Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example

We study a perturbed Floquet Hamiltonian $K+\beta V$ depending on a coupling constant $\beta$. The spectrum $\sigma(K)$ is assumed to be pure point and dense. We pick up an eigen-value, namely $0\in\sigma(K)$, and show the existence of a function $\lambda(\beta)$ defined on $I\subset\R$ such that $\lambda(\beta) \in \sigma(K+\beta V)$ for all $\beta\in I$, 0 is a point of density for the set $I$, and the Rayleigh-Schr\"odinger perturbation series represents an asymptotic series for the function $\lambda(\beta)$. All ideas are developed and demonstrated when treating an explicit example but some of them are expected to have an essentially wider range of application.Comment: Latex, 24 pages, 51

Nowhere to Run; Nowhere to Hide: The Reality of Being a Law Library Director in Times of Great Opportunity and Significant Challenges

This is an edited version of remarks presented at \u27Nowhere to Run, Nowhere to Hide\u27: The Reality of Being a Law Library Director in Times of Great Opportunity and Significant Challenges, January 5, 2015, at the Association of American Law Schools Annual Meeting, Washington, D.C

Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.Comment: In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some typo

The Realities of Evaluating Educational Technology in School Settings

\ua9 2024 Copyright held by the owner/author(s).HCI researchers are increasingly interested in the evaluation of educational technologies in context, yet acknowledge that challenges remain regarding the logistical, material and methodological constraints of this approach to research [18, 53].Through the analysis of the authors\u27 contributed thematic research vignettes, the following article exposes the practical realities of evaluating educational technologies in school settings. This includes insights into the planning stages of evaluation, the relationship between the researcher and the school environment, and the impact of the school context on the data collection process.We conclude by providing an orientation for the design of HCI educational technology research undertaken in school contexts, providing guidance such as considering the role of modular research design, clarifying goals and expectations with school partners, and reporting researcher positionality

The SKA Particle Array Prototype: The First Particle Detector at the Murchison Radio-astronomy Observatory

We report on the design, deployment, and first results from a scintillation detector deployed at the Murchison Radio-astronomy Observatory (MRO). The detector is a prototype for a larger array -- the Square Kilometre Array Particle Array (SKAPA) -- planned to allow the radio-detection of cosmic rays with the Murchison Widefield Array and the low-frequency component of the Square Kilometre Array. The prototype design has been driven by stringent limits on radio emissions at the MRO, and to ensure survivability in a desert environment. Using data taken from Nov.\ 2018 to Feb.\ 2019, we characterize the detector response while accounting for the effects of temperature fluctuations, and calibrate the sensitivity of the prototype detector to through-going muons. This verifies the feasibility of cosmic ray detection at the MRO. We then estimate the required parameters of a planned array of eight such detectors to be used to trigger radio observations by the Murchison Widefield Array.Comment: 17 pages, 14 figures, 3 table

Attenuation and modification of the ballast water microbial community during voyages into the Canadian Arctic

Aim: Ballast water is a major vector of non-indigenous species introductions world-wide. Our understanding of population dynamics of organisms entrained in ballast is largely limited to studies of zooplankton and phytoplankton. Bacteria are more numerous and diverse than zooplankton or phytoplankton, yet remain comparatively understudied. We apply a metagenomics approach to characterize changes in the microbial ballast water community over the course of three voyages on one ship, and assess the effects of ballast water exchange (BWE), spring/summer sampling month and time since voyage start. Location: Quebec City and Deception Bay, Quebec, and the coastal marine region offshore of eastern Canada. Methods: We used universal primers to Ion Torrent sequence a fragment of the bacterial 16S ribosomal DNA for samples collected over three voyages of one ship between Quebec City and Deception Bay in June, July and August 2015. We compared richness (total number of species in the community) and diversity (accounts for both species abundance and evenness) using linear mixed-effects analysis and compared community composition using non-metric multidimensional scaling and permutational multivariate analysis of variance. Initial comparisons were between months. Subsequent analyses focused on each month separately. Results: Ion Torrent sequencing returned c. 2.9 million reads and revealed monthly differences in diversity and richness, and in community structure in ballast water. June had higher richness and diversity than either July or August, and showed most clearly the effect of BWE on the microbial community. Main conclusions: Our results suggest that environmental conditions associated with different spring/summer sampling months drive differences in microbial diversity in ballast water. This study showed that BWE removes some components of the freshwater starting microbial community and replaces them with other taxa. BWE also changed proportional representation of some microbes without removing them completely. It appears that some taxa are resident in ballast tanks and are not removed by BWE. © 2017 John Wiley & Sons Lt

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

Ni-substituted sites and the effect on Cu electron spin dynamics of YBa2Cu{3-x}NixO{7-\delta}

We report Cu nuclear quadrupole resonance experiment on magnetic impurity Ni-substituted YBa$_2$Cu$_{3-x}$Ni$_x$O$_{7-\delta}$. The distribution of Ni-substituted sites and its effect on the Cu electron spin dynamics are investigated. Two samples with the same Ni concentration $x$=0.10 and nearly the same oxygen content but different $T_c$'s were prepared: One is an as-synthesized sample (7-$\delta$=6.93) in air ($T_c$$\approx 80 K$), and the other is a quenched one (7-$\delta$=6.92) in a reduced oxygen atmosphere ($T_c$$\approx 70 K$). The plane-site $^{63}$Cu(2) nuclear spin-lattice relaxation for the quenched sample was faster than that for the as-synthesized sample, in contrast to the $^{63}$Cu(1) relaxation that was faster for the as-synthesized sample. This indicates that the density of plane-site Ni(2) is higher in the quenched sample, contrary to the chain-site Ni(1) density which is lower in the quenched sample. From the analysis in terms of the Ni-induced nuclear spin-lattice relaxation, we suggest that the primary origin of suppression of $T_c$ is associated with nonmagnetic depairing effect of the plane-site Ni(2).Comment: 7 pages, 5 figure