The main objective of the dissertation is to formulate a .system for financial analysis and planning in the Costa Rican economy. First, a tentative structure within which a model of the financial system can be organized is outlined, and the corresponding statistical tables are constructed for the period 1961-1975. It is expected that such tables will be periodically updated and incorporated into a series of publications which describe and analyze financial developments in Costa Rica. The study then analyzes the evolution of the Costa Rican financial system based on the generated data and a set of well-known financial indicators. Finally, alternative linear financial models are formulated and estimated; they are the basis for an analysis of financial interdependence, i.e., the process through which sectoral investment and/or saving decisions generate indirect financi~l consequences in the rest of the economy. Some interesting findings of the study, related to the analysis of financial developments during the period 1961-1975, are the observed rapid growth of the relative size of the Costa Rican financial super-structure, coupled with an accelerated process of monetization of the economy. In addition the importance of the foreign sector in the financial.activities of the country shows a considerable increase. The empirical evidence that emerges from estimating alternative linear financial models suggests a considerable degree of financial interdependence, with the government sector taking a predominant role in the generation of financial multiplier effects. It also indicates that the definition of sectoral preferences over liability holdings as a behavioral assumption in the underlying model, explains the pattern of sectoral financial behavior in the Costa Rican economy more effectively than the alternative assumption that preferences are defined over asset holdings. / Thesis / Doctor of Philosophy (PhD)

Nous avons développé une nouvelle méthode de microscopie par effet électro-optique linéaire (effet Pockels), dite PLEOM, permettant de cartographier la susceptibilité du deuxième ordre Chi(2) d'un matériau non-centrosymétrique [1, 2]. Cette méthode est complémentaire de la microscopie de génération de seconde harmonique, et s’en distingue par différents aspects physiques et pratiques. Grâce à une détection interférométrique stabilisée, le retard de phase provoqué par une variation d'indice locale du matériau non-linéaire sous l'effet d'un champ électrique est détecté à 10-6 radians près, ouvrant la voie à l'imagerie d'échantillons biologiques ou au suivi du mouvement de nano-sondes [3]. PLEOM apporte un type de données nouveau, la "réponse en phase" du matériau, porteuse d'information physiques plus difficilement accessibles en microscopie biphotonique.Ce manuscrit décrit de nouveaux domaines de développement et d’application de PLEOM, qui a évolué vers une plateforme aux applications variées et multi-échelles, allant du nanométrique au millimétrique.Nous avons tout d’abord montré comment déterminer le vecteur de polarisation attaché à des nano-cristaux ferroélectriques uniques, en vue de leur utilisation comme nano-sondes. Cette nouvelle méthode permet, à notre connaissance de façon unique, de distinguer deux nano-cristaux mono-domaines d'orientations exactement opposées, dont les réponses en SHG ne peuvent pas être distinguées. Une image de phase électro-optique, combinée à un diagramme de polarisation, donne accès à l'orientation vectorielle d'un nano-cristal orienté aléatoirement dans le référentiel du laboratoire. Un verrou est ainsi levé pour des applications comme l'imagerie de nano-domaines ferroélectriques, celle de potentiels électrochimiques membranaires, où l'étude de la dynamique de rotation de molécules. Deux spécificités remarquables de PLEOM en font une méthode d'avenir : la faible intensité de pompage qui assure une bien meilleure biocompatibilité ainsi que la simplicité de la source laser continue utilisée.Nous avons ainsi pu utiliser PLEOM pour caractériser les domaines ferroélectriques d'un cristal de KTiOPO4 périodiquement réorienté en vue d’un quasi-accord de phase, ainsi que ceux d'un cristal bidimensionnel quasi-périodique de LiNbO3. Un retournement clair de la phase de 180 degree est observé au travers des parois de domaines, dont les coefficients électro-optiques apparaissent opposés dans le référentiel du laboratoire. PLEOM se présente ainsi comme un outil de caractérisation non destructif des propriétés de ces cristaux artificiels dont les motifs et les défauts (tels qu'une orientation localement incomplète) ont été caractérisés spatialement, et permet de mesurer localement leurs propriétés non-linéaires, dont le caractère tensoriel permet d’aller au-delà des informations acquises en microscopie classique.En outre, nous avons fait la preuve de principe d'une nouvelle expérience biomimétique, visant à étudier les potentiels membranaires cellulaires, en utilisant PLEOM sur des membranes phospholipidiques créées sur puce micro-fluidique et dopées en colorants. / Complementing Second-Harmonic Generation (SHG) microscopy, a new home-made nonlinear microscope named Pockels Linear Electro-Optical Microscopy (PLEOM) based on the linear electrooptic (Pockels) effect, has been developed and used to map the second-order susceptibility Chi(2) of non-centrosymmetric materials with high sensitivity due to a stabilized interferometric homodyne detection scheme [1, 2]. This enables PLEOM to detect the electrooptic phase retardation of light resulting from the variation of the refractive index of nonlinear materials down to 10-6 radian and to investigate nonlinear materials at the nano-scale [3] towards applications in imaging of biological samples and tracking of labels therein. With PLEOM, a new imaging method allows to access, besides the aplitude, the no less crucial phase response, which is not readily amenable to classical SHG microscopy. In the frame of this dissertation, we have further extended the range of applications of PLEOM to investigate nonlinear materials and structures from nano- to millimeter-scale.Firstly, we have proposed and demonstrated a new approach towards the full vector determination of the spontaneous polarization of single ferroelectric nano-crystals used as SHG nano-probes. This method allows to remove the ambiguity inherent to earlier polarization-resolved SHG microscopy experiments, and has permitted full determination of the orientation of single domain ferroelectric nano-crystals. The electrooptic phase response obtained in the form of phase images and polarization diagrams yields the full orientation in the laboratory frame of randomly dispersed single nano-crystals, together with their electric polarization dipole. The complete vector determination of the dipole orientation is a prerequisite to important applications including ferroelectric nano-domain orientation, membrane potential imaging and rotation dynamics of single biomolecules, especially by using a new low-cost non-invasive imaging method with a low intensity illumination beam.The ferroelectric domain pattern of periodically poled KTiOPO4 and of a two-dimensional decagonal quasi-periodic LiNbO3 nonlinear crystal was determined by local measurement of their electro-optically induced phase retardation. Owing to the sign reversal of the electrooptic coefficients upon domain inversion, a 180 degree (pi) phase shift is observed across domain barriers between domains with opposed orientations. PLEOM allows to reveal the nonlinear and electrooptic spatially modulated patterns in ferroelectric crystals in a non-destructive manner and to determine their poling period, duty cycle and short-range order as well as to detect local defects in the domain structure, such due to incomplete poling.In addition, we have also proposed and demonstrated a new method, based on the voltage dependence of the electrooptic dephasing, to mimic the membrane potential in cells, working at this stage on nonlinear dye containing phospholipidic membranes, grown in a microfluidic set-up.

This work investigates some aspects of the dynamics of non-invertible quasi-periodic circle maps, from the point of view of rotation numbers and their structure in parameter space.Circle maps and quasi-periodically forced circle maps have been widely used asa model for a broad range of physical phenomena. From the mathematical point of view they have also received considerable attention because of the many interesting features they exhibit.The system used is given by the maps: x_n = [ x_n-1 + a + b/(2pi) sin( 2pi x_n-1) + c sin( 2pi theta_n-1) ] mod 1, and, theta_n = theta_n-1 + omega.Where a, b and c are real constants. In addition, b and omega are restricted, respectively, to values larger than one and irrational.A fundamental part of this thesis consists of numerical approximations of rotation intervals using and adapting of the work of Boyland (1986) to the quasi-periodic case.Particular emphasis was given to the case of large coupling strength in quasi-periodicforcing.Examination of the computed rotation numbers for the large coupling case, together with previous claims suggesting that for large coupling strength the b-term could be neglected (see Ding (1989)), led to the formulation of an ergodic argument which is statistically supported. This argument indicates that, for this case, the qualitative behavior of rotation number depends linearly on a. It is also shown that the length of the rotation interval, when the transition from a trivial rotation interval (invertible case) to a non-trivial rotation interval occurs, it develops locally as a universal unfolding.A different map, piecewise monotone, and structurally similar to the maps defined to calculate the edges of rotation intervals in Boyland (1986), is studied to illustrate how the rotation number grows. The edges of rotation intervals are analytically calculated and matched with numerical observations.

Due essentially to the difficulties associated with obtaining explicit forms of stationary marginal distributions of non-linear stationary processes, appropriate characterizations of such processes are worked upon little. After discussing an elaborate motivation behind this thesis and presenting preliminaries in Chapter 1, we characterize, in Chapter 2, the stationary marginal distributions of certain non-linear multivariate stationary processes. To do so, we show that the stationary marginal distributions of these processes belong to specific skew-distribution families, and for a given skew-distribution from the corresponding family, a process, with stationary marginal distribution identical to that given skew-distribution, can be found. While conventional time series analysis greatly depends on the assumption of stationarity, measurements taken from many physical systems, which consist of both periodicity and randomness, often exhibit cyclostationarity (i.e., a periodic structure in their first- and second-order moments). Identifying the hourly global horizontal irradiances (GHIs), collected at a solar monitoring station of Saudi Arabia, as a cyclostationary process and considering the significant impact of that on the energy production in Saudi Arabia, Chapter 3 provides a temporal model of GHIs. Chapter 4 extends the analysis to a spatio-temporal cyclostationary modeling of 45 different solar monitoring stations of the Kingdom. Both the proposed models are shown to produce better forecasts, more realistic simulations, and reliable photovoltaic power estimates in comparison to a classical model that fails to recognize the GHI data as cyclostationary. Chapter 5 extends the notion of cyclostationarity to a novel and flexible class of processes, coined evolving period and amplitude cyclostationary (EPACS) processes, that allows periods and amplitudes of the mean and covariance functions to evolve and, therefore, accommodates a much larger class of processes than the cyclostationary processes. Thereafter, we investigate its properties, provide methodologies for statistical inference, and illustrate the presented methods using a simulation study and a real data example, from the heavens, of the magnitudes of the light emitted from the variable star R Hydrae. Finally, Chapter 6 summarizes the findings of the thesis and discusses its significance and possible future extensions.

Block copolymers can self-assemble into a variety of periodic nanostructures and therefore, are promising candidates for a diverse range of applications. While self-assembly of block copolymers has been widely studied and exploited, graft copolymers have remained far less explored in this context. One of the primary reasons for this is that the most commonly used methods to prepare graft copolymers leads to polymers that do not have precisely defined structures; specifically, controlling the precise location of the grafted segments is a synthetically difficult challenge. In typical chain polymerization processes, statistically random incorporation of monomers takes place and consequently, the periodicity of the grafted segment along the backbone is very difficult to control precisely; therefore, such methods cannot be utilized to prepare periodically grafted copolymers. Some recent efforts towards the preparation of sequence regulated copolymers using controlled radical polymerization in conjunction with periodic dosing of a commoner could provide an alternative to better regulate the periodicity, although this will also not be perfectly periodic. The only approach to control the periodicity perfectly is to utilize condensation polymerization approaches, wherein one of the monomers serve as a spacer whereas the other provides the opportunity to install the graft segment, as depicted in Scheme 1. One of the earliest examples of the utilization of a condensation approach to locate desired units at periodic intervals was reported by Wagener and co-workers using Acrylic Diene Metathesis (ADMET) process.1 ]n periodicity ]n graft segment Scheme 1. Synthetic scheme for the preparation of periodically grafted copolymers using condensation polymerization. From our lab, Roy et al. developed periodically grafted amphiphilic copolymers (PGAC), based on a readily available starting material, diethyl malonate;2 melt trans-esterification between diethyl malonate, containing a pendant hexaethylene glycol monomethyl ether (HEG) segment and 1,22-docosane diol resulted in PGAC wherein the hydrophilic oligo ethylene glycol units were placed on every 27th atom along the backbone (Scheme 2). Such PGAC underwent self-segregation and adopted a folded zigzag conformation, which was driven by the intrinsic immiscibility of the alkylene and HEG segments and was reinforced by the strong tendency for long chain alkylene segments to crystallize in a paraffinic lattice. However, one of the drawbacks of the above approach was that the hydrophilic pendant unit was installed at the monomer stage and consequently, the synthetic approach does not allow easy variation of the hydrophilic grafted segment; this limits the flexibility and any structural variation of the pendant segment would be synthetically tedious. 150 oC DBTDL 5 20 DBTDL = Dibutyltin dilaurate Scheme 2. Synthesis of PGAC, based on diethyl malonate, and immiscibility-driven folding of such PGACs. Mandal et al. developed a more general strategy for the synthesis of such periodically grafted systems; they prepared periodically clickable polyesters carrying propargyl groups at regular intervals, by the solution polycondensation of 2-propargyl-1,3-propanediol or 2,2-dipropargyl-1,3-propanediol and the acid chloride of 1,20-eicosanedioic acid. Such periodically clickable polyesters were shown to react quantitatively with a fluoroalkyl azide3 and PEG 350 azide4, thus allowing them to place different kinds of functionalities precisely along the backbone, as shown in Scheme 3. The immiscibility of the alkylene and fluoroalkyl/PEG segments caused the polymer chains to fold in a zigzag fashion, thereby facilitating the segregation of these segments, as observed earlier in the study by Roy et al.2 The objective of this study was to place various desired functionalities along the polymer backbone and examine their effect on the self-assembly behaviour and morphology of such periodically clicked systems. Scheme 3. Synthetic scheme for the generation of periodically clickable polyesters and their subsequent functionalization via Cu-catalysed click chemistry. In Chapter 2, we describe an alternative general strategy for the scalable synthesis of periodically graftable polyesters and their subsequent functionalization to generate a wide variety of periodically grafted systems. The importance of our approach lies in our choice of the monomer, which is based on itaconic acid, an inexpensive and bio-sourced molecule. We demonstrated that dibutyl itaconate can be melt-condensed with aliphatic diols to generate unsaturated polyesters (Scheme 4); importantly, we showed that the double bonds in the itaconate moiety remain unaffected during the melt polymerization. A particularly useful attribute of these polyesters is that the exo-chain double bonds are conjugated to the ester carbonyl and therefore, can serve as excellent Michael acceptors. A variety of organic thiols, such as alkane thiols, MPEG thiol, thioglycerol, derivative cysteine etc., were shown to quantitatively Michael-add to the exo-chain double bonds and generate interesting functionalized polyesters; similarly, organic amines, such as N-methylbenzylamine, diallyl amine and proline also underwent Michael addition across the double bond (Scheme 4). Thus, such poly(alkylene itaconate)s could be utilized to place diverse functionalities at regular intervals along the polymer backbone. Scheme 4. Preparation of periodically graftable polyesters, based on itaconic acid, and their subsequent modification by Michael addition. In Chapter 3, we examined a series of periodically grafted polyesters carrying long crystallizable alkylene (C-20) segments along the backbone and pendant polyethylene glycol monomethyl ether (MPEG) segments grafted at periodic intervals. Such periodically grafted amphiphilic copolymers (PGAC) having MPEG graft segments of varying lengths were prepared by utilizing the activated exo-chain double bonds in poly(icosyl itaconate) (PII) that carries a 20-carbon alkylene segment; MPEG thiols of varying lengths (TREG, 350, 550 and 750) were quantitatively grafted under standard Michael addition conditions to yield the required graft copolymers, as shown in Scheme 5. Scheme 5. Synthesis of a series of periodically grafted amphiphilic copolymers (PGAC) utilizing post-polymerization modification via Michael addition with MPEG thiols of varying lengths. The immiscibility of the backbone alkylene and pendant MPEG segments, and the strong propensity of the alkylene segments to crystallize in a paraffinic lattice, drive these systems to fold in a zigzag fashion and subsequently organize into a lamellar morphology, as shown in Scheme 6. Interestingly, all the graft copolymers exhibited a clear and invariant melting transition at ~44°C that suggested the crystallization of the backbone C-20 segment; the MPEG segments were, however, amorphous except in the case of polymers carrying MPEG 550/MPEG-750 segments, wherein a second melting transition corresponding to the independent crystallization of the PEG segment was also seen. SAXS studies indicated that all of the samples exhibited lamellar morphologies wherein more importantly, the inter-lamellar spacing was seen to increase linearly with the MPEG length (Scheme 6). This study provides a new design for controlling the dimensions of the microphase-separated nanostructures at significantly smaller length scales (sub-10 nm) than is typically possible using block copolymers. Scheme 6. Schematic representation of formation of lamellar morphology in PGACs and control of interlamellar spacing in such systems. In order to understand the influence of having a mixture of MPEG lengths on the self-assembled morphology, in Chapter 4 we prepared a series of PGACs by co-grafting the parent poly(icosyl itaconate) with a mixture of two different MPEG thiols, namely MPEG-350 and MPEG-750; the mole-ratios of these two PEGs were varied to generate co-grafted PGACs, carrying different amounts of the two MPEG segments randomly distributed along the chain (Scheme 7). Parallely, we also examined the behaviour of physical mixtures of two different PGACs, one bearing MPEG-350 and the other MPEG-750 grafts; keeping the total MPEG content constant, we sought to examine the differences in the behaviour of randomly co-grafted polymers and physical mixtures. Scheme 7. Preparation of co-grafted PGACs and physical mixtures of two different PGACs. The co-grafted PGACs also exhibited a lamellar morphology; interestingly, the inter- lamellar spacing increased linearly with the total volume of PEG domain. This suggested that despite the presence of MPEG segments of two different lengths in the co-grafted samples, there occurred a reorganization of the PEG chains within the amorphous domain ensuring that the condition of incompressibility is not violated, thereby giving rise to a weighted average interlamellar spacing, as shown in Scheme 8. In contrast, the SAXS patterns of the physical mixtures revealed the presence of two distinct lamellar domains in the sample; this indicated that the two homo-grafted samples do not mix and form separate lamellar domains. The self- segregation induced folding and subsequent crystallization of the central alkylene segments clearly appeared to dominate the final morphology. Scheme 8. Schematic depiction of the possible scenarios that could arise when MPEG segments of two different lengths, namely MPEG350 and MPEG750, are present in the PGACs; top panel depicts the co-grafted PGACs, whereas the bottom panel shows the case of mixtures of PGACs with two different MPEG lengths. In Chapter 5, we have dealt with the design and synthesis of chain-end functionalizable polyalkylene itaconates. Changing the monomer from dibutyl itaconate to dipropargyl itaconate and using it in controlled excess allowed us to generate chain-end functionalizable polymers containing propargyl groups at the chain ends, in addition to the exo-chain double bonds along the backbone, thereby providing the opportunity for orthogonal functionalization. In order to obtain three different telechelic polymers with target DPs (degree of polymerization) of 5, 10 and 20 respectively, 3 different mole ratios of the two monomers (dipropargyl itaconate and 1,20-eicosanediol) were used (Scheme 9). Scheme 9. Synthetic scheme for the generation of chain-end functionalizable polyalkylene itaconates. Orthogonal functionalization of the resultant polymers was carried out using thiol-Michael addition and Cu(I)-catalysed alkyne-azide cycloaddition (AAC), without interference between the functional handles present along the polymer backbone and the chain-end, respectively. Michael addition with triethylene glycol thiol and subsequent Cu-catalysed click reaction with MPEG 750 azide led to the generation of ABA type triblock copolymers where the middle block is a periodically grafted amphiphilic block and the two linear end blocks are hydrophilic in nature. Furthermore, such propargyl-terminated polyalkylene itaconates were used as macromonomers to prepare multiblock copolymers. The telechelic polymers were first treated with PEG 600 diazide, resulting in the formation of alternating multiblock copolymers; these multiblock copolymers were further reacted with thioglycerol to generate amphiphilic multiblock copolymers where one of the blocks is a periodically functionalized amphiphilc block, as depicted in Scheme 10. In both these amphiphilic block copolymer systems, a key feature is that the periodically functionalized amphiphilic block folds into a zigzag form, as evident from the presence of a nearly invariant melting peak corresponding to the crystallization of the alkylene segment. Scheme 10. Preparation of multiblock copolymers utilizing propargyl-terminated polyalkylene itaconates as a macromonomer. In summary, the thesis has demonstrated the design and synthesis of a series of novel amphiphilic copolymers using a bio-sourced monomer, wherein the driving theme is the immiscibility driven self-segregation that leads to the folding of the chain; these have been thoroughly examined using DSC, SAXS, WAXS, variable temperature FT-IR and AFM measurements. References (1) Berda, E. B.; Lande, R. E.; Wagener, K. B. Macromolecules 2007, 40, 8547. (2) Roy, R. K.; Gowd, E. B.; Ramakrishnan, S. Macromolecules 2012, 45, 3063. (3) Mandal, J.; Krishna Prasad, S.; Rao, D. S. S.; Ramakrishnan, S. Journal of the American Chemical Society 2014, 136, 2538. (4) Mandal, J.; Ramakrishnan, S. Langmuir 2015, 31, 6035.

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results.<p> A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification.<p> In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design.

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results.<p> A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification.<p> In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design.

From its beginning in the early 20th century, quantum theory has become progressively more important especially due to its contributions to the development of technologies. Quantum mechanics is crucial for current technology such as semiconductors, and also holds promise for future technologies such as superconductors and quantum computing. Despite of the success of quantum theory, its applications have been mostly limited to equilibrium or static systems due to 1. lack of experimental controllability of non-equilibrium quantum systems 2. lack of theoretical frameworks to understand non-equilibrium dynamics. Consequently, physicists have not yet discovered too many interesting phenomena in non-equilibrium quantum systems from both theoretical and experimental point of view and thus, non-equilibrium quantum physics did not attract too much attentions. / Physics

Most research on stock prices is based on the present value model or the more general consumption-based model. When applied to real economic data, both of them are found unable to account for both the stock price level and its volatility. Three essays here attempt to both build a more realistic model, and to check whether there is still room for bubbles in explaining fluctuations in stock prices. In the second chapter, several innovations are simultaneously incorporated into the traditional present value model in order to produce more accurate model-based fundamental prices. These innovations comprise replacing with broad dividends the more narrow traditional dividends that are more commonly used, a nonlinear artificial neural network (ANN) forecasting procedure for these broad dividends instead of the more common linear forecasting models for narrow traditional dividends, and a stochastic discount rate in place of the constant discount rate. Empirical results show that the model described above predicts fundamental prices better, compared with alternative models using linear forecasting process, narrow dividends, or a constant discount factor. Nonetheless, actual prices are still largely detached from fundamental prices. The bubble-like deviations are found to coincide with business cycles. The third chapter examines possible cointegration of stock prices with fundamentals and non-fundamentals. The output gap is introduced to form the non-fundamental part of stock prices. I use a trivariate Vector Autoregression (TVAR) model and a single equation model to run cointegration tests between these three variables. Neither of the cointegration tests shows strong evidence of explosive behavior in the DJIA and S&P 500 data. Then, I applied a sup augmented Dickey-Fuller test to check for the existence of periodically collapsing bubbles in stock prices. Such bubbles are found in S&P data during the late 1990s. Employing econometric tests from the third chapter, I continue in the fourth chapter to examine whether bubbles exist in stock prices of conventional economic sectors on the New York Stock Exchange. The ‘old economy’ as a whole is not found to have bubbles. But, periodically collapsing bubbles are found in Material and Telecommunication Services sectors, and the Real Estate industry group.

<p> In this work, tunable Mid-Infrared (IR) light sources based on quasi-phase matched (QPM) difference frequency generation (DFG) by periodically poled lithium niobate (PPLN) crystals are studied. The theory of DFG and the characteristics of lithium niobate crystals are described and analyzed. Characteristics of the wavelength tuning of QPM DFG by PPLN crystals are studied. In order to analyze in detail, simulation and experimental data of the widely tunable mid-IR laser source around 2 1- μm to 5 1- μm wavelength are presented. The simulations of DFG process by PPLN are conducted based on the nonlinear optics reported. In the experiment, a 1.064 μm Nd:YAG laser and a tunable Ti:sapphire laser are employed as the signal and pump lasers, respectively. Based on the studies of the wavelength tuning characteristics at different temperatures, an optimization procedure to achieve a maximum wavelength tuning range is proposed. The potential applications in gas detection of the mid-IR source are also described briefly. Recommendation for future works and potential applications of the PPLN DFG based mid-IR lasers are discussed. </p> / Thesis / Master of Applied Science (MASc)