Reciproc R25 (VDW, Munich, Germany), WaveOne Primary (VDW, Munich, Germany), Mtwo (Sweden & Martina, Padova, Italy), and Twisted File (TF; SybronEndo, Orange, CA) instruments used in continuous rotation or in 2 different reciprocating motions. METHODS A total of 180 nickel-titanium files from 4 brands mar...