Charged pion spectra and energy transfer following antiproton annihilation at rest in carbon and uranium

The momentum spectra of charged pions following antiproton annihilation at rest in carbon and uranium have been measured. This information complements our previous measurement of the neutral pion spectra. The total charged pion multiplicity is 2.84±0.10 and 2.47±0.09 for carbon and uranium, respectively, in good agreement with recent INC model predictions of 2.96 and 2.48 for the same quantities. However, structures predicted by the model near 200 MeV/c and 300 MeV/c related to delta-resonance production are not seen in the data. The total energy transfers to the nucleus are calculated to be 119±59 MeV(carbon) and 455±50 MeV(uranium). The possibility of exciting multifragmentation with a¯p beam impinging on heavy nuclei is discussed.     

Analysing the Need to Spend on Education

An earlier paper has put forward a methodology for measuring the ‘need to spend’ on education by local authorities. This paper examines the economic principles underlying the measurement of the need to spend, and finds some problems inherent in the earlier work. The measurement of spending need would nevertheless seem an essential step in the pursuit of territorial equity, particularly in the light of policy developments in the United Kingdom concerning local management of schools. The paper therefore identifies the areas where further clarification of key issues is required.     

Assessing Elementary Understanding of Multiplication Concepts

This article summarizes the basic concepts of multiplication and provides some evidence that the traditional third‐grade curriculum and instruction emphasizing memorization of multiplication facts produces much less understanding of the basic concepts of multiplication than a standards‐based curriculum and instruction emphasizing construction of number sense and meaning for operations. This study also describes a collection of assessment tasks that provided meaningful evidence of children's understandings of basic multiplication concepts, including understandings of the relationships between multiplication and addition.     

Extracting metabolite ions out of a matrix background by combined mass defect,neutral loss and isotope filtration

Mass defect, neutral loss and isotope filtration techniques were applied to electrospray ionization mass spectrometry (ESI‐MS) data obtained for in vivo and in vitro samples of drug metabolism studies. A combination of these post‐acquisition processing techniques was shown to be more powerful than the use of one of these tools alone for the detection in complex matrices of metabolites of candidate drugs with a characteristic isotope pattern (e.g. containing bromine, chlorine, or a high proportion of radiolabeled drug (¹²C/¹⁴C)) or characteristic neutral losses. In combination with ‘all‐in‐one’ data acquisition this methodology is able to perform software‐driven constant neutral loss scanning for an unlimited number of mass differences at any time after analysis. Highly selective MS chromatograms were obtained with excellent correlation with their corresponding radiochromatograms. Copyright © 2009 John Wiley & Sons, Ltd.     

Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities

We construct six unitary trace invariants for 2×2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We have discovered a curious trace identity for two unit-speed one-parameter subgroups of Sp(1). A modification gives an infinite family of trace identities for quaternions as well as for 2×2 complex matrices. We were not able to locate these identities in the literature. We prove two quaternionic versions of a well known characterization of triangularizable subalgebras of matrix algebras over an algebraically closed field. Finally we consider the problem of describing the semi-algebraic set of pairs (X,Y) of quaternionic n×n matrices which are simultaneously triangularizable. Even the case n=2, which we analyze in more detail, remains unsolved.     

Das Atomgewicht des Cadmiums

Ohne Zusammenfassung     

Ueber die Destillation von Formaldehyd

Ohne Zusammenfassung     

Halogen

Ohne Zusammenfassung