Rings, Group Rings, and Their Graphs

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. We define an undirected graph ᴦ(R) with nonzero zero-divisors as vertices and distinct vertices x and y are adjacent if xy=0 or yx=0. We investigate the Isomorphism Problem for zero-divisor graphs of group rings RG. Let Sk denote the sphere with k handles, where k is a non-negative integer, that is, Sk is an oriented surface of genus k. The genus of a graph is the minimal integer n such that the graph can be embedded in Sn. The annihilating-ideal graph of R is defined as the graph AG(R) with the set of ideals with nonzero annihilators as vertex such that two distinct vertices I and J are adjacent if IJ=(0). We characterize Artinian rings whose annihilating-ideal graphs have finite genus. Finally, we extend the definition of the annihilating-ideal graph to non-commutative rings.

British War Medal

This British War Medal was issued to those who had to leave their native shore in any part of the British Empire while they were on service. This is a silver circular medal, 3 1/2 cm in diameter. King George V is depicted on the front and St. George is on the back. This is accompanied by a watered silk ribbon which has a central band of gold and stripes of white, black and blue on both sides. "Lieut S. D. Woodruff" is engraved on the rim. This was issued 1914-1918.

Graffiti, memory and contested space : mnemonic initiatives following trauma and/or repression in Buenos Aires, Argentina

Graffiti, Memory and Contested Space: Mnemonic Initiatives Following Periods of Trauma and/or Repression in Buenos Aires, Argentina This thesis concerns the popular articulation ofmemory following periods or incidents of trauma in Argentina. I am interested in how groups lay claim to various public spaces in the city and how they convert these spaces into mnemonic battlegrounds. In considering these spaces of trauma and places of memory, I am primarily interested in how graffiti writing (stencils, spray-paint, signatures, etchings, wall-paintings, murals and installations) is used to make these spaces transmit particular memories that impugn official versions of the past. This thesis draws on literatures focused on popular/public memory. Scholars argue that memory is socially constructed and thus actively contested. Marginal initiatives such as graffiti writing challenge the memory projects of the state as well as state projects that are perceived by citizens to be 'inadequate,' 'inappropriate,' and/or as promoting the erasure of memory. Many of these initiatives are a reaction to the proreconciliation and pro-oblivion strategies of previous governments. I outline that the history of silences and impunity, and a longstanding emphasis on reconciliation at the expense of truth and justice has created an environment of vulnerable memory in Argentina. Popular memory entrepreneurs react by aggressively articulating their memories in time and in space. As a result of this intense memory work, the built landscape in Buenos Aires is dotted with mnemonic initiatives that aim to contradict or subvert officially sanctioned memories. I also suggest that memory workers in Argentina persistently and carefially use the sites of trauma as well as key public spaces to ensure official as well as popular audiences . The data for this project was collected in five spaces in Buenos Aires, the Plaza de Mayo, Plaza Congreso, La Republica Cromanon nightclub, Avellaneda Train Station and El Olimpo, a former detention centre from the military dictatorship.

The roles of ERK1/2 and PI3K in abnormal vascular functions in angiotensin II-infused hypertensive rats

Background: Ang II plays a major role in cardiovascular regulation. Recently, it has become apparent that vascular superoxide anion may play an important role in hypertension development. Treatment with antisense NAD(P)H oxidase or SOD decreased BP in Ang II-infused rats. Wang et al recently reported mice which lack one of the subunits of NAD(P)H oxidase developed hypertension at a much lower extent when compared to the wild type animals infused with Ang II, indicating that superoxide anion contributes to elevation in BP in the Ang II-infused hypertensive model. In the Ang II-infused hypertensive model, altered reactivity of blood vessels is often associated with the elevation of systolic blood pressure. We have observed abnormal tension development and impaired endothelium-dependent relaxation in the isolated aorta of Ang II-infused and DOCA-salt hypertensive rats. Recently, several other cellular signal molecules, including ERK1I2 and PI3K, have been determined to play important roles in the regulation of smooth muscle contraction and relaxation. ERKl/2 and PI3K pathways are also reported to contribute to Ang II induced cell growth, hypertrophy, remodeling and contraction. Moreover, these signaling pathways have shown ROS-sensitive properties. Therefore, the aim of the present study is to investigate the roles of ERKl12 and PI3K in vascular oxidative stress, spontaneous tone and impaired endothelium relaxation in Ang II-infused hypertensive model. Hypothesis: We hypothesize that the activation of ERKl12 and PI3K are elevated in response to an Ang II infusion for 6 days. The elevated activation of phospho-ERKl/2 and PI3K mediated the increased level of vascular superoxide anion, the abnormal vascular contraction and impaired endothelium-dependent vascular relaxation in Ang II-infused hypertensive rats. Methods: Vascular superoxide anion level is measured by lucigenin chemiluminescence. Spontaneous tone and ACh-induced endothelium-dependent relaxation was measured by isometric tension recording in organ chamber. The activity of ERK pathway will be measured by its Western blot of phosphorylation of ERK. PI3K activity was evaluated indirectly by Western blot of the phosphorylation of PDKl, a downstream protein of PI3K signaling pathway. The role of each pathway was also addressed via comparing the responses to the specific inhibitors. Results: Superoxide anion was markedly increased in the isolated thoracic aorta from Ang II-infused rats. There was spontaneous tone developed in rings from Ang II-induced hypertensive but not sham-operated normotensive rats. ACh-induced endothelium-dependent relaxation function is impaired in Ang II-infused hypertensive rats. Superoxide dismutase and NAD(P)H oxidase inhibitor, apocynin, inhibited the abnormal spontaneous tone and ameliorated impaired endothelium-dependent relaxation. The expression of phopho-ERKII2 was enhanced in Ang II-infused rats, indicating the activity of ERK1I2 could be increased. MEK1I2 inhibitors, PD98059 and U126, but not their inactive analogues, SB203580 and U124, significantly reduced the vascular superoxide anion in aortas from Ang II-infused rats. The MEK1I2 inhibitors reduced the spontaneous tone and improved the impaired endothelium-dependent relaxation in aorta of hypertension. These findings supported the role of ERKII2 signaling pathway in vascular oxidative stress, spontaneous tone and impaired endothelium-dependent relaxation in Ang II-infused hypertensive rats. The amount of phospho-PDK, a downstream protein of PI3K was increased in Ang II rats indicating the activity of PI3K activity was elevated. Strikingly, PI3K significantly inhibited the increase of superoxide anion level, abnormal spontaneous tone and restored endothelium-dependent relaxation in Ang II-infused hypertensive rats. These findings indicated the important role of PI3K in Ang II-infused hypertensive rats. Conclusion: ERKII2 and PI3K signaling pathways are sustained activated in Ang II-infused hypertensive rats. The activated ERKII2 and PI3K mediate the increase of vascular superoxide anion level, vascular abnormal spontaneous tone and impaired endothelium-dependent relaxation.

Synthesis of Chiral Benzimidazolylidenes from 1,10-Phenathrolines and 1,10-Phenathroline-2,9-dione /

A^-heterocyclic carbenes (NHCs) have become the focus of much interest as ancillary ligands for transition metal catalysts in recent years. Their structural variability and strong cy-donation properties have led to the preparation of demonstrably useful organometallic catalysts. Among the three general structural types of NHCs (imidazolylidenes, imidazolinylidenes, and benzimidazolylidenes), benzimidazolylidenes are the least investigated because of the limitation of current synthetic approaches. The preparation of chiral analogues is even more challenging. Previously, our group has demonstrated an alternative approach to synthesizing benzimidazolylidenes with a tetracyclic framework in three steps from 1,10-phenanthroline. This thesis is focused on approaches to chiral benzimidazolylidenes derived from substituted 1,10-phenanthrolines. A key step in the preparation of these ligands involves a reduction of the pyridyl rings in 1,10-phenanthrolines. Chirality can be introduced to phenanthrolines before, during, or after the reduction as illustrated by three approaches: 1) de novo construction of the phenanthroline from chiral ketones with endo and exo faces to provide a degree of diastereoselectivity during subsequent reduction; 2) introduction of substituents into the 2- and 2,9- position of phenanthroline by nucleophilic aromatic substitution, followed by a reduction-resolution sequence; and 3) use of the protected octahydrophenanthroline as a substrate for chiral induction a to nitrogen.

Chelated fluoroboron cations : synthesis and multinuclear nmr studies

The preparation of chelated difluoroboron cations (DD)BF2+, where DD is a saturated polydentate tertiary-amine or polydentate aromatic ligand, has been systematically studied by using multinuclear solution and solid state nuclear magnetic resonance spectroscopy and fast atom bombardment mass spectrometry. Three new methods of synthesis of (DD)BF2+ cations are reported, and compared with the previous method of reacting a chelating donor with Et20.BF3. The methods most effective for aromatic donors such as 1,1O-phenanthroline are ineffective for saturated polydentate tertiary-amines like N,N,N' ,Nil ,Nil-pentamethyldiethylenetriamine. Polydentate tertiary-amine donors that form 5-membered rings upon bidentate chelation were found to chelate effectively when the BF2 source contained two leaving groups (a heavy halide and a Lewis base such as pyridine =pyr or isoxazole =ISOX), i.e., pyr.BF2X (X = CI or Br), ISOX.BF2X and (pyr)2BF2+. Those that would form 6membered rings upon chelation do not chelate by any of the four methods. Polydentate aromatic ligands chelate effectively when the BF2 source contained a weak Lewis base, e.g., ISOX.BF3, ISOX.BF2X and Et20.BF3. Bidentate chelation by polydentate tertiaryamine and aromatic donors leads to nmr parameters that are significantly different then their (D)2BF2+ relatives (D =monod~ntate t-amines or pyridines). The chelated haloboron cations (DD)BFCI+, and (DD)BFBr+ were generated from D.BFX2 adducts for all ligands that form BF2+ cations above. In addition, the (DD)BCI2+ and (DD)BBr2+ cations were formed from D.BX3 adducts by the chelating aromatic ligands, except for the aromatic ligand 1,8-bis(dimethylamino)naphthalene, which formed only the (DD)BF2+ cation, apparently due to its extreme steric hindrance. Chelation by a donor is a two-step reaction. For polydentate tertiary-amine ligands, the two rates appear to be very dependent on the two possible leaving groups on the central boron atom. The order of increasing ease of displacement for the donors was: pyr < Cl < Br < ISOX. The rate of chelation by polydentate aromatic ligands appears to be dependent on the displacement of the first ligand from the boron. The order of increasing ease of displacement for the donors was: pyr < CI < ISOX ~ Br < Et20.

Reactions of polyhalogenated aromatic compounds and related ethers with metal/ammonia solutions

This work contains the results of a series of reduction studies on polyhalogenated aromatic compounds and related ethers using alkali metals in liquid ammonia. In general, polychlorobenzenes were reduced to t he parent aromatic hydrocarbon or to 1 ,4-cyc1ohexadiene, and dipheny1ethers were cleaved to the aroma tic hydrocarbon and a phenol. Chlorinated dipheny1ethers were r eductive1y dechlorinated in the process. For example, 4-chlorodipheny1- ether gave benzene and phenol. Pentach1orobenzene and certain tetrachlorobenzenes disproportionated to a fair degree during the reduction process if no added proton source was present. The disproportionation was attributed to a build-up of amide ion. Addition of ethanol completely suppressed the formation of any disproportionation products. In the reductions of certain dipheny1ethers , the reduction of one or both of the dipheny1ether rings occurred, along with the normal cleavage. This was more prevalent when lithium was the metal used . As a Sidelight, certain chloropheno1s were readily dechlorinated. In light of these results, the reductive detoxification of the chlorinated dibenzo-1,4-dioxins seems possible with alkali metals in l iquid ammonia.

Reactions of various aromatic nitro-compounds and anthraquinones with selected bases and nucleophiles

The Introducti on deals mainly with hi storical studies on aryne chemi stry and ring closure via arynes , hydride replacement from aromatic rings by nucleophi les, c l eavage of anthr aquinones in basic medium and the Leuckart reaction . This work can be divided into two main s ect i ons. Section I is concerned with the investigation of t he reaction of some aromatic ni t ro-compounds with potassamide in l iquid ammonia. 3-Amino-4- nitrobenzophenone was obtained from the reacti on of 4-nitrobenzophenone with t his reagent, toge t her with benzoic acid formed in a competing Haller-Bauer reaction. Nitrobenzene under these conditions gave a complex mixture from which 2-phenylphenol was isolated; a reaction i nvolving benzyne may be i nvo l ved. 4-Nitrodiphenyl sulfone gave 4-aminodiphenyl sulfone and 4-nitroani l ine. 4-Ethoxydiphenyl sulfone and 4-ethoxynitrobenzene were isolated when ethanol was used as a co-solvent in the reaction. Oxidative coupling reactions were observed with nitrotoluenes. 4-Nitrotoluene gave 4,4t-dinitrobibenzyl which i n a pro longed reaction gave 4,4t-dinitros t ilbene . 2-Nitrotoluene gave 2 , 2 t-dinitrobibenzyl, but not the corresponding stilbene derivative even after a longer time . A rather i nteresting result was obtained with 1-nitro-2,4,6- trimethylbenzene which gave a stilbene derivative only. Also the corresponding stilbene was obtained from bis-(4-nitrophenyl)-methane in a rather slow r eaction with this reagent . Section II deals wi th (i) the preparation of 5-chloro- 1-N-methyl aminoanthraquinone and a new synthesis of N-methyl acridones and (ii) treatment of chloro-anthraquinones with fo rmamide and a new synthesis of chloro-anthracenes . 5-Chloro-1 -N-methylaminoanthraqui none was synthesised f rom 1,5-dichloroanthraquinone by treatment with N-methylformamide. Treatment of 5-chloro-1-N-methylaminoanthraquinone with potassamide in liquid ammonia or with potassium t-butoxide i n t-butylbenzene gave N-methylacridone-1-carboxylic acid. This pleasing result, t he outcome of r i ng opening and alter native ring closure, is being extended to related ring systems.

Particle swarm optimization for two-connected networks with bounded rings

The Two-Connected Network with Bounded Ring (2CNBR) problem is a network design problem addressing the connection of servers to create a survivable network with limited redirections in the event of failures. Particle Swarm Optimization (PSO) is a stochastic population-based optimization technique modeled on the social behaviour of flocking birds or schooling fish. This thesis applies PSO to the 2CNBR problem. As PSO is originally designed to handle a continuous solution space, modification of the algorithm was necessary in order to adapt it for such a highly constrained discrete combinatorial optimization problem. Presented are an indirect transcription scheme for applying PSO to such discrete optimization problems and an oscillating mechanism for averting stagnation.

The new blockbuster film sequel : changing cultural and economic conditions within the film industry

Film sequels are a pervasive part of film consumption practices and have become an important part of the decision making process for Hollywood studios and producers. This thesis indicates that sequels are not homogenous groups of films, as they are often considered, but offer a variety of story construction and utilize a variety of production methods. Three types of blockbuster sequel sets are identified and discussed in this thesis. The Traditional Blockbuster Sequel Set, as exemplified by Back to the Future (1985, 1989, 1990) films, is the most conventional type of sequel set and capitalizes on the winning formula of the first film in the franchise. The MultiMedia Sequel Set, such as The Matrix (1999,2003) trilogy, allows the user/viewer to experience and consume the story as well as the world of the film through many different media. The Lord a/ the Rings (2001, 2002, 2003) set of films is an illustration of The Saga Sequel Set where plot lines are continuous over the entire franchise thus allowing the viewer to see the entire set as a unified work. The thesis also demonstrates how the blockbuster sequel sets, such as the Pirates a/ the Caribbean (2003, 2006, 2007) franchise, restructure the production process of the Hollywood film industry.