The extremal algebra on two hermitians with square 1

Let Ea(u,v) be the extremal algebra determined by two hermitians u and v with u2 = v2 = 1. We show that: Ea(u,v) = {f=gu:f,g ε C(T)}, where T is the unit circle; Ea(u,v) is C*-equivelant to C*(G), where G is the infinite dihedral group; most of the hermitian elements k od Ea(u,v) have the property that kn is hermitian for all odd n but for no even n; any two hermitian words in G generate an isometric copy of Ea(u,v) in Ea(u,v)

Cement Raw Materials in Indiana

Indiana Geological Survey Bulletin 15Limestone that is chemically suitable and easily accessible for cement manufacture can be found at many places in Indiana in the Mississippian limestones and to a more limited extent in the Devonian limestones. Clay, shale, and gypsum, also used in manufacturing cement, are readily available close to limestone reserves. Five areas in Indiana are most favorable for establishing cement plants: Bloomington-Spencer-Gosport, Paoli-Mitchell-Bedford, Greencastle, central Clark County, and southern Harrison County; a sixth area, east of Logansport, also may have limestone suitable for cement manufacture. Five of these areas are close to railroad lines and fuel supplies; the southern Harrison County area is favorably situated for barge transportation on the Ohio River. Reserves of mineral raw materials in 5 of the areas probably are sufficient to supply a cement plant for 50 years. Surface study does not permit an accurate appraisal of the Logansport area, but it probably also has sufficient reserves.Indiana Department of Conservatio

High-Calcium Limestone and Dolomite in Indiana

Indiana Geological Survey Bulletin 27High-Calcium limestone and dolomite suitable for industrial use exist in Indiana. Selected measured stratigraphic sections and chemical and spectrographic analyses are used to evaluate high-Calcium limestone and dolomite. Regions favorable for quarrying high-Calcium limestone and dolomite are the region of outcrop of Mississippian rocks and to a lesser extent the region of outcrop of Devonian rocks. Dolomite can also be found in the region of outcrop of Silurian rocks, particularly in northern Indiana.Indiana Department of Conservatio

Modeling Current and Future High-Cadence Surveys of Repeating FRB Populations

In recent years, the CHIME (Canadian Hydrogen Intensity Mapping Experiment) interferometer has revealed a large number of Fast Radio Bursts (FRBs), including a sizable population that demonstrates repeating behavior. This transit facility, employing a real-time FRB search pipeline, continually scans the sky with declinations between $-10^{\circ}$ and $90^{\circ}$ for events with fluences $\gtrapprox 0.4$ Jy ms. We simulate a population of repeating FRBs by performing Monte Carlo simulations of underlying source populations processed through a mock CHIME/FRB observing pipeline. Assuming intrinsic repeater rates follow a Poisson distribution, we test assumptions about the burst populations of the repeater sample, and construct models of the FRB sample assuming various cosmological distributions. We infer the completeness of CHIME/FRB observations as a function of observing cadence and redshifts out to 0.5. We find that, if all simulated bursts have a fixed Poisson probability of repetition over their integrated time of observation, repeating burst detections across comoving volume should continue to grow near linearly on the order of decades. We predict that around 170 of the current CHIME/FRB one-off sources will ultimately repeat. We also make projections for FRB repeaters by future facilities and demonstrate that the number of repeaters they find could saturate on a $\sim$3 yr timescale.Comment: 10 pages, 7 figure

Compositional analyses of the associations between sedentary time, different intensities of physical activity, and cardiometabolic biomarkers among children and youth from the United States

Introduction : Compositional data analysis is one appropriate method for co-dependent data, even when data are collected for a subdivision of the 24-hour period, such as the waking day. Objectives were to use compositional analyses to examine the combined and relative associations of sedentary time (ST), light-intensity physical activity (LPA), moderate-intensity physical activity (MPA), and vigorous-intensity physical activity (VPA) with cardiometabolic biomarkers in a representative sample of children and youth. Methods : This cross-sectional study included 2544 participants aged 6-17 years from the 2003-2006 United States National Health and Nutrition Examination Survey. ST (= 7 METs) were accelerometer-derived. Cardiometabolic biomarkers included waist circumference, body mass index (BMI) z-score, HDL-cholesterol, C-reactive protein, and blood pressure. Triglycerides, glucose, insulin, and LDL-cholesterol were measured in a fasting sub-sample of adolescents (n = 670). Compositional linear regression models were conducted. Results : The composition of ST, LPA, MPA, and VPA was significantly associated with BMI z-score, log waist circumference, systolic and diastolic blood pressure, HDL-cholesterol, and log plasma glucose (variance explained: 1-29%). Relative to the other three behaviors, VPA was negatively associated with BMI z-score (gamma VPA = -0.206, p = 0.005) and waist circumference (gamma VPA = -0.03, p = 0.001). Conversely, ST was positively associated with waist circumference (gamma ST = 0.029, p = 0.013). ST and VPA were also positively associated with diastolic blood pressure (gamma ST = 2.700, p = 0.018; gamma VPA = 1.246, p = 0.038), relative to the other behaviors, whereas negative associations were observed for LPA (gamma LPA = -2.892, p = 0.026). Finally, VPA was positively associated with HDL-cholesterol, relative to other behaviors (gamma VPA = 0.058, p<0.001). Conclusions : The ST and physical activity composition appears important for many aspects of cardiometabolic health in children and youth. Compositions with more time in higher-intensity activities may be better for some aspects of cardiometabolic health

Some extremal algebras for hermitians

We study three extremal Banach algebras: (a) generated by two hermitian unitaries; (b) generated by an element of norm 1 all of whose odd positive powers are hermitian; (c) generated by an element of norm 1 all of whose even positive powers are hermitian. In all three cases the numerical range is found for various elements. The second algebra is shown to be isometrically isomorphic to a subalgebra of the first. The third algebra is identified with a space of functions

Natural resource management and development discourses in the Caribbean: reflections on the Guyanese and Jamaican experience

International discourses on environment and development help to shape global shared understandings of environmental issues. This paper describes the environment and development history of Guyana and Jamaica through pre-colonial, colonial, independence and market liberalisation stages. Two opposing discourses are used to frame this history: a dominant global environmental discourse characterised by technical and ‘scientific’ expertise and hierarchical governance; and a counter-discourse emphasising local control over natural resources. This analysis serves as a first step in surfacing and understanding the highly complex and multifaceted nature of environmental issues in these locations. However, we conclude with the recognition that further work should go beyond a bipolar analysis to one taking a critical, multidimensional approach, to promote more sustainable management of natural resources than has previously taken place

Compositional analysis of the associations between 24-h movement behaviours and health indicators among adults and older adults from the Canadian health measure survey

This study investigated the association between the allocation of time-use over the 24-h day between sleep, sedentary behaviour (SB), light-intensity physical activity (LPA) and moderate-to-vigorous-intensity physical activity (MVPA)) and health indicators. A cross-sectional analysis of Canadian Health Measures Survey data was undertaken using compositional data analysis. SB, LPA and MVPA were derived from Actical accelerometers, whilst sleep was self-reported by respondents. The analysis was stratified by age; adults (aged 18⁻64 years; n = 6322) and older adults (65⁻79 years; n = 1454). For adults, beneficial associations were observed between larger proportions of MVPA relative to time in other behaviours and body mass index (BMI), waist circumference, aerobic fitness, resting heart rate, high-density lipoprotein (HDL) cholesterol, triglycerides, blood glucose and insulin levels. More time spent in sleep relative to other movement behaviours was deleteriously associated with aerobic fitness, HDL cholesterol, insulin, C-reactive proteins and grip strength but beneficially with low-density lipoprotein cholesterol. Relative time spent in LPA was deleteriously associated with BMI and beneficially with triglycerides and grip strength. In older adults, these associations were blunted or disappeared but larger proportions of MVPA were associated with better mental health. The importance to health of MVPA when explicitly considered relative to other movement behaviours was confirmed

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Guest Editorial: GLADD, The Association of LGBTQ+ Doctors and Dentist