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.

Producción y gestión de la industria lítica de Atxoste (Álava): Una aproximación a las sociedades Epipaleolíticas y Mesolíticas del alto Ebro

1000 p. (Anexos: 929-965 p.; bibliografía 965-1000 p.). Capítulos de discusión y conclusiones en castellano y francés.

Electron energy-loss spectroscopy study of polyatomic molecular systems under pyrolytic conditions

The technique of variable-angle, electron energy-loss spectroscopy has been used to study the electronic spectroscopy of the diketene molecule. The experiment was performed using incident electron beam energies of 25 eV and 50 eV, and at scattering angles between 10° and 90°. The energy-loss region from 2 eV to 11 eV was examined. One spin-forbidden transition has been observed at 4.36 eV and three others that are spin-allowed have been located at 5.89 eV, 6.88 eV and 7.84 eV. Based on the intensity variation of these transitions with impact energy and scattering angle, and through analogy with simpler molecules, the first three transitions are tentatively assigned to an n → π* transition, a π - σ* (3s) Rydberg transition and a π → π* transition.

Thermal decomposition of chlorodifluoromethane, chloroform, dichloromethane and chloromethane under flash-vacuum pyrolysis conditions (900-1100°C) was investigated by the technique of electron energy-loss spectroscopy, using the impact energy of 50 eV and a scattering angle of 10°. The pyrolytic reaction follows a hydrogen-chloride α-elimination pathway. The difluoromethylene radical was produced from chlorodifluoromethane pyrolysis at 900°C and identified by its X^1 A_1 → A^1B_1 band at 5.04 eV.

Finally, a number of exploratory studies have been performed. The thermal decomposition of diketene was studied under flash vacuum pressures (1-10 mTorr) and temperatures ranging from 500°C to 1000°C. The complete decomposition of the diketene molecule into two ketene molecules was achieved at 900°C. The pyrolysis of trifluoromethyl iodide molecule at 1000°C produced an electron energy-loss spectrum with several iodine-atom, sharp peaks and only a small shoulder at 8.37 eV as a possible trifluoromethyl radical feature. The electron energy-loss spectrum of trichlorobromomethane at 900°C mainly showed features from bromine atom, chlorine molecule and tetrachloroethylene. Hexachloroacetone decomposed partially at 900°C, but showed well-defined features from chlorine, carbon monoxide and tetrachloroethylene molecules. Bromodichloromethane molecule was investigated at 1000°C and produced a congested, electron energy-loss spectrum with bromine-atom, hydrogen-bromide, hydrogen-chloride and tetrachloroethylene features.

Ground-state energy shifts of H-like Ti under dense and hot plasma conditions

In this study, by adopting the ion sphere model, the self-consistent. field method is used with the Poisson-Boltzmann equation and the Dirac equation to calculate the ground-state energies of H-like Ti at a plasma electron density from 10(22) cm(-3) to 10(24) cm(-3) and the electron temperature from 100 eV to 3600 eV. The ground-state energy shifts of H-like Ti show different trends with the electron density and the electron temperature. It is shown that the energy shifts increase with the increase in the electron density and decrease with the increase in the electron temperature. The energy shifts are sensitive to the electron density, but only sensitive to the low electron temperature. In addition, an accurately fitting formula is obtained to fast estimate the ground-state energies of H-like Ti. Such fitted formula can also be used to estimate the critical electron density of pressure ionization for the ground state of H-like Ti.

I. Foehn winds of southern California. II. Foehn wind cyclo-genesis. III. Weather conditions associated with the Akron disaster. IV. The Los Angeles storm of December 30, 1933 to January 1, 1934

I. Foehn winds of southern California.
An investigation of the hot, dry and dust laden winds occurring in the late fall and early winter in the Los Angeles Basin and attributed in the past to the influences of the desert regions to the north revealed that these currents were of a foehn nature. Their properties were found to be entirely due to dynamical heating produced in the descent from the high level areas in the interior to the lower Los Angeles Basin. Any dust associated with the phenomenon was found to be acquired from the Los Angeles area rather than transported from the desert. It was found that the frequency of occurrence of a mild type foehn of this nature during this season was sufficient to warrant its classification as a winter monsoon. This results from the topography of the Los Angeles region which allows an easy entrance to the air from the interior by virtue of the low level mountain passes north of the area. This monsoon provides the mild winter climate of southern California since temperatures associated with the foehn currents are far higher than those experienced when maritime air from the adjacent Pacific Ocean occupies the region.

II. Foehn wind cyclo-genesis.
Intense anticyclones frequently build up over the high level regions of the Great Basin and Columbia Plateau which lie between the Sierra Nevada and Cascade Mountains to the west and the Rocky Mountains to the east. The outflow from these anticyclones produce extensive foehns east of the Rockies in the comparatively low level areas of the middle west and the Canadian provinces of Alberta and Saskatchewan. Normally at this season of the year very cold polar continental air masses are present over this territory and with the occurrence of these foehns marked discontinuity surfaces arise between the warm foehn current, which is obliged to slide over a colder mass, and the Pc air to the east. Cyclones are easily produced from this phenomenon and take the form of unstable waves which propagate along the discontinuity surface between the two dissimilar masses. A continual series of such cyclones was found to occur as long as the Great Basin anticyclone is maintained with undiminished intensity.

III. Weather conditions associated with the Akron disaster.
This situation illustrates the speedy development and propagation of young disturbances in the eastern United States during the spring of the year under the influence of the conditionally unstable tropical maritime air masses which characterise the region. It also furnishes an excellent example of the superiority of air mass and frontal methods of weather prediction for aircraft operation over the older methods based upon pressure distribution.

IV. The Los Angeles storm of December 30, 1933 to January 1, 1934.
This discussion points out some of the fundamental interactions occurring between air masses of the North Pacific Ocean in connection with Pacific Coast storms and the value of topographic and aerological considerations in predicting them. Estimates of rainfall intensity and duration from analyses of this type may be made and would prove very valuable in the Los Angeles area in connection with flood control problems.

A simple approach for the estimation of food consumption from growth rates at different environmental conditions and its application to juvenile cod (Gadus morhua L.) of a fjordic sea loch on the west coast of Scotland

Abstract Growth and condition of fish are functions of available food and environmental conditions. This led to the idea of using fish as a “consumption sensor” for the measurement of food intake over a defined period of time. A bio-physical model for the estimation of food consumption was developed based on the von Bertalanffy model. Whereas some of the input variables of the model, the initial and final lengths and masses of a fish and the temperature within the time period considered can easily be measured, internal characteristics of the species have to be determined indirectly. Three internal parameters are used in the model: the maintenance consumption at 0°C, the temperature dependence of this consumption and the food efficiency, the percentage of the ingested food utilized. Estimates of the parameters for a given species can be determined by feeding experiments. Here, data from published feeding experiments on juvenile cod, Gadus morhua L., were used to validate the model. The average of the relative error for the food intake predicted by the model for individual fish was about 24 %, indicating that fish used the food with different efficiencies. However, grouping the fish according to size classes and temperature lowered the relative error of the predicted food intake for the group to typically 5 %. For a group containing all fish of the feeding experiment the relative prediction error was about 2 %. Zusammenfassung Wachstum und Kondition der Fische sind von der verfügbaren Nahrung und von Umweltbedingungen abhängig. Dies führte zur Idee, Fisch als „Konsum-Sensor“ für die Messung der Nahrungsaufnahme über einen definierten Zeitraum zu verwenden. Auf Grundlage des von Bertalanffy-Modells wurde ein bio-physikalisches Modell zur Schätzung der Futteraufnahme entwickelt. Während einige der Eingangsgrößen des Modells leicht gemessen werden können (Anfangs- und Endlänge und -körpermasse der Fische und die Temperatur innerhalb des betrachteten Zeitraum), können interne Parameter der betrachteten Art nur indirekt bestimmt werden. Drei interne Parameter werden in dem Modell verwendet: Die Erhaltungskonsumtion bei 0° C, die Temperaturabhängigkeit dieser Rate und der Wirkungsgrad der Nahrung (der Anteil der Nahrung ,der aufgenommen und verwendet und nicht ungenutzt wieder ausgeschieden wird). Die Modellparameter für eine bestimmte Art können durch Fütterungsversuche bestimmt werden. Um das Modell zu validieren wurden Daten aus veröffentlichten Fütterungsversuchen mit juvenilen Kabeljau (Gadus morhua L.) verwendet. Modell und Wirklichkeit weichen in der Regel voneinander ab. Der durchschnittliche relative Fehler der durch das Modell vorhergesagten Nahrungsaufnahme betrug für Einzelfische etwa 24%, was darauf hinweist, dass einzelne Fisch die Nahrung mit unterschiedlichen Wirkungsgraden verwerten. Allerdings senkte die Gruppierung der Fische nach Größenklassen und Temperatur den relativen Vorhersagefehler für die Nahrungsaufnahme der Gruppe auf etwa 5%. Für alle Fische im Fütterungsversuch ist der relative Vorhersagefehler etwa 2%.

Worsening water quality conditions at Inner Puno Bay, Lake Titicaca, Peru, and their effect on Lemna spp. biomass

Although there have been a number of studies on aquatic conditions and the flora and fauna of Lake Titicaca over many decades, most of this work has been centred on the offshore regions of the main lake. Water quality there has been degrading and abundant growth of Lemna spp. has been developing. Lemna spp., commonly called floating duck-weed or ‘lenteja de agua’ in Puno, occurs perennially in most parts of the inner Puno Bay shore-line. In this article, the authors compare water quality changes over recent decades in shore-line regions of Inner Puno Bay and their possible effects on the distribution, abundance and biomass of Lemna spp..

A study of flow conditions near the substratum in an experimental channel [Translation from: Verhandlungen der Internationalen Vereinigung fur Theoretische und Angewandte Limnologie 18, 718-725, 1972]

In a slow flow, on a smooth uniform substratum, a limited bed allows the existence of currents slow enough for benthic invertebrates. These conditions rarely occur naturally. The investigations carried out in this work aimed, on an intermediary scale, to define the influence of irregularities in the substratum on flow near the bottom. The substrata used were made of glass marbles. The investigations were carried out in a transparent channel of 70 cm in length and a rectangular section 10 x 5 cm. The data was analysed to study the general evolution of flow in terms of average speeds and the appearance of the turbulence near the bottom.

Reference-growth rate – a simple and handy parameter summarizing the influence of environmental conditions

Abstract Environmental changes may have an impact on life conditions of the fish, e.g. food supply for the fish. The prevailing environmental conditions apply evenly to all age groups of one stock. Small fish have high growth rates, whereas large fish grow with low rates. But, it can be shown on the basis of the von Bertalanffy-growth model that it is sufficient to know only the growth rate of one single age group to compute the growth rates of all other age groups. The growth rate of a reference fish GRF (e.g. a fish with a body mass of 1 kg) was introduced as a reference growth describing the current food condition of all age groups of the stock. As an example a time series of the reference-growth rate of the northern cod stock (NAFO, 3K) was computed for the time span 1979 to 1999. For the northern cod stock it can be observed that environmental conditions caused growth rates below the long-term mean for seven years in a row. After a prolonged hunger period the fish stock collapsed in 1992 also by the impact of fisheries - and this was probably not a coincidence. Now, with the reference-growth rate GRF a simple and handy parameter was found to summarize the influence of the environmental conditions on growth and other derived models and therefore makes it easier to compute the influence of environmental changes within stock assessment. Zusammenfassung Veränderungen der Umwelt können Auswirkungen auf die Lebensbedingungen der Fische haben, z. B. auf das Nahrungsangebot der Fische. Die vorherrschenden Umgebungsbedingungen wirken gleichmäßig auf alle Altersgruppen eines Bestandes, wobei typischer Weise kleineFische hohe Wachstumsraten haben, während die großen Fische mit niedrigen Raten wachsen. Auf der Grundlage des von Bertalanffy-Wachstumsmodells kann gezeigt werden, dass es ausreicht, nur die Wachstumsrate von einer einzigen Altersgruppe zu kennen, um die Wachstumsraten von allen anderen Altersgruppen berechnen zu können. Die Wachstumsrate eines Referenz-Fisches (z.B. eines Fisches mit einer Körpermasse von 1 kg) wurde als Referenz-Wachstum GRF eingeführt, die den aktuellen Zustand des Nahrungsangebots füralle Altersgruppen des Bestandes beschreibt. Als Beispiel wurde einer Zeitreihe der Referenz-Wachstumsraten des nördlichen Kabeljaubestandes (NAFO, 3K) für die Zeitsraum 1979 bis 1999 berechnet. Für diesen Kabeljaubestand war zu beobachten, dass Umgebungsbedingungen für sieben Jahre in Folge Wachstumsraten unter dem langjährigen Mittelwert verursachten. Nach einer längeren Hungerperiode kollabierte dieser Fischbestand im Jahr 1992 auch durch den Einfluß der Fischerei - und dies war sicher kein Zufall. Jetzt, mit der Referenz-Wachstumsrate GRF, ist ein einfacher und handlicher Parameter gefunden, der es gestattet den Einfluss der Umweltbedingungen auf die Wachstumsbedingungen und andere davon abgeleitete Modelle zusammenzufassen. Dies macht es einfach, den Einfluss von Umweltveränderungen innerhalb der Bestandsabschätzungen zu berechnen.

Concerning the current conditions and transport of sand in the shallow water areas off the coast of the south-eastern North Sea [Translation from: Hamburger Kustenforschung 29 [pages 41-43 only], 1974]

With the aid of the German Research Association in the central programme 'Sand movements in the German coastal region', an investigation into the current conditions in the shallow water areas of the coasts of the south-eastern North Sea between Sylt and the Weser estuary was carried out by the author. Foundations of the work are 19 continuous current recordings in five profiles normal to the coast from years 1971 to 1973. Off the coasts of the south-eastern North Sea varying tidal currents impinge; they are currents whose directions may vary periodically through all points of the compass. They are caused by the circulating tides in the North Sea (Amphidromien). The turning flow movement experiences a deformation in the very shallow coastal waters, and as it happens the flow turning movement in the case of high tide continues right up onto the outer flats, while here and in the fore-lying shallow water areas around the time of low water (on account of the small depths of waters), there prevails a more variable current. A result of this hydrodynamical procedure is the development of counter currents. This partial translation of the original paper provides the summary of this study of of the mudflat areas between the Elbe and Weser.

Feeding of Gammarus lacustris Sars under different conditions of habitation [Translation from: [Trophic relations of freshwater invertebrates.] (ed. G. G. Vinberg) pp.94-98. Leningrad, Zool.Inst.AN SSSR, 1980]

The amphipod Gammarus lacustris, a regular representative of lacustrine communities, often plays a significant role in the transformation of matter and energy. The object of the present work was to clarify the quantitative side of the feeding of the amphipod under different conditions of habitation. Experimental works on determination of the rate of consumption of food and its dependence on body-weight were carried out in the summer periods 1975-1978 on three water-bodies of the Krasnoyarsk region, of different conditions of habitation for the amphipods.

Influence of recording conditions on crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals

The influence of the recording conditions, including the widths of the recording beams, the width ratio of the recording beams, and the recording angles, on the properties of crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals is studied. A theoretical model that combines the band transport model with two-dimensional coupled-wave theory is proposed. The numerical calculations of the space-charge field, the intensity profiles of the diffracted beam, and the diffraction efficiency are presented. (C) 2006 Optical Society of America.