The disjunctivities of ω-languages

An ω-language over a finite alphabet X is a set of infinite sequences of letters of X. Consider congruences IL and Pω, L on X* and a congruence OL on Xω introduced by an ω-language L. IL, Pω, L, and OL are called the infinitary syntactic-congruence, the principal congruence and the ω-syntactic congruence of L, respectively. If IL (Pω, L, OL) is the equality then L is called an I-disjunctive (P-disjunctive, O-disjunctive, respectively) ω- language. Properties concerning such ω-languages are explored and relations between these ω-languages are also studied

Unintended Consequences of Water Legislation

The population of Texas is expected to double by 2060. The Texas Lower Rio Grande Valley is one area in which alternative water sources and potable treatment methods are being sought to support a rapid population growth. An emerging and promising approach to expanding potable water supplies is brackish groundwater desalination. Due to recent technology developments in desalination membranes and increasing prices of surface water rights, the economics of desalination have become competitive with conventional treatment methods. The seemingly comparable competitive economics relationship between conventional and desalination treatments was impacted by Floor Amendment 60 of Texas Senate Bill 3, which was an attempt to meet the increased demand for municipal water. This amendment established the price at which irrigation water in the Valley can convert to municipal water, as a result of urban/residential development of agricultural land, at 68 percent of the market price, effective January 1, 2008. Preliminary economic and financial investigations suggest this legislation could affect the adoption of water treatment technology. This paper identifies and analyzes the economic and financial implications, both intended and unintended, of Floor Amendment 60 on the Valley water market, and the associated adoption of alternative technologies for producing potable water.Resource /Energy Economics and Policy,

Claisen Rearrangements of Heterocycles

This thesis is divided into five chapters. Chapter 1 is a review of de-aromatisation processes achieved by sigmatropic rearrangement. It covers the two main types of sigmatropic rearrangements, namely [2,3]- and [3,3]-rearrangement. Chapter 2 introduces the decarboxylative Claisen rearrangement (dCr) reaction and the aim to investigate its viability on more elaborate heterocyclic substrates is discussed. Research efforts into the synthesis of 3-sulfonyl-6-alkenyl-1,4-dioxan-2-ones are detailed. Chapter 3 discusses the extension of this methodology towards N-alkylmorpholinones. The first section examines 5,6-divinyl cis-morpholinones and L-alanine-derived trans-morpholinones as Claisen precursors, whereby stereospecific Ireland–Claisen rearrangement of L-alanine-derived trans-morpholinones was achieved. The second section details the synthesis of a novel L-proline-derived bicyclic morpholinone. However, attempted rearrangement led to degradation of product instead. The third section details the synthesis of 6-thienyl and 6-furanyl morpholinones, along with attempted Ireland–Claisen rearrangements and dCr reactions. Chapter 4 describes research efforts into the de-aromatising sigmatropic rearrangement of azide- and phthalimide-containing thienyl acyclic precursors. dCr Reaction of a cyanoacetate-containing substrate followed by unprecedented cyclisation led to the formation a highly-conjugated tetracycle and the mechanism of its formation is discussed. Chapter 5 provides experimental procedures and characterisation data

Topo-Climatic effects of fuel loading in ponderosa pine (Pinus ponderosa) forests of the Colorado Rocky Mountains

A key restoration focus is the mitigation and prevention of intense wildfires. This is done using a regularly prescribed fire regime and forest thinning practices to reduce surface fuel loads. Prediction of fuel loads at the forest floor is pivotal when assessing the hazard level a forest fire may present. Scientists already have much data correlating fuel characteristics to fire effects and behavior. However, links between montane climate variability and relative effects on fuel load characteristics have not been extensively explored in the Front Range and southwestern Colorado. This study system was uniquely located along a North-South monsoonal gradient and encompasses variable aspects, slopes, and elevations, providing topographic differences within the species’ range in Colorado. This research resampled forest fuels in old-growth ponderosa pine forest plots initially taken in 1994 (Robertson & Bowser, 1999). Additionally, we analyzed FIA (forest inventory and analysis) fuel type datasets. To accomplish this, we used two different scales: 1) a 1994-2021 coarse woody debris resample and 2) a large-scale analysis of Colorado’s downed woody material from forest inventory and analysis (FIA) datasets