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Articles 1 - 30 of 57
Full-Text Articles in Physical Sciences and Mathematics
Multiscale Strain Analysis, Timothy Donald Breitzman
Multiscale Strain Analysis, Timothy Donald Breitzman
LSU Doctoral Dissertations
The mathematical homogenization and corrector theory relevant to prestressed heterogeneous materials in the linear-elastic regime is discussed. A suitable corrector theory is derived to reconstruct the local strain field inside the composite. Based on this theory, we develop an inexpensive numerical method for multi scale strain analysis within a prestressed heterogeneous material. The theory also provides a characterization of the macroscopic strength domain. The strength domain places constraints on the homogenized strain field which guarantee that the actual strain in the heterogeneous material lies inside the strength domain of each material participating in the structure.
Hydrophobic Guar Gum Derivatives Prepared By Controlled Grafting Processes For Hydraulic Facturing Applications, Ahmad Bahamdan
Hydrophobic Guar Gum Derivatives Prepared By Controlled Grafting Processes For Hydraulic Facturing Applications, Ahmad Bahamdan
LSU Doctoral Dissertations
The synthesis of new water soluble guar gum derivatives is described. Introduction of polyalkoxyalkyleneamide grafts to guar gum or hydroxyopropyl guar was achieved in a three step process: carboxymethylation with sodium chloroacetate, esterification with dimethyl sulfate and amidation with a series of polyalkoxyalkylene-amines. The process steps were followed using infrared spectroscopy; the grafted guar derivatives were characterized using FT-IR and 1H NMR. A series of hydroxypropyl guar derivatives with degrees of carboxymethylations ranging from 0.15-0.25 were modified with polyalkoxyalkyleneamines with molecular weights ranging from 300-3000. The ratio of oxypropylene to oxoethylene units in the polyalkoxyalkyleneamines was varied from 9/1 …
Nitrate Reduction And Methane Formation As Influenced By Iron-Centered Intermediate Redox Processes In Rice Soils, Bin Huang
LSU Doctoral Dissertations
Rice fields are a major source of the greenhouse gases methane (CH4) and nitrous oxide (N2O) and contribute to nitrate (NO3-) pollution in waters. Ferric iron (Fe3+) and manganic manganese (Mn4+) are two intermediate alternative electron acceptors (AEAs) capable of regeneration in freshwater soils. In this investigation, the influences of iron-centered intermediate redox processes on NO3- reduction and CH4 formation in rice soils were studied using soil slurries, soil columns, and potted rice. Reduction of Fe3+-centered intermediate AEAs was mainly mediated by obligate anaerobes …
Stm And Arpes Studies Of Epitaxial Multilayer Ag On Cu(110) And Ni(110), Weichang Zhao
Stm And Arpes Studies Of Epitaxial Multilayer Ag On Cu(110) And Ni(110), Weichang Zhao
LSU Doctoral Dissertations
Ag nanostructures of multilayer coverages (< 30 monolayers) epitaxially self-assembled on Cu(110) and Ni(110) have been explored by scanning tunneling microscopy (STM), angle-resolved photoelectron emission spectroscopy (ARPES), and low energy electron diffraction (LEED). We have studied varied nanostructure morphologies self-assembled depending on different deposition/annealing processes and coverages, their atomic structures, growth behaviors and mechanisms, and the electronic structures of nanowires. At nominal coverages of 1.2 ML < ¦È < ~10 ML, there are two epitaxial structures on Cu(110) and Ni(110). One is a Ag(110) multilayer film, which has a superstructure with lateral periodic units of eight and three/four substrate lattice constants along [¯110] and along [001] respectively. Another is that of Ag(110) nanowires surrounded by pseudohexagonal Ag(111) monolayer. The Ag(110) nanowires are triangular in cross section. The two side surfaces are faceted and the long axis is atomically straight along [¯110]. Typical lengths are within the range of 100 ~ 5000 Å, widths 70 ~ 300 Å, side slopes 10 ~ 30º, and heights 5 ~ 60 Å. The Ag nanowires present extraordinary anisotropy with observed aspect ratios (length:width) of up to 20:1. The Ag(110) nanowires are in-registry with the substrate along [001], but not along [¯110]. At coverages of ~ 10 ML < ¦È < ~25 ML, there also exist two different nanostructures, the nanowires and a Ag(110) atomically-flat film with some pits as deep as down to the substrate and a one-dimensional quasiperiodic superstructure along [001]. There are two basic separations of the superstructural stripes: one is three lattices wide (~11 Å) and the other is two lattices wide (~7 Å). Both of nanostructures are stable at temperature up to at least 200 ¡ãC and not inter-transformable. The growth of the nanowires is driven by the elastic strain mechanism, but the growth of the atomically-flat film is driven by electronic growth mechanism originated from the electron quantum confinement in the vertical direction of the film. The ARPES of the nanowires shows dispersion in the vertical and the [¯110] directions, but no dispersion in the [001] direction because of the limited width (~ 200 Å).
The Twiggs Clay: Mineralogy, Origin, And Industrial Properties Of An Upper Eocene Opaline Claystone In The Coastal Plain Province Of Georgia, U.S., Lori G. Eversull
The Twiggs Clay: Mineralogy, Origin, And Industrial Properties Of An Upper Eocene Opaline Claystone In The Coastal Plain Province Of Georgia, U.S., Lori G. Eversull
LSU Doctoral Dissertations
The Twiggs Clay is an upper Eocene claystone found as discontinuous deposits downdip of the Fall Line in the Coastal Plain Province of eastern and central Georgia. A distinctive facies of the Twiggs is found in two lenses near the town of Wrens. The nature, origin, and potential commercial application of this resource are examined. Four strata and two mineralogic assemblages are recognized in the Wrens deposit. The lower three strata are near white in color and very low in density. These strata are mineralogically similar and are composed predominantly of disordered silica and smectite. The smectite is dioctahedral, and …
Parallel Molecular Dynamics Simulations Of Pressure-Induced Structural Transformations In Cadmium Selenide Nanocrystals, Nicholas Jabari Ouma Lee
Parallel Molecular Dynamics Simulations Of Pressure-Induced Structural Transformations In Cadmium Selenide Nanocrystals, Nicholas Jabari Ouma Lee
LSU Doctoral Dissertations
Parallel molecular dynamics (MD) simulations are performed to investigate pressure-induced solid-to-solid structural phase transformations in cadmium selenide (CdSe) nanorods. The effects of the size and shape of nanorods on different aspects of structural phase transformations are studied. Simulations are based on interatomic potentials validated extensively by experiments. Simulations range from 105 to 106 atoms. These simulations are enabled by highly scalable algorithms executed on massively parallel Beowulf computing architectures. Pressure-induced structural transformations are studied using a hydrostatic pressure medium simulated by atoms interacting via Lennard-Jones potential. Four single-crystal CdSe nanorods, each 44Å in diameter but varying in length, in the …
An Evaluation Of The Enantiomeric Recognition Of Amino Acid Based Polymeric Surfactants And Cyclodextrins Using Spectroscopic And Chromatographic Methods, Bertha Cedillo Valle
An Evaluation Of The Enantiomeric Recognition Of Amino Acid Based Polymeric Surfactants And Cyclodextrins Using Spectroscopic And Chromatographic Methods, Bertha Cedillo Valle
LSU Doctoral Dissertations
The scope of this dissertation is to explore the enantiomeric recognition properties of amino acid based polymeric surfactants using a combination of analytical techniques including chromatographic and spectroscopic methods. Chapter 1 includes an introduction to chirality and chiral separations using capillary electrophoresis. Using cyclodextrin modified micellar electrokinetic chromatography (CD-MEKC), the enantioseparation of three binaphthyl derivatives using native alpha- and beta-cyclodextrins in combination with various diastereomers of chiral polymeric surfactants (PS) was examined. A reversal of enantiomeric order was observed with the enantiomers of (1,1 S-binaphthyl-2,2 S-diamine (BNA) and (1,1 S-binaphthol (BOH) due to a competition between the two chiral selectors …
Long-Term Freshwater Input And Sediment Load From Three Tributaries To Lake Pontchartrain, Louisiana, Kangsheng Wu
Long-Term Freshwater Input And Sediment Load From Three Tributaries To Lake Pontchartrain, Louisiana, Kangsheng Wu
LSU Doctoral Dissertations
Lake Pontchartrain and the drainage basin have experienced environmental degradation because of human settlement, land use and climate changes. A thorough understanding of hydrologic trends and variability associated with the changes is critical for sustainable water resources management and ecosystem restoration in the region. This study examined freshwater inflow (1940-2002) and suspended solids loadings (1978-2001) from three upper Lake Pontchartrain watersheds that contribute to the lake estuary: the Amite, Tickfaw, and Tangipahoa river watersheds. The relationships of freshwater inflow and suspended solids loadings with climate variables and population growth were investigated. Using observed daily discharge, a spatially-distributed hydrologic model (SWAT) …
Synthesis, Characterization And Application Of Polymeric Surfactants In Micellar Electrokinetic Chromatography: Use Of Ionic Liquids As Modifiers, Simon M. Mwongela
Synthesis, Characterization And Application Of Polymeric Surfactants In Micellar Electrokinetic Chromatography: Use Of Ionic Liquids As Modifiers, Simon M. Mwongela
LSU Doctoral Dissertations
The goal of the research presented in this dissertation is to synthesize, characterize, and apply a novel chiral amino acid-based surfactant and achiral sulfate-based surfactants for the effective separations of chiral and achiral compounds in micellar electrokinetic chromatography (MEKC). The first part of this research involves novel synthesis, characterization, and application of polysodium oleyl-L-leucyl-valinate (poly-L-SOLV) for the separation of chiral compounds in MEKC. Surface tensiometry, proton nuclear magnetic resonance, infrared spectroscopy, densitometry and analytical ultracentrifugation were used as the characterization techniques. Optimal MEKC separating conditions were established by varying surfactant concentration, buffer concentration and pH, applied voltage, and capillary temperature. …
Dynamical Systems With Time Delay, Norma Ortiz
Dynamical Systems With Time Delay, Norma Ortiz
LSU Doctoral Dissertations
In this dissertation, we study necessary conditions and weak invariance properties of dynamical systems with time delay. A number of results have been obtained recently that refine necessary conditions of optimal solutions for nonsmooth dynamical systems without time delay. In this dissertation, we examine the extension of some of these results to problems with time delay. In particular, we study the generalized problem of Bolza with the addition of delay in the state and velocity variables and refer to this problem as the Neutral Problem of Bolza. We consider the relationship between the generalized problem of Bolza with time delay …
Shear Induced Orientation In Polymer-Clay Solutions And Their Influence On The Structure In Multilayered Films, Matthew Michael Malwitz
Shear Induced Orientation In Polymer-Clay Solutions And Their Influence On The Structure In Multilayered Films, Matthew Michael Malwitz
LSU Doctoral Dissertations
The influence of shear on viscoelastic solutions of poly(ethylene oxide) (PEO) and clay (Cloisite, CNA) was investigated by rheology and small angle neutron scattering (SANS) under shear. These measurements determined the shear-induced orientation of the clay and the polymer as well as their relaxation behavior after cessation of shear. Comparison of PEO-CNA solutions (~100 nm diameter platelets) to previously studied PEO-Laponite gels (~30 nm diameter platelets) found that the orientation of CNA platelets occurs at much lower shear rates. Additionally, the relaxation times were much longer for CNA platelets than for Laponite platelets. From these solutions and gels, multilayered nanocomposite …
Broadcast In Sparse Conversion Optical Networks Using Fewest Converters, Tong Yi
Broadcast In Sparse Conversion Optical Networks Using Fewest Converters, Tong Yi
LSU Doctoral Dissertations
Wavelengths and converters are shared by communication requests in optical networks. When a message goes through a node without a converter, the outgoing wavelength must be the same as the incoming one. This constraint can be removed if the node uses a converter. Hence, the usage of converters increases the utilization of wavelengths and allows more communication requests to succeed. Since converters are expensive, we consider sparse conversion networks, where only some specified nodes have converters. Moreover, since the usage of converters induces delays, we should minimize the use of available converters. The Converters Usage Problem (CUP) is to use …
Error Estimates For Stabilized Approximation Methods For Semigroups, Sarah Campbell Mcallister
Error Estimates For Stabilized Approximation Methods For Semigroups, Sarah Campbell Mcallister
LSU Doctoral Dissertations
In this work we analyze error estimates for rational approximation methods, and their stabilizations, for strongly continuous semigroups. Chapter 1 consists of a brief survey of time discretization methods for semigroups. In Chapter 2, we demonstrate a new method for obtaining convergent approximations in the absence of stability for strongly continuous semigroups with arbitrary initial data. In Section 2.2, we state the stabilization result in more general form and show that this method can be used to improve known error estimates by a magnitude of up to one half for smooth initial data. In Section 2.3, we give concrete examples …
Molecular Recognition And Its Underlying Mechanisms In Molecularly Imprinted Polymers, Ryan Simon
Molecular Recognition And Its Underlying Mechanisms In Molecularly Imprinted Polymers, Ryan Simon
LSU Doctoral Dissertations
Molecular recognition in molecularly imprinting polymers (MIPs) is governed by two mechanisms: pre-organization of functional groups and shape specificity of the binding site. While pre-organization of functional groups has been studied extensively, shape specificity of the binding site has not been rigorously explored. The goal of this research is to determine the influence of shape specificity on molecular recognition in MIPs (Chapter 2). Once shape selectivity was proven to play a vital role in molecular recognition, it was important to determine if pre-organization of functional groups or shape specificity was the dominating factor in determining molecular recognition in the binding …
Stability In Dynamical Polysystems, George Cazacu
Stability In Dynamical Polysystems, George Cazacu
LSU Doctoral Dissertations
A dynamical polysystem consists of a family of continuous dynamical systems, all acting on a given metric space. The first chapter of the present thesis shows a generalization of control systems via dynamical polysystems and establishes the equivalence of the two notions under certain lipschitz condition on the function defining the dynamics. The remaining chapters are focused on a basic theory of dynamical polysystems. Some topological properties of limit sets are described in Chapter 2. Chapters 3 and 4 provide characterizations for various notions of strong stability. Chapter 5 makes use of the theory of closed relations to study Lyapunov …
Capillary And Microchip Gel Electrophoresis Using Multiplexed Fluorescence Detection With Both Time-Resolved And Spectral-Discrimination Capabilities: Applications In Dna Sequencing Using Near-Infrared Fluorescence, Li Zhu
LSU Doctoral Dissertations
Increasing the information content obtainable from a single assay and system miniaturization has continued to be important research areas in analytical chemistry. The research presented in this dissertation involves the development of a two-color, time-resolved fluorescence microscope for the acquisition of both steady-state and time-resolved data during capillary and microchip electrophoresis. The utility of this hybrid fluorescence detector has been demonstrated by applying it to DNA sequencing applications. Coupling color discrimination with time-resolved fluorescence offers increased multiplexing capabilities because the lifetime data adds another layer of information. An optical fiber-based fluorescence microscope was constructed, which utilized fluorescence in near-IR region, …
Effects Of Body Size On Goose Behavior: Lesser Snow Goose And Ross's Goose, Jon Einar Jonsson
Effects Of Body Size On Goose Behavior: Lesser Snow Goose And Ross's Goose, Jon Einar Jonsson
LSU Doctoral Dissertations
Body size is highly variable among geese, both at intra- and interspecific levels. Interspecific variation in several behaviors has been attributed to differences in body size in geese: incubation constancy, tendency to maintain family units, and time spent foraging. Body size has important physiological implications for birds, mostly because mass-specific metabolic rate is greater for birds of smaller mass. The Body-size Hypothesis predicts that smaller species deplete their energy reserves at relatively faster rates than do larger species. Hypotheses and conclusions concerning effects of body size on waterfowl behavior often are based on comparisons of species that confront different climates, …
Enantioselective Syntheses And Chemical Investigations Of Plant-Derived Bioactive Volatile Compounds, Anne Marie Sauer
Enantioselective Syntheses And Chemical Investigations Of Plant-Derived Bioactive Volatile Compounds, Anne Marie Sauer
LSU Doctoral Dissertations
Research, inspired by nature, provides ample opportunity for discovery, ingenuity, and creative endeavor. For these reasons, the work and accomplishments presented herein focus on the total syntheses and related investigations of a variety of natural product derivatives, specifically (+)-nootkatone and jasmone. While the former consists of several independent projects: (a) an enantioselective synthetic route to (+)-nootkatone and derivatives, (b) examination of the valencane ring system, (c) determination of the absolute configuration of (+)-nootkatone, and (d) rearrangements of various sesquiterpenoid derivatives; the latter focuses on the construction ofƒndelta, epsilon-unsaturated carbonyl compounds, hetero Pauson-Khand substrates, via [3,3]-sigmatropic rearrangements.
Denitrification And Greenhouse Gas Emissions From Cultivated And Wetland Alluvial Soils, Sami Ullah
Denitrification And Greenhouse Gas Emissions From Cultivated And Wetland Alluvial Soils, Sami Ullah
LSU Doctoral Dissertations
Agricultural development in the Mississippi River Basin has contributed to an 3-fold increase in NO3 loading of the river. Increased NO3 loading is a primary cause of eutrophication in the northern Gulf of Mexico. Identification of best management practices (BMPs) to reduce NO3 loss and wetlands restoration to remove NO3 through denitrification are critically needed. The objectives of this research were to determine factors controlling denitrification potential of different landscape units in an agricultural watershed and quantify the effects of BMPs and organic C amendments on denitrification rates of cultivated lands and restored forested wetlands. N2O, CH4 and CO2 emissions …
Macroinvertebrate Community Of Ecology Of Lowland, Subtropical Streams In Louisiana, Michael Douglas Kaller
Macroinvertebrate Community Of Ecology Of Lowland, Subtropical Streams In Louisiana, Michael Douglas Kaller
LSU Doctoral Dissertations
Freshwater ecosystems, particularly streams and rivers, have been the subject of prodigious research. Unfortunately, in comparison to neighboring regions, the Gulf of Mexico coastal plain has not received as much attention. Therefore, I collected data on the macroinvertebrates of these streams to begin the understanding of the relationships between community structure and environmental characteristics. In contrast to the hypothesized ancestral streams of these macroinvertebrates, coastal plain streams are commonly devoid of rocks leaving only woody debris as usable hard substrates and are typically lower in dissolved oxygen. I examined habitat selection by colonization of woody debris with large and small …
Biologically Inspired Learning System, Patrick Mcdowell
Biologically Inspired Learning System, Patrick Mcdowell
LSU Doctoral Dissertations
Learning Systems used on robots require either a-priori knowledge in the form of models, rules of thumb or databases or require that robot to physically execute multitudes of trial solutions. The first requirement limits the robot’s ability to operate in unstructured changing environments, and the second limits the robot’s service life and resources. In this research a generalized approach to learning was developed through a series of algorithms that can be used for construction of behaviors that are able to cope with unstructured environments through adaptation of both internal parameters and system structure as a result of a goal based …
Synthetic Development And Application Of Compounds With Biological Relevance, Jeffery Caleb Clark
Synthetic Development And Application Of Compounds With Biological Relevance, Jeffery Caleb Clark
LSU Doctoral Dissertations
Nature has provided a vast number of compounds that have medicinal application. The use of these compounds provided by nature however, is limited by the amount of a specific compound that nature provides. The synthesis of these molecules and their derivatives provides an even greater number of compounds for biological screening. Various pyrroles, the heterocyclic building blocks of porphyrins, can be prepared synthetically over several steps. The implementation of carboranes on pyrrole rings intrinsically provides substrates that can be converted into porphyrins bearing carborane substituents. The condensation of these carboranylpyrroles with carboranylaldehydes provides carboranylporphyrins bearing a higher order of carborane …
Boundary Effects On Non-Equilibrium Localized Structures In Spatially Extended Systems, Aniruddha Yadav
Boundary Effects On Non-Equilibrium Localized Structures In Spatially Extended Systems, Aniruddha Yadav
LSU Doctoral Dissertations
A study of the effects of system boundaries on bistable front propagation in nonequilibrium reaction-diffusion systems is presented. Two model partial differential equations displaying bistable fronts, with distinct experimental motivations and mathematical structure, are examined in detail utilizing simulations and perturbation techniques. We see that propagating fronts in both models bounce, trap, pin, or oscillate at the boundary, contingent on the imposed boundary condition, initial front speed and distance from the boundary. The similarities in front boundary interactions in these two models is traced to the fact that they display the same front instability (Ising-Bloch bifurcation) that controls the speed …
The Stable Isotope Stratigraphy And Paleosols Of North America's Most Southern Exposure Of Late Paleocene/Early Eocene Fossiliferous Continental Deposits: Documenting The Initial Eocene Thermal Maximum In Big Bend National Park, Texas, Paul David White
LSU Doctoral Dissertations
A chemostratigraphic section across the Paleocene/Eocene boundary, using the stable isotopes of carbon and oxygen, has been developed for North America's most southern exposure of early Paleogene continental deposits in which the boundary is constrained by fossil mammals. A negative carbon excursion has been identified within C24r. The range in d13C values is from -8.1 to -13.2‰. Until the development of the chemostratigraphic section it was uncertain if the earliest Eocene was recorded in Big Bend. An early Wasatchian (Wa1) fossil site occurs stratigraphically higher than the carbon excursion and has yielded the stratigraphically lowest Hyracotherium in the …
The Stereoselective Synthesis Of The Butyrolactone-Bridged [8-5-5] Tricyclic Ring Systems Of (+/-)-Asteriscanolide Via The Titanium-Mediated Hetero-Pauson-Khand Reaction, Mohamed G. Sherriff
The Stereoselective Synthesis Of The Butyrolactone-Bridged [8-5-5] Tricyclic Ring Systems Of (+/-)-Asteriscanolide Via The Titanium-Mediated Hetero-Pauson-Khand Reaction, Mohamed G. Sherriff
LSU Doctoral Dissertations
The stereoselective construction of the tricyclic ring system of asteriscanolide from cyclooctadiene has been achieved. The synthesis involves two main steps; the synthesis of the aldehyde precursor(5)and the titanium-mediated cabocyclization of 5 to make the three rings of 43 stereoselectively.
Active Security Mechanisms For Wireless Sensor Networks And Energy Optimization For Passive Security Routing, Lydia Ray
LSU Doctoral Dissertations
Wireless sensor networks consisting of numerous tiny low power autonomous sensor nodes provide us with the remarkable ability to remotely view and interact with the previously unobservable physical world. However, incorporating computation intensive security measures in sensor networks with limited resources is a challenging research issue. The objective of our thesis is to explore different security aspects of sensor networks and provide novel solutions for significant problems. We classify security mechanisms into two categories - active category and passive category. The problem of providing a secure communication infrastructure among randomly deployed sensor nodes requires active security measurements. Key pre-distribution is …
Characterization Of A Modified Poly(Propylene Imine) Dendrimer Host System, Amy D. Morara
Characterization Of A Modified Poly(Propylene Imine) Dendrimer Host System, Amy D. Morara
LSU Doctoral Dissertations
The research in this dissertation focuses on the design of a novel redox-responsive host system that has the ability to encapsulate guest molecules. The host at hand is a tri(ethylene oxide), TEO, pyrrole-terminated PPI dendrimer that possesses water-solubility as a result of the presence of the TEO chains on the pyrrole groups and redox-responsive activity from the pyrrole groups after their oligomerization. The pyrrole moieties at the periphery of the dendrimer exhibit the ability to be oligomerized by oxidation chemistry, and this is shown to aid in the retention and egress of guest molecules located within the dendrimer interior. These …
Population Dynamics Of Clausocalanus Furcatus (Copepoda, Calanoida) In The Northern Gulf Of Mexico, Hongsheng Bi
Population Dynamics Of Clausocalanus Furcatus (Copepoda, Calanoida) In The Northern Gulf Of Mexico, Hongsheng Bi
LSU Doctoral Dissertations
Copepods are important components of marine ecosystems. Understanding copepod population dynamics can help interpret variations in both primary producers and higher trophic levels. Egg production, stage duration, and stage-specific mortality rates are key parameters describing copepod population dynamics. Estimation of stage-specific mortality is complicated due to a complex life history, patchiness, and sampling biases. This study was undertaken to quantify the population dynamics of the copepod Clausocalanus furcatus in the northern Gulf of Mexico and to assess the utility of available mortality estimation methods in a highly advective environment. Zooplankton samples were taken every 12h from March 18-April 6, and …
Komatiites Of The Weltevreden Formation, Barberton Greenstone Belt, South Africa: Implications For The Chemistry And Temperature Of The Archean Mantle, Keena Kareem
LSU Doctoral Dissertations
The komatiites of the 3.29 Ga Weltevreden Formation, Barberton Greenstone Belt, South Africa represent extremely magnesian lavas derived from the Archean mantle. Three related papers are presented on aspects of the temperature and composition of the Archean mantle, and surface alteration processes. Petrographical and geochemical analyses confirm that olivines from the komatiites retain much of their original igneous character, containing fresh olivines, pyroxenes, and chromites. The olivines from the Weltevreden Formation are extremely magnesian, with Fo contents up to 95.6. Primitive mantle normalized Gd/Yb values near 1, and Al2O3/TiO3 values of 26-33 for these rocks …
Virtual Strings For Closed Curves With Multiple Components And Filamentations For Virtual Links, William Schellhorn
Virtual Strings For Closed Curves With Multiple Components And Filamentations For Virtual Links, William Schellhorn
LSU Doctoral Dissertations
The theory of filaments on oriented chord diagrams can be used to detect some non-classical virtual knots. We extend existing filament techniques to virtual links with more than one component and give examples of virtual links that these techniques can detect as non-classical. Given a signed Gauss word underlying an oriented chord diagram, we describe how to construct a finite sequence of integers that encodes all of the filament information for the diagram. We also introduce a square array of integers called a MIN-square that summarizes the filament information about all of the signed Gauss words having a given Gauss …