The transition fundions for the correlated random walk with two absorbing boundaries are derived by means of a combinatorial construction which is based on Krattenthaler's Theorem for counting lattice paths with turns. Results for walks with one boundary and for unrestricted walks are presented as special cases. Finally we give an asymptotic formula, which proves to be useful for computational purposes. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Variable Selection has always been a very important problem in statistics. We often meet situations where a huge data set is given and we want to find out the relationship between the response and the corresponding variables. With a huge number of variables, we often end up with a big model even if we delete those that are insignificant. There are two reasons why we are unsatisfied with a final model with too many variables. The first reason is the prediction accuracy. Though the prediction bias might be small under a big model, the variance is usually very high. The second reason is interpretation. With a large number of variables in the model, it's hard to determine a clear relationship and explain the effects of variables we are interested in. A lot of variable selection methods have been proposed. However, one disadvantage of variable selection is that different sizes of model require different tuning parameters in the analysis, which is hard to choose for non-statisticians. Xin and Zhu advocate variable ranking instead of variable selection. Once variables are ranked properly, we can make the selection by adopting a threshold rule. In this thesis, we try to rank the variables using Least Angle Regression (LARS). Some shrinkage methods like Lasso and LARS can shrink the coefficients to zero. The advantage of this kind of methods is that they can give a solution path which describes the order that variables enter the model. This provides an intuitive way to rank variables based on the path. However, Lasso can sometimes be difficult to apply to variable ranking directly. This is because that in a Lasso solution path, variables might enter the model and then get dropped. This dropping issue makes it hard to rank based on the order of entrance. However, LARS, which is a modified version of Lasso, doesn't have this problem. We'll make use of this property and rank variables using LARS solution path.

Optimal trade execution aims at balancing price impact and timing risk. With respect to the mathematical formulation of the optimization problem, we primarily focus on Mean Variance (MV) optimization, in which the two conflicting objectives are maximizing expected revenue (the flip side of trading impact) and minimizing variance of revenue (a measure of timing risk). We also consider the use of expected quadratic variation of the portfolio value process as an alternative measure of timing risk, which leads to Mean Quadratic Variation (MQV) optimization. We demonstrate that MV-optimal strategies are quite different from MQV-optimal strategies in many aspects. These differences are in stark contrast to the common belief that MQV-optimal strategies are similar to, or even the same as, MV-optimal strategies. These differences should be of interest to practitioners since we prove that the classic Almgren-Chriss strategies (industry standard) are MQV-optimal, in contrary to the common belief that they are MV-optimal. From a computational point of view, we extend theoretical results in the literature to prove that the mean variance efficient frontier computed using our method is indeed the complete Pareto-efficient frontier. First, we generalize the result in Li (2000) on the embedding technique and develop a post-processing algorithm that guarantees Pareto-optimality of numerically computed efficient frontier. Second, we extend the convergence result in Barles (1990) to viscosity solution of a system of nonlinear Hamilton Jacobi Bellman partial differential equations (HJB PDEs). On the numerical aspect, we combine the techniques of similarity reduction, non-standard interpolation, and careful grid construction to significantly improve the efficiency of our numerical methods for solving nonlinear HJB PDEs.

Molecular dynamics (MD) is a computer simulation of physical movements of atoms and molecules. MD has now been widely used in materials, biochemical and pharmaceutical research. In recent years, zirconium phosphate (ZrP) compounds developed a new type of multi-function mediated porous materials, which the crystalline £\-zirconium phosphate (£\-ZrP) is a cationic layered compounds, with a neat layer structure and easy to design. Cetyl trimethyl ammonium bromide (CTAB) is a cationic surfactant, it¡¦s one kind of ammonium salt of a long carbon chain as hydrophobic groups. Ion exchange can occur with other exchangeable cations. In this study, we first use CTAB inserted into £\-ZrP interlayer to prepare £\-ZrP-CTAB material. Second, we add phenol solution in the system, and use molecular dynamics simulations to observe the solution¡¦s penetration and adsorption. The result shows that pure water can permeate through £\-ZrP CTAB membrane, and pure phenol will be adsorbed by the £\-ZrP-CTAB membrane. If we add phenol solution, the water molecules can pass through the £\-ZrP-CTAB membrane but phenol molecule can¡¦t. It can achieve the effect of separation of the mixed solution. Last we simulate phenolate solution system. The result shows that the number of phenolate molecule enter the membrane is less than phenol molecule in phenol solution. This result is also consistent with the experiments mentioned in the literature.

Urea aqueous solution is ubiquitously used to denature protein. Regardless of its extensive use, the mechanism is still unclear and remains an active field of study. There have been two proposed mechanisms, the direct and indirect. The indirect mechanism, which attributes the ability of urea of changing water structure, is susceptible since many research works show that there is little effect of urea on water structure. The current study provided evidence for the indirect mechanism by demonstrating that the introduction of urea slightly changes the water structure in the hydrophobic interfacial areas. In the current study, the urea aqueous solution systems with either gas-liquid or hydrophobic interface are studied by MD simulations, and the structures of water near the interfacial areas are analyzed in terms of density, orientation and number of hydrogen bonds. For each kind of interface, systems with four different urea concentrations are included, ranging from 0M to 8M. The results show slight change of water structure by the urea solute on the hydrophobic interface in terms of the orientation and number of hydrogen bonds per water molecule.

Ammonia is one of valuable chemicals, which are commonly used, in various industrial factors. It is also a typical pollutant, and has a long-term impact on human health for its toxicity characteristics. This study investigated the reaction mechanism of gas-liquid phase in oxidation of ammonia in WAO and SCO processes over copper catalysts. As for lack of the research on activated center of copper catalyst for a long time, it was still not exactly unknown what center was going on affecting activity. Therefore, we conducted the physical and chemical properties on surface of catalyst to realize conversion/activity in oxidation of ammonia over nanoscale copper catalyst. Achievements in oxidation of liquid phase ammonia in WAO process over nanoscale Cu-La-Ce catalysts are as follows: (1) The raising on conversion of ammonia is significantly by adding the molar ratio 7:2:1 of Cu-La-Ce catalyst. (2) The higher temperature the higher conversion, and the increasing space velocity of influent the lower conversion. (3) The reaction rate in WAO process over 7:2:1 catalyst increases with initial pH increasing of solution, 95% conversion of ammonia can be achieved under alkalinity condition. (4) Oxygen supply can promote the decomposition of ammonia at high temperature, above 95% conversion of ammonia can be achieved when total pressure raises at 4.0 MPa. (5) The characteristic peaks of CuO, La2O3 and CeO2 showed from XRD tests indicate the coordination by three peaks probably causes the excellent activity in Cu-La-Ce catalysts; UV-Vis and FTIR analysis results show CuO species dominates the reaction mechanism of liquid phase of WAO process over Cu-La-Ce catalyst which can be used to adsorb the oxygen atom in proceeding the oxidation of ammonia. (6) AEM and TEM analysis results show the outlook of catalyst sites are almost nearly circular and its particle sizes are concentrated in range of nanoscale level; and by EDS and Mapping tests proof elements of Cu, La and Ce are indeed the major components in this catalyst. Achievements in oxidation of liquid phase ammonia in WAO process over nanoscale Cu-ACF catalysts are as follows: (1) The dose of copper on activated carbon fiber support (denoted by ACF) is important in treatment efficiency of pollutants removal; adding at least 5% of copper dosage which can maintain Cu to be a state of +2, it has the catalytic capacity to convert the ammonia in solution. (2) The optimal conversion obtained in 99% under 463 K and 400 mg/l, shows Cu-ACF is also an alterative catalyst. (3) The higher temperature the higher conversion, and the lower nitrogen is. (4) The higher oxygen pressure the higher conversion. (5) From analysis results of BET, FTIR and EA show ACF support has high BET surface area and oxygen-containing function groups, it causes an increasing activity of metal in reaction for the higher activated sites and metal dispersed uniformly on ACF; XRD tests indicate the coordination by CuO and ACF probably causes the excellent activity over Cu-ACF catalysts; UV-Vis and FTIR analysis results show species CuO and ACF both dominate the reaction mechanism of liquid phase of WAO process over Cu-ACF catalyst. (6) AEM and TEM analysis results show the outlook of catalyst sites are almost Nearly long narrowed tube and its diameters are concentrated in range of nanoscale level; and by EDS and XRF (Mapping) tests proof elements of Cu and P are indeed the major components in this catalyst. Achievements in oxidation of gas phase ammonia in SCO process over nanoscale Cu-Ce catalysts are as follows: (1) The great conversion over Cu-Ce catalyst (molar ratio 6:4) obtained under 463 K and 400 mg/l. (2) The higher initial concentration of ammonia the lower conversion is probably due to the intermediates out of completely decomposed in catalytic reaction. (3) From analysis results of BET and EA show this catalyst have high BET surface area and empty hole of oxygen-containing on surface, it causes an increasing activity of metal in reaction for the higher activated sites; XRD tests indicate the coordination by CuO and CeO2 probably causes good activity over Cu-Ce catalysts; UV-Vis and FTIR analysis results show species CuO and CeO2 both dominate the reaction mechanism of gas phase of ammonia in SCO process over Cu-CeO2 catalyst. (4) AEM and TEM analysis results show the outlook of catalyst sites are almost nearly circular and its particle sizes are concentrated in range of nanoscale level; and by EDS and Mapping tests proof elements of Cu and Ce are indeed the major components in this catalyst. Achievements in oxidation of gas phase ammonia in SCO process over nanoscale Pt-Pd-Rh catalyst coated on ceramics are as follows: (1) The 99% conversion over this catalyst can be obtained at 623 K; the higher initial concentration of ammonia ranging from 500 to 1000 mg/l the lower conversion is found. (2) The large amount of N2 and minor amount of NO and NO2 are found in the products after this reaction. (3) XRD tests indicate the coordination by Pt, PdO, Rh and CeO2 probably causes the excellent activity over this catalyst; UV-Vis and FTIR analysis results show species PdO and CeO2 both dominate the reaction mechanism of gas phase of ammonia in SCO process over Pt-Pd-Rh catalyst. (4) AEM and TEM analysis results show the higher initial concentration the higher aged the ceramic support, and the wider sintering of Al2O3 coating layer is. (5) By EDS, XRF and Mapping tests proof elements of Pt, Pd and Rh are indeed the major components dispersed on this ceramic catalyst.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 258-270). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 103-116). Available also in a digital version from Dissertation Abstracts.

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