Quivers and Three-Dimensional Lie Algebras

We study a family of three-dimensional Lie algebras $L_\mu$ that depend on a continuous parameter $\mu$. We introduce certain quivers, which we denote by $Q_{m,n}$ $(m,n \in \mathbb{Z})$ and $Q_{\infty \times \infty}$, and prove that idempotented versions of the enveloping algebras of the Lie algebras $L_{\mu}$ are isomorphic to the path algebras of these quivers modulo certain ideals in the case that $\mu$ is rational and non-rational, respectively. We then show how the representation theory of the quivers $Q_{m,n}$ and $Q_{\infty\times\infty}$ can be related to the representation theory of quivers of affine type $A$, and use this relationship to study representations of the Lie algebras $L_\mu$. In particular, though it is known that the Lie algebras $L_\mu$ are of wild representation type, we show that if we impose certain restrictions on weight decompositions, we obtain full subcategories of the category of representations of $L_\mu$ that are of finite or tame representation type.Comment: 18 page

Endangered Precedent: Interpreting Agency Action and the Duty to Consult Under Section 7 of the ESA in Light of \u3cem\u3eKaruk\u3c/em\u3e

Following the designation of the West Coast coho salmon as a threatened species under the Endangered Species Act, and the ensuing designation of the Klamath River system in the Pacific Northwest as critical habitat for the species, the indigenous Karuk Tribe challenged the U.S. Forest Service’s mining permit approval practices in Karuk Tribe of California v. U.S. Forest Service. Under Section 7 of the ESA, an agency must consult with one of two outside resources in instances where the agency’s actions “may affect” an endangered population. In reversing the district court’s denial of summary judgment on the Tribe’s ESA claim, the Ninth Circuit held that the Forest Service’s approval of mining applications without consultation constituted discretionary agency action that may affect the region’s coho salmon population. This Comment argues that this broad interpretation of agency action accurately reflects Section 7’s requirements. Furthermore, because this standard is clear, courts should apply this broad interpretation in future cases to avoid inconsistency and protect the environment in accord with congressional intent

Summary of Progressive Gulf Ins. Co. v. Faehnrich, 130 Nev. Adv. Op. 19

The Court determined whether Nevada public policy precludes giving effect to a choice-of-law provision in an insurance contract made by parties residing outside Nevada that would deny Nevada residents injured in Nevada recovery under NRS 485.3091

A Tale of Two Codes: The Influence of \u3cem\u3eAlbuquerque\u3c/em\u3e and \u3cem\u3eWashington\u3c/em\u3e on Green Building

Green building has become an increasingly important piece of the American economy. Two cases from the past five years addressed this burgeoning field: Air Conditioning, Heating and Refrigeration Institute v. City of Albuquerque and Building Industry Association of Washington v. Washington State Building Code Council. As a result of these decisions, legislators would be wise to explicitly evidence their desires when updating or enacting local buildings codes to guard against the potential for severability in the event that the federal Energy Policy and Conservation Act preempts part of the code. So long as they do so, legislators should be able to include both performance- and prescriptive-based paths for compliance. If the state or municipality must choose a single path to compliance, however, it would be most beneficial to emphasize performance-based paths because a credit-based system provides a builder with more flexibility, which will benefit both the project and the environment

Summary of St. Mary v. Damon, 129 Nev. Adv. Op. 68

The Court determined three issues: 1) whether the Nevada Parentage Act and its underlying policies allows for a child to have two legal mothers; 2) whether the parties’ co- parenting agreement was a surrogacy agreement; and 3) whether the same-sex parties’ co- parenting agreement is consistent with Nevada’s public policies or void as unlawful or against public policy

How is gambling related to perceived parenting style and/or family environment for college students?

Background and aims: The relationship between college student gambling, parenting styles, and family environments is a neglected area of gambling research. Do parenting styles indirectly influence problem gambling behaviors via family environments? Do poor family environments, characterized by high levels of conflict and low levels of cohesion, increase the likelihood of problem gambling among youth? This study explored the interrelationships among college students' current gambling behaviors and a) having an emotionally close and supportive family environment, b) having nagging and critical parents, c) having an authoritative mother, and d) frequency of alcohol consumption. Methods and results: Survey data were collected from 450 undergraduate students enrolled in introductory psychology classes at two state universities in a southern state. Feeling that one has nagging and critical parents was associated with gambling in more venues, while the opposite was true for having emotionally close and supportive families. However, perceptions of having authoritative mothers were not related to gambling. The results also showed that more frequent alcohol consumption was associated with higher odds of gambling in casinos, playing cards for money, betting on sports, gambling on the Internet, higher gambling losses, and a larger number of gambling venues. Conclusions: As with any exploratory research, there are several unique lines of inquiry that can, and should, follow from these findings, including more research on how college students' attitudes toward gambling activities may have begun prior to college and been influenced by their feelings about their homes and parents

FLOWSHEET FOR ALUMINUM REMOVAL FROM SLUDGE BATCH 6

Samples of Tank 12 sludge slurry show a substantially larger fraction of aluminum than originally identified in sludge batch planning. The Liquid Waste Organization (LWO) plans to formulate Sludge Batch 6 (SB6) with about one half of the sludge slurry in Tank 12 and one half of the sludge slurry in Tank 4. LWO identified aluminum dissolution as a method to mitigate the effect of having about 50% more solids in High Level Waste (HLW) sludge than previously planned. Previous aluminum dissolution performed in a HLW tank in 1982 was performed at approximately 85 C for 5 days and dissolved nearly 80% of the aluminum in the sludge slurry. In 2008, LWO successfully dissolved 64% of the aluminum at approximately 60 C in 46 days with minimal tank modifications and using only slurry pumps as a heat source. This report establishes the technical basis and flowsheet for performing an aluminum removal process in Tank 51 for SB6 that incorporates the lessons learned from previous aluminum dissolution evolutions. For SB6, aluminum dissolution process temperature will be held at a minimum of 65 C for at least 24 days, but as long as practical or until as much as 80% of the aluminum is dissolved. As planned, an aluminum removal process can reduce the aluminum in SB6 from about 84,500 kg to as little as 17,900 kg with a corresponding reduction of total insoluble solids in the batch from 246,000 kg to 131,000 kg. The extent of the reduction may be limited by the time available to maintain Tank 51 at dissolution temperature. The range of dissolution in four weeks based on the known variability in dissolution kinetics can range from 44 to more than 80%. At 44% of the aluminum dissolved, the mass reduction is approximately 1/2 of the mass noted above, i.e., 33,300 kg of aluminum instead of 66,600 kg. Planning to reach 80% of the aluminum dissolved should allow a maximum of 81 days for dissolution and reduce the allowance if test data shows faster kinetics. 47,800 kg of the dissolved aluminum will be stored in Tank 8 and 21,000 kg will be stored in saltcake via evaporation. Up to 77% of the total aluminum planned for SB6 may be removed via aluminum dissolution. Storage of the aluminum-laden supernate in Tank 8 will require routine evaluation of the free hydroxide concentration in order to maintain aluminum in solution. Periodic evaluation will be established on concurrent frequency with corrosion program samples as previously established for aluminum-laden supernate from SB5 that is stored in Tank 11

Copper(I) Complexes of Heterocyclic Thiourea Ligands

The coordination of heterocyclic thiourea ligands (L = N-(2-pyridyl)-N′-phenylthiourea (1), N-(2-pyridyl)-N′-methylthiourea (2), N-(3-pyridyl)-N′-phenylthiourea (3), N-(3-pyridyl)-N′-methylthiourea (4), N-(4-pyridyl)-N′-phenylthiourea (5), N-(2-pyrimidyl)-N′-phenylthiourea (6), N-(2-pyrimidyl)-N′-methylthiourea (7), N-(2-thiazolyl)-N′-methylthiourea (8), N-(2-benzothiazolyl)-N′-methylthiourea (9), N,N′-bis(2-pyridyl)thiourea (10) and N,N′-bis(3-pyridyl)thiourea (11)) with CuX (X = Cl, Br, I, NO3) has been investigated. CuX:L product stoichiometries of 1:1–1:5 were found, with 1:1 being most common. X-ray structures of four 3-coordinate mononuclear CuXL2 complexes (CuCl(6)2, CuCl(7)2, CuBr(6)2, and CuBr(9)2) are reported. In contrast, CuBr(1)2 is a 1D sulfur-bridged polymer. CuIL structures (L = 7, 8) are 1D chains with corner-sharing Cu2(μ-I)2 and Cu2(μ-S)2 units, and CuCl(10) is a 2D network having μ-Cl and N-/S-bridging L. Two [CuL2]NO3 structures are reported: a mononuclear 4-coordinate copper complex with chelating ligands (L = 10) and a 1D link-chain with N-/S-bridging L (L = 3). Two ligand oxidative cyclizations were encountered during crystallization. CuI crystallized with 6 to produce zigzag ladder polymer [(CuI)2(12)]·½CH3CN (12 = N-(pyrimidin-2-yl)benzo[d]thiazol-2-amine) and CuNO3 crystallized with 10 to form [Cu2(NO3)(13)2(MeCN)]NO3 (13 = dipyridyltetraazathiapentalene)

Convenient Synthesis of Copper (I) Thiolates and Related Compounds

Copper (I) salts of various anions including thiolates, diethyl dithiocarbamate, diethyl dithiophosphate, trithiocyanurate, 1-cyano-3-methylisothiourea, 2-aminothiazole, and tetrakis(1-imidazolyl)borate are conveniently synthesized by reducing copper (II) sulfate in aqueous ammonia. The addition of phosphine ligands to several of the products is demonstrated, and the crystal structure of [Cu2(MBT)2(DPPE)3] · Et2O (MBT = 2-mercaptobenzothiazolate, DPPE = 1,2-bis(diphenylphosphino)ethane) is reported