A variety of new mean value theorems are presented along with interesting proofs and generalizations of the standard theorems. Three proofs are given for the ordinary Mean Value Theorem for derivatives, the third of which is interesting in that it is independent of of Rolle's Theorem. The Second Mean Value Theorem for derivatives is generalized, with the use of determinants, to three functions and also generalized in terms of nth order derivatives. Observing that under certain conditions the tangent line to the curve of a differentiable function passes through the initial point, we find a new type of mean value theorem for derivatives. This theorem is extended to two functions and later in the paper an integral analog is given together with integral mean value theorems. Many new mean value theorems are presented in their respective settings including theorems for the total variation of a function, the arc length of the graph of a function, and for vector-valued functions. A mean value theorem in the complex plane is given in which the difference quotient is equal to a linear combination of the values of the derivative. Using a regular derivative, the ordinary Mean Value Theorem for derivatives is extended into Rn, n>1.

Thermoelectric devices allow for direct conversion of heat into electricity as well as solid-state refrigeration. The skutterudite family of compounds continues to be of considerable interest both scientifically and technologically due to their unique physical properties, in particular as promising thermoelectric materials. In this thesis, the basic thermoelectric phenomena and some background history on skutterudites will be reviewed. Rhombohedral derivatives of the cubic skutterudite CoSb3, namely Co4-xFexGe6Se6 with x=0, 1, 1.5 (p-type) and rare-earth filled Ce0.13Co4Ge6Se6 and Yb0.14Co4Ge6Se6 (n-type), were synthesized and their synthesis and low temperature transport properties will be discussed. Reitveld refinement and elemental analysis were used to identify the structure and stoichiometry of these compositions. Both Fe substitution and rare-earth filling reduced the thermal conductivity compared with Co4Ge6Se6 skutterudite derivative. In addition the electrical and thermal properties of these compounds are greatly affected by doping. This fundamental investigation reveals new insight and is intended as part of the continuing effort to explore different skutterudite compositions and structure types for potential thermoelectric applications.

Electricity markets around the world have gone through, or are currently in a deregulation phase. As a result, power companies that formerly enjoyed a monopoly are now facing risks. In order to cover (hedge) these risks, futures markets have emerged, in parallel with the spot price markets. Then, markets of more complex derived products have appeared to better hedge the risk exposures of power suppliers and consumers. An Affine Jump Diffusion (AJD) framework is presented here to coherently model the dynamics of the spot price of electricity and all the futures contracts. The non-storability of electricity makes it indeed impossible to use it in hedging strategies. Futures contracts, however, are standard financial contracts that can be stored and used in hedging strategies. We thus propose to consider the set of futures contracts as the primary commodities to be modelled and jointly estimate the parameters of the spot and futures prices based on their historical time series. The estimation is done by Maximum Likelihood, using a Kalman Filter recursive algorithm that has been updated to account for non-Gaussian errors. This procedure has been applied to the German European Energy index (EEX) based in Frankfurt for electricity, to the Brent for Crude oil, and to the NBP for natural gas. The AJD framework is very powerful because the characteristic function of the underlying stochastic variables can be obtained just by solving a system of complex valued ODEs. We took advantage of this feature and developed a novel approach to estimate expectations of arbitrary functions of random variables that does not require the probability density function of the stochastic variables, but instead, their characteristic function. This approach, relying on the Parseval Identity, provided closed form solutions for options with payoff functions that have an analytical Fourier transform. In particular, European calls, puts and spread options could be computed as well as the value of multi-fuel power plants that can be viewed as an option to exchange the most economic fuel of the moment against electricity. A numerical procedure has also been developed for options with payoff functions that do not have an analytical Fourier transform. This numerical approach is indeed using a Fast Fourier Transform of the payoff function, and can be used in Dynamic Programming algorithms to price contracts with endogenous exercise strategies. Finally, it is showed that the (mathematical) partial derivatives of these contracts, often referred to as the Greeks, could also be computed at low cost. This allows to build hedging strategies to shape the risk profile of a given producer, or consumer.

The supramolecular interactions of small organic molecules with different host molecules are investigated in this dissertation. Additionally, the author also describes the self-assembly mechanisms in hydrogen bonding motif. These studies were carried out by many techniques including, NMR, cyclic voltammetry, steady state voltammetry, mass spectroscopy, UV-visible spectroscopy and fluorescence spectroscopy. Chapter 1 introduces the science of supramolecular chemistry and the background of cucurbiturils, one of the most important host molecules studied in this research work. It describes the structures and binding behaviors of each host molecule. Additionally, the selectivity and binding properties in the host-guest interactions involved cucurbiturils are discussed. Chapter 2 compares the electrochemical properties of cationic and neutral ferrocene derivatives upon addition of cucurbiturils. It is observed that the cationic ferrocene compounds bind to cucurbit[7]uril much stronger compared to the neutral ferrocene compounds. The positive charged side chains favor to interact with cucurbit[7]uril portals and thus stabilize the complexes. Besides, the author describes a simple analytical method to determine the binding constants by a competitive binding with a standard reference compound, cobaltocenium, which is reported to bind strongly to cucurbit[7]uril. Chapter 3 described the research of the pH-dependent binding affinity between cucurbit[7]uril and ferrocene guests. The electrochemical behavior of ferrocene moiety in aqueous solution was investigated by cyclic voltammetry in the presence of cucurbit[7]uril in acidic and basic environment respectively. The protonation and deprotonation processes affect the binding behaviors of the ferrocene residues with cucurbit[7]uril. Chapter 4 describes the synthesis and characterization of a new series of 4-phenyl-pyridinium derivatives. These compounds contain a phenyl-pyridinium residue which is favorable to be bound by cucurbit[8]uril. The 1:1 and 1:2 host-guest binding stoichiometries are both observed by UV-visible spectroscopy. These new compounds can be dimerized encapsulated inside the cucurbit[8]uril portals without being electrochemical reduced. Chapter 5 is a brief introduction into the science of hydrogen bonding. This chapter investigates the application of multiple hydrogen-bonding in supramolecular chemistry extensively. Multiple hydrogen bonds with their directionality and reversibility are of great interest and importance in the design and investigations of well-defined supramolecular assemblies. The potential of hydrogen bonding is limitless and is still developing. Chapter 6 describes the synthesis and photochemical behaviors of a series of ureido-pyrimidione derivatives. All of the DDAA derivatives form stable, non-covalent dimers in non-polar solvents. The dimeric molecular assemblies of these hydrogen bonding motifs in their DDAA pyrimidinedione units are investigated by NMR, X-ray crystallography, fluorescence spectroscopy and computations. Additionally, their hetero-dimerization is well studied by fluorescence spectroscopy. The observation and comparison of fluorescence quenching on the photochemical fluorophore for each compound by ferrocene-DDAA and isopropyl-DDAA reveal the electron transfer process through the quadruple hydrogen bonding motifs.

No description available.

The dynamical behaviors of tricarboxylic acid derivative, 1,3,5-tris(carbox- ymethoxy) benzene[TCMB, C6H3(OCH2COOH)3] on an Au surface is investigated by molecular dynamics. A TCMB molecule adsorbed on the Au(111) substrate is first probed into the structure arrangement. It founds that there are four possible conformations of the TCMB molecule that is adsorbed on the Au(111) substrate. The main difference on its conformation is the orientation of its functional group, which lead the molecule that forms the lock-and-key (LAK) behavior and prompts the molecule that become more stable on the substrate. As this result, the LAK behavior directly affects the trajectories of movement and dynamical behaviors. Another topic is to observe the behavior of TCMB molecule on Au(110) and Au(100) surface, respectively. As well as the result of the TCMB molecule adsorbed on the Au(111) substrate, it also shows a different behavior on dynamical behaviors when the TCMB molecule adsorbed on the Au(110) and Au(100) substrate. Moreover, we found that the diffusion direction of TCMB molecule is dependent on the arrangement of the adsorbed surface. From the observation of the trajectory of the TCMB molecule, we found that diffusion range is most wide on Au(100) plane. The translational direction of TCMB molecule tend to move on the <110> direction as the molecule is migrate on the Au(100) plane, whereas that tend to move on the [1ī0] direction as the molecule is migrate on the Au(110) plane. From the description above, we know that TCMB molecule with different conformations on different plane of surface arrangement displays different trajectories of movement and dynamical behaviors. Therefore, in order to understand the dynamical behaviors of TCMB monolayer on gold surface. In this work, the temperature effect on the adsorption behavior and the dynamic behavior of TCMB monolayer structure on the Au(111) substrate are investigated. From the calculation of the cohesive energy between molecules and the interaction energy between the molecule and the Au(111) substrate, we found that there are significant changes in cohesive energy and interaction energy at specific temperatures, which can be attributed to the deformation of the monolayer structure. Finally, the mean square displacement (MSD), diffusion coefficient(D) and distance between the molecule and the Au(111) substrate are calculated to investigate the diffusion property and motion behavior of TCMB monolayer at specific temperatures.

The S&P 500 Index is a leading indicator of U.S. equities and is meant to reflect the risk and return on the U.S. stock market. Many derivatives based on the S&P 500 are available to investors. The S&P 500 Futures of the Chicago Mercantile Exchange and the S&P 500 Index Options of the Chicago Board Options Exchange are both actively traded. My thesis argues that the S&P 500 Index is only a summary statistic designed to reflect the evolution of the stock market. It is not the value of a self-financed tradable portfolio, and its modifications do not coincide with changes of the value of any mimicking portfolio, due to the particular way the S&P 500 Index is computed and maintained. Therefore, the Spot-Futures Parity and the Put-Call Parity do not hold for the S&P 500 Index and its derivatives. Furthermore, its derivatives cannot be priced by using the standard option pricing models, which assume that the underlying asset is tradable. Chapter One analyzes why the S&P 500 Index does not represent the value of a self-financed tradable portfolio and why it cannot be replaced by the value of a tracker such as the SPDR. In particular, we show that the nonlinear and extreme risk dynamics of the SPDR and of the S&P 500 Index are very different. Chapter Two provides empirical evidence that the non-tradability of the S&P 500 Index can explain the Put-Call Parity deviations. Even after controlling for the liquidity risk of the options, we find that the Put-Call Parity implied dividends depend significantly on the option strike. In Chapter Three, we develop an affine multi-factor model to price coherently various derivatives such as forwards and futures written on the S&P 500 Index, and European put and call options written on the S&P 500 Index and on the S&P 500 futures. We consider the cases when the underlying asset is self-financed and tradable and when it is not, and show the difference between them. When the underlying asset is self-financed and tradable, an additional arbitrage condition has to be introduced and implies additional parameter restrictions.

This study examines the issue of tax neutrality of the income tax treatment of credit swaps in Canada in domestic context. It analyzes the applicable tax regime consisting of rules on tax characterization, timing and tax rates through the lenses of symmetry, consistency and certainty approaches. The study argues that the Canadian tax policy focuses on achieving symmetry in income tax treatment, rather than consistency. This is because introducing consistency would contradict the fundamental principles of the Canadian law. The study finds that the current tax regime is only partially neutral because symmetry has not been achieved in respect to credit swaps entered between non-financial organizations. To enhance symmetry, the study proposes to adopt a mandatory mark-to-market basis of taxation of credit swaps for the non-financial organizations. Further, to make income tax treatment more certain, the study proposes that the CRA should issue a non-binding guidance on credit swaps.

This study examines the issue of tax neutrality of the income tax treatment of credit swaps in Canada in domestic context. It analyzes the applicable tax regime consisting of rules on tax characterization, timing and tax rates through the lenses of symmetry, consistency and certainty approaches. The study argues that the Canadian tax policy focuses on achieving symmetry in income tax treatment, rather than consistency. This is because introducing consistency would contradict the fundamental principles of the Canadian law. The study finds that the current tax regime is only partially neutral because symmetry has not been achieved in respect to credit swaps entered between non-financial organizations. To enhance symmetry, the study proposes to adopt a mandatory mark-to-market basis of taxation of credit swaps for the non-financial organizations. Further, to make income tax treatment more certain, the study proposes that the CRA should issue a non-binding guidance on credit swaps.

The S&P 500 Index is a leading indicator of U.S. equities and is meant to reflect the risk and return on the U.S. stock market. Many derivatives based on the S&P 500 are available to investors. The S&P 500 Futures of the Chicago Mercantile Exchange and the S&P 500 Index Options of the Chicago Board Options Exchange are both actively traded. My thesis argues that the S&P 500 Index is only a summary statistic designed to reflect the evolution of the stock market. It is not the value of a self-financed tradable portfolio, and its modifications do not coincide with changes of the value of any mimicking portfolio, due to the particular way the S&P 500 Index is computed and maintained. Therefore, the Spot-Futures Parity and the Put-Call Parity do not hold for the S&P 500 Index and its derivatives. Furthermore, its derivatives cannot be priced by using the standard option pricing models, which assume that the underlying asset is tradable. Chapter One analyzes why the S&P 500 Index does not represent the value of a self-financed tradable portfolio and why it cannot be replaced by the value of a tracker such as the SPDR. In particular, we show that the nonlinear and extreme risk dynamics of the SPDR and of the S&P 500 Index are very different. Chapter Two provides empirical evidence that the non-tradability of the S&P 500 Index can explain the Put-Call Parity deviations. Even after controlling for the liquidity risk of the options, we find that the Put-Call Parity implied dividends depend significantly on the option strike. In Chapter Three, we develop an affine multi-factor model to price coherently various derivatives such as forwards and futures written on the S&P 500 Index, and European put and call options written on the S&P 500 Index and on the S&P 500 futures. We consider the cases when the underlying asset is self-financed and tradable and when it is not, and show the difference between them. When the underlying asset is self-financed and tradable, an additional arbitrage condition has to be introduced and implies additional parameter restrictions.