The stochastic exit problem for dynamical systems

The problem of "exit against a flow" for dynamical systems subject to small Gaussian white noise excitation is studied. Here the word "flow" refers to the behavior in phase space of the unperturbed system's state variables. "Exit against a flow" occurs if a perturbation causes the phase point to leave a phase space region within which it would normally be confined. In particular, there are two components of the problem of exit against a flow:

i) the mean exit time

ii) the phase-space distribution of exit locations.

When the noise perturbing the dynamical systems is small, the solution of each component of the problem of exit against a flow is, in general, the solution of a singularly perturbed, degenerate elliptic-parabolic boundary value problem.

Singular perturbation techniques are used to express the asymptotic solution in terms of an unknown parameter. The unknown parameter is determined using the solution of the adjoint boundary value problem.

The problem of exit against a flow for several dynamical systems of physical interest is considered, and the mean exit times and distributions of exit positions are calculated. The systems are then simulated numerically, using Monte Carlo techniques, in order to determine the validity of the asymptotic solutions.

Some problems of edge waves and standing waves on beaches

Some problems of edge waves and standing waves on beaches are examined.

The nonlinear interaction of a wave normally incident on a sloping beach with a subharmonic edge wave is studied. A two-timing expansion is used in the full nonlinear theory to obtain the modulation equations which describe the evolution of the waves. It is shown how large amplitude edge waves are produced; and the results of the theory are compared with some recent laboratory experiments.

Traveling edge waves are considered in two situations. First, the full linear theory is examined to find the finite depth effect on the edge waves produced by a moving pressure disturbance. In the second situation, a Stokes' expansion is used to discuss the nonlinear effects in shallow water edge waves traveling over a bottom of arbitrary shape. The results are compared with the ones of the full theory for a uniformly sloping bottom.

The finite amplitude effects for waves incident on a sloping beach, with perfect reflection, are considered. A Stokes' expansion is used in the full nonlinear theory to find the corrections to the dispersion relation for the cases of normal and oblique incidence.

Finally, an abstract formulation of the linear water waves problem is given in terms of a self adjoint but nonlocal operator. The appropriate spectral representations are developed for two particular cases.

Topics in bifurcation theory

I. Existence and Structure of Bifurcation Branches

The problem of bifurcation is formulated as an operator equation in a Banach space, depending on relevant control parameters, say of the form G(u,λ) = 0. If dimN(G_u(u_O,λ_O)) = m the method of Lyapunov-Schmidt reduces the problem to the solution of m algebraic equations. The possible structure of these equations and the various types of solution behaviour are discussed. The equations are normally derived under the assumption that G^O_λεR(G^O_u). It is shown, however, that if G^O_λεR(G^O_u) then bifurcation still may occur and the local structure of such branches is determined. A new and compact proof of the existence of multiple bifurcation is derived. The linearized stability near simple bifurcation and "normal" limit points is then indicated.

II. Constructive Techniques for the Generation of Solution Branches

A method is described in which the dependence of the solution arc on a naturally occurring parameter is replaced by the dependence on a form of pseudo-arclength. This results in continuation procedures through regular and "normal" limit points. In the neighborhood of bifurcation points, however, the associated linear operator is nearly singular causing difficulty in the convergence of continuation methods. A study of the approach to singularity of this operator yields convergence proofs for an iterative method for determining the solution arc in the neighborhood of a simple bifurcation point. As a result of these considerations, a new constructive proof of bifurcation is determined.

Detailed properties of high redshift galaxies

Galaxies evolve throughout the history of the universe from the first star-forming sources, through gas-rich asymmetric structures with rapid star formation rates, to the massive symmetrical stellar systems observed at the present day. Determining the physical processes which drive galaxy formation and evolution is one of the most important questions in observational astrophysics. This thesis presents four projects aimed at improving our understanding of galaxy evolution from detailed measurements of star forming galaxies at high redshift.

We use resolved spectroscopy of gravitationally lensed z ≃ 2 - 3 star forming galaxies to measure their kinematic and star formation properties. The combination of lensing with adaptive optics yields physical resolution of ≃ 100 pc, sufficient to resolve giant Hii regions. We find that ~ 70 % of galaxies in our sample display ordered rotation with high local velocity dispersion indicating turbulent thick disks. The rotating galaxies are gravitationally unstable and are expected to fragment into giant clumps. The size and dynamical mass of giant Hii regions are in agreement with predictions for such clumps indicating that gravitational instability drives the rapid star formation. The remainder of our sample is comprised of ongoing major mergers. Merging galaxies display similar star formation rate, morphology, and local velocity dispersion as isolated sources, but their velocity fields are more chaotic with no coherent rotation.

We measure resolved metallicity in four lensed galaxies at z = 2.0 − 2.4 from optical emission line diagnostics. Three rotating galaxies display radial gradients with higher metallicity at smaller radii, while the fourth is undergoing a merger and has an inverted gradient with lower metallicity at the center. Strong gradients in the rotating galaxies indicate that they are growing inside-out with star formation fueled by accretion of metal-poor gas at large radii. By comparing measured gradients with an appropriate comparison sample at z = 0, we demonstrate that metallicity gradients in isolated galaxies must flatten at later times. The amount of size growth inferred by the gradients is in rough agreement with direct measurements of massive galaxies. We develop a chemical evolution model to interpret these data and conclude that metallicity gradients are established by a gradient in the outflow mass loading factor, combined with radial inflow of metal-enriched gas.

We present the first rest-frame optical spectroscopic survey of a large sample of low-luminosity galaxies at high redshift (L < L*, 1.5 < z < 3.5). This population dominates the star formation density of the universe at high redshifts, yet such galaxies are normally too faint to be studied spectroscopically. We take advantage of strong gravitational lensing magnification to compile observations for a sample of 29 galaxies using modest integration times with the Keck and Palomar telescopes. Balmer emission lines confirm that the sample has a median SFR ∼ 10 M_sun yr^−1 and extends to lower SFR than has been probed by other surveys at similar redshift. We derive the metallicity, dust extinction, SFR, ionization parameter, and dynamical mass from the spectroscopic data, providing the first accurate characterization of the star-forming environment in low-luminosity galaxies at high redshift. For the first time, we directly test the proposal that the relation between galaxy stellar mass, star formation rate, and gas phase metallicity does not evolve. We find lower gas phase metallicity in the high redshift galaxies than in local sources with equivalent stellar mass and star formation rate, arguing against a time-invariant relation. While our result is preliminary and may be biased by measurement errors, this represents an important first measurement that will be further constrained by ongoing analysis of the full data set and by future observations.

We present a study of composite rest-frame ultraviolet spectra of Lyman break galaxies at z = 4 and discuss implications for the distribution of neutral outflowing gas in the circumgalactic medium. In general we find similar spectroscopic trends to those found at z = 3 by earlier surveys. In particular, absorption lines which trace neutral gas are weaker in less evolved galaxies with lower stellar masses, smaller radii, lower luminosity, less dust, and stronger Lyα emission. Typical galaxies are thus expected to have stronger Lyα emission and weaker low-ionization absorption at earlier times, and we indeed find somewhat weaker low-ionization absorption at higher redshifts. In conjunction with earlier results, we argue that the reduced low-ionization absorption is likely caused by lower covering fraction and/or velocity range of outflowing neutral gas at earlier epochs. This result has important implications for the hypothesis that early galaxies were responsible for cosmic reionization. We additionally show that fine structure emission lines are sensitive to the spatial extent of neutral gas, and demonstrate that neutral gas is concentrated at smaller galactocentric radii in higher redshift galaxies.

The results of this thesis present a coherent picture of galaxy evolution at high redshifts 2 ≲ z ≲ 4. Roughly 1/3 of massive star forming galaxies at this period are undergoing major mergers, while the rest are growing inside-out with star formation occurring in gravitationally unstable thick disks. Star formation, stellar mass, and metallicity are limited by outflows which create a circumgalactic medium of metal-enriched material. We conclude by describing some remaining open questions and prospects for improving our understanding of galaxy evolution with future observations of gravitationally lensed galaxies.

Aluminium in Fisch und Fischereierzeugnissen

Recent reports associating aluminium with several skeletal (osteomalacia) and neurological disorders (encephalopathy and Alzheimer’s disease) in humans suggest that exposure to aluminium may pose a hazard to health. This requires the examination of aluminiumcontent in different foodstuffs. Therefore, an analytical method for the determination of aluminium in fish and fishery products, especially in fishery products packaged in aluminium cans, was developed using graphite furnace atomic absorption spectrometry. Fillets of lean and fatty fish showed aluminium levels lower than 1mg/kg wet weight, muscle of crustacean, molluscan and shellfish had apparently higher aluminium levels (up to 20 mg/kg wet weight). The aluminium content in some aluminum-canned herring was much higher than the content found in herring caught in the North Sea. These results indicate that aluminium is taken up by the herring fillets in aluminium cans, presumably through the slight and slow dissolution of aluminium from the can wall, due to some defects in the protective lacquer layer. A comparison of the aluminium levels measured in canned herring with the average aluminium-intake (normally between 3 and 5 mg/day) or with the provisional tolerable daily intake of 1mg/kg body weight per day (WHO 1989) indicated, that the aluminium content of the edible part of aquatic food does not play a significant role. High consumption of fish fillets does not pose any health risk.

Some ecological roles of Hippopotamus (Hippopotamus amphibious Linn. 1758) in fish production: possibilities for integrated fish-cum Agric production system

The common hippopotamus (Hippopotamus amphibious Linn. 1758) contributes to the productivity of aquatic systems where it lives. This paper reviews ecological roles of the hippo in this regard. Desk review of available literature information complemented with field observations were employed in the data collection. The ecological roles of the common hippopotamus being presented draw examples from East, West, Central and South African sub regions. The nutritional importance of the amphibious hippopotamus to rural communities was highlighted. In Southern Ethiopia, the Bodi, Bacha and Mura tribes eat hippo meat and this has led to severe hunting consequences on the wild populations of the animal. The important relationships between the hippopotamus and fish were presented. Hippopotamuses usually defecate in water and their excrements enrich the nutrients in the water resulting in favourable conditions for large fish populations. Some fish, including Labeo spp. were observed to feed on the micro-organisms and algae that grow on the skin of the hippotamus. A strong case was made for hippo-cum-fish integrated farm development in Nigeria based on ecological relationships so observed between the amphibious mammals and fish. This is one of the meeting points of fisheries and wildlife management that should be exploited for the benefits of the teeming Nigerian population

The LIN-3 gene of the nematode C. elegans is the vulval-inducing signal

The development of the vulva of the nematode Caenorhabditis elegans is induced by a signal from the anchor cell of the somatic gonad. Activity of the gene lin-3 is required for the Vulval Precursor Cells (VPCs) to assume vulval fates. It is shown here that lin-3 encodes the vulval-inducing signal.

lin-3 was molecularly cloned by transposon-tagging and shown to encode a nematode member ofthe Epidermal Growth Factor (EGF) family. Genetic epistasis experiments indicate that lin-3 acts upstream of let-23, which encodes a homologue of the EGF-Receptor.

lin-3 transgenes that contain multiple copies of wild-type lin-3 genomic DNA clones confer a dominant multivulva phenotype in which up to all six of the VPCs assume vulval fates. The properties of these trans genes suggest that lin-3 can act in the anchor cell to induce vulval fates. Ablation of the gonadal precursors, which prevents the development of the AC, strongly reduces the ability of lin-3 transgenes to stimulate vulval development. A lin-3 recorder transgene that retains the ability to stimulate vulval development is expressed specifically in the anchor cell at the time of vulval induction.

Expression of an obligate secreted form of the EGF domain of Lin-S from a heterologous promoter is sufficient to induce vulval fates in the absence of the normal source of the inductive signal. This result suggests that Lin-S may act as a secreted factor, and that Lin-S may be the sole vulval-inducing signal made by the anchor cell.

lin-3 transgenes can cause adjacent VPCs to assume the 1° vulval fate and thus can override the action of the lateral signal mediated by lin-12 that normally prevents adjacent 1° fates. This indicates that the production of Lin-3 by the anchor cell must be limited to allow the VPCs to assume the proper pattern of fates of so 3° 3° 2° 1° 2° 3°.

Molecular genetics of the Drosophila eyes absent gene

The Drosophila compound eye has provided a genetic approach to understanding the specification of cell fates during differentiation. The eye is made up of some 750 repeated units or ommatidia, arranged in a lattice. The cellular composition of each ommatidium is identical. The arrangement of the lattice and the specification of cell fates in each ommatidium are thought to occur in development through cellular interactions with the local environment. Many mutations have been studied that disrupt the proper patterning and cell fating in the eye. The eyes absent (eya) mutation, the subject of this thesis, was chosen because of its eyeless phenotype. In eya mutants, eye progenitor cells undergo programmed cell death before the onset of patterning has occurred. The molecular genetic analysis of the gene is presented.

The eye arises from the larval eye-antennal imaginal disc. During the third larval instar, a wave of differentiation progresses across the disc, marked by a furrow. Anterior to the furrow, proliferating cells are found in apparent disarray. Posterior to the furrow, clusters of differentiating cells can be discerned, that correspond to the ommatidia of the adult eye. Analysis of an allelic series of eya mutants in comparison to wild type revealed the presence of a selection point: a wave of programmed cell death that normally precedes the furrow. In eya mutants, an excessive number of eye progenitor cells die at this selection point, suggesting the eya gene influences the distribution of cells between fates of death and differentiation.

In addition to its role in the eye, the eya gene has an embryonic function. The eye function is autonomous to the eye progenitor cells. Molecular maps of the eye and embryonic phenotypes are different. Therefore, the function of eya in the eye can be treated independently of the embryonic function. Cloning of the gene reveals two cDNA's that are identical except for the use of an alternatively-spliced 5' exon. The predicted protein products differ only at the N-termini. Sequence analysis shows these two proteins to be the first of their kind to be isolated. Trangenic studies using the two cDNA's show that either gene product is able to rescue the eye phenotype of eya mutants.

The eya gene exhibits interallelic complementation. This interaction is an example of an "allelic position effect": an interaction that depends on the relative position in the genome of the two alleles, which is thought to be mediated by chromosomal pairing. The interaction at eya is essentially identical to a phenomenon known as transvection, which is an allelic position effect that is sensitive to certain kinds of chromosomal rearrangements. A current model for the mechanism of transvection is the trans action of gene regulatory regions. The eya locus is particularly well suited for the study of transvection because the mutant phenotypes can be quantified by scoring the size of the eye.

The molecular genetic analysis of eya provides a system for uncovering mechanisms underlying differentiation, developmentally regulated programmed cell death, and gene regulation.

Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion

The nonlinear dynamics of 1.6-mu m fs laser pulses propagating in fused silica is investigated by employing a full-order dispersion model. Different from the x-wave generation in normally dispersive media, a few-cycle spatiotemporally compressed soliton wave is generated with the contrary contributions of anomalous group velocity dispersion (GVD) and self-phase-modulation. However, at the tailing edge of the pulse forms a shock wave which generates separate and strong supercontinuum peaked at 670 nm. It is also the origin of conical emission formed both in time and frequency domain with the contribution of normal GVD at visible light.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

飞秒激光脉冲在正色散固体材料中的自压缩

实验研究了正色散固体介质中的激光脉冲自压缩现象，证明了无需任何外加色散补偿情况下，固体透明介质中的自聚焦传输过程可使高功率飞秒激光脉冲实现时域脉冲压缩，并详细研究了输出脉冲的时域和频域特性随入射脉冲强度的演化规律．实验结果表明脉冲自压缩量随入射脉冲强度的增加呈递增趋势，然而当入射光强增大到足以引起超连续谱及锥形辐射产生时，脉冲时域形状会发生分裂．此外还发现发散光束入射情况下同样可以观察到脉冲自压缩现象．

[R_Logroño_Muralla] Documentación geométrica del Cubo del Revellín (Logroño, La Rioja)

[ES] Documentación del exterior y del interior del cubo de la muralla de Logroño. Esta torre tiene una forma aproximadamente cilíndrica de 10 metros de radio. Al interior se compone de dos niveles, el superior (antiguo teatro) que forma una estancia circular con un pilar en el centro y el inferior que consiste en una estancia abovedada. Además se ha documentado una galería de acceso.

负啁啾高强度飞秒脉冲在正常色散材料中传输特性研究

利用块状正常色散材料作非线性介质，实验研究了负啁啾强激光飞秒脉冲在正常色散材料的传输过程中，脉冲波形及频谱随入射脉冲能量的变化特性．实验发现，负啁啾脉冲经过材料后激光光谱在被整形和压缩的同时，脉冲宽度也被压缩．实验获得的压缩脉冲宽度短于相等光谱宽度下的双曲正割转换极限脉冲宽度。数值模拟结果显示，在实验条件下模拟结果具有同样的变化特性．

圆偏振光和线偏振光在正常色散材料中的时空自压缩

实验研究了圆偏振和线偏振高强度飞秒激光脉冲在正常色散材料中传输时的时空自压缩现象。实验中利用BK7玻璃作为正色散材料，比较研究了不同偏振入射情况下脉冲波形及频谱的变化规律。圆偏振光入射时，可以获得更短脉冲宽度的压缩脉冲和更窄的光谱宽度。在圆偏振光入射条件下，50fs入射脉冲成功地自压缩到了19fs，获得了大于2．5倍的压缩倍率。所以利用圆偏振光可以获得更短压缩脉冲，更大能量，更好光束质量的激光。

Learning and management skills: the internationalization of Grupo Arcor. Analysis from a process-based approach

This paper analyzes the path of the international expansion of Grupo Arcor, an Argentine multinational company specializing in confectionery. The objective is to entify corporate strategies and business learning that led this Latin American firm to establish itself as one of the leading manufacturers in confectionery industry ,particularly in the 21st Century. The analysis is primarily qualitative in order to identify the economic dimension as a determinant in the internationalization process; a processbased approach from the Uppsala Model is used for this. However, the study is also complemented with a regression analysis to test if the firm was driven to expand internationally by the expectations on the degree of globalization of the industry and the accumulation of experience in foreign markets, and if the company was influenced by psychic distance in choosing the location of its investment; given the influence of these variables in Grupo Arcor business strategies. Our findings suggest that Grupo Arcor, was able to become global due to strategies such as vertical integration, diversification of products and geographical markets (based on psychic distance) and indeed some strategies were consequence of the globalization of the sector and the accumulation of experience in foreign markets.