Title: Dynamic model for estimation of radon concentration in buildings Author: Barbora Vaňková Department: Department of probability and mathematical statistics Supervisor: Ing. Marek Brabec, Ph.D. Supervisor's e-mail address: mbrabec@cs.cas.cz Abstract: In the present work there is described the method for estimation of functi- onal data from discrete values and basic methods of functional data analysis. 1

Banks finance their operations in several ways, by shareholders equity, receiving deposits from customers and by borrowing from investors and other financial institutions. One widely used approach is to issue a bond. Bonds issued on the foreign capital markets is a way to increase the financing options and mitigate risk exposure. When a bank converts foreign capital to domestic capital, there is a degree of currency risk involved. One commonly used instrument for converting capital from one currency to another is a cross currency swap. Since the Global Financial Crisis 2007-2009 regulations imposed by regulators have increased. Banks are required to have sound risk management practises where risk exposure is estimated. In response to recent regulations banks have several departments which assess and follow up risks taken in the operations. As a result, at least two systems are used when valuing financial instruments, one where all trades are conducted, the front office system, and one where risk exposure is estimated, the risk system. The aim of this project is to investigate why there is a discrepancy between the two systems. We will also analyse how this discrepancy affects risk measures. By replicating the two systems’ valuation it is possible to distinguish why there is a discrep- ancy between the systems, regarding the valuation of cross currency basis swaps. When the replication is in place, risk measure calculations are conducted to enable analysis of the impact on risk measures. There are two main differences found between the two systems and how they value a cross currency basis swap: (i) how the underlying risk factors are used; and (ii) how an upcoming cash flow is settled. The effect of these discrepancies are that the risk system overestimate the risk exposure compared with the front office system. / Banker finansierar sin verksamhet på flera olika sätt, %har flera möjligheter att, t.ex. genom eget kapital, inlåning och upplåning från investerare och andra finansiella institutioner. Ett vanligt förfarande är att emittera en obligation, där obligationer emitterade på den utländska kapitalmarknaden är ett sätt att öka finansieringsalternativen och därmed minska riskexponeringen mot den inhemska marknaden. När en bank konverterar utländskt kapital till kapital i den nationella valutan, finns en viss valutarisk inblandad. Ett vanligt instrument för att växla kapital från en valuta till en annan är en valutaswappar. Allt sedan den Globala Finanskrisen 2007-2009 har regleringen från tillsynsmyndigheter ökat. Banker är skyldiga att ha sunda riskhanteringsstrategier för att uppskatta sin riskexponering. Till följd av nya regleverk har banker idag flera avdelningar vilka estimerar och följer upp risker som tas i verksamheten. Ett resultat av detta är att åtminstone två system används vid värdering av finansiella instrument, ett system där all handel utförs, och ett där riskexponeringen estimeras. Syftet med detta projekt är att undersöka eventuella skillnader i värderingen av valutabasisswappar och vidare analysera hur detta påverkar olika riskmått. Det verkar vara en diskrepans mellan de två systemen där finansiella instrument värderas, speciellt med avsende på valutabasisswappar. Genom att replikera de två systemens värdering är det möjligt att urskilja varför det finns en diskrepans. Replikering av de två systemen låg till grund för beräkningen av riskmått samt analysen av hur skillnaderna påverkar dessa. % Resultat De huvudsakliga skillnaderna mellan de två systemen avsenede värderingen av valutabasisswappar är: (i)hur de underliggande riskfaktorerna används, och (ii) hur nästkommande kassaflöde (kupong) bestäms. Effekten av dessa skillnader är att systemet där riskexponering estimeras övervärderar risken jämfört med om risken skulle estimerats i systemet där all handel utförs.

Accurate rainfall forecasting using weather radar imagery has always been a crucial and predominant task in the field of meteorology [1], [2], [3] and [4]. Competitive Radial Basis Function Neural Networks (CRBFNN) [5] is one of the methods used for weather radar image based forecasting. Recently, an alternative CRBFNN based approach [6] was introduced to model the precipitation events. The difference between the techniques presented in [5] and [6] is in the approach used to model the rainfall image. Overall, it was shown that the modified CRBFNN approach [6] is more computationally efficient compared to the CRBFNN approach [5]. However, both techniques [5] and [6] share the same prediction stage. In this thesis, a different GRBFNN approach is presented for forecasting Gaussian envelope parameters. The proposed method investigates the concept of parameter dependency among Gaussian envelopes. Experimental results are also presented to illustrate the advantage of parameters prediction over the independent series prediction.

Chien Siu-Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract (English) / Abstract (Chinese) / Acknowledgements / Table of Contents / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian-2 Method / Chapter 1.2 --- The Gaussian-3 Method / Chapter 1.3 --- The G3 Method with Reduced Moller-Plesset Order and Basis Set / Chapter 1.4 --- Calculated Thermochemical Data / Chapter 1.5 --- Remark on the Location of Transition State / Chapter 1.6 --- Scope of the Thesis / Chapter 1.7 --- References / Chapter Chapter 2 --- "Energetics and Structures of the Carbonyl Chloride Radical, Oxalyl Chloride, and Their Cations" --- p.6 / Chapter 2.1 --- Introduction / Chapter 2.2 --- Computational Methods / Chapter 2.3 --- Results and Discussion / Chapter 2.3.1 --- Carbonyl Chloride and Its Cation / Chapter 2.3.2 --- The anti and syn Conformers of Oxalyl Chloride and Oxalyl Chloride Cation / Chapter 3.3.3 --- The anti and gauche Conformers of (ClCO) 2 and the TS Linking Them / Chapter 2.4 --- Conclusions / Chapter 2.5 --- Publication Note / Chapter 2.6 --- References / Chapter Chapter 3 --- "An Isomeric Study of N5, N5+，and N5- : A Gaussian-3 Investigation" --- p.17 / Chapter 3.1 --- Introduction / Chapter 3.2 --- Computational Methods / Chapter 3.3 --- Results and Discussion / Chapter 3.3.1 --- "The N5 Isomers """ / Chapter 3.3.2 --- The N5+ Isomers / Chapter 3.3.3 --- The N5- Isomers / Chapter 3.3.4 --- Comparison of the G3 and G3(MP2) Results / Chapter 3.4 --- Conclusions / Chapter 3.5 --- Publication Note / Chapter 3.6 --- References / Chapter Chapter 4 --- Thermochemistry of Hydrochlorofluorosilanes : An Ab Initio Gaussian-3 Study --- p.28 / Chapter 4.1 --- Introduction / Chapter 4.2 --- Computational Methods / Chapter 4.3 --- Results and Discussion / Chapter 4.3.1 --- Heats of Formation for Neutral HCFSis / Chapter 4.3.2 --- Ionization Energies / Chapter 4.3.3 --- Electron Affinities / Chapter 4.3.4 --- Proton Affinities / Chapter 4.3.5 --- Acidities / Chapter 4.3.6 --- G3 versus G3(MP2) / Chapter 4.4 --- Conclusions / Chapter 4.5 --- Publication Note / Chapter 4.6 --- References / Chapter Chapter 5 --- A Gaussian-3 Study of the Photodissociation Channels of Thiirane --- p.48 / Chapter 5.1 --- Introduction / Chapter 5.2 --- Computational Methods / Chapter 5.3 --- Results and Discussion / Chapter 5.3.1 --- The Heats of Reactions / Chapter 5.3.2 --- The Dissociation Channels Taking Place at the Ground State / Chapter 5.3.3 --- The Dissociation Channels Taking Place at Excited States / Chapter 5.4 --- Conclusions / Chapter 5.5 --- References / Chapter Chapter 6 --- A Gaussian-3 Study of the VUV Photoionization and Photodissociation of Chloropropylene Oxide --- p.59 / Chapter 6.1 --- Introduction / Chapter 6.2 --- Computational Methods / Chapter 6.3 --- Results and Discussion / Chapter 6.3.1 --- Ionization Energy / Chapter 6.3.2 --- Dissociation Channels / Chapter 6.4 --- Conclusions / Chapter 6.5 --- Publication Note / Chapter 6.6 --- References / Chapter Chapter 7 --- Conclusions --- p.69 / Appendix A The Gaussian-n (n=l-3) Theoretical Models --- p.71 / Chapter A.1 --- The G1 and G2 Theories / Chapter A.2 --- The G3 Theory / Chapter A.3 --- The G3(MP2) Theory / "Appendix B Calculation of Enthalpy at 298 K,H298" --- p.74

Li Chi-Lun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Table of Contents --- p.iv / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Remark on the Location of Transition Structures --- p.1 / Chapter 1.2 --- Scope of the Thesis --- p.1 / Chapter 1.3 --- References --- p.2 / Chapter Chapter 2 --- "A Gaussian-3 Study on the Photodissociation of Phenylacetylene and Formation of 1,3,5-Hexatriyne" --- p.5 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Computational Method --- p.7 / Chapter 2.3 --- Results and Discussion --- p.8 / Chapter 2.3.1 --- Phenylacetylene → Acetylene + Benzyne --- p.8 / Chapter 2.3.2 --- "Phenylacetylene → Acetylene + (Z)-3 -Hexene- 1,5-diyne" --- p.9 / Chapter 2.3.3 --- "(Z)-3-Hexene-l,5-diyne / (E)-3 -Hexene-1,5-diyne → 1,3,5-Hexatriyne and Molecular Hydrogen" --- p.9 / Chapter 2.3.4 --- Evaluation of Thermochemical Data --- p.10 / Chapter 2.3.5 --- Evaluation of Ion Energetics Data --- p.10 / Chapter 2.4 --- Conclusions --- p.10 / Chapter 2.5 --- References --- p.11 / Chapter Chapter 3 --- A Gaussian-3 Study of the Photoionization and Dissociative Photoionization Channels of Cyanoethylene --- p.21 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Computational Method --- p.22 / Chapter 3.3 --- Results and Discussion --- p.23 / Chapter 3.3.1 --- Bond Cleavage Reactions --- p.23 / Chapter 3.3.2 --- Dissociation Channels Involving Transition Structures --- p.25 / Chapter 3.4 --- Conclusions --- p.25 / Chapter 3.5 --- References --- p.26 / Chapter Chapter 4 --- "A Gaussian´ؤ2 Study of Structures, Energetics, and Reactions of C2H3S- Anions" --- p.34 / Chapter 4.1 --- Introduction --- p.35 / Chapter 4.2 --- Computational Method --- p.35 / Chapter 4.3 --- Results and Discussion --- p.36 / Chapter 4.3.1 --- Thioformylmethyl Anion --- p.37 / Chapter 4.3.2 --- Thioacetyl Anion --- p.37 / Chapter 4.3.3 --- Cyclic C2H3S- Ions --- p.37 / Chapter 4.3.4 --- CH2SCH- --- p.38 / Chapter 4.3.5 --- 2-Thiovinyl Anion --- p.38 / Chapter 4.3.6 --- 1-Thiovinyl Anion --- p.39 / Chapter 4.3.7 --- Intramolecular Rearrangements of 1- --- p.39 / Chapter 4.3.8 --- Intramolecular Rearrangements of Cyclic C2H3S- ions and 1´ؤThiovinyl Anion --- p.39 / Chapter 4.4 --- Conclusions --- p.40 / Chapter 4.5 --- References --- p.40 / Chapter Chapter 5 --- "Theoretical Studies of Transition Metal Complexes: Bond Energies for Fe+-D, Fe+-H2O, and Fe+-CO" --- p.51 / Chapter 5.1 --- Introduction --- p.52 / Chapter 5.2 --- Computational Method --- p.53 / Chapter 5.3 --- Results and Discussion --- p.54 / Chapter 5.3.1 --- Fe+-D --- p.54 / Chapter 5.3.2 --- Fe+-CO --- p.54 / Chapter 5.3.3 --- Fe+-H2O --- p.55 / Chapter 5.4 --- Conclusions --- p.56 / Chapter 5.5 --- References --- p.57 / Chapter Chapter 6 --- Ab Initio Study of the Charge-Delocalized and -Localized Form of the Rhodizonate Dianion --- p.61 / Chapter 6.1 --- Introduction --- p.62 / Chapter 6.2 --- Computational Method --- p.63 / Chapter 6.3 --- Results and Discussion --- p.64 / Chapter 6.3.1 --- Charge-Localized C6062- --- p.64 / Chapter 6.3.2 --- Charge-Delocalized C6062- --- p.64 / Chapter 6.4 --- Conclusions --- p.65 / Chapter 6.5 --- References --- p.66 / Chapter Chapter 7 --- "Franck-Condon Factor Simulated Spectra of the Cations of cis-2-Butene,trans-2-Butene, Isobutene, cis-Dichloroethene, and trans-Dichloroethene" --- p.71 / Chapter 7.1 --- Introduction --- p.72 / Chapter 7.2 --- Computational Method --- p.72 / Chapter 7.3 --- Results and Discussion --- p.73 / Chapter 7.3.1 --- cis-2-Butene Cation --- p.73 / Chapter 7.3.2 --- trans-2-Butene Cation --- p.74 / Chapter 7.3.3 --- cis-Dichloroethene Cation --- p.75 / Chapter 7.3.4 --- trans-Dichloroethene Cation --- p.76 / Chapter 7.3.5 --- Isobutene --- p.76 / Chapter 7.4 --- Conclusions --- p.77 / Chapter 7.5 --- References --- p.77 / Chapter Chapter 8 --- Conclusions --- p.88 / Appendix A --- p.89 / Appendix B --- p.91 / Appendix C --- p.92

Based on the combined surface and volume RWG (Rao-Wilton-Glisson) basis functions, a simulator of a patch antenna on a finite dielectric substrate using the Method of Moments (MoM) has been implemented in Matlab. The metal surface is divided into planar triangular elements whereas the (inhomogeneous) dielectric volume is divided into tetrahedral elements. The structure under study is comprised of a typical patch antenna consisting of a single patch above a finite ground plane, and a probe feed. The performance of the solver is studied for different mesh configurations. The results obtained are tested by comparison with the commercial ANSOFT HFSS v8.5 and WIPL-D simulators. The former uses a large number of finite elements (up to 30,000) and adaptive mesh refinement, thus providing the reliable data for comparison. Behavior of the most sensitive characteristic ¡V antenna input impedance ¡V is tested, close to the first resonant frequency. The error in the resonant frequency is estimated at different values of the relative dielectric constant ƒÕr, which ranges from 1 to 20. The reported results show reasonable agreement. However, the solver needs to be further improved.

Lam Chow Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references. / Abstracts in English and Chinese. / Thesis Examination Committee --- p.i / Abstract --- p.ii / Acknowledgements --- p.iv / Table of Contents --- p.v / List of Tables --- p.vii / List of Figures --- p.viii / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian-3 Method --- p.1 / Chapter 1.2 --- The G3 Method with Reduced MΦller- Plesset Order and Basis Set --- p.2 / Chapter 1.3 --- Density Functional Theory (DFT) --- p.3 / Chapter 1.4 --- Calculation of Thermodynamical Data --- p.3 / Chapter 1.5 --- Remark on the Location of Transition Structures --- p.3 / Chapter 1.6 --- Natural Bond Orbital (NBO) Analysis --- p.4 / Chapter 1.7 --- Scope of the Thesis --- p.4 / Chapter 1.8 --- References --- p.5 / Chapter Chapter 2 --- Theoretical Study of Tri-s-triazine and Its Derivatives --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Methods of Calculation --- p.9 / Chapter 2.3 --- Results and Discussion --- p.9 / Chapter 2.3.1. --- Property of Tri-s-triazine --- p.9 / Chapter 2.3.2. --- Substituent Effects on the Properties of the Tri-s-triazine Parent Molecule --- p.10 / Chapter 2.3.3. --- Heats of Formation of Derivatives of Tri-s-triazine --- p.20 / Chapter 2.4 --- Conclusion --- p.22 / Chapter 2.5 --- References --- p.22 / Chapter Chapter 3 --- A Gaussian-3 Study of the Dissociative Photoionization of Acetone --- p.25 / Chapter 3.1 --- Introduction --- p.25 / Chapter 3.2 --- Methods of Calculation --- p.26 / Chapter 3.3 --- Results and Discussion --- p.26 / Chapter 3.3.1. --- "Formation of m/z = 42 (CH2CO+.),43 (CH3CO+) Ions" --- p.31 / Chapter 3.3.2. --- Formation of m/z = 43 (c-CH2CHO+) and m/z = 15 (CH3+) Ions --- p.32 / Chapter 3.3.3. --- Formation of m/z = 57 (CH3COCH2+) Ions --- p.37 / Chapter 3.3.4. --- Formation of m/z = 39 (C3H3+) Ions --- p.38 / Chapter 3.4 --- Conclusion --- p.40 / Chapter 3.5 --- Publication Note --- p.40 / Chapter 3.6 --- References --- p.40 / Chapter Chapter 4 --- "A G3(MP2) Study of the C3H60+. Isomers Fragmented from l,4-Dioxane+" --- p.42 / Chapter 4.1 --- Introduction --- p.42 / Chapter 4.2 --- Methods of Calculation --- p.43 / Chapter 4.3 --- Results and Discussion --- p.44 / Chapter 4.3.1. --- "Formation of C3H60+. Isomers 1 and 2 via Fragmentation of 1,4-Dioxane+" --- p.44 / Chapter 4.3.2. --- Reaction with Acetonitrile --- p.55 / Chapter 4.3.3. --- Reaction with Formaldehyde --- p.57 / Chapter 4.3.4. --- Reaction with Ethylene --- p.61 / Chapter 4.3.5. --- Reaction with Propene --- p.63 / Chapter 4.4 --- Conclusion --- p.67 / Chapter 4.5 --- Publication Note --- p.68 / Chapter 4.6 --- References --- p.68 / Chapter Chapter 5 --- A Computational Study of the Photodissociation Channels of Chloroiodomethane --- p.71 / Chapter 5.1 --- Introduction --- p.71 / Chapter 5.2 --- Methods of Calculation --- p.73 / Chapter 5.3 --- Results and Discussion --- p.74 / Chapter 5.3.1 --- CH2C1 + I(2P1/2) and CH2C1 + I(2P3/2) Channels --- p.77 / Chapter 5.3.2 --- "CH2I + C1(2P3/2,1/2) Channel" --- p.78 / Chapter 5.3.3 --- CHI + HC1 Channel --- p.80 / Chapter 5.3.4 --- CH2 + IC1 Channel --- p.81 / Chapter 5.4 --- Conclusion --- p.82 / Chapter 5.5 --- Publication Note --- p.83 / Chapter 5.6 --- References --- p.83 / Chapter Chapter 6 --- Conclusion --- p.86 / Appendix A --- p.87 / Appendix B --- p.89

Lui, Fung Yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 83-92). / Abstracts in English and Chinese. / Acknowledgement --- p.iii / Abbreviation --- p.xii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Related Work --- p.6 / Chapter 1.2.1 --- Parametric Optimization Method and Radial Basis Functions --- p.6 / Chapter 1.3 --- Contribution and Organization of the Dissertation --- p.7 / Chapter 2 --- Level Set Method for Structure Shape and Topology Optimization --- p.8 / Chapter 2.1 --- Primary Ideas of Shape and Topology Optimization --- p.8 / Chapter 2.2 --- Level Set models of implicit moving boundaries --- p.11 / Chapter 2.2.1 --- Representation of the Boundary via Level Set Method --- p.11 / Chapter 2.2.2 --- Hamilton-Jacobin Equations --- p.13 / Chapter 2.3 --- Numerical Techniques --- p.13 / Chapter 2.3.1 --- Sign-distance function --- p.14 / Chapter 2.3.2 --- Discrete Computational Scheme --- p.14 / Chapter 2.3.3 --- Level Set Surface Re-initialization --- p.16 / Chapter 2.3.4 --- Velocity Extension --- p.16 / Chapter 3 --- Structure Topology Optimization with Discrete Level Sets --- p.18 / Chapter 3.1 --- A Level Set Method for Structural Shape and Topology Optimization --- p.18 / Chapter 3.1.1 --- Problem Definition --- p.18 / Chapter 3.2 --- Shape Derivative: an Engineering-oriented Deduction --- p.21 / Chapter 3.2.1 --- Sensitivity Analysis --- p.23 / Chapter 3.2.2 --- Optimization Algorithm --- p.28 / Chapter 3.3 --- Limitations of Discrete Level Set Method --- p.30 / Chapter 4 --- RBF based Parametric Level Set Method --- p.32 / Chapter 4.1 --- Introduction --- p.32 / Chapter 4.2 --- Radial Basis Functions Modeling --- p.33 / Chapter 4.2.1 --- Inverse Multiquadric (IMQ) Radial Basis Functions --- p.38 / Chapter 4.3 --- Parameterized Level Set Method in Structure Topology Optimization --- p.39 / Chapter 4.4 --- Parametric Shape and Topology Structure Optimization Method with Radial Basis Functions --- p.42 / Chapter 4.4.1 --- Changing Coefficient Method --- p.43 / Chapter 4.4.2 --- Moving Knot Method --- p.45 / Chapter 4.4.3 --- Combination of Changing Coefficient and Moving Knot method --- p.46 / Chapter 4.5 --- Numerical Implementation --- p.48 / Chapter 4.5.1 --- Sensitivity Calculation --- p.48 / Chapter 4.5.2 --- Optimization Algorithms --- p.49 / Chapter 4.5.3 --- Numerical Examples --- p.52 / Chapter 4.6 --- Summary --- p.65 / Chapter 5 --- Conclusion and Future Work --- p.80 / Chapter 5.1 --- Conclusion --- p.80 / Chapter 5.2 --- Future Work --- p.81 / Bibliography --- p.83

Algebraic geometry is the study of systems of polynomial equations in one or more variables. Thinking of polynomials as functions reveals a close connection between affine varieties, which are geometric structures, and ideals, which are algebraic objects. An affine variety is a collection of tuples that represents the solutions to a system of equations. An ideal is a special subset of a ring and is what provides the tools to prove geometric theorems algebraically. In this thesis, we establish that a variety depends on the ideal generated by its defining equations. The ability to change the basis of an ideal without changing the variety is a powerful tool in determining a variety. In general, the quotient and remainder on division of polynomials in more than one variable are not unique. One property of a Groebner basis is that it yields a unique remainder on division. To prove geometric theorems algebraically, we first express the hypotheses and conclusions as polynomials. Then, with the aid of a computer, apply the Groebner Basis Algorithm to determine if the conclusion polynomial(s) vanish on the same variety as the hypotheses.

In order to reduce air pollution and reduce the amount of traffic on highways in the western United States, certain states have set up worksite trip reduction programs. Employers in these states must comply with worksite trip reduction laws and submit trip reduction plans to their respective regulatory agency each year. These plans are currently evaluated manually, and are either rejected or accepted by the agency. There are two major flaws in this system; the first is the amount of time required by the agency to review a plan could be a matter of months, and the second is that human reviewers have subjective opinions regarding the effectiveness of plans. The purpose of this thesis is to develop computer models using Radial Basis Function neural networks, with centers built using the k-means clustering algorithm. These networks will be compared against the performance of a commercial neural network-modeling program known as Predict, as well as the traditional method of selecting RBF neurons from the training set.