The energy of gaseous molecules

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The haber process at merseburg (saxony)

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Phase retrieval on circles and lines

Let $f$ and $g$ be analytic functions on the open unit disc $\mathbb D$ such that $|f|=|g|$ on a set $A$. We give an alternative proof of the result of Perez that there exists $c$ in the unit circle $\mathbb T$ such that $f=cg$ when $A$ is the union of two lines in $\mathbb D$ intersecting at an angle that is an irrational multiple of $\pi$, and from this deduce a sequential generalization of the result. Similarly, the same conclusion is valid when $f$ and $g$ are in the Nevanlinna class and $A$ is the union of the unit circle and an interior circle, tangential or not. We also provide sequential versions of this result and analyse the case $A=r\mathbb T$. Finally, we examine the most general situation when there is equality on two distinct circles in the disc, providing a result or counterexample for each possible configuration.Comment: 14 pages, 1 figur

Model spaces and Toeplitz kernels in reflexive Hardy spaces

This paper considers model spaces in an Hp setting. The existence of unbounded functions and the characterisation of maximal functions in a model space are studied, and decomposition results for Toeplitz kernels, in terms of model spaces, are establishedFCT/Portuga

Kernels of unbounded Toeplitz operators and factorization of symbols

We consider kernels of unbounded Toeplitz operators in Hp(C+) in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in Hp(C+), we describe the kernels of Toeplitz operators whose symbol possesses a certain factorization involving two different Hardy spaces and we establish relations between the kernels of two operators whose symbols differ by a factor which corresponds, in the unit circle, to a non-integer power of z. We apply the results to describe the kernels of Toeplitz operators with non-vanishing piecewise continuous symbols.This work was partially supported by FCT/Portugal through UID/MAT/04459/2020. The research of M. T. Malheiro was partially supported by Portuguese Funds through FCT/Portugal within the Projects UIDB/00013/2020 and UIDP/00013/2020

A class of quasicontractive semigroups acting on Hardy and Dirichlet space

This paper provides a complete characterization of quasicontractive C0-semigroups on Hardy and Dirichlet space with a prescribed generator of the form Af = Gf ′. We show that such semigroups are semigroups of composition operators, and we give simple sufficient and necessary condition on G. Our techniques are based on ideas from semigroup theory, such as the use of numerical ranges

Preparing athletes and teams for the Olympic Games: experiences and lessons learned from the world's best sport psychologists

As part of an increased effort to understand the most effective ways to psychologically prepare athletes and teams for Olympic competition, a number of sport psychology consultants have offered best-practice insights into working in this context. These individual reports have typically comprised anecdotal reflections of working with particular sports or countries; therefore, a more holistic approach is needed so that developing practitioners can have access to - and utilise - a comprehensive evidence-base. The purpose of this paper is to provide a panel-type article, which offers lessons and advice for the next generation of aspiring practitioners on preparing athletes and teams for the Olympic Games from some of the world’s most recognised and experienced sport psychologists. The sample comprised 15 sport psychology practitioners who, collectively, have accumulated over 200 years of first-hand experience preparing athletes and/or teams from a range of nations for six summer and five winter Olympic Games. Interviews with the participants revealed 28 main themes and 5 categories: Olympic stressors, success and failure lessons, top tips for neophyte practitioners, differences within one’s own consulting work, and multidisciplinary consulting. It is hoped that the findings of this study can help the next generation of sport psychologists better face the realities of Olympic consultancy and plan their own professional development so that, ultimately, their aspirations to be the world’s best can become a reality

Nitrogen use efficiency of ¹⁵N urea applied to wheat based on fertiliser timing and use of inhibitors

Improving fertiliser nitrogen (N) use efficiency is essential to increase productivity and avoid environmental damage. Using a 15N mass balance approach, we investigated the effects of five N fertiliser management strategies to test the hypothesis that increasing uptake of applied N by wheat improves productivity and reduces loss of N in a semi-arid environment. Three experiments were conducted between 2012 and 2014. Treatments included urea application (50 kg N/ha) at sowing with and without nitrification inhibitor (3,4-dimethylpyrazole phosphate, DMPP) and surface broadcast with and without urease inhibitor (n-butyl thiophosphoric triamide, NBPT) at the end of tillering plus an unfertilised control. It was found that deferring fertiliser application until the end of tillering decreased losses of fertiliser N (35–52%) through increasing uptake by the crop and or recovery in the soil at harvest, while maintaining yield except when rainfall following application was low. In this case, deferring application reduced fertiliser uptake (− 71%) and grain yield (− 18%) and increased recovery of N in the soil (+ 121%). Use of DMPP or NBPT reduced N loss where seasonal conditions were conducive to denitrification during winter (DMPP) and volatilisation or denitrification later in the season (NBPT). Their effect on grain yield was less significant; DMPP increased yield (+ 3–31%) in all years and NBPT increased yield (+ 7–11%) in 2 of 3 years compared to unamended urea. The majority of crop N uptake was supplied from soil reserves and as a result, crop recovery of applied N was not strongly related to grain yield response

A dedicated greedy pursuit algorithm for sparse spectral representation of music sound

A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal as a linear superposition of as few spectral components as possible, without affecting the quality of the reproduction. A representation of this nature is said to be sparse. In the present context sparsity is accomplished by greedy selection of the spectral components, from an overcomplete set called a dictionary. The proposed algorithm is tailored to be applied with trigonometric dictionaries. Its distinctive feature being that it avoids the need for the actual construction of the whole dictionary, by implementing the required operations via the fast Fourier transform. The achieved sparsity is theoretically equivalent to that rendered by the orthogonal matching pursuit (OMP) method. The contribution of the proposed dedicated implementation is to extend the applicability of the standard OMP algorithm, by reducing its storage and computational demands. The suitability of the approach for producing sparse spectral representation is illustrated by comparison with the traditional method, in the line of the short time Fourier transform, involving only the corresponding orthonormal trigonometric basis