Combining Bio- and Chemo-Catalysis for the Conversion of Bio-Renewable Alcohols: Homogeneous Iridium Catalysed Hydrogen Transfer Initiated Dehydration of 1,3-Propanediol to Aldehydes

Combining whole cell biocatalysis and chemocatalysis in a single reaction sequence avoids unnecessary separations, and the associated waste and energy consumption. Bacterial fermentation has been employed to convert waste glycerol from biodiesel production into 1,3-propanediol. This 1,3-propanediol can be extracted selectively from the aqueous fermentation broth using ionic liquids. 1,3-propanediol in ionic liquid solution was converted to propanal by hydrogen transfer initiated dehydration (HTID) catalysed by a Cp*IrCl2(NHC) (Cp* = pentamethylcyclopentadienyl; NHC = carbene ligand) complex. The use of an ionic liquid solvent enabled the reaction to be performed under reduced pressure, facilitating the isolation of the product, and improving the reaction selectivity. The Ir(III) catalyst in ionic liquid was found to be highly recyclable.

Detecting localized homogeneous anomalies over spatio-temporal data

The last decade has witnessed an unprecedented growth in availability of data having spatio-temporal characteristics. Given the scale and richness of such data, finding spatio-temporal patterns that demonstrate significantly different behavior from their neighbors could be of interest for various application scenarios such as – weather modeling, analyzing spread of disease outbreaks, monitoring traffic congestions, and so on. In this paper, we propose an automated approach of exploring and discovering such anomalous patterns irrespective of the underlying domain from which the data is recovered. Our approach differs significantly from traditional methods of spatial outlier detection, and employs two phases – i) discovering homogeneous regions, and ii) evaluating these regions as anomalies based on their statistical difference from a generalized neighborhood. We evaluate the quality of our approach and distinguish it from existing techniques via an extensive experimental evaluation.

Experimental Saltwater Intrusion in Coastal aquifers Using Automated Image Analysis: Applications to Homogeneous Aquifers.

This paper presents the applications of a novel methodology to quantify saltwater intrusion parameters in laboratory-scale experiments. The methodology uses an automated image analysis procedure, minimizing manual inputs and the subsequent systematic errors that can be introduced. This allowed the quantification of the width of the mixing zone which is difficult to measure in experimental methods that are based on visual observations. Glass beads of different grain sizes were tested for both steady-state and transient conditions. The transient results showed good correlation between experimental and numerical intrusion rates. The experimental intrusion rates revealed that the saltwater wedge reached a steady state condition sooner while receding than advancing. The hydrodynamics of the experimental mixing zone exhibited similar
traits; a greater increase in the width of the mixing zone was observed in the receding saltwater wedge, which indicates faster fluid velocities and higher dispersion. The angle of intrusion analysis revealed the formation of a volume of diluted saltwater at the toe position when the saltwater wedge is prompted to recede. In addition, results of different physical repeats of the experiment produced an average coefficient of variation less than 0.18 of the measured toe length and width of the mixing zone.

The Riemann-Hilbert method applied to the theory of orthogonal polynomials

Doutoramento em Matemática

Temperature modelling of an homogeneous medium using genetically selected RBF (LIC)

Temperature modelling of human tissue subjected to ultrasound for therapeutic use is essencial for an accurate instrumental assessment and calibration. In this paper punctual temperature modeling of a homogeneous medium, radiated by therapeutic ultrasound, is presented.

Transverse Vibrations in Beams Supported by a Piece-Wise Homogeneous Visco- Elastic Foundation

Transversal vibrations induced by a load moving uniformly along an infinite beam resting on a piece-wise homogeneous visco-elastic foundation are studied. Special attention is paid to the additional vibrations, conventionally referred to as transition radiations, which arise as the point load traverses the place of foundation discontinuity. The governing equations of the problem are solved by the normalmode analysis. The solution is expressed in a form of infinite sum of orthogonal natural modes multiplied by the generalized coordinate of displacement. The natural frequencies are obtained numerically exploiting the concept of the global dynamic stiffness matrix. This ensures that the frequencies obtained are exact. The methodology has restrictions neither on velocity nor on damping. The approach looks simple, though, the numerical expression of the results is not straightforward. A general procedure for numerical implementation is presented and verified. To illustrate the utility of the methodology parametric optimization is presented and influence of the load mass is studied. The results obtained have direct application in analysis of railway track vibrations induced by high-speed trains when passing regions with significantly different foundation stiffness.

Unveiling Shi’i Religious Identities: Case Studies of Hijab in Culturally Homogeneous Canadian Schools

This qualitative case study explored 10 young female Shi’i Muslim Arabic-Canadian students’ experiences associated with wearing the Hijab (headscarf) within their home, community, and predominantly White Canadian public elementary school environments. The study integrated several bodies of scholarly theories in order to examine the data under a set of comprehensive lenses that more fully articulates and theorizes on the diversity of female Shi’i Muslim Canadian students’ experiences. These theories are: identity theories with a focus on religious identity and negative stereotypes associated with Muslims; feminism and the Hijab discourses; research pertaining to Muslims in school settings; and critical race theory. In order to readdress the dearth of information about Shi’is’ experiences in schools, this study provides an in-depth case study analysis in which the methodology strategies included 10 semi-structured in-depth interviews, 2 focus-group meetings, and the incorporation of the researcher’s fieldnotes. Data analysis revealed the following themes corresponding to participants’ experiences and values in their social worlds of home, community, and schools: (a) martyrdom and self-sacrifice as a means for social justice; (b) transformational meaning of the Hijab; (c) intersectionality between culture, religion, and gender; and (d) effects of visits “back home” on participants’ religious identities. Additional themes related to participants’ school experiences included: (a) “us versus them” mentality; (b) religious and complex secular dialogues; (c) absence of Muslim representations in monocultural schools; (d) discrimination; (e) remaining silent versus speaking out; and (f) participants’ strategies for preserving their identities. Recommendations are made to integrate Shi’i Muslim females’ identity within the context of Islam and the West, most notably in relation to: (a) the role of Muslim community in nondiverse settings as a space that advances and nurtures Shi’i Muslim identity; and (b) holistic and culturally responsive teaching that fosters respect of others’ religiosity and spirituality. This study makes new inroads into feminist theorizing by drawing conceptual links between these previously unknown connections such as the impact of the historical female exemplary role model and the ritual stories on the experiences of Muslim females wearing the Hijab.

Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

Certain problems concerning polynomials and transcendental entire functions of exponential type

Soit $\displaystyle P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ un polynôme de degré $n$ et $\displaystyle M:=\sup_{|z|=1}|P(z)|.$ Sans aucne restriction suplémentaire, on sait que $|P'(z)|\leq Mn$ pour $|z|\leq 1$ (inégalité de Bernstein). Si nous supposons maintenant que les zéros du polynôme $P$ sont à l'extérieur du cercle $|z|=k,$ quelle amélioration peut-on apporter à l'inégalité de Bernstein? Il est déjà connu [{\bf \ref{Mal1}}] que dans le cas où $k\geq 1$ on a $$(*) \qquad |P'(z)|\leq \frac{n}{1+k}M \qquad (|z|\leq 1),$$ qu'en est-il pour le cas où $k < 1$? Quelle est l'inégalité analogue à $(*)$ pour une fonction entière de type exponentiel $\tau ?$ D'autre part, si on suppose que $P$ a tous ses zéros dans $|z|\geq k \, \, (k\geq 1),$ quelle est l'estimation de $|P'(z)|$ sur le cercle unité, en terme des quatre premiers termes de son développement en série entière autour de l'origine. Cette thèse constitue une contribution à la théorie analytique des polynômes à la lumière de ces questions.

Development of Shape Descriptors Based on Legendre Polynomials and Content-Based Retrieval of Scoliosis Images

The wealth of information available freely on the web and medical image databases poses a major problem for the end users: how to find the information needed? Content –Based Image Retrieval is the obvious solution.A standard called MPEG-7 was evolved to address the interoperability issues of content-based search.The work presented in this thesis mainly concentrates on developing new shape descriptors and a framework for content – based retrieval of scoliosis images.New region-based and contour based shape descriptor is developed based on orthogonal Legendre polymomials.A novel system for indexing and retrieval of digital spine radiographs with scoliosis is presented.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Orthogonal polynomials and recurrence equations, operator equations and factorization

This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.

A generic formula for the values at the boundary points of monic classical orthogonal polynomials

In a previous paper we have determined a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type σ(x)y"n(x)+τ(x)y'n(x)-λnyn(x)=0. In this paper, we give another such formula which enables us to present a generic formula for the values of monic classical orthogonal polynomials at their boundary points of definition.

Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.