We apply anisotropic Banach space methods together with operator renewal theory to obtain polynomial rates of decay of correlations for a class of generalized baker's transformations. The polynomial rates were proved for a smaller class of observables in a 2013 paper of Bose and Murray by fundamentally different methods. Our approach provides a direct analysis of the Frobenius-Perron operator associated to a generalized baker's transformation in contrast to the paper of Bose and Murray where decay rates are obtained for a factor map and lifted to the full map. / Graduate

In eukaryotes, mRNA is in constant flux between an actively translating state and translationally repressed states. Specifically, mRNA degradation and repression factors compete with translation factors to direct mRNAs out of translation for storage or decay. This process often leads to formation of cytoplasmic aggregates. P-bodies are granules that contain mRNA and degradation factors, suggesting they are sites of mRNA decay or storage. Stress granules form in response to stress conditions and contain mRNAs and translation factors.P-bodies and stress granules consist of mRNPs of different compositions, believed to mature and transition between the states. It is proposed that mRNAs transition between the two granules. In the work described below, we use <italic>Saccharomyces cerevisiae</italic> to demonstrate that a decay factor, Dhh1 is capable of existing in both P-body and stress granule mRNPs. This suggests that a decay factor can be part of two different mRNP complexes. Additionally, we identify two novel components of the stress granule mRNPs, Pbp4 and Lsm12, and determine that they are not essential for stress granule formation. Lastly, we show that the stress granule mRNP factor, Pab1, is not absolutely required for stress granule formation.An important aspect of cytoplasmic mRNA regulation is mRNA quality control. One example of this is nonsense-mediated mRNA decay (NMD), whereby aberrant mRNAs containing premature termination codons are targeted for decay, and can be localized to P-bodies. Upf1-3 and the mRNA decapping complex, Dcp2/Dcp1 are essential for NMD, which requires Upf1 interaction with stalled ribosomal/mRNA complexes to target aberrant mRNA for decapping and degradation. How Dcp2/Dcp1 is recruited to aberrant mRNA is poorly understood.Here, we show by yeast two-hybrid assays that an interaction between Dcp2 and Upf1 is mediated by the decapping stimulator Edc3. Interestingly, Edc3 and Upf2 share overlapping binding sites on the Upf1 N-terminal domain. The decapping stimulator, Pat1, also interacts on the Upf1 N-terminus, but Edc3 and Pat1 are not essential for NMD. Surprisingly, the Upf1-Edc3 interaction does not promote or negatively regulate NMD. Thus, the Upf1-Edc3 and Upf1-Pat1 interactions likely regulate a subset of mRNA transcripts, or are essential for proper NMD under different environmental conditions.

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We present results for the matrix elements relevant for proton decay in Grand Unified Theories (GUTs), using two methods. In the indirect method, we rely on an effective field theory description of proton decay, where we need to estimate two low energy constants. We then relate these low energy constants to the proton decay matrix elements using leading order chiral perturbation theory. In the direct method, we calculate the required matrix elements directly; this is computationally more expensive, but the calculation has no systematic error from the use of chiral perturbation theory. The calculations are performed with 2+1 flavors of domain wall fermions on lattices of size 163 × 32 and 243 × 64 with a fifth dimension of length 16. We work at fixed inverse lattice spacing, a−1 = 1.73(3) GeV, leading to physical volumes of (1.8 fm)3 and (2.7 fm)3 for the 163 × 32 and 243 × 64 lattices respectively. In the first four chapters we present the background theory. We start with a brief review of the standard model and the motivation for GUTs. We show that GUTs must lead to proton decay, and that the proton lifetime is an experimentally testable prediction which can be used to constrain GUT parameters, or rule out classes of GUT which predict a minimum lifetime shorter than the experimental minimum bound. We then review continuum and lattice QCD, including outlines of the lattice methods used to calculate the proton decay matrix elements. In the last three chapters we present the results and analysis. We calculate the nucleon and pion two–point correlation functions, and determine their ground state masses and amplitudes. These quantities will then be used to calculate the matrix elements using the indirect and direct methods outlined above. The matrix elements can then be combined with experimental bounds on the proton lifetime to bound parameters of individual GUTs.

The decay B → K*l^+l^-, where the l^+l^- can be e^+e^- or μ^+μ^-, resulting from the b → s flavour changing neutral current decay is highly sensitive to the presence of new physics. The angular observables describing the K* polarisation (FL) and the forward backward asymmetry (AFB) are first measured in two regions of di-lepton mass squared using a dataset of 384 million BB pairs collected by the BaBar detector on the PEP-II rings at SLAC. A second measurement was made in four regions of di-lepton mass squared using a dataset of 468 million BB pairs.

This thesis presents measurements of the branching fractions B(Ds -> lvl) and mea- surements of the pseudoscalar decay constant, fDs , using all the data acquired at the BaBar detector at SLAC National Accelerator Laboratory, which were collected from September 1999 to April 2007, and comprised 531 fb-1. The following mea- surements are made: B(Ds -> eve) = (6:11 +/-0:38 +/- 0:33) * 10-3, B(Ds -> tvt) = (5:06 +/- 0:34 +/- 0:50) * 10-2 , and a limit B(Ds -> eve) < 1:46 * 10-4 is obtained. Using these measurements a value of fDs = 252 +/- 6 +/- 7 +/- 1MeV is obtained, where the first uncertainties account for the statistical limitations of the data, the second uncertainties account for the systematic uncertainties, and the third uncertainties account for uncertainties associated with other physical constants (dominated by the lifetime of the Ds meson).

The possibilities of differentiating linkage positions and anomeric configurations of small oligosaccharides by negative ion mode MALDI using anion attachment followed by PSD are investigated. By careful initial adjustment of the focusing mirror ratios allowing acquisition of the peaks of interest within the same PSD segment, it is possible to obtain highly reproducible relative ion abundances. Discrimination of different linkage types is achieved by analysis of structurally-informative diagnostic peaks offered by PSD spectra of chloride adducts of oligosaccharides, whereas the relative peak intensities of selected diagnostic fragment pairs make differentiation of anomeric configuration possible. F- and Ac- cannot form anionic adducts with the oligosaccharides in significant yields. However, Br-, I- and NO3- anionic adducts consistently appear in higher abundances relative to [M - H]-, just like Cl-. Mildly acidic saccharides form both deprotonated molecules and anionic adducts, making it possible to simultaneously detect neutral and acidic oligosaccharides via anion attachment. PSD of [oligosaccharide + Cl]- yields structurally-informative fragment ions that retain the charge on the sugar molecule rather than solely forming Cl-, whereas PSD of Br-, I- and NO3- adducts of oligosaccharides yield the respective anions as the main product ions without offering structural information concerning the sugar. PSD of the chloride adduct of saccharides containing 1-2 linkages also yields chlorine-containing fragment ions. MALDI-TOF-MS and LDI-TOF-MS are shown to be useful for characterization of ultra-small titania nanoparticles. Peak maxima in MALDI-TOF mass spectra are found to correlate with nanoparticle size. The size distributions of TiO2 nanoparticles, obtained from MALDI- and LDI-TOF-MS are in good agreement with parallel TEM observations. PSD analysis of inorganic x nanomaterials is performed and valuable information about the structure of analytes has been obtained. A group of inorganic nitrate and perchlorate salts of forensic and health interest are investigated by LDI- and MALDI-TOF MS. In each case, a series of characteristic cluster ions are predominant in the negative-ion mode. The number and identity of metal atoms and anions in the recorded cluster ions can be positively identified by their m/z values, distinctive isotopic patterns and characteristic PSD fragmentation patterns.

Neste trabalho estudamos o decaimento do potencial de um plasma, inicialmente distribuído de maneira uniforme num sólido dielétrico, submetido a um potencial inicial conhecido. A possibilidade de recombinação entre os portadores positivos e negativos constituintes do plasma é considerada. Usando o método das características obtemos o potencial e a configuração espacial de portadores para qualquer instante bem como, a carga residual nos eletrodos ao final do processo. Dois casos particulares são igualmente resolvidos: no primeiro, a mobilidade relativa dos portadores é relacionada ao coeficiente de recombinação entre eles através da relação de Langevin e, no segundo, considera-se que os portadores não se recombinam. No desenvolvimento da solução ao problema surge, também, uma considerável quantidade de informações à respeito da dinâmica dos portadores no interior do dielétrico / In the present work we studied the decay of the potential of a plasma which is initially uniformely distributed in a solid from a given initial value.. The possibility of recombination between the positive and negative charge carriers of the plasma is also considered. Using the method of characteristics, we obtained the potential and space distribution of charge carries for any time and also residual charge in the electrodes at end of the process. Two particular cases are considered. In the first case, the relative mobility of charge carriers is related to their recombination coefficient through Langevin\'s relation and, in the second case, the recombination of charge carrier is absent.. The solution affords considerable information about the charge dynamics inside the dielectric solid

In this thesis, we study a two fluid system which describes the motion of two charged particles in a strict neutral incompressible plasma. We study the well-posdness of the system in both space dimensions two and three. Regardless of the size of the initial data, we prove the global well-posedness of the Cauchy problem when the space dimension is two. In space dimension three, we construct global weak-solutions, and we prove the local well-posedness of Kato-type solutions. These solutions turn out to be global when the initial data are sufficiently small. We also study the stability of the solution around zero given that the initial data is small and has sufficient regularity. It turns out that our system is a system of regularity-loss and the L2 norm of lower derivatives of the solution decays. At last, this two fluid system can be used to derive the classic MHD at least formally. Arsenio, Ibrahim and Masmoudi (2015) proved that the two fluid system converges to MHD under some constraints. We showed numerically that the two fluid system converges to MHD with no such constraint and found the approximate converge rate. / Graduate