Cyclic, f-Cyclic, and Bicyclic Decompositions of the Complete Graph into the 4-Cycle with a Pendant Edge.

In this paper, we consider decompositions of the complete graph on v vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of: (1) a single cycle of length v, (2) f fixed points and a cycle of length v − f, or (3) two disjoint cycles. The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, f-cyclic, and bicyclic Q-decompositions of Kv

The spectrum of bicyclic antiautomorphisms of directed triple systems

AbstractA transitive triple, (a,b,c), is defined to be the set {(a,b),(b,c),(a,c)} of ordered pairs. A directed triple system of order v, DTS(v), is a pair (D,β), where D is a set of v points and β is a collection of transitive triples of pairwise distinct points of D such that any ordered pair of distinct points of D is contained in precisely one transitive triple of β. An antiautomorphism of a directed triple system, (D,β), is a permutation of D which maps β to β−1, where β−1={(c,b,a)|(a,b,c)∈β}. In this paper we complete the necessary and sufficient conditions for the existence of a directed triple system of order v admitting an antiautomorphism consisting of two cycles

Decompositions of the Complete Mixed Graph by Mixed Stars

In the study of mixed graphs, a common question is: What are the necessary and suffcient conditions for the existence of a decomposition of the complete mixed graph into isomorphic copies of a given mixed graph? Since the complete mixed graph has twice as many arcs as edges, then an obvious necessary condition is that the isomorphic copies have twice as many arcs as edges. We will prove necessary and suffcient conditions for the existence of a decomposition of the complete mixed graphs into mixed stars with two edges and four arcs. We also consider some special cases of decompositions of the complete mixed graph into partially oriented stars with twice as many arcs as edges. We employ difference methods in most of our constructions when showing suffciency.

Saturated Hydrocarbon Analysis of Liberty State Park Soils

Contaminated soils have been a concern in New Jersey since the Industrial Revolution (Gallagher, 2008). One site in particular has a variety of contaminants and is near the coast of Jersey City in Liberty State Park. Liberty State Park has been impacted by three significant changes. It was first a wetland in the 1600s, then became a New York dump site, and finally a railyard for the Central Railroad of New Jersey (Stanislaw, 2013). The whole land mass has mixed contaminants, including trace elements, heavy metals, organic wastes, and organic compounds. Currently, most of the state park has been dredged out and filled with “reclaimed landfill”. Only 102 out of the park\u27s 490 hectares were left unremediated and this is the area that is under research. Even with this site still being highly contaminated, it has abundant plant life that has followed a relatively normal succession. In normal conditions, one might expect that contaminants would interfere with plant growth because they would impede different enzymatic functions of the plant. The goal of this study is to find out what contaminants are present in the LSP soils. There are four subplots and a reference site that my research group studied: HMF, 146, 43, 25F, and 25R. HMF or Hutcheson Memorial Forest is a natural preserve that Native Americans used for agriculture. The sites 146, 43, 25F, and 25R are in different locations within the restricted, unremediated section of Liberty State Park (LSP) and have different levels of contamination and plant life. This thesis reports on a category of organic compounds called saturated hydrocarbons. Depending on how contaminated each individual site is, the abundance of the specific saturated compounds may vary. The numerous findings prove that HMF is a natural site by having fewer hydrocarbons, as revealed by gas chromatography-mass spectrometry (GCMS). It also proves that 25R is the most organically contaminated site by its highest abundance of hydrocarbons out of all of the sites. Chapter 1 (Introduction): presents the background of the two site (HMF and LSP) and prepares the reader for the complex topics discussed in the following chapters and describes the significance of this study. Chapter 2 (Environmental Forensics): explains techniques used to investigate specific chemical compounds, how they relate to biotic processes, and how the chemical compounds affect the ecosystem. Chapter 3: (Experimental Methods): goes into the specifics of the analytical techniques and how they apply when examining soil contamination. Chapter 4: (Results and Discussions): shows the results from the experiment and interprets the data. Chapter 5: (Environmental Toxicology/Impacts): explains the health impact of each studied category of compounds, how the compounds enrich the actual sites, and compare overall contaminants (LSP) to the uncontaminated site (HMF). Chapter 6: (Conclusions): draws a final picture of what all the above evidence means, what we should do next, and how does the entire study relate to the people/communities that visit the LSP park now

Growth of unsaturated, cyclic, and polycyclic aromatic hydrocarbons: Reactions under the conditions of the interstellar medium

Hydrocarbons, in particular polycyclic aromatic hydrocarbons (PAHs), have been long discussed to be carriers of interstellar infrared (IR) emission and ultraviolet (UV) absorption features. Yet, their origin in dense phases of the interstellar medium (ISM), such as molecular clouds, remains unclear. In this work, growth mechanisms based on ion-molecule reactions between cationic PAHs/hydrocarbons and methyne (CH) were investigated. The reaction type and the precursor were derived and selected from known chemical and physical properties of the ISM. These chemical reactions were characterised by calculating branching ratios (based on cross sections) and capture rate coefficients, minimum reaction paths, reaction enthalpies, thermal equilibrium constants, and microcanonic isomerisation and radiative deactivation rate coefficients. In order to cope with the variety of reaction parameters, a hierarchic workflow scheme was set up. First, the reaction potential energy surface was sampled by molecular dynamics simulations. Then, minimum energy paths of the most probable reaction channels were investigated. Finally, molecular and kinetic properties of stationary points were calculated. The quantum chemical level of theory was increased at each step from DFTB (tight-binding density-functional), to DFT, and finally to post-Hartree-Fock methods. Results on CH based hydrocarbon growth showed the transition from non-cyclic hydrocarbons to cyclic and aromatic structures and from cyclic to polycyclic aromatic hydrocarbons. Additionally, the reactive collisions between hydrocarbons and CH were found to produce sufficient energy for isomerisation and fragmentation processes even at ultra low temperatures. In all, the results indicate that methyne might be a proper precursor for the formation of large interstellar PAHs.Kohlenwasserstoffe, insbesondere polyzyklische Kohlenwasserstoffe (engl. PAHs), werden seit einigen Jahren als Mitverursacher interstellar IR-Emissions- und UV-Absorptionsbanden angesehen und diskutiert. Dabei ist die Herkunft dieser Moleküle in den dichten Phasen des interstellaren Mediums (ISM) aber noch nicht aufgeklärt. In dieser Arbeit wurden daher die Bildungsmechanismen, welche auf Ion-Molekül-Reaktionen zwischen kationischen PAHs und Kohlenwasserstoffen und dem Molekül CH beruhen, untersucht. Sowohl der Reaktionstyp als auch der Präkursor wurden anhand von bekannten physikalischen und chemischen Eigenschaften des ISM abgeleitet und ausgewählt. Die Analyse der chemischen Reaktionen basierte auf Berechnungen zur Produktzusammensetzung und Einfangsratenkoeffizienten (welche wiederum aus berechneten Reaktionsquerschnitten hervorgingen) Minimumenergiepfade (MEP), Reaktionsenthalpien, thermische Gleichgewichtskonstanten und mikrokanonische Isomerisierungs- und Strahlungsdeaktivierungs-Ratenkoeffizienten. Um der Vielzahl an Reaktionsparameter gerecht zu werden, wurden die Berechnungsmethoden entsprechend eines hierarischen Fließschemas kombiniert. Hierzu wurden zuerst durch Molekulardynamik-Simulationen die Reaktionspotentialenergieflächen abgerastert. Auf der nächsten Stufe wurden statistisch bedeutsame Reaktionskanäle bezüglich ihrer Minimumenergiepfade untersucht. Den Abschluss bildete die Berechnung molekularer und kinetischer Charakteristika stationärer Punkte auf einem MEP. Entsprechend dieses Schemas wurde die quantenchemische Genauigkeit auf jeder Stufe von approximativer DFT über DFT zu post-Hartree-Fock verändert. Die Ergebnisse des CH-basierten Kohlenwasserstoffwachstums zeigten einen Übergang von nichtzyklischen zu zyklischen and aromatischen Strukturen, sowie von zyklischen zu polyzyklischen Kohlenwasserstoffen. Außerdem zeigte sich, dass reaktive Kollisionen zwischen Kohlenwasserstoffen und CH auch bei Tiefsttemperaturen immer ausreichend Energie für Isomerisierungs- und Fragmentationsprozesse liefert. Die Ergebnisse dieser Arbeit lassen den Schluss zu, dass CH ein geeigneter Präkursor für die Bildung großer interstellarer PAH ist

The aromatic character of [10]annulenes and dicupra[10]annulenes from current density calculations

We have investigated the aromatic properties of seven low-lying isomers of [10]annulene and of the recently synthesized dicupra[10]annulene compounds that were crystallised with two or four lithium counterions (Wei et al., J. Am. Chem. Soc., 2016, 138, 60-63). The molecular structures of the [10]annulene conformers and the dicupra[10]annulenes with bulky trimethylsilyl (TMS) and phenyl groups, as well as the corresponding unsubstituted dicupra[10]annulenes were optimised using density functional theory, employing a semiempirical dispersion correction to consider van der Waals interactions. The structures of the hydrocarbon annulenes were subsequently optimised at the SCS-MP2/def2-QZVPD level. Single-point coupled-cluster calculations with explicit treatment of the electron correlation CCSD(F12)(T) were performed to obtain the relative energies of the hydrocarbon annulenes. Four of the conformations lie close in energy relative to each other. Three substituted and three unsubstituted dicupra[10]annulene structures with either four, two or no Li+ counterions were investigated. Magnetically induced current densities calculated using the GIMIC program were used for the assessment of the aromatic properties of the studied molecules. The conformations of [10] annulene with lowest energies are non-aromatic. The calculations revealed that the electron donation of the lithium atoms to the dicupra[10]annulene core significantly affects the electronic and molecular structures of the dicupra[10]annulenes. The annulene ring is non-planar for all studied dicupra[10]annulenes except for the unsubstituted one with four Li+ counterions, which was also found to be the only molecule that sustains a strong diatropic ring current around the dicupra[10]annulene ring. The other five dicupra[10]annulenes sustain very weak net ring currents and can be considered non-aromatic.Peer reviewe

Synthetic and computational investigations into reaction pathways towards complex heterocyclic ring systems

Tetrazocines are eight-membered rings possessing four nitrogen atoms. The development of new synthetic routes to novel heterocyclic systems has remained a critical branch of synthetic organic chemistry due to potential applications in biomimetics and pharmaceuticals, such as dyes and explosives. 1,2,3,5-tetrazocines were originally proposed as an intermediate in the formation of 1,3a,6,6atetrahydroimidazo[4,5-c]pyrazole (a promising anti-fungal agent) from the irradiation of 2,3a,4,6a-tetraphenyl-3,3a,4,5,6,6a hexahydropyrrolo-[2,3-d]-1,2,3-triazole. One of our main aims was to synthesise novel 1,2,3,5-tetrazocines that possessed three phenyl and one methyl group(s) attached to the eight-membered ring, as previously synthesised 1,2,3,5-tetrazocines are of the tetra-phenyl variety. Adopting the established synthetic route in the pursuit of novel 1,2,3,5-tetrazocines proved difficult however, as the asymmetric nature of the 1,2,3,5-tetrazocine precursors (dihydrazones) resulted in altered reactivity as compared with their symmetric equivalents, this finding was rationalised using distributed multipole analysis. Ab initio calculations (B3LYP/6-31G(d)) indicate that for an underivatised 1,2,3,5- tetrazocine, the planar (aromatic) structure is the most stable, though this is not observed experimentally, presumably due to steric repulsions between the large aromatic substituents often used to stabilise these molecules. Excluding the planar geometry, we found that there is a significant thermodynamic stabilisation of 1,2,3,5- tetrazocine over the 1,3a,6,6a-tetrahydroimidazo[4,5-c]pyrazole, providing a novel route to heterocyclic systems