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Ph.D. / After giving basic definitions concerning additive hereditary properties of graphs, this document is divided into three main sections, concerning minimal reducible bounds, minimal forbidden subgraphs and prime ideals. We prove that every irreducible property has at least one minimal reducible bound, and that if an irreducible property P is contained in a reducible property R, then there is a minimal reducible bound for P contained in R. In addition we show that every reducible property serves as a minimal reducible bound for some irreducible property. Several applications of these results are given in the case of hom-properties, mainly to show the existence of minimal reducible bounds of certain types. We prove that every degenerate property has a minimal reducible bound where one factor is the class of edgeless graphs and provide evidence that this may also be true for an arbitrary irreducible property. We also consider edge partitions and we show that the results for minimal decomposable bounds are similar to those for minimal reducible bounds. The second set of results deals with minimal forbidden subgraphs of graph properties. We show that every reducible property has infinitely many minimal forbidden subgraphs since the set of all the cyclic blocks making up these graphs is infinite. Finally we consider the lattice of all additive hereditary properies and study the prime ideals in this lattice. We give an example of a prime ideal that is not co-principal and give some requirements that non co-principal prime ideals should satisfy. 'vVe prove that the set of properties with bounded chromatic number is not a prime ideal by showing that a property P with bounded chromatic number can be written as the intersection of two properties with unbounded chromatic number if and only if P contains all trees.

The spin-lattice relaxation time T₁ has been measured in gaseous CH₄ as a function of density at room temperature. The density region investigated is from 0.006 to 7.0 amagats and T₁ passes through a minimum near 0.04 amagats. The spin-rotation interaction is the dominant relaxation mechanism in gaseous CH₄. Since the spin-rotation constants are accurately known for CH₄, the results provide a check on the existing theory of spin-lattice relaxation for spherical top molecules. An interesting feature was the failure of commonly used theoretical expressions for the density dependence of T₁ to fit the experimental data. A reasonable explanation is that the centrifugal distortion of the CH₄ molecule is indirectly contributing to the spin-lattice relaxation. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

archives@tulane.edu / Prostheses have enabled many people with bone injuries to achieve a quality of life that would be difficult without the advances in biomedical engineering and materials sciences. Exploration of alternatives to current methods of prosthetic bone development will result in more options from both the physician and patient perspective for the replacement of bone and the use of bone substitutes. Thus, new bone prostheses can be customized to a patient’s needs. To address rising healthcare costs, 3D printed bone substitutes are enabling affordable and customizable bone replacements. In this study, we designed a strong yet lightweight structural matrix to substitute bone grafts in cases of comminuted fracture of tibial bone. The artificial matrix is inspired by structural components called voxels that have been demonstrated to be feasible in the areas of aerospace for fixed and morphing wing flight. The basis of this voxel matrix is derived from units of hollow eight-sided faces formed from 12 connected struts. In this study, we have produced and simulated a lattice that can resemble natural bone performance. This bone facsimile has been evaluated using finite element analysis to suggest an optimal voxel density and beam width at which the internal structure has a high elastic modulus to relative density ratio for use as a scaffold during bone reconstruction. A lattice-based implant was designed and evaluated using finite-element analysis for osteosarcoma-afflicted long bones such as the tibia. This study should pave the way for bone implants made of strong but lightweight structures can help patients regain the faculties of natural bone. Ultimately, this structure would be constructed from biocompatible materials that provide nutrients for natural bone regeneration processes. With this, the structure would reabsorb completely into the healing bone, after providing a matrix upon which osteoblasts can form new bone. / 1 / Afsheen Sajjadi

In this thesis some general results on uniform frames are established and then, after defining a 'uniform sigma frame', the correspondence between the two is explored via the 'uniform cozero part' of a uniform frame. It is shown that the Lindelof uniform frames and the uniform sigma frames are in fact equivalent as categories, and that properties of, and constructions using separable uniform frames can be obtained by considering the uniform cozero part. For example, the Samuel compactification of a separable uniform frame can be obtained via the Samuel compactification (in the sigma frame sense) of the underlying cozero part of the uniform frame. Throughout the thesis, choice principles such as the axioms of choice and countably dependent choice, are used, and generally without mention.

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<p> A high temperature polymorph of α-Cu2P2O7 was found above 70°C. The lattice parameters and space groups of both phases were determined from X-ray photographs. The crystal structures of α and β-Cu2P2O7 were refined by crystallographic least squares analysis and the molecular geometry obtained was compared with that of other closely related compounds of the transition metal ion pyrophosphate series. The central oxygen atom was found to have enhanced thermal motion or disorder in agreement with I.R. spectroscopic studies of Lazarev. The bond lengths obtained for the P2O7^4- ion were discussed in reference to values predicted by Cruickshank. Evidence of a Jahn-Teller effect was found in the case of the Cu++ ion. A description is given of a relatively efficient method of measuring intensities of Bragg reflections, using a single crystal diffractometer.</p> / Thesis / Master of Science (MSc)

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