On the Mumford-Tate conjecture for Abelian varieties with reduction conditions

In this thesis we study Galois representations corresponding to abelian varieties with certain reduction conditions. We show that these conditions force the image of the representations to be "big," so that the Mumford-Tate conjecture (:= MT) holds. We also prove that the set of abelian varieties satisfying these conditions is dense in a corresponding moduli space.

The main results of the thesis are the following two theorems.

Theorem A: Let A be an absolutely simple abelian variety, End° (A) = k : imaginary quadratic field, g = dim(A). Assume either dim(A) ≤ 4, or A has bad reduction at some prime ϕ, with the dimension of the toric part of the reduction equal to 2r, and gcd(r,g) = 1, and (r,g) ≠ (15,56) or (m -1, m(m+1)/2). Then MT holds.

Theorem B: Let M be the moduli space of abelian varieties with fixed polarization, level structure and a k-action. It is defined over a number field F. The subset of M(Q) corresponding to absolutely simple abelian varieties with a prescribed stable reduction at a large enough prime ϕ of F is dense in M(C) in the complex topology. In particular, the set of simple abelian varieties having bad reductions with fixed dimension of the toric parts is dense.

Besides this we also established the following results:

(1) MT holds for some other classes of abelian varieties with similar reduction conditions. For example, if A is an abelian variety with End° (A) = Q and the dimension of the toric part of its reduction is prime to dim( A), then MT holds.

(2) MT holds for Ribet-type abelian varieties.

(3) The Hodge and the Tate conjectures are equivalent for abelian 4-folds.

(4) MT holds for abelian 4-folds of type II, III, IV (Theorem 5.0(2)) and some 4-folds of type I.

(5) For some abelian varieties either MT or the Hodge conjecture holds.

On the local Tamagawa number conjecture for Tate motives

There is a wonderful conjecture of Bloch and Kato that generalizes both the analytic Class Number Formula and the Birch and Swinnerton-Dyer conjecture. The conjecture itself was generalized by Fukaya and Kato to an equivariant formulation. In this thesis, I provide a new proof for the equivariant local Tamagawa number conjecture in the case of Tate motives for unramified fields, using Iwasawa theory and (φ,Γ)-modules, and provide some work towards extending the proof to tamely ramified fields.

Comparación de la rugosidad media y máxima obtenida mediante diferentes instrumentos: análisis del filtro y Lc empleados

[ES]Este trabajo pretende analizar la influencia que tiene la longitud de corte elegida y el filtro empleado en la medida de la rugosidad. Se realizan medidas de rugosidad en tres probetas que han sido sometidas a diferentes procesos de fabricación (fresado, rectificado y electroerosión). Además, se utilizan tres instrumentos diferentes para la medición. Tras realizar las medidas, se comparan los resultados y se extraen las conclusiones

LC-MS based methods for phytosterols determination in oenological matrices. Targeted metabolomic study of Rioja grape varieties

221 p.+ anexos

Judd-Ofelt analysis of spectra and experimental evaluation of laser performance of Tm3+ doped Lu2SiO5 crystal

This paper reports that the TM3+:Lu2SiO5 (Tm:LSO) crystal is grown by Czochralski technique. The room-temperature absorption spectra of Tm:LSO crystal are measured on a b-cut sample with 4 at.% thulium. According to the obtained Judd-Ofelt intensity parameters Omega(2)=9.3155 x 10(-20) cm(2), Omega(4)=8.4103 x 10(-20) cm(2), Omega(6)=1.5908 x 10(-20) cm(2), the fluorescence lifetime is calculated to be 2.03 ms for F-3(4) -> H-3(6) transition, and the integrated emission cross section is 5.81 x 10(-18) cm(2). Room-temperature laser action near 2 mu m under diode pumping is experimentally evaluated in Tm:LSO. An optical-optical conversion efficiency of 9.1% and a slope efficiency of 16.2% are obtained with continuous-wave maximum output power of 0.67 W. The emission wavelengths of Tm:LSO laser are centred around 2.06 mu m with spectral bandwidth of similar to 13.6 nm.

Dynamics in dye-doped LC systems in presence of trans-cis isomerism

The excitation as well as relaxation dynamics of dye-doped nematic liquid crystal cells has been explored both experimentally and theoretically. Overshoots in the build up of the probe signal diffracted from gratings written onto dye-doped liquid crystal systems have often been observed. The overshoot behaviour makes the accurate measurement of nonlinear optical (NLO) response magnitude difficult and ambiguous. Moreover, it complicates the understanding of the dynamics and the physics of the NLO processes. On the basis of the system with trans-cis isomerisation as a mechanism of the NLO effect the quantitative model has been built to describe the experimental results which we observe. The two unknown material parameters: diffusion coefficient and cis species lifetime are calculated from the relaxation data. A quantitative model of the signal build-up uses these parameters. The calculated dynamic behaviour based on this model correlates very well with the experimental data. The model is used to predict the performance of the system with various dopant diffusion properties.

B itte r an d Sw e e t /Um am i Ta s te Re c ep to rs w ith D iffe ren tly Evo lu tio n a ry Pa thw ays

通过生物信息学和系统发育学分析,研究了苦味受体和甜味/鲜味受体的进化途径。结果显示,苦味受体 和甜味/鲜味受体在进化上具有远相关,并且具有不同的进化途径,提示这可能是导致这些受体具有不同功能,传 导不同味觉的原因。

Quantitative Determination of Microcystins in Rat Plasma by LC-ESI Tandem MS

A rapid and sensitive method was developed and validated for the determination of MCYST (microcystin)-RR, -LR, and [Dha(7)] MCYST-LR in rat plasma by liquid chromatography-tandem mass spectrometry. The analytes were extracted from rat plasma by protein precipitation, followed by solid-phase extraction. Liquid chromatography with electrospray ionization mass spectrometry, operating in selected reaction monitoring (SRM) mode, was used to quantify MCYST-RR, -LR, and [Dha(7)] MCYST-LR in rat plasma. The recoveries for each analyte in rat plasma ranged from 70.8 to 88.7%. The calibration curve was linear within the range from 0.005 to 1.25 mu g mL(-1). The limit of detection were 1.4, 1.0, 0.6 ng mL(-1) for MCYST-RR, -LR, and [Dha(7)] MCYST-LR. The overall precision was determined on three different days. The values for within- and between-day precision in rat plasma were within 15%. This method was applied to the identification and quantification of microcystins in rat plasma with acute exposure of microcystins via intravenous injection.

Determinations of residual furazolidone and its metabolite, 3-amino-2-oxazolidinone (AOZ), in fish feeds by HPLC-UV and LC-MS/MS, respectively

The antibacterial drug furazolidone belonging to the group of nitrofuran antibacterial agents has been widely used as an antibacterial and antiprotozoal feed additive for poultry, cattle, and farmed fish in China. During application a large proportion of the administered drug may reach the environment directly or via feces. Although the use of furazolidone is prohibited in numerous countries, there are indications of its illegal use. It is known that furazolidone can be rapidly metabolized to 3-amino-2-oxazolidinone (AOZ) in the body of the target organism. In this study, a total of 21 fish feed samples, including 17 commercial fish feeds from local markets in China (representing 15 different formulations) and 4 fish feeds obtained from Germany and Turkey, respectively, are analyzed to determine whether the drug is still illegally used or commercially available feeds are contaminated by this drug. High-performance liquid chromatography (HPLC) and liquid chromatography-electrospray ionization tandem mass spectrometry (LC-ESI-MS/MS) methods have been implemented to determine furazolidone and its metabolite AOZ in fish feeds containing animal protein, respectively. An efficient and convenient cleanup method for the determination of furazolidone in fish feeds is developed, and a simple cleanup method for the determination of AOZ is used. Method recoveries for samples used were determined as 87.7-98.3% for furazolidone at two spike levels of 2.0 and 5.0 ng g(-1) and as 95.6-102.8% for AOZ at spike levels of 0.4 and 0.8 ng g(-1). Limits of detections were 0.4 ng g(-1) for furazolidone and 0.05 ng g(-1) for AOZ. The established methods are therefore suitable for the determination of furazolidone and its metabolite AOZ in fish feeds at trace contamination levels. Using the established methods, all fish feed samples have been proved to be furazolidone negative; however, AOZ is tested in 16 of 17 fish feeds obtained from local markets in the Hubei province of China, with a positive rate as high as 94.1%.