On bosets and fundamental semigroups

The term boset was coined by Patrick Jordan, both as an abbreviation of biordered set, and as a generalisation of poset, itself an abbreviation of partially ordered set. A boset is a set equipped with a partial multiplication and two intertwining reflexive and transitive arrow relations which satisfy certain axioms. When the arrow relations coincide the boset becomes a poset. Bosets were invented by Nambooripad (in the 1970s) who developed his own version of the theory of fundamental regular semigroups, including the classical theory of fundamental inverse semigroups using semilattices, due to Munn (in the 1960s). A semigroup is fundamental if it cannot be shrunk homomorphically without collapsing its skeleton of idempotents, which is a boset. Nambooripad constructed the maximum fundamental regular semigroup with a given boset of idempotents. Fundamental semigroups and bosets are natural candidates for basic building blocks in semigroup theory because every semigroup is a coextension of a fundamental semigroup in which the boset of idempotents is undisturbed. Recently Jordan reproved Nambooripad's results using a new construction based on arbitrary bosets. In this thesis we prove that this construction is always fundamental, which was previously known only for regular bosets, and also that it possesses a certain maximality property with respect to semigroups which are generated by regular elements. For nonregular bosets this constuction may be regular or nonregular. We introduce a class of bosets, called sawtooth bosets, which contain many regular and nonregular examples, and correct a criterion of Jordan's for the regularity of this construction for sawtooth bosets with two teeth. We also introduce a subclass, called cyclic sawtooth bosets, also containing many regular and nonregular examples, for which the construction is always regular

On bosets and fundamental semigroups

The term boset was coined by Patrick Jordan, both as an abbreviation of biordered set, and as a generalisation of poset, itself an abbreviation of partially ordered set. A boset is a set equipped with a partial multiplication and two intertwining reflexive and transitive arrow relations which satisfy certain axioms. When the arrow relations coincide the boset becomes a poset. Bosets were invented by Nambooripad (in the 1970s) who developed his own version of the theory of fundamental regular semigroups, including the classical theory of fundamental inverse semigroups using semilattices, due to Munn (in the 1960s). A semigroup is fundamental if it cannot be shrunk homomorphically without collapsing its skeleton of idempotents, which is a boset. Nambooripad constructed the maximum fundamental regular semigroup with a given boset of idempotents. Fundamental semigroups and bosets are natural candidates for basic building blocks in semigroup theory because every semigroup is a coextension of a fundamental semigroup in which the boset of idempotents is undisturbed. Recently Jordan reproved Nambooripad's results using a new construction based on arbitrary bosets. In this thesis we prove that this construction is always fundamental, which was previously known only for regular bosets, and also that it possesses a certain maximality property with respect to semigroups which are generated by regular elements. For nonregular bosets this constuction may be regular or nonregular. We introduce a class of bosets, called sawtooth bosets, which contain many regular and nonregular examples, and correct a criterion of Jordan's for the regularity of this construction for sawtooth bosets with two teeth. We also introduce a subclass, called cyclic sawtooth bosets, also containing many regular and nonregular examples, for which the construction is always regular

Accelerator mass spectrometry 14C determination in CO2 produced from laser decomposition of aragonite

Author Posting. © John Wiley & Sons, 2008. This is the author's version of the work. It is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Rapid Communications in Mass Spectrometry 22 (2008): 3443-3449, doi:10.1002/rcm.3745.Determination of 14C in aragonite (CaCO3) decomposed thermally to CO2 using an yttrium‐aluminum‐garnet doped neodymium laser is reported. Laser decomposition accelerator mass spectrometer (LD‐AMS) measurements reproduce AMS determinations of 14C from conventional reaction of aragonite with concentrated phosphoric acid. The lack of significant differences between these sets of measurements indicate that LD‐AMS radiocarbon dating can overcome the significant fractionation that has been observed during stable isotope (C and O) laser decomposition analysis of different carbonate minerals. The laser regularly converted nearly 30% of material removed to CO2 despite being optimized for ablation, where laser energy breaks material apart rather than chemically altering it. These results illustrate promise for using laser decomposition on the front‐end of AMS systems that directly measure CO2 gas. The feasibility of such measurements depends on 1. the improvement of material removal and/or CO2 generation efficiency of the laser decomposition system and 2. the ionization efficiency of AMS systems measuring continuously flowing CO2.This work was funded on a competitive basis by the Cecil H. and Ida M. Green Technology Innovation Award of Woods Hole Oceanographic Institution

Digital optical recorder-reproducer system

A mass archival optical recording and reproduction system includes a recording light source such as a laser beam focussed and directed upon an acousto-optic linear modulator array (or page composer) that receives parallel blocks of data converted from a serial stream of digital data to be stored. The page composer imparts to the laser beam modulation representative of a plurality of parallel channels of data and through focussing optics downstream of the page composer parallel arrays of optical spots are recorded upon a suitable recording medium such as a photographic film floppy disc. The recording medium may be substantially frictionlessly and stably positioned for recording at a record/read station by an air-bearing platen arrangement which is preferably thermodynamically non-throttling so that the recording film may be positioned in the path of the information-carrying light beam in a static or dynamic mode. During readout, the page composer is bypassed and a readout light beam is focussed directly upon the recording medium containing an array of previously recorded digital spots, a sync bit, data positioning bits, and a tracking band. The readout beam which has been directed through the recording medium is then imaged upon a photodetector array, the output of which may be coupled to suitable electronic processing circuitry, such as a digital multiplexer, whereby the parallel spot array is converted back into the original serial data stream

The Heart of the Matter: Health Status of Aged Care Clients Receiving Home- and Community-Based Care

Objective. To determine the current health status of home based elderly clients receiving government funded aged care packages. Design. Prospective Observational study. Setting. Community based, home care program in Australia. Participants. Community-dwelling older adults receiving aged care packages. Measurements. A comprehensive test battery of physical, mental and social scales were completed including a Caregiver Strain Index where appropriate. Results. 37% of the 334 subjects were male and the mean age was 81 ± 8 years. Physical functioning was low compared to the Australian population. Depression was highly prevalent with 15.9% severely depressed and 38.7% mildly depressed. 26% of clients screened positive for dementia. Relatively good levels of social support were reported, however social networking activity levels were low. Sixty one percent of clients had caregivers, of whom 63.3% had high levels of strain. Strain was higher in caregivers of clients on higher levels of care (78.5% versus 50.6% highly strained). Conclusion. The data suggests that as a group there is a high degree of comorbidity, and depression, dementia and caregiver strain are highly prevalent. The findings may aid administrators and health policy planners in directing resources to key areas impacting on health outcomes in this group

The effect of the COVID-19 pandemic on domestic violence and child abuse

In response to the COVID-19 pandemic, many governments around the world have implemented lockdown or mass quarantine measures. While the purpose of these measures is to prevent the spread of the virus, they have had important social consequences. To determine the effect that pandemic-related isolation and quarantine measures have had on domestic violence and child abuse, we analyzed Canadian police calls for service data from 2015 to 2020. Our findings indicate that calls for service related to both domestic violence and child abuse have significantly increased during the pandemic. In light of these findings, we make recommendations for both government officials responsible for pandemic management and policing organizations on how to prevent increases in domestic violence and child abuse during future lockdowns

NASA Global Precipitation Measurement (GPM) mission ground and satellite observations for ICE-POP: Status Update

No abstract availabl

Software development for continuous-gas-flow AMS

Author Posting. © Elsevier B.V., 2008. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 266 (2008): 2233-2237, doi:10.1016/j.nimb.2008.03.001.The National Ocean Sciences Accelerator Mass Spectrometry (NOSAMS) Facility at Woods Hole Oceanographic Institution is presently completing installation of a novel continuous-flow AMS system. A multi-year development of an AMS microwave gas ion source in collaboration with Atomic Energy Canada Limited (AECL), Chalk River, has preceded this final step of an implementation that is expected to add a new dimension to 14C AMS. National Instruments, NIM, and CAMAC modules have been programmed with LabVIEW on a Windows XP platform to form the basis for data acquisition. In this paper we discuss possible applications and include simulations of expected data acquisition scenarios like real-time AMS analysis of chromatograms. Particular attention is given to issues of synchronization between rapidly changing input amplitudes and signal processing cycles in hardware and software.This work is supported by the United States National Science Foundation under Cooperative Agreement OCE-0228996

Rethinking How External Pressure Can Suppress Dendrites in Lithium Metal Batteries

We offer an explanation for how dendrite growth can be inhibited when Li metal pouch cells are subjected to external loads, even for cells using soft, thin separators. We develop a contact mechanics model for tracking Li surface and sub-surface stresses where electrodes have realistically (micron-scale) rough surfaces. Existing models examine a single, micron-scale Li metal protrusion under a fixed local current density that presses more or less conformally against a separator or stiff electrolyte. At the larger, sub-mm scales studied here, contact between the Li metal and the separator is heterogeneous and far from conformal for surfaces with realistic roughness: the load is carried at just the tallest asperities, where stresses reach tens of MPa, while most of the Li surface feels no force at all. Yet, dendrite growth is suppressed over the entire Li surface. To explain this dendrite suppression, our electrochemical/mechanics model suggests that Li avoids plating at the tips of growing Li dendrites if there is sufficient local stress; that local contact stresses there may be high enough to close separator pores so that incremental Li+ ions plate elsewhere; and that creep ensures that Li protrusions are gradually flattened. These mechanisms cannot be captured by single-dendrite-scale analyses

A Radio Pulsar/X-ray Binary Link

Radio pulsars with millisecond spin periods are thought to have been spun up by transfer of matter and angular momentum from a low-mass companion star during an X-ray-emitting phase. The spin periods of the neutron stars in several such low-mass X-ray binary (LMXB) systems have been shown to be in the millisecond regime, but no radio pulsations have been detected. Here we report on detection and follow-up observations of a nearby radio millisecond pulsar (MSP) in a circular binary orbit with an optically identified companion star. Optical observations indicate that an accretion disk was present in this system within the last decade. Our optical data show no evidence that one exists today, suggesting that the radio MSP has turned on after a recent LMXB phase.Comment: published in Scienc