Bimodules over Cartan MASAs in von Neumann Algebras, Norming Algebras, and Mercer's Theorem

In a 1991 paper, R. Mercer asserted that a Cartan bimodule isomorphism between Cartan bimodule algebras A_1 and A_2 extends uniquely to a normal *-isomorphism of the von Neumann algebras generated by A_1 and A_2 [13, Corollary 4.3]. Mercer's argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel [15, Theorem 2.5]. Unfortunately, the arguments in the literature supporting [15, Theorem 2.5] contain gaps, and hence Mercer's proof is incomplete. In this paper, we use the outline in [16, Remark 2.17] to give a proof of Mercer's Theorem under the additional hypothesis that the given Cartan bimodule isomorphism is weak-* continuous. Unlike the arguments contained in [13, 15], we avoid the use of the Feldman-Moore machinery from [8]; as a consequence, our proof does not require the von Neumann algebras generated by the algebras A_i to have separable preduals. This point of view also yields some insights on the von Neumann subalgebras of a Cartan pair (M,D), for instance, a strengthening of a result of Aoi [1]. We also examine the relationship between various topologies on a von Neumann algebra M with a Cartan MASA D. This provides the necessary tools to parametrize the family of Bures-closed bimodules over a Cartan MASA in terms of projections in a certain abelian von Neumann algebra; this result may be viewed as a weaker form of the Spectral Theorem for Bimodules, and is a key ingredient in the proof of our version of Mercer's theorem. Our results lead to a notion of spectral synthesis for weak-* closed bimodules appropriate to our context, and we show that any von Neumann subalgebra of M which contains D is synthetic. We observe that a result of Sinclair and Smith shows that any Cartan MASA in a von Neumann algebra is norming in the sense of Pop, Sinclair and Smith.Comment: 21 pages, paper is a completely reworked and expanded version of an earlier preprint with a similar titl

Trends in wintertime climate in the northeastern United States: 1965–2005

Humans experience climate variability and climate change primarily through changes in weather at local and regional scales. One of the most effective means to track these changes is through detailed analysis of meteorological data. In this work, monthly and seasonal trends in recent winter climate of the northeastern United States (NE-US) are documented. Snow cover and snowfall are important components of the region\u27s hydrological systems, ecosystems, infrastructure, travel safety, and winter tourism and recreation. Temperature, snowfall, and snow depth data were collected from the merged United States Historical Climate Network (USHCN) and National Climatic Data Center Cooperative Network (COOP) data set for the months of December through March, 1965–2005. Monthly and seasonal time series of snow-covered days (snow depth \u3e2.54 cm) are constructed from daily snow depth data. Spatial coherence analysis is used to address data quality issues with daily snowfall and snow depth data, and to remove stations with nonclimatic influences from the regional analysis. Monthly and seasonal trends in mean, minimum, and maximum temperature, total snowfall, and snow-covered days are evaluated over the period 1965–2005, a period during which global temperature records and regional indicators exhibit a shift to warmer climate conditions. NE-US regional winter mean, minimum, and maximum temperatures are all increasing at a rate ranging from 0.42° to 0.46°C/decade with the greatest warming in all three variables occurring in the coldest months of winter (January and February). The regional average reduction in number of snow-covered days in winter (−8.9 d/decade) is also greatest during the months of January and February. Further analysis with additional regional climate modeling is required to better investigate the causal link between the increases in temperature and reduction in snow cover during the coldest winter months of January and February. In addition, regionally averaged winter snowfall has decreased by about 4.6 cm/decade, with the greatest decreases in snowfall occurring in December and February. These results have important implications for the impacts of regional climate change on the northeastern United States hydrology, natural ecosystems, and economy

THE IMPACT OF FEDERALISM ON EDUCATION FINANCE: A COMPARATIVE ANALYSIS *

Drawing on the implications suggested by several recent studies in comparative public policy, this article examines the impact of the structure of intergovernmental relations on the patterns of distribution of educational funds. The fundamental hypothesis underlying this analysis is that differences in this structure, and in particular the distinction between federal and unitary systems of government, are systematically related to differences in distribution across and within nations. The variations in total educational allocations among eighteen nations in Europe and North America are considered in order to discover whether the aggregate funding of education, relative to a nation's wealth, is related to the structure of intergovernmental relations. Then, in a more intensive analysis, the intranational patterns of distribution are compared in four federal and four unitary systems. This analysis suggests that there is a significant difference between the two types of system in the degree to which educational policy outputs equalize the territorial disparities in wealth and effect a redistribution of funds within the nation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74630/1/j.1475-6765.1974.tb00752.x.pd

Truthmakers and modality

This paper attempts to locate, within an actualist ontology, truthmakers for modal truths: truths of the form or . In section 1 I motivate the demand for substantial truthmakers for modal truths. In section 2 I criticise Armstrong’s account of truthmakers for modal truths. In section 3 I examine essentialism and defend an account of what makes essentialist attributions true, but I argue that this does not solve the problem of modal truth in general. In section 4 I discuss, and dismiss, a theistic account of the source of modal truth proposed by Alexander Pruss. In section 5 I offer a means of (dis)solving the problem

The rise and fall of the Malvinoxhosan (Malvinokaffric) bioregion in South Africa: Evidence for Early-Middle Devonian biocrises at the South Pole

Global reconstructions, inclusive of environments and ecosystems, and biodiversity counts for the Devonian Period are often done so at the expense of high latitude regions given a historical lack of data presented from these areas. This has bearing on the recognition of biocrises (events marked by extinctions and faunal turnovers) at high latitudes as well as their controls and potential correlation with global, regional, and local tempos. The appearance and disappearance of high-latitude endemic Malvinoxhosan (synonymous with the “Malvinokaffric Realm” which it supersedes) marine invertebrate faunas from West Gondwana are often overlooked, in part owing to difficulties in correlating fossil-bearing strata with global frameworks given the absence and rarity of several key index taxa as well as detailed biostratigraphic appraisals in which to draw regional interbasinal correlations and comparisons. The Early to Middle Devonian Series of South Africa (upper Table Mountain, Bokkeveld and lower Witteberg groups) are a classic Malvinoxhosan-bearing section recording the rise of these endemic faunas, as well as their decline and replacement by cosmopolitan faunas. A detailed biostratigraphy of this interval was created following an assessment of fossil material curated at the Council for Geoscience and Iziko South African Museum, Cape Town as well as from literature. These data suggest that the Malvinoxhosan bioregion persisted as a cohesive unit during Rietvlei-Baviaanskloof to Waboomberg deposition (Pragian/Emsian-early Givetian) given that many representative taxa are found in these strata, however showing a trend of decreasing diversity with little origination through time. Above this interval, few representative taxa are known to continue into the upper Bokkeveld and Witteberg groups, disappearing entirely by the deposition of the Blinkberg Formation. The few fossils that are known in these strata and those succeeding it (e.g., the Swartruggens Formation) are entirely cosmopolitan in identity. Using novel multivariate statistical methods (non-metric multidimensional scaling and cluster analysis) in conjunction with network analysis (NA), the data were interrogated to indicate potential groupings of strata according to their fossil content as well as to track faunal changes through time. These analyses suggest the presence of at least seven to eight interval assemblage biozones housed within at least three larger faunal complexes (Eo-Malvinoxhosan, Malvinoxhosan and Post-Malvinoxhosan) based on their constituent faunal makeup. A closer inspection of these faunal complexes and interval assemblage biozones show a stepped decline in biodiversity with little to no origination and recovery through time that may be correlated with local base-level change at varying orders of magnitude. Declines in biodiversity show selectivity for taxa with epifaunal and semi-infaunal habits with respect to infaunal, deep infaunal and nektonic taxa. Environmental conditions associated with the collapse of the Malvinoxhosan bioregion are thought to have been catastrophic as few new (often short-ranging) immigrants are registered in Post-Malvinoxhosan strata. Further to this, those faunas that are prevalent in Post-Malvinoxhosan strata (e.g., Tropidoleptus) those with known high environmental tolerance and were already present in the region prior to the collapse of the Malvinoxhosan bioregion. Lastly, the observed biodiversity changes in South Africa with respect to local base-level show remarkable similarities with several time equivalent locales in South America suggesting that the decline and extinction of the Malvinoxhosan biota was regional and that the biostratigraphy presented herein has regional application. Here, it is thought regional tectonic controls are suggested to have brought on sea-level changes and entrained warmer waters into higher latitudes against the backdrop of overall rising temperatures from the late Givetian onwards. Whilst the decline of the Malvinoxhosan bioregion might associated with global Middle Devonian biocrises (e.g., Kačák; Taghanic) insufficient age constraints for these strata are available at present to make direct comparisons. Furthermore, an adequate driver for global sea-level change during the Devonian Period, needs to be established to tease out global and local signals in constructed local sea-level curves to establish if these changes (and their effects in changes in biodiversity) are truly global in extent

Stability and placement of Ag/AgCl quasi-reference counter electrodes in confined electrochemical cells

Nanoelectrochemistry is an important and growing branch of electrochemistry that encompasses a number of key research areas, including (electro)catalysis, energy storage, biomedical/environmental sensing, and electrochemical imaging. Nanoscale electrochemical measurements are often performed in confined environments over prolonged experimental time scales with nonisolated quasi-reference counter electrodes (QRCEs) in a simplified two-electrode format. Herein, we consider the stability of commonly used Ag/AgCl QRCEs, comprising an AgCl-coated wire, in a nanopipet configuration, which simulates the confined electrochemical cell arrangement commonly encountered in nanoelectrochemical systems. Ag/AgCl QRCEs possess a very stable reference potential even when used immediately after preparation and, when deployed in Cl– free electrolyte media (e.g., 0.1 M HClO4) in the scanning ion conductance microscopy (SICM) format, drift by only ca. 1 mV h–1 on the several hours time scale. Furthermore, contrary to some previous reports, when employed in a scanning electrochemical cell microscopy (SECCM) format (meniscus contact with a working electrode surface), Ag/AgCl QRCEs do not cause fouling of the surface (i.e., with soluble redox byproducts, such as Ag+) on at least the 6 h time scale, as long as suitable precautions with respect to electrode handling and placement within the nanopipet are observed. These experimental observations are validated through finite element method (FEM) simulations, which consider Ag+ transport within a nanopipet probe in the SECCM and SICM configurations. These results confirm that Ag/AgCl is a stable and robust QRCE in confined electrochemical environments, such as in nanopipets used in SICM, for nanopore measurements, for printing and patterning, and in SECCM, justifying the widespread use of this electrode in the field of nanoelectrochemistry and beyond