A non-trivial example of an L-topological space, the fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.

For the first time, the Z0 boson angular distribution in the center-of-momentum frame is measured in proton-proton collisions at sqrt(S) = 7 TeV at the CERN LHC. The data sample, recorded with the CMS detector, corresponds to an integrated luminosity of approximately 36 pb-1. Events in which there is a Z0 and at least one jet, with a jet transverse momentum threshold of 20 GeV and absolute jet rapidity less than 2.4, are selected for the analysis. Only the Z0’s muon decay channel is studied. Within experimental and theoretical uncertainties, the measured angular distribution is in agreement with next-to-leading order perturbative QCD predictions.

Let U be an n-dimensional vector space over an algebraically closed field. Let [formula omitted] denote the [formula omitted] space spanned by all Grassmann products [formula omitted]. Subsets of vectors of [formula omitted] denoted by [formula omitted] and [formula omitted] are defined as follows [formula omitted]. A vector which is in [formula omitted] or is zero is called pure or decomposable. Each vector in [formula omitted] is said to have rank one. Similarly each vector in [formula omitted] has rank two. A subspace of H of [formula omitted] is called a rank two subspace If [formula omitted] is contained in [formula omitted]. In this thesis we are concerned with investigating rank two subspaces. The main results are as follows: If dim [formula omitted] such that every nonzero vector [formula omitted] is independent in U. The rank two subspaces of dimension less than four are also characterized. / Science, Faculty of / Mathematics, Department of / Graduate

A generalization of a theorem of N.R. 0'Brian, zeroes of holomorphic vector fields and the Grothendieck residue, Bull. London Math. Soc, 7 (1975) is given. The theorem of Riemann-Roch and Hirzebruch for V-equivariant holomorphic vector bundles is obtained, via holomorphic vector fields, in the case all zeroes of the holomorphic vector field V are isolated. The Bruhat decomposition of G/B is obtained from the G -action on G/B . It is shown that a theorem of A. Bialynicki-Birula, Some theorems on actions of algebraic groups, Ann. of Math. 98, 480-497 (1973) is the generalization of the Bruhat decomposition on G/B , which was a conjecture of B. Iversen. The existence of a G -action on G/P with only one fixed a point is proved, where G is a connected linear algebraic group defined over an algebraically closed field k of characteristic zero and P is a parabolic subgroup of G . The following is obtained P = N[sub G](Pu) = {geG: Adg(Pu) = Pu} where G is a connected linear algebraic group, P is a parabolic subgroup of G and P^ is the tangent space of the set of unipotent elements of P at the identity. An elementary proof of P = N[sub G](P) = {geG: gPg ⁻¹=P} is given, where G is a connected linear algebraic group and P is a parabolic subgroup of G . / Science, Faculty of / Mathematics, Department of / Graduate

Influenza infection occurs in as much as 5–15% of the world population, resulting in 3–5 million cases of severe illness and up to 500,000 deaths annually. According to the CDC, on average 24% of all influenza positive respiratory samples during 2001 to 2011 tested positive for Influenza B. Influenza has two main surface glycoproteins, neuraminidase (NA) and hemagglutinin (HA), HA being responsible for the binding of the virus to the host cell. Currently, seasonal influenza vaccines are produced using two strains of Influenza A and one or two strains of Influenza B viruses recommended by the World Health Organization (WHO). These vaccines are mainly targeting the head domain of the HA protein, which mutates constantly, hence the need for annual vaccine updates. The goal of this research is to develop an experimental universal vaccine against influenza B and increase our knowledge to help pave the way for finding a one-time vaccination alternative, reducing the need for a yearly flu shot. To achieve the above, protection and toxicity studies were conducted in DBA/2 mice immunized with a designed HA2 adenoviral-vectored vaccine targeting the HA stem region of influenza B. Results showed that this designed vaccine was able to confer 100% survival protection, this was supported by lower viral titer in trachea and lung tissues. Additionally, we studied the influence of CD40L as a targeting adjuvant, by analyzing its effect on the humoral and cellular immune response, where results showed that it has a significant effect by inducing a higher TH1-bias response. This research is the first report that leads us to a better understanding of the potential use of a conserved consensus HA2 sequence to induce protection against influenza B virus.

Human head and body lice are obligatory hematophagous ectoparasites that belong to a single species Pediculus humanus. Only body lice, however, are vectors of the infections gram-negative bacteria Bartonella quintana. Due to their near identical genomes, yet differential vector competency, head and body lice provide an ideal model system to study an insects ability to gain or lose vector competency. Using our in vitro louse rearing system, we have infected both head and body lice with a blood containing B. quintana in order to detect differences in B. quintana proliferation between head and body lice as well as transcriptional regulation of immune-related genes. B. quintana proliferates rapidly in body lice after 6 days post-infection, but declines in head lice after 4 days post-infection, possibly explaining, in part, the differential vector competence between the two insects. A transcriptome analysis using whole lice followed by qPCR verification of head and body lice immune-related genes was then conducted using uninfected, versus B. quintana infected lice to identify potential genes involved in vector competence. The immune-related genes Defensin 1, Fibrinogen-related protein and Spaetzle, were differentially regulated between head and body lice and were identified as potential targets for future research. Previously studied immune-related genes, PGRP, Defensin 1 and Defensin 2 transcription levels were also assessed in body louse midgut using qPCR following B. quintana infection. In this case, B. quintana infection did not result in significant effects on the transcript levels of these genes in midgut tissue. Overall transcriptional profiles of head and body lice genomes were notably different, including difference in the expression of 18.3 % of immune related genes, a finding that strongly supports the contention that immune system differences between head and body lice are the primary reason for difference in vector capacity.

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This analysis studies the reaction ep → e′p′ϕ in the kinematical range 1.6 ≤ Q² ≤ 3.8 GeV² and 2.0 ≤ W ≤ 3:0 GeV at CLAS. After successful signal identification, total and differential cross sections are measured and compared to the world data set. Comparisons are made to the predictions of the Jean-Marc Laget(JML) model based on Pomeron plus 2-gluon exchange. The overall scaling of the total cross section was determined to be 1/Q^4.6±1.7 which is compatible within errors to the Vector Meson Dominance prediction of 1/Q⁴ as well as to the expected behavior of a quark and gluon exchange-dominated model described by Generalized Parton Distributions of 1/Q⁶. The differential cross section dσ/dφ was used to determine that the s-channel helicity conservation (SCHC) assumption is valid within the precision of the current data. SCHC leads to a simple expression for the decay angular distribution from which R, the ratio of the longitudinal to the transverse cross section, can be extracted. Under the assumption of SCHC, we determine R = 1.33 ± 0.18 at an average Q² of 2.21 GeV² which leads to a determination of the longitudinal cross section σ_L = 5.3 ± 1.3 nb for exclusive ϕ production. / Ph. D.

We studied the reaction 𝑒𝑝 → 𝑒′𝑝′𝜙 with a 4.2 GeV incident electron beam in the region of the electroproduction variables Q² from 0.7 to 2.2 GeV² and W from 2.0 to 2.6 GeV. The data were taken and analyzed at the Thomas Jefferson National Accelerator Facility. For the first time, we observe the expected t-slope dependence on Q² and Δ𝜏 in 𝜙 vector meson production. We find that the width of the forward 𝜙-meson diffraction peak increases rapidly as the interaction time decreases below cΔ𝜏 ≈ 1 fm. Within a simple optical model framework, the data show that 𝜙 meson has a smaller size than the 𝜌. The measured 𝜙 cross-section dependence on Q² is in a good agreement with previous measurements and well-described by the phenomenological Pomeron-exchange model. Our cross-section data do not favor the standard Vector Meson Dominance and 𝑠𝑠̅-knockout model predictions. From the angular distribution of the decay 𝜙 → 𝐾⁺𝐾⁻, assuming the 𝑠-channel helicity conservation, we extracted the longitudinal-to-transverse cross-section ratio, 𝑅, and Vector Meson Dominance scaling parameter, 𝜉², which are consistent with the previous measurements and the model expectations. / Ph. D.

Fused Deposition Modeling is a rapid prototyping technique in which miniature extruders melt filaments of polymeric materials. The extruder is mounted to an X/Y stage, and a computer controls the machine so that the polymer is deposited in only the appropriate locations. Material is deposited on one layer at a time so that the desired shape is built from the bottom up. While Fused Deposition Modeling has many advantages, it is poorly suited for large parts or for parts with thick walls due to the amount of time that is required to fabricate them. One strategy to reduce the build time is to implement multiple independent extrusion-heads. This thesis addresses various issues and concerns that arise while designing a multiple independent extrusion-head Fused Deposition Modeling system. The greatest design challenges and most critical issues are identified, and then solutions are presented. Physical samples and experiments verify feasibility when possible. Suitable material deposition strategies have been formulated to allow multiple independent extrusion heads to work simultaneously to reduce build time while allowing for a larger build envelope. These strategies produce parts that have nearly identical mechanical properties as those made on a single-head machine. This work seeks to provide information that is useful for designing a multiple independent extrusion-head Fused Deposition Modeling, regardless the number of extrusion heads or machine configuration. Implementing multiple independent extrusion heads will greatly reduce the fabrication time while allowing for a larger build envelope. / Master of Science