Magnetic translation groups as group extension

Extensions of a direct product T of two cyclic groups Z_n1 and Z_n2 by an Abelian (gauge) group G with the trivial action of T on G are considered. All possible (nonequivalent) factor systems are determined using the Mac Lane method. Some of resulting groups describe magnetic translation groups. As examples extensions with G=U(1) and G=Z_n are considered and discussed.Comment: 10 page

Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Quantifying uncertainty in the measurement of arsenic in suspended particulate matter by Atomic Absorption Spectrometry with hydride generator

Arsenic is the toxic element, which creates several problems in human being specially when inhaled through air. So the accurate and precise measurement of arsenic in suspended particulate matter (SPM) is of prime importance as it gives information about the level of toxicity in the environment, and preventive measures could be taken in the effective areas. Quality assurance is equally important in the measurement of arsenic in SPM samples before making any decision. The quality and reliability of the data of such volatile elements depends upon the measurement of uncertainty of each step involved from sampling to analysis. The analytical results quantifying uncertainty gives a measure of the confidence level of the concerned laboratory. So the main objective of this study was to determine arsenic content in SPM samples with uncertainty budget and to find out various potential sources of uncertainty, which affects the results. Keeping these facts, we have selected seven diverse sites of Delhi (National Capital of India) for quantification of arsenic content in SPM samples with uncertainty budget following sampling by HVS to analysis by Atomic Absorption Spectrometer-Hydride Generator (AAS-HG). In the measurement of arsenic in SPM samples so many steps are involved from sampling to final result and we have considered various potential sources of uncertainties. The calculation of uncertainty is based on ISO/IEC17025: 2005 document and EURACHEM guideline. It has been found that the final results mostly depend on the uncertainty in measurement mainly due to repeatability, final volume prepared for analysis, weighing balance and sampling by HVS. After the analysis of data of seven diverse sites of Delhi, it has been concluded that during the period from 31st Jan. 2008 to 7th Feb. 2008 the arsenic concentration varies from 1.44 ± 0.25 to 5.58 ± 0.55 ng/m3 with 95% confidence level (k = 2)

Freezing/perfusion microscope stage

This invention relates to a microscope stage assembly for use in combination with magnification apparatus. The stage assembly includes a support assembly, temperature control assembly and fluid control assembly. The stage assembly provides for continuous visual observation of an object being magnified while at the same time controlling the thermal and fluid environment of the object. Physical and chemical changes to an object can be viewed continuously.Board of Regents, University of Texas Syste

Coupled States of the System of Two Free Electrons on a Single Star

A classification scheme of quantum states for the system of two free electrons in a cubic box, confined to a single star of quasi-momentum is proposed within a Racah-Wigner type of approach. Coupling of angular momenta of the atomic case is here substituted by Mackey theorem for transitive representations, which provides a crystalline analogue of orbital angular momentum - the resultant orbit of the geometric symmetry group. The action of the Pauli group is combined with that of the octahedral group which yields the connection between spin (i.e. the singlet or triplet pairing of electrons) and statistic of the positional factor. Resultant singlets and doublets - irreducible representations of the octahedral group, exhibit an ordinary Landau diamagnetic behaviour, whereas triplets are paramagnetic. A relation between the Mackey star and the star of resultant momentum is discussed

Outcomes Assessment: A Pilot Study

Outcomes assessment and continuous improvement are essential elements of educational programs. Emphasis on assessment is based primarily upon the requirements of accrediting agencies, but also on the perceived value of assessment in satisfying the demands for accountability in an increasingly competitive environment. Educational research has shown that measurement of educational outcomes can be used to inform an institution about educational goals that are being satisfied and those that are not. This information can motivate and direct efforts to improve curricula. This article describes a pilot study of the implementation of a Web-based (TrueOutcomes[C]) assessment process in a technology program and examines the effectiveness of the process in terms of student and faculty buy-in and whether the process produces useful data and reports for accreditation and continuous improvement. Three accrediting agencies were associated with this study. Two directly impact Southwest Missouri State University (SMSU) and the third was included because of its impact on the development and application of the software. These agencies and their impact are briefly described in this article