Quasirepresentations of amenable groups: Unbounded tame quasirepresentations

Continuing the study of representations of amenable groups, we discuss a model case in which a (not necessarily bounded) Banach space quasirepresentation of an amenable group is close to an ordinary representation of the group in the same space.     

Representations associated to quasirepresentations of amenable groups with zero multiplication of defect operators

A direct construction of representations associated to dual quasirepresentations with zero multiplication of defect operators for amenable groups is given.     

Radiocarcinogenesis: Results fromin vitro,experiments

Summary Transformation frequencies induced in cell systems by low- and high-LET radiations are compared and analysed as a function of LET and dose protraction. At acute dose rates, the dose-response curve with low-LET radiations shows a complex shape: the transformation frequency increases with the dose by a power of less than 1 in the interval (0.25÷1.5) Gy; a power of about 2 from 1.5 Gy to 4.5 Gy, where it reaches its maximum value and then remains constant. High-LET radiation transformation frequencies increase with dose by a power of 2 from 0.1 to 2 Gy after which they remain constant. RBE values increase with LET up to 140 ke V/μm and then decrease. The transformation frequency is reduced following dose fractionation or dose rate reduction with low-LET radiation, whereas it is enhanced with high-LET radiation, such as 0.85 MeV neutrons. Values of RBE for transformation up to 50 can be evaluated for neutrons. Various models that have been proposed to explain these results are analysed and compared.

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Riassunto Si riportano i risultati di uno studio della frequenza di trasformazione indotta in cellule in coltura da radiazione ionizzante in funzione della dose, del LET e della distribuzione temporale della dose. Per radiazioni a basso LET, l’andamento della curva dose-effectto è piuttosto complesso: la frequenza di trasformazione cresce con una potenza della dose minore di 1 nella regione di dosi (0.25÷1.5) Gy, di circa 2 nella regione da 1.5 Gy a 4.5 Gy oltre la quale si mantiene costante. La frequenza di trasformazione indotta da radiazioni ad alto LET aumenta con la dose con una potenza di 2 tra 0.1 e 2 Gy dove raggiunge il suo valore massimo e poi si mantiene costante. I valori di RBE aumentano con il LET fino a 140 keV/μm e poi decrescono in analogia con quanto trovato per altri effetti quqli la mortalità e l’aberrazione cromosomica. Il frazionamento e la riduzione dell’intensità di dose di radiazione a basso LET producono una diminuzione dell’incidenza di trasformazione; al contrario, alcune radiazioni ad alto LET quali neutroni da 0.85 MeV si sono mostrate molto piú efficaci, mostrando un netto aumento della frequenza di trasformazione quando la dose viene somministrata in piú frazioni od a ridotta intensità nell’intervallo di dosi minori di 1.5 Gy. Alla luce di questi dati si discutono e si analizzano diversi modelli d’induzione della trasformazione proposti in letteratura.

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Резюме Частоты преобразований, индуцированные в клеточных системах излучениями с малыми и высокими ЛПЭ, сравниваются и анализируются в зависимости от ЛПЭ и дозы облучения. При больших интенсивностях кривая ?дозаотклик? при излучениях с малыми ЛПЭ обнаруживает сложное поведение: частоты преобразований увеличиваются с дозой, как степенная функция с показателем меньше 1 в интервале (0.25÷1.5) Gy; потом с показателем 2 в интервале от 1.5 до 4.4 Gy, где достигают максимальной величины, а затем остаются постоянными. Частоты преобразованнй при излучениях с высокими ЛПЭ увеличиваются с дозой, как степенная функция с показателем 2 в интервале от 0.1 до 2 Gy, а затем остаются постоянными. Величины RBE увеличиваются с ЛПЭ вплоть до 140 кэВ/мкм, а затем уменьшаются. Частота преобразований уменьшается с уменьшением интенсивности дозы в случае излучений с низкими ЛПЭ, тогда как для излучений с высокими ЛПЭ, например, нейтроны с энергией 0.85 МэВ, частота преовразований возрастает. Для нейтронов можно оценить величины RBE для преобразований вплоть до 50. Анализируются и сравниваются различные модели, предложенные для объяснения этих результатов.

     

Microwave response of high-T c superconducting crystals: Results, problems, and prospects

The results of studying temperature behavior of the microwave surface impedance Z _s (T) and conductivity tensor $\hat \sigma (T)$ (T) of high-T _c superconducting (HTSC) single crystals are analyzed. The emphasis is on the experimental facts that are inconsistent with the known electrodynamic concepts of conductivity mechanisms in these materials. Possible reasons for the inconsistency are discussed in the context of structural features of the HTSC crystals, and the outlook for future investigations is outlined.     

Gravitational fields,spinor fields,and groups of motions

The problem of finding the most general spinor field possessing the same symmetry as a given gravitational field is solved for every group of motions. Its connection with the resolution of Einstein-Dirac equations is briefly pointed out.Aspirant du Fonds National Belge de la Recherche Scientifique.     

Double focus interferometers and errors the influence of their sample setting errors

Double Focus interferometers are attractive for reducing the influence of ambient conditions due to their common-path configuration. This paper describes the influence of sample setting errors in these interferometers. They have been divided into two types, i.e. the normal illumination type and the oblique illumination type. For each type, an equation of the measurement error due to sample setting error has been derived with Gaussian optics. The measurement error of the normal illumination type becomes a parabolic function of the position on the sample surface. The derived error equations have been verified by ray tracing and by experiment. The error of the oblique type is smaller than that of the normal type.     

Monopoles,braid groups,and the dirac operator

Using the relation between the space of rational functions on , the space ofSU(2)-monopoles on ³, and the classifying space of the braid group, see [10], we show how the index bundle of the family of real Dirac operators coupled toSU(2)-monopoles can be described using permutation representations of Artin's braid groups. We also show how this implies the existence of a pair consisting of a gauge fieldA and a Higgs field on ³ whose corresponding Dirac equation has an arbitrarily large dimensional space of solutions.The first author was supported by a grant from the NSF     

Fields,statistics and non-Abelian gauge groups

We examine field theories with a compact groupG of exact internal gauge symmetries so that the superselection sectors are labelled by the inequivalent irreducible representations ofG. A particle in one of these sectors obeys a parastatistics of orderd if and only if the corresponding representation ofG isd-dimensional. The correspondence between representations of the observable algebra and representations ofG extends to a mapping of the intertwining operators for these representations preserving linearity, tensor products and conjugation. Although we assume no explicit commutation property between fields, the commutation relations of fields of the same irreducible tensor character underG at spacelike separations are largely determined by the statistics parameter of the corresponding sector. For fields of conjugate irreducible tensor character the observable part of the commutator (anticommutator) vanishes at spacelike separations if the corresponding sector has para-Bose (para-Fermi) statistics.     

Gauge theories, vertex models, and quantum groups

It is known that the Jones polynomial of knot theory, and its generalizations, are closely related to the integrable “vertex models” of two-dimensional statistical mechanics, and to quantum groups. In this paper, an attempt is made to show on a priori grounds, starting only from general covariance of three-dimensional Chern-Simons gauge theory and two-dimensional “duality”, why this must be so.     

Unified theory of weak,strong, and electromagnetic interactions: Gauge transformation groups and gauge fields

An attempt is made to construct a unified theory of the weak, strong, and electro-magnetic interactions, based on a generalization of the Weinberg-Salam theory [1]. The groups of gauge transformations leaving the Lagrangian of the bispinor field invariant are discussed. It is shown that in order to preserve this invariance in transition from global to local transformations it is necessary to introduce seven gauge compensation fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 19–23, May, 1982.     

Induced-charge errors in charge-transfer measurement: Brush discharges between charged,insulating discs and earthed,conductive spheres

Charge-transfer measurements made with fast-response, unshielded probes will, in principle, underestimate charge-transfers because of induced-charge errors. It is, however, difficult to know when the degree of underestimation is significant or to allow for it quantitatively because information on the magnitude of these errors is fragmented. Consequently, when measurements are done for electrostatic hazard assessment, unsafe equipment could wrongly be classified as safe. To rectify this situation, and thus contribute to improving charge-transfer test methods in static electricity standards, we have systematically calculated induced-charge errors in brush discharges between insulating discs and earthed spheres. Errors are expressed as the charge-collection efficiency, which is the ratio of charge transfer in the external measurement circuit to charge transfer across the discharge gap. Key results are the worst-case efficiencies at the charge-transfer ignition-thresholds suggested for different classes of flammable material (60 nC, 30 nC and 10 nC for gas group IIa, IIb and IIc materials respectively). For 60 nC transfers and with our best estimate of post-discharge conditions on the disc surface, the worst-case charge-collection efficiency is 0.56, which indicates the error-allowance needed for safe assessment. For 30 nC or 10 nC transfers, the charge-collection efficiency is both smaller (～0.2), and considerably more sensitive to gap geometry. Consequently, it is not recommended to use charge-transfer measurements with fast, unshielded probes to assess electrostatic hazards for gas group IIb or IIc materials.