A network flow approach to a common generalization of Clar and Fries numbers

Clar number and Fries number are two thoroughly investigated parameters of plane graphs emerging from mathematical chemistry to measure stability of organic molecules. We consider first a common generalization of these two concepts for bipartite plane graphs, and then extend it to a framework on general (not necessarily planar) directed graphs. The corresponding optimization problem can be transformed into a maximum weight feasible tension problem which is the linear programming dual of a minimum cost network flow (or circulation) problem. Therefore the approach gives rise to a min-max theorem and to a strongly polynomial algorithm that relies exclusively on standard network flow subroutines. In particular, we give the first network flow based algorithm for an optimal Fries structure and its variants

Two essays in computational optimization: computing the clar number in fullerene graphs and distributing the errors in iterative interior point methods

Fullerene are cage-like hollow carbon molecules graph of pseudospherical sym- metry consisting of only pentagons and hexagons faces. It has been the object of interest for chemists and mathematicians due to its widespread application in various fields, namely including electronic and optic engineering, medical sci- ence and biotechnology. A Fullerene molecular, Γ n of n atoms has a multiplicity of isomers which increases as N iso ∼ O(n 9 ). For instance, Γ 180 has 79,538,751 isomers. The Fries and Clar numbers are stability predictors of a Fullerene molecule. These number can be computed by solving a (possibly N P -hard) combinatorial optimization problem. We propose several ILP formulation of such a problem each yielding a solution algorithm that provides the exact value of the Fries and Clar numbers. We compare the performances of the algorithm derived from the proposed ILP formulations. One of this algorithm is used to find the Clar isomers, i.e., those for which the Clar number is maximum among all isomers having a given size. We repeated this computational experiment for all sizes up to 204 atoms. In the course of the study a total of 2 649 413 774 isomers were analyzed.The second essay concerns developing an iterative primal dual infeasible path following (PDIPF) interior point (IP) algorithm for separable convex quadratic minimum cost flow network problem. In each iteration of PDIPF algorithm, the main computational effort is solving the underlying Newton search direction system. We concentrated on finding the solution of the corresponding linear system iteratively and inexactly. We assumed that all the involved inequalities can be solved inexactly and to this purpose, we focused on different approaches for distributing the error generated by iterative linear solvers such that the convergences of the PDIPF algorithm are guaranteed. As a result, we achieved theoretical bases that open the path to further interesting practical investiga- tion

Convexity deficit of benzenoids

In 2012, a family of benzenoids was introduced by Cruz, Gutman, and Rada, which they called convex benzenoids. In this paper we introduce the convexity deficit, a new topological index intended for benzenoids and, more generally, fusenes. This index measures by how much a given fusene departs from convexity. It is defined in terms of the boundary-edges code. In particular, convex benzenoids are exactly the benzenoids having convexity deficit equal to 0. Quasi-convex benzenoids form the family of non-convex benzenoids that are closest to convex, i.e., they have convexity deficit equal to 1. Finally, we investigate convexity deficit of several important families of benzenoids

The fine structure of condensed ring compounds

This thesis deals with the fine structure of the aromatic hydrocarbons and the heterocyclic compound indazole. The author's contributions are given in the attached reprints from the Journal of the Chemical Society, while the typescript gives an account of the theories involved as well as some work not yet published.Certain considerations outlined in the publications are expanded.Part I gives a general survey of the subject, and Part II deals more particularly with those topics related to the author's work

The Synthesis of Highly Substituted Aromatics and the Reaction of Alkene Pi Systems with Vinyl Cations

Aldol cyclotrimerizations have been used to achieve the rational chemical synthesis of both fullerenes and fullerene fragments in the past. Under certain conditions this reaction produces the corresponding cyclotetramer which has sometimes been regarded as an undesired byproduct. This work details efforts to synthesize and use these cyclotetramers toward a synthesis of a C240 fullerene fragment. One principal focus in this work is tridecacyclene, a cyclic tetramer of acenaphthylene given its name by our group for its thirteen rings. Relatively low yields for the synthesis of tridecacyclene and its derivatives drove us to investigate the mechanism of its formation and attempt to optimize its production. During this process, novel dione products were isolated from the attempted cyclotetramerization of two dimeric species. Characterization of these products by X-ray crystallography gave valuable insight into the reaction pathway, leading us to a new proposed mechanism of formation for the cyclotetramerization products observed in these aldol reactions. β-hydroxy-α-diazoketones are suitable progenitors to vinyl cation intermediates whose use in chemical synthesis is relatively unexplored. As part of an extensive project to develop the chemistry of vinyl cations for use in carbon-carbon bond forming reactions to build important molecular scaffolds, a range of β-hydroxy-α-diazoketones containing a pendent nucleophilic alkene were synthesized. Treatment of these compounds with Lewis acids gave either lactone or cyclopentenone products depending on the substrate used. Proposed herein is a mechanism involving a key acylium intermediate which, depending on the position of the pendent alkene, results in different product outcomes. In a collaborative effort to further investigate the known anti-cancer properties of fusarochromanone, a fungal metabolite that is isolated from Fusarium-infected feed from cold climates, a large-scale synthesis of this natural product was explored. An efficient, scalable synthesis of the previously prohibitively expensive amidochromanone starting material has been achieved and its elaboration to fusarochromanone has been demonstrated

Systematics and evolution of Gomphrena (Amaranthaceae) with an emphasis on the species in Bolivia

Summary The dissertation investigates Gomphrena L. and allied genera with morphological and molecular data in order to test the phylogenetic relationships and to better understand the evolutionary history of this linage. An emphasis is on the actual Gomphrena clade and as well the diversity in Bolivia. Gomphrena (Gomphrenoideae) is the largest genus of the Amaranthaceae with an estimated number of 120 species. The areas of main diversity of this genus comprise South America with about two thirds of the species, Central and North America (about 15%), and Australia (about 20%). This genus largely grows in tropical climates. Some of the species are used as medicinal plants, and a few are cultivated as ornamental plants exhibiting attractive pigmentation in their tepals. The first chapter presents the state of knowledge and a general introduction into Gomphrena. It is important to note that previous molecular phylogenetic studies revealed that Gomphrena in the widely used circumscription of Schinz (1934) is a polyphyletic group. These past studies included only few species of Gomphrena and distinguished two main clades. The first clade includes the type species of the genus, G. globosa L., and certain Australian and American species, plus the allied genera Gossypianthus Hook., Lithophila Sw., and Philoxerus R.Br. (= Blutaparon Raf.) with not fully understood relationships. This group of Gomphrena s. str. is here called “Gomphrena clade” whereas the second group that includes G. elegans Mart., G. mandonii R.E.Fr. and others is part of a lineage called Pfaffia clade (not studied here). In addition, the first chapter presents the complex taxonomic history of Gomphrena. The second chapter focuses on the morphological characteristics of the Gomphrena clade. As a result 22 vegetative and floral morphological characters were defined with their respective states and assessed for 27 representative samples. The photosynthesis type (absence or presence of C 4 photosynthesis) was coded in the form of a single trait including morpho-anatomical characteristics. For chapter three a combined data set of chloroplast sequences (matK-trnK + trnL-F + rpl16) of the Gomphrena clade (including the allied segregate genera) and outgroups from Gomphrenoideae was analyzed with parsimony (MP), maximum likelihood (ML) and Bayesian inference (BI) methods. The 22 morphological characters were optimized on the Bayesian Maximum clade credibility tree using Bayes Traits. The results show that most vegetative characters including the annual life form have evolved multiple times, whereas some floral character states were identified as synapomorphies. An important result reveals that many of the nine characters defined for the androecium, most of which were used historically for the pre- phylogenetic delimitation of Gomphrena and other genera, appear homoplastic. The presence of a fused stamen tube without stamen tube appendages (but with lateral filament appendages in some species) is confined to the Gomphrenoid clade (Gomphrena clade plus Froelichia, iv Xerosiphon, and the Pfaffia clade) whereas the Alternantheroid clade (here represented by Pedersenia) differs by the presence of stamen tube appendages. The important character is the difference between inner and outer tepals showing that all members of the newly found core C 4 Gomphrena clade have a difference in the size of the two inner tepals. To the contrary, all other species present five tepals of similar size. Another interesting result is the detection of pseudanthia, acting as a visual attractant for pollinators. The pseudanthial leaves are typical for a “Mostly Andean clade”. But pseudanthial leaves also were derived two more times independently in G. boliviana and allies and G. meyeniana and allied. The combined plastid tree also shows with high support that the species of Philoxerus, Lithophila and Gossypianthus are nested within the core C 4 Gomphrena clade. For this reason, it is proposed here to include the three genera into Gomphrena and a respective treatment is provided. The extended taxon sampling for matK-trnK (80 samples) and nrITS (82 samples) show that most of the major lineages are congruently resolved between plastid and nuclear data with one exception in the early branching G. mollis - rupestris clade (that is C3). It is sister to all C 4 species of Gomphrena in the nrITS tree whereas it appears as a second branch after the G. prostrata - Guilleminea clade in all plastid trees. Ancestral character state reconstruction shows that C 4 photosynthesis arose in the common ancestor of the Gomphrena clade plus Froelichia but reversed back to C 3 in the lineage of G. mollis and G. rupestris. The age of the crown group of the core C 4 Gomphrena clade plus Froelichia is inferred as 18 Ma (10.2-28.4, 95% HPD), which corresponds to the mid-Miocene climatic optimum (c. 18-16 Ma) when an increase in temperature and aridity and later drop in concentrations of CO 2 occurred. This result is also consistent with the emergence of C 4 photosynthesis in Chenopodiaceae and Poaceae. The core Gomphrena clade stands out by being a C 4 clade that diversified at least twice into high elevation Andean environments. Species such as G. fuscipellita (growing at elevations of 3600-4300 m) and G. meyeniana Walp. (3200-4700 m) constitute at the moment the highest populations of any herb C 4 . The mostly Andean clade diverged around 8 Ma (4.0-13.6, 95 % HPD) from lowland ancestors whereas the crown group has an age of just 4.3 Ma (1.8-10.3. 95% HPD). The majority of the species from the inter Andean dry valleys, Prepuna and Puna ecoregions in the extensively sampled matK-trnK and ITS trees are included in two major subclades of the “Mostly Andean clade”. The molecular time divergence estimate concurs with the maximum Andean mountain upheaval that occurred at 5 Ma, which created new habitats through the geomorphological and climatic modifications. The dry climates led to the recent and multiple evolution of annual species such as G. phaeotricha, G. pallida or G. umbellata. The sister of the Mostly Andean clade is the Australian clade., The results of this thesis (chapter 3) show with high support that the disjunctly distributed Australian species are closely related to the coastal species of Lithophila and Philoxerus. The latter is distributed on the Pacific coast of central America includes morphologically similar species that are endemics on the Galapagos islands. the same applies to Lithophila with one widely distributed Caribbean species and Galapagos endemics. The species of Lithophila and Philoxerus present adaptations to live in high concentrations of salt such as fleshy leaves, adventitious roots allowing vegetative reproduction from broken-off stems. The current distribution of Philoxerus vermicularis is restricted to the west coast of tropical Africa, and the species has not further extended into Africa, which decreases the possibilities for dispersal between Africa and Australia. The stem age of the clade comprising Lithophila, Philoxerus and the Australian Gomphrena spp. 10 Ma (5.7-16.9 95 % HPD). This confirms that the disjunction occurred recently so that Gondwanan vicariance is not possible a tectonic. It is therefore hypothesized that the dispersal to Australia involved long distance dispersal (LDD). Ancestors of Lithophila or Philoxerus -like plants came across the Pacific Ocean, perhaps even from Galapagos that acted as a stepping stone through marine currents such as the South Ecuatorial Current, which then leads over into the East Australian current and which were present since about 6 Ma. The chapter four provides a taxonomic treatment for the species of the core C 4 Gomphrena clade in Bolivia, including keys for identification detailed morphological descriptions and distribution maps. In the introductory part to this chapter dot distribution maps are presented, which are layed over by maps with environmental data in order to better standardize the habitat types of the species for the descriptions of their respective ecology. The results are based on extensive field and herbarium studies and now recognize 30 species of core Gomphrena in Bolivia, which is an increase in eight over the state of knowledge in the Catálogo de Plantas Vasculares de Bolivia that was published in 2014 with 22 species of core Gomphrena. These eight species represent discoveries new to science

Part 1: Towards the Synthesis of Pyrene Zigzag Cyclacenes, Part 2: New Methods for the Synthesis of Conjugated Polymers

Part 1: Carbon nanotubes (CNTs) are allotropes of carbon that have emerged as candidates for implementation in electronic devices ranging from transistors to solar cells. Unfortunately, the behavior of CNTs is highly dependent on their structure and modern synthetic methods for generating CNTs are not able to provide uniform samples for electronic applications. Recently, the synthesis of cycloparaphenylenes (CPPs), which closely resemble metallic CNTs, has been elucidated and has since been further expanded to allow for the CPPs of varying diameters and subunits. More importantly, CPPs were also shown to allow for the controlled bottom-up synthesis of CNTs, opening the door towards the concise synthesis of CNTs. Herein, we will outline our synthetic attempts towards the synthesis of zigzag cyclacenes and how the creation of a zigzag nanobelt could bring forth the defined synthesis of semiconducting zigzag nanotubes. Drawing inspiration from previous attempts at cyclacenes and the successful synthesis of CPPs, we set out to construct a zigzag macrocycle using a Diels-Alder approach with pyrene as the backbone of the cycle. We were able to successfully construct the cyclic precursor to the cyclacene following numerous attempts; however, isolation of the fully aromatized product was not accomplished because the strain exhibited by the cycle led to an over reduction. Our search to create cyclacenes led us towards phosphonium salts as a new method for the mild creation of benzyne. Unfortunately, the phosphonium benzyne performed poorly due to regioselectivity issues, but in trying to create the aryl phosphonium salts, we created a new route towards these compounds. Herein, we will describe our development of a metal free synthesis of aryl phosphonium salts. When aryl halides are irradiated with UV light in the presence of a phosphine, the two species can couple leading to the formation of the phosphonium salt. The reaction is amenable to a variety of phosphines and can proceed with aryl chlorides, iodides, bromides, and pseudohalides. Part 2: Conjugated polymers have gained a great deal of interest as these compounds can be used as active materials and enable the creation of lightweight, flexible, and low-cost electronic devices. Critical to the advancement of these technologies is the creation of new synthetic methods and facile access to material. Herein, we will outline the development of new synthetic techniques for the creating conjugated polymers. First, we will discuss the development of a new metal free dehydrative polymerization of thiazole N-oxides. Drawing inspiration from nature and from the industrial synthesis of commodity polymers, such as PET and nylon-6,6, we developed a new transformation that can dimerize thiazole N-oxides in the absence of a metal with the formal loss of water being the sole byproduct. This methodology was later extended onto bifunctional monomers and allowed for the synthesis of conjugated polymers in quantitative yield and good molecular weights. Secondly, we will discuss the design and synthesis of a new palladium precatalyst for the synthesis of conjugated polymers through direct arylation polymerization. Conjugated polymers are mostly synthesized using transition metal couplings such as Stille or Suzuki couplings; however, these methods require pre- functionalization and can leave behind toxic byproducts. Direct arylation polymerization has recently emerged as a new technique for synthesizing conjugated polymers; however, the nature of the propagating species means that conjugated polymers created this way are more prone to branching/crosslinking defects. We designed a palladium precatalyst specifically for direct arylation polymerization that can reduce unwanted functionalization while providing good molecular weights, high yields, lower loadings, and improved thermal properties

The Independent and Montgomery Transcript, V. 89, Thursday, April 9, 1964, [Number: 45]

[8] p. Accept and Defend the Truth. Newspaper published in Collegeville, Pa. Weekly. Contains local, county, state and national news, editorials, letters, classified and local business advertisements.https://digitalcommons.ursinus.edu/independent_montgomery/1547/thumbnail.jp