Two-point one-dimensional δ\delta-δ′\delta^\prime interactions: non-abelian addition law and decoupling limit

In this contribution to the study of one dimensional point potentials, we prove that if we take the limit $q\to 0$ on a potential of the type $v_0\delta({y})+{2}v_1\delta'({y})+w_0\delta({y}-q)+ {2} w_1\delta'({y}-q)$, we obtain a new point potential of the type ${u_0} \delta({y})+{2 u_1} \delta'({y})$, when $u_0$ and $u_1$ are related to $v_0$, $v_1$, $w_0$ and $w_1$ by a law having the structure of a group. This is the Borel subgroup of $SL_2({\mathbb R})$. We also obtain the non-abelian addition law from the scattering data. The spectra of the Hamiltonian in the exceptional cases emerging in the study are also described in full detail. It is shown that for the $v_1=\pm 1$, $w_1=\pm 1$ values of the $\delta^\prime$ couplings the singular Kurasov matrices become equivalent to Dirichlet at one side of the point interaction and Robin boundary conditions at the other side

Engineering Start-Up Packages: Mixed Methods Analysis of Composition and Implications for Early-Career Professional Formation

This paper is an evidence-based practice paper. In competitive research environments, many universities and engineering colleges utilize start-up or recruitment packages to attract potential candidates. These costs are distributed across multiple cost centers within the university ecosystem. Potential engineering faculty candidates may sign a probationary contract and are provided with role statements during onboarding processes. Within the role statement, research has been the primary area that is catalyzed with start-up funding. Typically, start-up funding has prescribed purposes by category. According to the 2019 American Society for Engineering Education (ASEE) Engineering Research Council (ERC) Startup Package Survey, 77.6% of the start-up packages were negotiated by categories. While start-up packages are well-known tools for recruitment in engineering, their composition, categories and cost-center distribution are less well described. Methods: Start-up packages (n=29) for assistant tenure-track engineering faculty hired between 2013-2019 within a midsize college of engineering at an emerging R1 were analyzed. The mixed methods study utilized descriptive analysis, themes and tree map charts to conceptualize and characterize the categories used. The study examined one question: How are the categories of assistant tenure track engineering faculty start-up packages different or similar across multiple departments? Results: The study contributes to the knowledge about early career engineering faculty professional formation. Specifically, the study revealed start-up packages as critical stimuli for the transition from graduate/postdoctoral student to paid assistant tenure track professor. Start-up package negotiations occurred where there are expectations and actions that are formative and not well described a priori. Discussion: Assistant tenure track professors had start-up packages that varied by department between 2013-2019. This study acknowledged that the seven cohorts did not all begin with the same start-ups within their six-year cycle. Some departments provided new candidates with less than $100,000 each while others invested over$430,000 per candidate. Based on the data, the survey and other secondary data examined some general recommendations were identified. Importantly, the data may be seen as a starting point for having informed conversations with others in the ecosystem and engineering faculty who are mentoring students and early career faculty. Limitations: The limitations of the study are that the data were sampled from early career faculty in the western US which may have different costs of living depending on the area. The data were collected as secondary data to demonstrate the significant investments institutions have in early career faculty and that this was a potential motivator and/or variable for grant writing and research

Recent progress in the development of a solar neutron tracking device (SONTRAC)

We report the results of recent calibration data analysis of a prototype scintillating fiber tracking detector system designed to perform imaging, spectroscopy and particle identification on 20 to 250 MeV neutrons and protons. We present the neutron imaging concept and briefly review the detection principle and the prototype description. The prototype detector system records ionization track data on an event-by-event basis allowing event selection criteria to be used in the off-line analysis. Images of acrylic phantoms from the analysis of recent proton beam calibrations are presented as demonstrations of the particle identification, imaging and energy measurement capabilities. The measured position resolution is \u3c 500 micrometers . The measured energy resolution is 14.2 percent at 35 MeV. The detection techniques employed can be applied to measurements in a variety of disciplines including solar and atmospheric physics, radiation therapy and nuclear materials monitoring. These applications are discussed briefly as are alternative detector configurations and future development plans

On the macroion virial contribution to the osmotic pressure in charge-stabilized colloidal suspensions

Our interest goes to the different virial contributions to the equation of state of charged colloidal suspensions. Neglect of surface effects in the computation of the colloidal virial term leads to spurious and paradoxical results. This pitfall is one of the several facets of the danger of a naive implementation of the so called One Component Model, where the micro-ionic degrees of freedom are integrated out to only keep in the description the mesoscopic (colloidal) degrees of freedom. On the other hand, due incorporation of wall induced forces dissolves the paradox brought forth in the naive approach, provides a consistent description, and confirms that for salt-free systems, the colloidal contribution to the pressure is dominated by the micro-ionic one. Much emphasis is put on the no salt case but the situation with added electrolyte is also discussed

Colloidal hard-rod fluids near geometrically structured substrates

Density functional theory is used to study colloidal hard-rod fluids near an individual right-angled wedge or edge as well as near a hard wall which is periodically patterned with rectangular barriers. The Zwanzig model, in which the orientations of the rods are restricted to three orthogonal orientations but their positions can vary continuously, is analyzed by numerical minimization of the grand potential. Density and orientational order profiles, excess adsorptions, as well as surface and line tensions are determined. The calculations exhibit an enrichment [depletion] of rods lying parallel and close to the corner of the wedge [edge]. For the fluid near the geometrically patterned wall, complete wetting of the wall -- isotropic liquid interface by a nematic film occurs as a two-stage process in which first the nematic phase fills the space between the barriers until an almost planar isotropic -- nematic liquid interface has formed separating the higher-density nematic fluid in the space between the barriers from the lower-density isotropic bulk fluid. In the second stage a nematic film of diverging film thickness develops upon approaching bulk isotropic -- nematic coexistence.Comment: 9 pages, 9 figure

How Leaders Invest Staffing Resources for Learning Improvement

Analyzes staffing challenges that guide school leaders' resource decisions in the context of a learning improvement agenda, staff resource investment strategies that improve learning outcomes equitably, and ways to win support for differential investment

A scintillating plastic fiber tracking detector for neutron and proton imaging and spectroscopy

We report the results of recent calibration data analysis of a prototype scintillating fiber tracking detector system designed to perform imaging, spectroscopy and particle identification on 20 to 250 MeV neutrons and protons. We present the neutron imaging concept and briefly review the detection principle and the prototype description. The prototype detector system records ionization track data on an event-by-event basis allowing event selection criteria to be used in the off-line analysis. Images of acrylic phantoms from the analysis of recent proton beam calibrations (14 to 65 MeV range) are presented as demonstrations of the particle identification, imaging and energy measurement capabilities. The measured position resolution is c 500 pm. The measured energy resolution (AE/E, FWHM) is 14.2% at 35 MeV. An effective technique for track identification and data compression is presented. The detection techniques employed can be applied to measurements in a variety of disciplines including solar and atmospheric physics, radiation therapy and nuclear materials monitoring. These applications are discussed briefly as are alternative detector configurations and future development plans

Young Children’s Ideas About Astronomy

Young children express interest and understanding about science topics through everyday conversations with parents. Little is known about how much interest preschool-aged children show in astronomy. Using a diary report methodology, we asked parents in three communities in coastal California to keep track of conversations with their three to five-year-old children about nature. The communities varied in demographics, including one community with predominantly European-American families, one community with predominantly Latinx families, and one community with families from a variety of backgrounds. Overall, young children showed interest in astronomy through initiation and engagement in conversations about a variety of astronomical objects and events; this was consistent across gender, age, and community. Across all three communities, conversations about astronomy accounted for approximately 15% of the conversations about nature, ranking in the top three most frequent topics for each group. Children initiated the vast majority of conversations with their parents, including those about astronomy. Within astronomy, children were most interested in the sun, moon, stars, and day or night sky. Thus, while science educators may see astronomy as too complex for young children, children observe and comment on astronomical phenomena as part of their everyday life. Finding ways to support educators and parents in talking with children about these observations may productively build on this early astronomy interest and position children for greater understanding and engagement in this domain

The relationship of aging, complete tooth loss, and having a dental visit in the last 12 months

OBJECTIVES: To evaluate the extent to which dental health care visits in the past year differed among older adults with and without edentulism. MATERIAL AND METHODS: We conducted a cross-sectional study using the 2017 Medical Expenditure Panel Survey among participants aged \u3e /=50 years (n = 10,480, weighted = 112,116,641). Two self-reported outcome variables were used: loss of all teeth from upper and lower jaws (yes/no) and dental visit in the last 12 months (yes/no). Logistic models were used to estimate adjusted odds ratios (aOR) and 95% confidence intervals (CI). RESULTS: Overall, 11.4% of the non-institutionalized U.S. population aged \u3e /=50 years were edentulous; the prevalence was higher in those with advanced age. Adherence to annual oral health visits was 16% among those with edentulism, 52% among those without. The prevalence of dental care visits in the past year was higher among those with advanced age without edentulism, but for those with edentulism, the odds of visiting a dental care provider was lower in all age groups compared to those 50-59 years ((60-69 years): aOR: 0.58, CI:0.36-0.95; (70-79 years): aOR: 0.51, CI: 0.30-0.88; ( \u3e /= 80 years): aOR: 0.45, CI: 0.26-0.80)). CONCLUSION: Although the prevalence of edentulism was higher in those with advanced age, oral health visits during the last 12 months were less frequent in older adults with edentulism. Interventions to improve adherence to dental care recommendations in the growing aging population are warranted