Shape Theory

Dydak, Jerzy; Segal, Jack

doi:10.1007/bfb0067572

Cited by 72 publications

(31 citation statements)

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“…also 6,7] that Tn is free abelian on these n generators; we have just seen that it operates trivially on lm(Hqix). Because X is finite-dimensional, there is a largest degree r such that HrY # 0.…”

mentioning

confidence: 80%

Homotopy Idempotents on Finite-Dimensional Complexes Split

Hastings¹,

Heller²

1982

Proceedings of the American Mathematical Society

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mentioning

confidence: 80%

Homotopy Idempotents on Finite-Dimensional Complexes Split

Hastings¹,

Heller²

1982

Proceedings of the American Mathematical Society

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“…The approximate displacements in r and r·φ that arise from a small transverse component of the magnetic field, for a perfectly aligned electric field E = (0, 0, E z ) and a (nearly) parallel magnetic field B = (B r , B rφ , B z ), are (for details, see Refs. [21] and [22]):…”

Section: Distortions From Field Inhomogeneitiesmentioning

confidence: 99%

“…Fortunately, this was provided for at large radius by ∼16 mm wide overlaps 21) of the barrel RPCs [6], and-for physics tracks-at small radius by the beam point. For throughgoing cosmic-muon tracks that pass close to the TPC axis, the closest point of approach to the 19) Here, and elsewhere in this paper, whenever there is a double sign the upper sign refers to the magnetic field orientation B = (0, 0, B z ) with B z > 0, and the lower sign to the opposite magnet polarity.…”

Section: Distortions From Field Inhomogeneitiesmentioning

confidence: 99%

The HARP Time Projection Chamber: Characteristics and physics performance

Ammosov

Bolshakova

Boyko

et al. 2008

Nuclear Instruments and Methods in Physics Research Section A:

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The HARP spectrometer that took data at the CERN Proton Synchrotron in 2001 and 2002 had as large-angle detector system a Time Projection Chamber (TPC) surrounded by Resistive Plate Chambers. The design of the TPC, experience with its operation, and its good physics performance are described. The successful recovery from track distortions arising from inhomogeneities of the electric and magnetic fields in the TPC volume is discussed.A. Bolshakova INTRODUCTIONThe HARP experiment arose from the realization that the differential cross-sections of hadron production in the collisions of low-momentum protons with nuclei were known only within a factor of two to three. Consequently, the HARP spectrometer was designed to carry out a programme of systematic and precise measurements of hadron production by protons and pions with momenta from 1.5 to 15 GeV/c. The experiment was performed at the CERN Proton Synchrotron in 2001 and 2002 with a set of targets ranging from hydrogen to lead. With a view to achieving nearly 4π acceptance, the HARP detector combined a large-angle spectrometer with a forward spectrometer. The latter consisted of a dipole magnet and drift chambers for momentum measurement, and a threshold Cherenkov counter, a time-of-flight wall, and an electromagnetic calorimeter for particle identification. The large-angle spectrometer comprised a cylindrical Time Projection Chamber (TPC) and an array of Resistive Plate Chambers (RPCs) around and behind the TPC. The purpose of the TPC was track reconstruction and particle identification by dE/dx. The purpose of the RPCs was to complement the particle identification by dE/dx by time of flight, especially to distinguish between electrons and pions in the momentum range 150-250 MeV/c where the specific ionization of electrons and pions is too close for their separation.This paper describes the HARP TPC, the experience with its operation, and its physics performance.The TPC had to be designed, constructed and commissioned within a brief period of 17 months. Under this time pressure a few per se minor mishaps occurred which, however, had quite some consequences for the quality of the raw data. Part of this paper is dedicated to the-so we hope-interesting discovery of, and the recovery from, these errors. This paper also sets the record straight with respect to the TPC performance reported in Refs.[1] and [2]. It justifies and details our criticism thereof [3,4]. PERFORMANCE: OBJECTIVES AND RESULTSThe experiment was carried out in the T9 beam of the CERN Proton Synchrotron that had a maximum momentum of p = 15 GeV/c. Thus in the large-angle region, the detector was to handle comfortably transverse momenta up to p T ∼ 2 GeV/c. A, say, 2σ separation (2.3% misidentification probability) between positive and negative charges at p T = 2 GeV/c called for a resolution σ(1/p T ) not worse than about 0.25 (GeV/c) −1 . Table 1 summarizes the key parameters of the TPC, and compares objectives with the achieved results. In later sections, the table entries will be discuss...

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“…Let the compact metric space Z be shape dominated by the finite CW complex X (see [4] for information on shape theory). Then CW complex, then d°u' and d'ou are mutually inverse shape morphisms, so Z is shape equivalent to CW complex.…”

Section: (B) Additional Information In the Finite-dimensional Casementioning

confidence: 99%

“…Compact metric spaces shape dominated by finite CW complexes are called FANR's (or ANSR's in [4]). The above says that the FANR Z has the shape of a CW complexe if and only if any one of the homotopy idempotents on finite complexes associated with Z splits.…”

Section: (B) Additional Information In the Finite-dimensional Casementioning

confidence: 99%

Splitting homotopy idempotents which have essential fixed points

Geoghegan¹

1981

Pacific J. Math.

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Shape Theory

Cited by 72 publications

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Homotopy Idempotents on Finite-Dimensional Complexes Split

Homotopy Idempotents on Finite-Dimensional Complexes Split

The HARP Time Projection Chamber: Characteristics and physics performance

Splitting homotopy idempotents which have essential fixed points

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