We consider three problems in this dissertation, all under the unifying theme of random matrix products. The first and second problems are concerned with weak convergence in stochastic matrices and circulant matrices, respectively, and the third is concerned with the numerical calculation of the Lyapunov exponent associated with some random Fibonacci sequences. Stochastic matrices are nonnegative matrices whose row sums are all equal to 1. They are most commonly encountered as transition matrices of Markov chains. Circulant matrices, on the other hand, are matrices where each row after the first is just the previous row cyclically shifted to the right by one position. Like stochastic matrices, circulant matrices are ubiquitous in the literature.In the first problem, we study the weak convergence of the convolution sequence mu to the n, where mu is a probability measure with support S sub mu inside the space S of d by d stochastic matrices, d greater than or equal to 3. Note that mu to the n is precisely the distribution of the product X sub 1 times X sub 2 times and so on times X sub n of the mu distributed independent random variables X sub 1, X sub 2, and so on, X sub n taking values in S. In [CR] Santanu Chakraborty and B.V. Rao introduced a cyclicity condition on S sub mu and showed that this condition is necessary and sufficient for mu to the n to not converge weakly when d is equal to 3 and the minimal rank r of the matrices in the closed semigroup S generated by S sub mu is 2. Here, we extend this result to any d bigger than 3. Moreover, we show that when the minimal rank r is not 2, this result does not always hold.The second problem is an investigation of weak convergence in another direction, namely the case when the probability measure mu's support S sub mu consists of d by d circulant matrices, d greater than or equal to 3, which are not necessarily nonnegative. The resulting semigroup S generated by S sub mu now lacking the nice property of compactness in the case of stochastic matrices, we assume tightness of the sequence mu to the n to analyze the problem. Our approach is based on the work of Mukherjea and his collaborators, who in [LM] and [DM] presented a method based on a bookkeeping of the possible structure of the compact kernel K of S.The third problem considered in this dissertation is the numerical determination of Lyapunov exponents of some random Fibonacci sequences, which are stochastic versions of the classical Fibonacci sequence f sub (n plus 1) equals f sub n plus f sub (n minus 1), n greater than or equal to 1, and f sub 0 equal f sub 1 equals 1, obtained by randomizing one or both signs on the right side of the defining equation and or adding a "growth parameter." These sequences may be viewed as coming from a sequence of products of i.i.d. random matrices and their rate of growth measured by the associated Lyapunov exponent. Following techniques presented by Embree and Trefethen in their numerical paper [ET], we study the behavior of the Lyapunov exponents as a function of the probability p of choosing plus in the sign randomization.

Η παρούσα εργασία πραγματεύεται το σχεδιασμό και τη δημιουργία εκπαιδευτικού λογισμικού για τη διδασκαλία της ομοιόμορφης σύγκλισης ακολουθιών πραγματικών συναρτήσεων. Η ομοιόμορφη σύγκλιση ακολουθιών πραγματικών συναρτήσεων είναι ένα μαθηματικό ζήτημα που αντιμετωπίζουν οι δευτεροετείς φοιτητές των Μαθηματικών Τμημάτων. Η εμπειρία τόσο των φοιτητών όσο και των εκπαιδευτικών έχει δείξει ότι η μάθηση αυτού του αντικειμένου με παραδοσιακές μεθόδους διδασκαλίας (π.χ., από έδρας διδασκαλία, ή εγχειρίδιο) παρουσιάζει δυσκολία στην κατασκευή των γραφικών παραστάσεων ακολουθιών πραγματικών συναρτήσεων. Στόχος του λoγισμικού UNICORN (UNIform COnvergence Resource Navigator) είναι να καλύψει αυτό το εκπαιδευτικό κενό διδάσκοντας την έννοια της ομοιόμορφης σύγκλισης μέσα από την κατασκευή και ανάλυση των γραφικών παραστάσεων. Ο σχεδιασμός του λογισμικού βασίστηκε κυρίως στην κονστρουκτιβιστική θεωρία μάθησης (constructivism). Το UNICORN είναι ένα ανοιχτό περιβάλλον που επιδιώκει να εμπλέξει ενεργά το φοιτητή στη μαθησιακή διεργασία και να ενεργοποιήσει τη δημιουργικότητά του. Η πλοήγηση του φοιτητή μέσα στο λογισμικό υποβοηθείται εν μέρει από κατευθυντήριες ερωτήσεις και διορθωτικό σχολιασμό (feedback), που βασίζονται στη θεωρία μάθησης του ινστραξιονισμού (instructionism). Το UNICORN κατασκευάστηκε με τη χρήση των προγραμμάτων Mathematica 4.0 (γραφικές παραστάσεις) και Macromedia Director 8.5 (κοινή επιφάνεια – interface), το υποπρόγραμμα BuddyApi (επικοινωνία UNICORN-Mathematica), και τη γλώσσα προγραμματισμού Lingo (λειτουργίες interface). Το λογισμικό είναι έτοιμο για πιλοτική χρήση και αξιολόγηση ως συμπληρωματικό εκπαιδευτικό υλικό και/ή ως εργαλείο μάθησης από απόσταση. / The present work discusses the design and development of educational software for teaching the uniform convergence of sequences of real functions. This advanced mathematical topic is taught during the second year of undergraduate studies in Mathematics Departments of Greek academic institutions. The experiences of both students and instructors agree that this topic is difficult to understand by using only traditional teaching methods (such as a lecture and the use of the blackboard). The reason is that it is difficult to draw manually graphical representations of the sequences of real functions. The educational software described here (named UNIform COnvergence Resource Navigator, or UNICORN) aims to cover this educational gap by teaching the concept of the uniform convergence of sequences of real functions through the construction and analysis of the respective graphical representations. The design of the educational software was mainly based on the teaching theory of constructivism. UNICORN is an open environment that aims to actively involve the user/learner in the learning process and to activate her creativity. The student’s navigation through the software is assisted by instructional questions and feedback, both of which are based on the learning theory of instructionism. UNICORN was developed with the help of Mathematica 4.0 (graphical representations), Director 8.5 (interface), and BuddiApi (communication between UNICORN and Mathematica). The software is ready for pilot testing and evaluation as supplementary teaching material and/or as a tool for long distance learning.

The one dimensional transient heat conduction equation was numerically modeled through matrix diagonalization and three time-discretization schemes. The discrete methods were first-order backward, second-order backward, and implicit finite difference schemes. All simulations used the central difference formula in the space dimension. Two relevant physical systems were considered: a uniformly conducting slab and a melting block of ice. The latter lead to a moving boundary system, or Stefan problem. The multiphysics of melting was numerically modeled through alternating updates of temperature and melt front profiles. Iterative simulations were run with regularly refined discretization meshes in both systems. In the case of the conducting slab, temperature at a fixed point in space and time was considered. For the Stefan problem, the melt front movement after a set time was the physical solution of interest. The accuracy of the convergent results was increased using Richardson acceleration and the Wynn's epsilon algorithm. Accuracy was improved for the moving boundary problem as well, but to a significantly lesser degree. The relative errors improved by five and two orders of magnitude for the conducting block and melting ice simulations, respectively. These relative errors were used to determine that matrix diagonalization is the most accurate numerical solution among the four considered. In both simulation convergence and acceleration potential, matrix diagonalization was superior to the implicit and explicit discretization solutions. However, matrix diagonalization required significantly more computational time. With the enhancement of convergence acceleration, the finite difference schemes obtained similar relative errors to the diagonalization model. This demonstrated the value of convergence acceleration in the classic dilemma for every programmer. There is always a balance struck between model sophistication, accuracy, and computational time. Convergence acceleration allows for a simpler numerical model to achieve comparable accuracy, and in less time than that required for sophisticated numerical models. The numerical models were also compared for stability through parameters that arose in each simulation. These parameters were the Courant-Friederichs-Lewy (CFL) condition and diagonalized eigenvalues. Though diagonalization was found to be the most accurate, it was determined that the backwards finite difference solutions are the easiest to evaluate for stability. In these solution methods, the CFL value allows the stability to be determined prior to running the simulation.

Conventional stereoscopic displays present a pair of stereoscopic images on a single and fixed image plane decoupled with the vergence and accommodation responses of the viewer. In consequence, these displays lack the capability of correctly rendering focus cues (i.e. accommodation and retinal blur) and may induce the discrepancy between accommodation and convergence. A number of visual artifacts associated with incorrect focus cues in stereoscopic displays have been reported, limiting the applicability of these displays for demanding applications and daily usage.In this dissertation, methods and apparatus for generating addressable focus cues in conventional stereoscopic displays are proposed. Focus cues can be addressed throughout a volumetric space, either through dynamically varying the focal distance of a display enabled by an active optical element or by multiplexing a stack of 2-D image planes. Optimal depth-weighted fusing functions are developed to fuse a number of discrete image planes into a seamless volumetric space with continuous and near-correct focus cues similar to the real world counterparts.The optical design, driving methodology, and prototype implementation of the addressable focus displays are presented and discussed. Experimental results demonstrate continuously addressable focus cues from infinity to as close as the near eye distance. Experiments to further evaluate the depth perception in the display prototype are conducted. Preliminary results suggest that the perceived distance and accommodative response of the viewer match with the addressable accommodation cues rendered by the display, approximating the real-world viewing condition.

This study sought to understand using qualitative methods why and how the Government of Singapore came to set-up organized research units (ORU) in her two autonomous universities - the National University of Singapore (NUS) and Nanyang Technological University (NTU). That is, are ORUs the chief means in transforming NUS and NTU into top WCUs? The underpinnings of the institutional theory in the globalized context, the theory of academic capitalism, and guidance by frameworks on educational policy transfer, as well as the glonacal heuristics, together with document and discourse analysis of published documents, aided in the design of this study.This study finds that key state and institutional actors in Singapore decided to emulate the key features of U.S.-originated organized research units to make R&D and innovation-led economic growth the vehicle of sustaining this global city-state's global competitiveness in the knowledge-economy and to better elevate the status of both NUS and NTU as world-class. Because global rankings have branding implications, catch-up nations and institutions should make serious attempts to balance the ranking-enhancement effort with their local, national, and regional science-research needs given the constraints of available capital and resources.

We study and analyze the performance of iterative equalization and decoding (IED) using an M-BCJR equalizer. We use bit error rate (BER), frame error rate simulations and extrinsic information transfer (EXIT) charts to study and compare the performances of M-BCJR and BCJR equalizers on precoded and non-precoded channels. Using EXIT charts, the achievable channel capacities with IED using the BCJR, M-BCJR and MMSE LE equalizers are also compared. We predict the BER performance of IED using the M-BCJR equalizer from EXIT charts and explain the discrepancy between the observed and predicted performances by showing that the extrinsic outputs of the $M$-BCJR algorithm are not true logarithmic-likelihood ratios (LLR's). We show that the true LLR's can be estimated if the conditional distributions of the extrinsic outputs are known and finally we design a practical estimator for computing the true LLR's from the extrinsic outputs of the M-BCJR equalizer.

Background: Family-business is considered to be the most frequent and complex form of business organization around the world. However, recently there has been a large number of corporate scandals in such firms especially at the board level (e.g. Parmalat). Within the framework of two corporate governance models characterized by the Continental European and the Anglo-Saxon model, boards of directors hold a central position. This position becomes of great importance when talking about public companies and more specifically in public family-controlled companies. The concentration of ownership is the main characteristic of the Continental European, which is the most workable form of corporate governance for family-controlled business. Nevertheless, family-controlled companies acting under the Anglo-Saxon model have also been able to operate successfully. Therefore, we will investigate if there is a convergence of corporate governance in family-controlled companies across frontiers focusing mainly on boards’ structures and composition as well as ownership, and the sub-committees. Purpose: The overall purpose of this thesis is to contribute to the understanding of Corporate Governance in public Family-controlled firms which are in the Swedish and United Kingdom stock market. More specifically, investigate whether the boards’ structures and composition, as well as ownership and the existence of sub-committees show similarities or not in Family-controlled firms acting within the framework of an Anglo-Saxon and Continental model of Corporate Governance Method: A quantitative approach was used to fulfill the purpose of this thesis. Furthermore, the top 10 family-controlled companies with highest market-capitalization have been selected from both countries to constitute our sample. The empirical material was gathered mainly from the annual reports of the companies but also by contacting the companies by email or from articles in online newspapers. Conclusion: This study found that in some aspects of corporate governance convergence exists while in others it does not. Regarding board structures and composition, there is a convergence to “one tier board” and the presence of family members and employee representation in boards. On the other hand, when it comes to the sizes of the boards and number of independent directors in the boards we argue that convergence is not present.

No description available.

Darbe gaunama, jog silpno matų konvergavimo erdvės X prasme išlpaukia charakteringųjų transformacijų konvergavimas ir atvirkščiai, jeigu charakteringosios transformacijos konverguoja į funkcijas tolydžias nuliniame taške, tai iš čia išplaukia matų silpnas konvergavimas erdvės X prasme. / It is obtained, that the weak convergence in the sense of X implies the convergence of characteristic transforms, and, on the contrary, if the characteristic transforms converge weakly to the functions contiuous at zero, the from this the weak convergence in the sense of X for the probability measures fallows.

Darbe įrodyta diskreti ribinė teorema bendrųjų Dirichlė eilučių poklasiui meromorfinių funkcijų erdvėje. Pateiktas ribinio mato išreikštinis pavidalas. / The discrete limit theorem for general Dirichlet series in the space of meromorphic functions was proved in this paper. Expressed shape of limit measue was provided.