Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Intestinal microbes affect phenotypes and functions of invariant natural killer T cells in mice

Invariant natural killer T (iNKT) cells undergo canonical, Vα14-Jα18 rearrangement of the T-cell receptor (TCR) in mice; this form of the TCR recognizes glycolipids presented by CD1d. iNKT cells mediate many different immune reactions. Their constitutive activated and memory phenotype and rapid initiation of effector functions after stimulation indicate previous antigen-specific stimulation. However, little is known about this process. We investigated whether symbiotic microbes can determine the activated phenotype and function of iNKT cells.

Effective Length K-Factors For Flexural Buckling Strengths Of Web Members In Open Web Steel Joists

Open web steel joists are designed in the United States following the governing specification published by the Steel Joist Institute. For compression members in joists, this specification employs an effective length factor, or K-factor, in confirming their adequacy. In most cases, these K-factors have been conservatively assumed equal to 1.0 for compression web members, regardless of the fact that intuition and limited experimental work indicate that smaller values could be justified. Given that smaller K-factors could result in more economical designs without a loss in safety, the research presented in this thesis aims to suggest procedures for obtaining more rational values. Three different methods for computing in-plane and out-of-plane K-factors are investigated, including (1) a hand calculation method based on the use of alignment charts, (2) computational critical load (eigenvalue) analyses using uniformly distributed loads, and (3) computational analyses using a compressive strain approach. The latter method is novel and allows for computing the individual buckling load of a specific member within a system, such as a joist. Four different joist configurations are investigated, including an 18K3, 28K10, and two variations of a 32LH06. Based on these methods and the very limited number of joists studied, it appears promising that in-plane and out-of-plane K-factors of 0.75 and 0.85, respectively, could be used in computing the flexural buckling strength of web members in routine steel joist design. Recommendations for future work, which include systematically investigating a wider range of joist configurations and connection restraint, are provided.

The experimental combination of rTMS and fMRI reveals the functional relevance of parietal cortex for visuospatial functions

We combined repetitive transcranial magnetic stimulation (rTMS) and functional magnetic resonance imaging (fMRI) to investigate the functional relevance of parietal cortex activation during the performance of visuospatial tasks. fMRI provides information about local transient changes in neuronal activation during behavioural or cognitive tasks. Information on the functional relevance of this activation was obtained by using rTMS to induce temporary regional deactivations. We thereby turned the physiological parameter of brain activity into an independent variable controlled and manipulated by the experimenter and investigated its effect on the performance of the cognitive tasks within a controlled experimental design. We investigated cognitive tasks that were performed on the same visual material but differed in the demand on visuospatial functions. For the visuospatial tasks we found a selective enhancement of fMRI signal in the superior parietal lobule (SPL) and a selective impairment of performance after rTMS to this region in comparison to a control group. We could thus show that the parietal cortex is functionally important for the execution of spatial judgements on visually presented material and that TMS as an experimental tool has the potential to interfere with higher cognitive functions such as visuospatial information processing.

Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Carbon dioxide and climate impulse response functions for the computation of greenhouse gas metrics: a multi-model analysis

The responses of carbon dioxide (CO2) and other climate variables to an emission pulse of CO2 into the atmosphere are often used to compute the Global Warming Potential (GWP) and Global Temperature change Potential (GTP), to characterize the response timescales of Earth System models, and to build reduced-form models. In this carbon cycle-climate model intercomparison project, which spans the full model hierarchy, we quantify responses to emission pulses of different magnitudes injected under different conditions. The CO2 response shows the known rapid decline in the first few decades followed by a millennium-scale tail. For a 100 Gt-C emission pulse added to a constant CO2 concentration of 389 ppm, 25 ± 9% is still found in the atmosphere after 1000 yr; the ocean has absorbed 59 ± 12% and the land the remainder (16 ± 14%). The response in global mean surface air temperature is an increase by 0.20 ± 0.12 °C within the first twenty years; thereafter and until year 1000, temperature decreases only slightly, whereas ocean heat content and sea level continue to rise. Our best estimate for the Absolute Global Warming Potential, given by the time-integrated response in CO2 at year 100 multiplied by its radiative efficiency, is 92.5 × 10−15 yr W m−2 per kg-CO2. This value very likely (5 to 95% confidence) lies within the range of (68 to 117) × 10−15 yr W m−2 per kg-CO2. Estimates for time-integrated response in CO2 published in the IPCC First, Second, and Fourth Assessment and our multi-model best estimate all agree within 15% during the first 100 yr. The integrated CO2 response, normalized by the pulse size, is lower for pre-industrial conditions, compared to present day, and lower for smaller pulses than larger pulses. In contrast, the response in temperature, sea level and ocean heat content is less sensitive to these choices. Although, choices in pulse size, background concentration, and model lead to uncertainties, the most important and subjective choice to determine AGWP of CO2 and GWP is the time horizon.

2-methylthio-N$\sp6$-dimethylallyl modification of adenosine 37 of tRNAs in {\it Escherichia coli\/} K-12

The hypermodified, hydrophobic 2-methylthio-N$\sp6$-(dimethylallyl)-adenosine (ms${2{\cdot}6}\atop1$A) residue occurs $3\sp\prime$ to the anticodon in tRNA species that read codons beginning with U. The first step (i$\sp6$A37 formation) of this modification is catalyzed by dimethylallyl diphosphate:tRNA dimethyallyltransferase (EC 2.5.1.8), which is the product of the miaA gene. Subsequent steps were proposed to be catalyzed by MiaB and MiaC enzymes to complete the ms${2{\cdot}6}\atop1$A37 modification. The study of functions of the ms${2{\cdot}6}\atop1$A37 is very important because this modified base is one of the best candidates for a role in global control in response to environmental stress. This dissertation describes the further delineation of functions of the ms${2{\cdot}6}\atop1$A37 modification in E. coli K-12 cells. This work provides significant information on functions of tRNA modifications in E. coli cells to adapt to stressful environmental conditions. Three hypotheses were tested in this work.^ The first hypothesis tested was that non-optimal translation processes cause increased spontaneous mutagenesis by the induction of SOS response in starving cells. To test this hypothesis, I measured spontaneous mutation rates of wild type cells and various mutant strains which are defective in tRNA modification, SOS response, or oxidative damage repair. I found that the miaA mutation acts as a mutator that increased Lac$\sp+$ reversion rates and Trp$\sp+$ reversion frequencies of the wild-type cells in starving conditions. However, the lexA3(Ind)(which abolishes the induction of SOS response) mutation abolished the mutator phenotype of the miaA mutant. The recA430 mutation, not other identified SOS genes, decreased the Lac$\sp+$ reversion to a less extent than that of the lexA3(Ind) mutation. These results suggest that RecA together with another unidentified SOS gene product are responsible for the process.^ The second hypothesis tested was that MiaA protein binds to full-length tRNA$\sp{\rm Phe}$ molecules in form of a protein dimer. To test this hypothesis, three versions of the MiaA protein and seven species of tRNA substrates were purified. Binding studies by gel mobility shift assays, filter binding assays and gel filtration shift assays support the hypothesis that MiaA protein binds to full-length tRNA$\sp{\rm Phe}$ as a protein dimer but as a monomer to the anticodon stem-and-loop. These results were further supported by using steady state enzyme kinetic studies.^ The third hypothesis tested in this work was that the miaB gene in E. coli exists and is clonable. The miaB::Tn10dCm insertion mutation of Salmonella typhimurium was transduced to E. coli K-12 cells by using P$\sb1$ and P$\sb{22}$ bacteriophages. The insertion was confirmed by HPLC analyses of nucleotide profiles of miaB mutants of E. coli. The insertion mutation was cloned and DNA sequences adjacent to the transposon were sequenced. These DNA sequences were 86% identical to the f474 gene at 14.97 min chromosome of E. coli. The f474 gene was then cloned by PCR from the wild-type chromosome of E. coli. The recombinant plasmid complemented the mutant phenotype of the miaB mutant of E. coli. These results support the hypothesis that the miaB gene of E. coli exists and is clonable. In summary, functions of the ms${2{\cdot}6}\atop1$A37 modification in E. coli cells are further delineated in this work in perspectives of adaptation to stressful environmental conditions and protein:tRNA interaction. (Abstract shortened by UMI.) ^

Characterization of cellular and molecular functions of the p21 -activated kinase, Shk1, in the fission yeast, Schizosaccharomyces pombe

The p21-activated kinase, Shk1, is an essential serine/threonine kinase required for normal cell polarity, proper mating response, and hyperosmotic stress response, in the fission yeast, Schizosaccharomyces pombe. This study has established a novel role for Shk1 as a microtubule regulator in fission yeast and, in addition, characterized a potential biological substrate of Shk1. Cells defective in Shk1 function were found to exhibit malformed interphase and mitotic microtubules, are hypersensitive to the microtubule disrupting drug thiabendazole (TBZ), and are cold sensitive for growth. Microtubule disruption by TBZ results in a significant reduction of Shk1 kinase activity, which is restored after cells are released from the drug, thus providing a correlation between Shk1 kinase activity and active microtubule polymerization. Consistent with a role for Shk1 as a microtubule regulator, GFP-Shk1 fusion proteins localize to interphase microtubules and mitotic microtubule spindles. Furthermore, loss of Tea1, a presumptive microtubule regulator in fission yeast, exacerbates the growth and microtubule defects of cells deficient in Shk1 function, and results in illicit Shk1 localization. Moreover, loss of the Cdc2 inhibitory kinase Wee1, which has been implicated as a mediator of the Shk1 pathway, leads to significant microtubule defects. Intriguingly, Wee1 protein levels are markedly reduced both by partial loss of Shk1 function and by treatment with TBZ. These results suggest that Shk1 is required for proper regulation of microtubule dynamics in fission yeast and may interact with Tea1 and Wee1 in this regulatory process. ^ To further understand Shk1 function in fission yeast, a yeast two-hybrid screen for proteins that interact with the Shk1 catalytic domain was performed. This screen led to the identification of a novel protein, Skb10 (for S&barbelow;hk1 k&barbelow;inase b&barbelow;inding protein 10). Coprecipitation experiments demonstrated that Skb10 associates with Shk1 in S. pombe cells. (Abstract shortened by UMI.) ^

Determination of sulfite and manganese in sediments from the K/T boundary

The solid-state-physics technique of electron spin resonance (ESR) has been employed in an exploratory study of marine limestones and impact-related deposits from Cretaceous-Tertiary (KT) boundary sites including Spain (Sopelana and Caravaca), New Jersey (Bass River), the U.S. Atlantic continental margin (Blake Nose, ODP Leg 171B/1049/A), and several locations in Belize and southern Mexico within -600 km of the Chicxulub crater. The ESR spectra of SO3(1-) (a radiation-induced point defect involving a sulfite ion substitutional for CO3(2-) which has trapped a positive charge) and Mn(2+) in calcite were singled out for analysis because they are unambiguously interpretable and relatively easy to record. ESR signal strengths of calcite-related SO3(1-) and Mn(2+) have been studied as functions of stratigraphic position in whole-rock samples across the KT boundary at Sopelana, Caravaca, and Blake Nose. At all three of these sites, anomalies in SO3(1-) and/or Mn(2+) intensities are noted at the KT boundary relative to the corresponding background levels in the rocks above and below. At Caravaca, the SO3(1-) background itself is found to be lower by a factor of 2.7 in the first 30,000 years of the Tertiary relative to its steady-state value in the last 15,000 years of the Cretaceous, indicating either an abrupt and quasi-permanent change in ocean chemistry (or temperature) or extinction of the marine biota primarily responsible for fixing sulfite in the late Cretaceous limestones. An exponential decrease in the Mn(2+) concentration per unit mass calcite, [Mn(2+)], as the KT boundary at Caravaca is approached from below (1/e characteristic length =1.4 cm) is interpreted as a result of post-impact leaching of the seafloor. Absolute ESR quantitative analyses of proximal impact deposits from Belize and southern Mexico group naturally into three distinct fields in a twodimensional [SO3(1-)]-versus-[Mn(2+)] scatter plot. These fields contain (I) limestone ejecta clasts, (II) accretionary lapilli, and (III) a variety of SO3(1-) -depleted/Mn(2+) enriched impact deposits. Data for the investigated non-impact-related Cretaceous and Tertiary marine limestones (Spain and Blake Nose) fall outside of these three fields. With reference to thes enon-impact deposits, fields I, II, and III can be respectively characterized as Mn(2+) -depleted, SO3(1-) -enhanced, and SO3(1-) -depleted. It is proposed that (1) field I represents calcites from the Yucatin Platform, and that the Mn(2+) -depleted signature can be used as an indicator of primary Chicxulub ejecta in deep marine environments and (2) field II represents calcites that include a component formed in the vapor plume, either from condensation in the presence of CO2/SO3(1-) -rich vapors, or reactions between CaO and CO2/SO3 rich vapors, and that this SO3(1-) -enhanced signature can be used as an indicator of impact vapor plume deposits. Given these two propositions, the ESR data for the Blake Nose deposits are ascribed to the presence of basal coarse calcitic Chicxulub ejecta clasts, while the finer components that are increasingly represented toward the top are interpreted to contain high- SO3(1-) calcite from the vapor plume. The apparently-undisturbed Bass River deposit may contain even higher concentrations of vapor-plume calcite. None of the three components included in field III appear to be represented at distal, deep marine KT-boundary sites; this field may include several types of impact-related deposits of diverse origins and diagenetic histories.

Tissue metal concentrations and metal transfer functions of Glaucous Gulls (Larus hyperboreus) from Bjørnøya and Jan Mayen

Heavy metals (Cd, Cu, Fe, Mn and Zn) concentrations were determined in different tissues (muscle, kidney, liver, brain, gonads, heart and feathers) of Glaucous Gulls (Larus hyperboreus) from Bjornoya and Jan Mayen. The age and spatial dependent variations in heavy metals were quantified and interpreted in view of the three chemometric techniques, i.e. non-parametric Mann-Whitney U test, redundancy gradient analysis and detrended correspondence analysis. The Glaucous Gulls from Bjornoya contained significantly higher (p < 0.05) levels of Cd, Cu and Zn than those inhabited Jan Mayen. Adult birds were characterized by greater (p < 0.01) concentration of muscle, hepatic and renal heavy metals in comparison to chicks. Insignificantly higher slope constant Zn/Cd for the liver than for the kidney may reflect insignificant Cd exposure. Estimate of transfer factor (TF) allows us to assess variations in heavy metal concentrations during the individual development of Glaucous Gulls. It may be stated that there is a distinct increase of bioaccumulation of all the studied metals during subsequent stages of the bird life.

Transporte electrogénico en el colon de ratas privadas de sodio : bloqueo de canales epiteliales versus inhibición de la NA, K-ATPASA

La privación dietaria de sodio estimula la secreción de aldosterona. En el colon de rata, la aldosterona elevada aumenta la absorción de Na+, pero además torna electrogénico el mecanismo de absorción (normalmente electroneutro). Dicho transporte electrogénico puede suprimirse mediante el bloqueo de los canales epiteliales de Na+ en la membrana apical o la inhibición de la Na, KATPasa de la membrana basolateral. La absorción electrogénica de sodio está estrechamente acoplada al metabolismo aerobio, pero se desconoce si el bloqueo de los canales de Na+ reduce el consumo de oxígeno en igual medida que la inhibición de la Na, K-ATPasa. Se obtuvieron preparados de mucosa aislada del colon distal de ratas alimentadas con una dieta hiposódica por 10 días. Se determinó simultáneamente la corriente de cortocircuito y el consumo de oxígeno en condición basal y luego del bloqueo de canales de Na+ con amilorida (n=12) o de la Na, K-ATPasa con uabaína (n=12). Ambos tratamientos redujeron la corriente de cortocircuito en igual medida (>80%), pero la reducción en el consumo de oxígeno fue mayor con uabaína que con amilorida (p<0.03). Esto se debe probablemente a que la Na, KATPasa cumple otras funciones, además del transporte transepitelial de Na+, que son suprimidas por la uabaína pero no por la amilorida.

40Ar/39Ar single-crystal dating of detrital muscovite and K-feldspar of ODP Holes 116-717A and 116-718C

Detrital K-feldspars and muscovites from Ocean Drilling Program Leg 116 cores that have depositional ages from 0 to 18 Ma have been dated by the 40Ar/39Ar technique. Four to thirteen individual K-feldspars have been dated from seven stratigraphic levels, each of which have a very large range, up to 1660 Ma. At each level investigated, at least one K-feldspar yielded an age minimum which is, within uncertainty, identical to the age of deposition. One to twelve single muscovite crystals from each of six levels have also been studied. The range of muscovite ages is less than that of the K-feldspars and, with one exception, reveal only a 20-Ma spread in ages. As with the K-feldspars, each level investigated contains muscovites with mineral ages essentially identical to depositional ages. These results indicate that a significant portion of the material in the Bengal Fan is first-cycle detritus derived from the Himalayas. Therefore, the significant proportion of sediment deposited in the distal fan in the early to mid Miocene can be ascribed to a significant pulse of uplift and erosion in the collision zone. Moreover, these data indicate that during the entire Neogene, some portion of the Himalayan orogen was experiencing rapid erosion (<= uplift). The lack of granulite facies rocks in the eastern Himalayas and Tibetan Plateau suggests that very rapid uplift must have been distributed in brief pulses in different places in the mountain belt. We suggest that the great majority of the crystals with young apparent ages have been derived from the southern slope of the Himalayas, predominantly from near the main central thrust zone. These data provide further evidence against tectonic models in which the Himalayas and Tibetan plateaus are uplifted either uniformly during the past 40 m.y. or mostly within the last 2 to 5 m.y.