The Libyan Intervention and its Broader Implications

The Texas Orato

On the rank of Leopoldt's and Gross's regulator maps

We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect for an arbitrary extension of number fields. As an application, we prove new cases of Gross's finiteness conjecture (also known as the Gross-Kuz'min conjecture) beyond the classical abelian case, and we show that Gross's $p$-adic regulator has at least half of the conjectured rank. We also describe and compute non-cyclotomic analogues of Gross's defect.Comment: 20 pages, comments welcome

GOP Minority Undermines Rule of Law

The Texas Orato

Fine-Only Offenses in Texas

In Texas, “fine-only” criminal offenses are pervasive, and have placed millions of Texans in jail. Traffic violations are well-known, but even non-drivers face boundless criminalization. This report analyzes primary material, such as case law and training documents. Secondary sources and direct observation, litigation of civil and criminal cases in justice court, provided evidence of de facto practices. Ultimately, these fines and fees constitute discretionary regressive taxes. Lacking representation, those who cannot afford to pay enter a vicious cycle, landing into modern-day debtors' prisons. The Legislature passed tepid reforms in 2017 and 2019, but far more is needed to live up to our promise of a just, fair society.Plan II Honors Progra

The New World Order: An Arab Assessment

What is meant by the New Global Order, and how did the Gulf Crisis constitute a turning point? Let me state at the outset that the United Nations Security Council was energized, and to some extent overused during the Gulf Crisis, because Iraq\u27s invasion of Kuwait constituted a clear violation of the United Nations Charter, and also the Arab League Charter. There might have been mitigating circumstances; there might have been certain provocations; but in the final analysis they did not warrant the invasion and the total occupation of another Arab country. I think this should be stated as clearly as possible in order also to state that the Arab League, in its summit meeting in Cairo in August 1990, was in my opinion, pre-empted from undertaking its own functions in resolving a basically inter-Arab dispute

Immobilized titanium dioxide for emerging contaminant removal in wastewater

There have been rising concerns about emerging contaminants that are not efficiently removed by conventional wastewater treatment plants. TiO2 photocatalysis is one of the promising routes for sustainable wastewater treatment. Research on the use of TiO2 photocatalysis for water/wastewater treatment for the removal of persistent non-biodegradable emerging water pollutant is active worldwide. Since the mid-1970s the viability of photocatalytic degradation of organic compounds in water using TiO2 was demonstrated. More than 1,000 substances have been degraded using TiO2. Despite the extensive research on photocatalytic oxidation using TiO2, pilot and demonstration plants through the last four decades are still countable. Widespread use of photocatalytic treatment of water and wastewater require the development of an innovative photocatalytic reactor that is efficient, reliable, simple to construct, easy to maintain, has low energy consumption, low capital and operating cost and provides easy separation of catalyst after treatment ends. In an attempt to develop this desired photo-reactor, three photo-reactors were designed and constructed: the slurry water-bell photo-reactor, the immobilized water-bell photo-reactor and the immobilized tray photo-reactor. The slurry water-bell photo-reactor is based on generating a thin water film to allow for solar light penetration for photo-catalyst activation and continuous oxygenation. Recirculating the reaction solution at a high flow rate ensures good mixing and avoids dead zones in the photo-reactor. the reactor performance for degradation of phenol, as a model compound, was evaluated using commercial TiO2. Factors affecting the degradation efficiency were studied including catalyst loading, light intensity, initial pollutant concentration, oxidant addition and exposure time. Dissolved oxygen levels, temperature and pH were monitored through all the conducted tests. The performance of the slurry water-bell was compared with other photo-reactors using two benchmarks: the degradation rate constant and the reactor throughput. The reactor throughput is a function of the treated volume, treatment duration and reactor area footprint, thus it is as a versatile indicator for comparison between reactors of different types and geometries as well as selection of reactor configurations suitable for scale-up and commercialization. TiO2 was immobilized on sand grains for use as dispersed photo-catalyst in the water-bell reactor. Immobilization of TiO2 was conducted by two methods; direct immobilization using sol-gel synthesis and binding with epoxy coating. Photo-catalyst abrasion was encountered. The strong mixing conditions and flow through the recirculating pump resulted in high abrasion of the photo-catalyst off the sand surface. The tray photo-reactor was developed to avoid the high friction of the photo-catalyst particles in the recirculating pump while maintain fulfilling all the other photocatalytic process requirements of light penetration, continuous oxygen supply, and turbulent flow. The immobilized tray photocatalytic reactor uses a fixed-bed of TiO2 supported on sand grains. The reactor maintains a thin water film over the supported TiO2 catalytic bed. TiO2 was immobilized on the sand grains using 3 different immobilization approaches: 1) direct immobilization using the sol gel technique, 2) coating with TiO2/cement grout; and (3) binding with TiO2-epoxy coating. Reactor performance for the degradation of phenol as a model compound was evaluated for the three photo-catalysts. Immobilization of TiO2 on sand particles using epoxy was successful in achieving the highest phenol degradation and resistance to abrasion. The water turbidity remained unchanged indicating photo-catalyst resistance to abrasion even after multiple use of the catalytic bed. Successful operation of the tray photo-reactor in the continuous mode was also achieved. The performance of the immobilized tray photo-reactor was compared with other photo-reactors using three benchmarks: the initial degradation rate, the reactor throughput and turbidity. The immobilized tray photo-reactor is suitable for scale-up and commercialization due to five distinctive features which are: modular design; integrated storage; passive oxygenation; absence of need for UV transmitting components that are susceptible to breakage and optical losses, and simple and cheap components

Immersions into manifolds without conjugate points

Many differential geometric concepts such as (isometric) immersion, stability, etc., realized in Euclidean spaces proved to be also realized in manifolds without conjugate points while other concepts are found to be strictly associated with Euclidean spaces. In fact, this thesis may be considered as a trial for finding out to what extent geometric phenomena in Euclidean spaces are still l valid in manifolds without conjugate points. In the introduction, we have quoted the necessary background material for the following chapters. Specially, we have concentrated on the geometry of submanifolds. The interesting problem of rigidity of submanifolds lies in three different categories : finite rigidity, continuous rigidity and infinitesimal rigidity. These three types of rigidity have been studied in hyperbolic spaces in chapter I, sections 1 and 2. K. Nomizu, B. Snmyth (1969) and S. Braidi, C.C. Hsuing (1970) studied some geometric properties of immersed submanifolds in Euclidean sphere essentially the behaviour of the second fundamental form and the Gauss map. In chapter II (sections 1, 2) we have carried out similar study for immersed submanifolds in hyperbolic spaces which shows some deviations from the corresponding one in Euclidean sphere. Since B.Y. Chen's paper (1973) which established the geometric concept of stability of submanifolds in Euclidean spaces, other geometers tried to extend this concept to non-Euclidean spaces. In chapter II (section 3) we share this development through studying stability of surfaces in hyperbolic 3-dimensional space. The most interesting part of our thesis is the last chapter which deals with tight and taut (convex-minimal) immersions in manifolds without conjugate points. Some geometric concepts such as (spherical) two-piece property, h-two-piece property, total (absolute) curvature,... e t c . , have been introduced. Relations between the above concepts have been adopted. We expect for this part to receive more attention in the future to discover more results and to generalize other Euclidean concepts which we did not touch