Most drugs undergo passive transport during absorption and distribution in the body. It is desirable to predict passive permeation of future drug candidates in order to increase the productivity of the drug discovery process. Unlike drug-receptor interactions, there is no receptor map for passive permeability because the process of transport across the lipid bilayer involves multiple mechanisms. This work intends to increase the understanding of permeation of drug-like molecules through lipid bilayers. Drug molecules in solution typically form various species due to ionization, complexation, etc. Therefore, species specific properties must be obtained to bridge the experiment and simulations. Due to the volume contrast between intra- and extravesicular compartments of liposomes, minor perturbations in ionic and binding equilibria become significant contributors to transport rates. Using tyramine as a model amine, quantitative numerical models were developed to determine intrinsic permeability coefficients. The microscopic ionization and binding constants needed for this were independently measured. The partition coefficient in 1,9-decadiene was measured for a series of compounds as a quantitative surrogate for the partitioning into the hydrocarbon region of the bilayer. These studies uncovered an apparent long-range interaction between the two polar substituents that caused deviations in the microscopic pKa values and partition coefficient of tyramine from the expected values. Additionally the partition coefficients in the preferred binding region of the bilayer were also measured by equilibrium uptake into liposomes. All-atom molecular dynamics simulations of lipid bilayers containing tyramine, 4- ethylphenol, or phenylethylamine provided free energies of transfer of these solutes from water to various locations on the transport path. The experimentally measured partition coefficients were consistent with the free energy profiles in showing the barrier in the hydrocarbon region and preferred binding region near the interface. The substituent contributions to these free energies were also quantitatively consistent between the experiments and simulations. Specific interactions between solutes and the bilayer suggest that amphiphiles are likely to show preferred binding in the head group region and that the most of hydrogen bonds involving solutes located inside the bilayer are with water molecules. Solute re-orientation inside the bilayer lowers the partitioning barrier by allowing favorable interactions.

Fluorinated systems are defined by unique properties that offer advantages in drug delivery, material synthesis and industrial applications. In comparison to their hydrocarbon counterparts, the design of fluorinated solutes for tailored applications is limited by the inability to predict the effect of fluorination on phase behavior. This work examines and interprets the influence of fluorination on the phase behavior of fluorinated solutes and surfactants, with emphasis on their impact on vesicle bilayers. Thermodynamic partitioning of functionalized series of fluorinated and hydrocarbon nicotinate prodrugs fashioned to promote solubility in a fluorocarbon solvent (perfluorooctyl bromide; PFOB) is measured. Predictive approaches are also employed to describe partitioning of these nicotinates between immiscible phases relevant to drug delivery. The findings reveal no strong correlation of the partitioning trends with biological markers of cytotoxicity and prodrug uptake for PFOB mediated delivery. However, partitioning in model membranes (liposomes), which, increases with the hydrophobicity of the perhydrocarbon nicotinates, suggests incorporation in a cellular matrix is chain length dependent. The impact of incorporating fluorinated surfactants in catanionic vesicles, which form spontaneously in dilute aqueous solutions and serve as potential substitutes to conventional meta-stable liposome-based vesicles, is studied. Much larger isotropic vesicle regions are observed in the phase map of the partially fluorinated catanionic surfactant pair, cetylpyridinium bromide/ sodium perfluorooctanoate (CPB/SPFO) than in fully fluorinated HFDPC (1,1,2,2,-tetrahydroperfluorododecyl pyridinium chloride )/SPFO. Fluorescence probing of the vesicle bilayers suggest more fluid bilayers in CPB/SPFO than in HFDPC/SPFO due to better chain packing in the fully fluorinated bilayer. However, the vesicle region is expanded in more asymmetric fluorinated bilayers of HFDPC/SPFH (sodium perfluorohexanoate). The increased chain asymmetry in HFDPC/SPFH results in reduced packing density and more fluid bilayers than in HFDPC/SPFO. The robustness of CPB/SPFO and HFDPC/SPFO vesicles is demonstrated in the synthesis of silica hollow spheres by templating and the retention of encapsulated solutes. Higher colloidal stability of the silica spheres is achieved in HFDPC/SPFO relative to CPB/SPFO due to the barrier effect of the fluorinated bilayer. Similarly, higher solute retention in HFDPC/SPFO is observed. The modulation of phase behavior with fluorination offers opportunities in tunable applications of fluorinated bilayers.

The partition of India that accompanied that nation's independence in 1947 created the additional state of Pakistan; by 1971, this Pakistan had fractured into the two independent states of Pakistan and Bangladesh. This dissertation seeks to expand our temporal and spatial understanding of the sub-continent's partitioning by examining the experiences of a group of South Asian Muslims across time and space. As this dissertation will show, South Asia's partitioning includes more than the official history of boundary creation and division of assets, and more than the people's history of unbridled violence. I have oriented my investigation around a single institution, the Aligarh Muslim University, and spoken to former students of the 1940s and 1950s, whose young lives were shaped by the independence and partition of India. The memories of these former students of Aligarh University offer a lens for examining the "multiple realities" of partition and the decolonized experiences of South Asian Muslims. The educational institution at Aligarh, founded in 1875, had long been concerned with cultivating a sporting, activist, masculine identity among its students; Muslim League leaders further empowered that identity as they recruited students for election work in support of Pakistan. The students embraced the values of the demand for Pakistan that appeared to be consistent with the values engendered at Aligarh. This dissertation uncovers the history of these students throughout the 1947 partition and beyond. It explores unexpected histories of trauma among communities who "chose to stay" but later experienced a powerful discontinuity in independent India. It exposes contradictions evident in remembered histories from Pakistanis who express triumph and grief at the prospect of Pakistani independence. Finally, this dissertation assesses the position of Muslims after partition and how the "disturbances" that began in the late 1940s continue to affect them today in both lived and remembered experience. As a site for examining the "disturbances" of partition, Aligarh University proves to be a hub of a community that was and remains deeply disturbed by the changes partition wrought. / text

The scope of this research concerns the passive damping of structural vibrations by the use of viscoelastic layers. It is motivated by the need for efficient numerical tools to deal with the medium frequency behaviour of industrial viscoelastic sandwich products. The sandwich modelling technique is based on the use of an interface element: the two deformable plates are modelled by special plate elements while the intermediate dissipative layer is modelled with interface elements. This interface element is based on the first-order shear deformation theory and assume constant peel and shear stresses in the polymer thickness. This element couples the lower and upper layers without additional degrees of freedom. The partition of unity finite element method (PUFEM) is applied to the development of enriched Mindlin plate elements. The element shape functions are obtained as the product of partition of unity functions with arbitrary chosen enrichment functions. Polynomial enrichment leads to the generation of high-order polynomial shape functions and is therefore similar to a p-FEM technique. Numerical examples illustrate the use of both PUFEM Mindlin plate elements and interface elements for the simulation of viscoelastic sandwich structures.

Microbial fuel cells (MFC) are an emerging renewable technology which converts complex organic matter to electrical power using microorganisms as the biocatalyst. A variety of biological relevant organic matters such as glucose, acetate and ethanol have been utilized for the successful operation of a MFC. In this regard, the investigation of a MFC inoculated with ethanol oxidizing bacteria is of particular interest for this research due to its ability to simultaneously produce electricity while reducing ethanol pollution (a type of volatile organic carbon (VOC) pollutant) with potential use in modified biological air pollution control technology such as biofiltration. In this research, ethanol-oxidizing microbial species isolated from soil and compost samples were identified, with Acinetobacter calcoaceticus being the dominant strain. In order to understand the metabolism of the anode microbial cells, which is considered to be the key dictating the performance of a MFC, a systematic analysis/optimization of the growth rate and biomass production for A. calcoaceticus were carried out. A maximum specific growth rate with a final biomass concentration of 1.68 g/l was derived when aerated at a rate of 0.68 vvm. It has been recognized that one of the principle constraints in increasing the current density of MFCs is the electron transfer from the bacteria to the anode. In this sense, the addition of a redox mediator, which facilitates the process of the electron transfer, is desired for the efficient operation of a MFC. Thionine, methylene blue (MB), resorufin and potassium ferricyanide that have been profusely utilized as effective mediator compounds in many MFC studies, however, specific information on the biomass sorption of these compounds was lacking and therefore were selected for this research. All mediators tested were reduced biologically in A. calcoaceticus inoculated samples as indicated by the color transition from the pigmented oxidized form to the colorless reduced form. Subsequent tests on mediator color removal revealed that physical adsorption by the biomass, aggregation as well as precipitation accounted for a significant portion of the color loss for thionine and MB. It was speculated that the fraction of the initial mediator concentration sequestered, aggregated and/or precipitated no longer contributed to the electron transfer process, resulting in a current production which was proportional to the measurable mediator concentration remained in anode solution. To verify this hypothesis, chronoamperometric measurements were conducted for various mediator systems at known initial and measurable concentrations. The data obtained on the current produced were in good agreement with the theoretical predictions calculated from the actual mediator concentration, suggesting that the current produced depended on the concentration of mediator remaining in solution. Finally, the microbial reduction kinetics and the cytotoxicity of potassium ferricyanide were analyzed. The reduction of potassium ferricyanide followed zero order kinetics with the specific reduction rate increased as the initial mediator concentration increased from 1 mM to 200 mM. Inhibitory effects on cell growth were observed at initial potassium ferricyanide concentration of 50 mM.

在這篇論文中，我們希望用不同角度來重新探討一個古典的數學問題；點、線、面切割最多區域問題，雖然這個問題已經經由許多方法得到公式，例如：遞迴關係、差分方程式、歐拉公式、標準n維空間切割系統等等，並延伸出其他方面的問題，可以運用在很多地方，所以我們希望可以再找到更簡單易懂的論證方式，可以讓國中學生也能理解。 思考學生現有的數學觀念，我們發現利用不等式的數學觀念，藉由定義出一套有規則的系統以及數學歸納法，可以以更直接，簡單的理論驗證出此數學公式，最後我們更希望能將這理論推廣至n維度空間。 / In this research, we will discuss a classical mathematical question from different aspects. The question of maximizing the number of regions made up by points, lines and planes has been proved and developed many formulas, using Recurrence Relations, Difference Equations, and Euler's Formula etc., which can extend to other questions and apply to many areas. Therefore, we hope to find an easier way to prove it which may help middle school students to understand better. We find that we can use the concept of inequality from what the students learn so far. By defining a logical system and using Induction, we can prove this mathematical formula in an easier and more direct way. Finally we hope it can be generalized to n-dimensional space.

Ce travail de recherche s'inscrit dans le cadre de l'analyse vibroacoustique des structures complexes. Il propose une nouvelle approche énergétique utilisant le champ de densité d'énergie afin de simplifier une telle analyse. Cette approche est basée sur un modèle numérique stochastique construit à l'aide de l'approche probabiliste non paramétrique des incertitudes de modélisation et de paramètres. L'approche énergétique stochastique développée correspond à une nouvelle représentation du système vibroacoustique en terme des grandeurs énergétiques aléatoires. Un modèle vibroacoustique énergétique moyen est alors construit en prenant la moyenne statistique des grandeurs énergétiques. On dispose alors d'un modèle énergétique moyen pour analyser la vibroacoustique des systèmes complexes dans la bande des basses et des moyennes fréquences alors que la méthode SEA ne permet pas d'analyser cette bande de fréquence. L'analyse des propriétés des grandeurs énergétiques moyennes utilisées pour la construction du modèle vibroacoustique énergétique permet de construire une version simplifiée conduisant à un modèle énergétique simplifié pour lequel une méthodologie de partition structurale par zone est établie. Une application de cette approche énergétique et de la méthodologie de partition structurale par zone est présentée pour une voiture constituée d'une structure automobile couplée avec sa cavité acoustique interne

Spanning tree congestion was defined by Ostrovskii (2004) as a measure of how well a network can perform if only minimal connection can be maintained. We compute the parameter for several families of graphs. In particular, by partitioning a hypercube into pieces with almost optimal edge-boundaries, we give tight estimates of the parameter thereby disproving a conjecture of Hruska (2008). For a typical random graph, the parameter exhibits a zigzag behaviour reflecting the feature that it is not monotone in the number of edges. This motivates the study of the most congested graphs where we show that any graph is close to a graph with small congestion. Next, we enumerate independent sets. Using the independent set polynomial, we compute the extrema of averages in trees and graphs. Furthermore, we consider inverse problems among trees and resolve a conjecture of Wagner (2009). A result in a more general setting is also proved which answers a question of Alon, Haber and Krivelevich (2011). After briefly considering polynomial invariants of general graphs, we specialize into trees. Three levels of tree distinguishing power are exhibited. We show that polynomials which do not distinguish rooted trees define typically exponentially large equivalence classes. On the other hand, we prove that the rooted Ising polynomial distinguishes rooted trees and that the Negami polynomial determines the subtree polynomial, strengthening results of Bollobás and Riordan (2000) and Martin, Morin and Wagner (2008). The top level consists of the chromatic symmetric function and it is proved to be a complete invariant for caterpillars.

The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the properties of the matrix A and its column submatrices. The analysis demonstrates that RBGS improves RGS more when given appropriate column-paving of the matrix, a partition of the columns into well-conditioned blocks. The main result yields a RBGS method that is more e cient than the simple RGS method.

A new approach for predicting octanol-water partition coefficients (Log P) of linear perfluorinated compounds, making use of the limited experimental data available, previous observations and the consistent similarities observed between the experimental and calculated (with electronic structure methods and using EPI suite) slopes of the linear plots of Log P values with the number of carbon atoms (N = 2 to 11) is described here. Eight families of linear organic compounds were investigated: carboxylic acids, perfluorinated carboxylic acids, sulfonic acids and perfluorinated sulfonic acids, together with their corresponding conjugate bases. To the best of our knowledge, this work reports the first application of density functional theory methods to the calculation of Log P values of perfluorinated compounds. A second part of the thesis, describes the study of the thermodynamic stability of the PFOA family of 39 structural isomers with the M06-2X, LC-ωPBE, B97D and B3LYP functionals and with the PM6 method. The PM6 results closely resemble the M06-2X results for neutral PFOAs, but greatly disagree regarding anions. The four functionals applied behave similarly from a qualitative point of view, but quantitatively speaking, the LC-ωPBE and B97D results are between the M06-2X and B3LYP stability results. M06-2X ranks highly substituted isomers as more stable than did B3LYP, and ranks less-branched isomers quite low in relative stability compared to B3LYP. Various similarities with a former PFOSs study applying the M06-2X and B3LYP functionals have been identified. The degree of branching within structural isomers cannot always be precisely determined, and is not the only aspect that determines thermodynamic stability; the pattern of substitution seems to also play a significant role. / Graduate