Dissertations / Theses on the topic 'Comparison theorems'

Nella tesi si studiano le varietà algebriche e in particolare quelle proiettive. Data una varietà algebrica definita sul campo complesso con la topologia di Zariski, si analizza la corrispondenza tra le proprietà topologiche di separatezza, completezza e irriducibilità e, rispettivamente, l'essere Hausdoff, la compattezza e la connessione dello spazio analitico associato. In particolare si dimostra che lo spazio proiettivo, e di conseguenza tutte le varietà proiettive, sono separate e complete. Si generalizza inoltre la nozione di varietà a quella di schema e si calcola la coomologia di fasci coerenti sullo spazio proiettivo. Si dimostra infine il teorema di dualità di Serre per fasci coerenti su uno schema proiettivo arbitrario.

In this thesis two classes of rational matrix differential resp. difference equations which contain the matrix Riccati equations of continuous- and discrete-time optimal control as particular cases are considered. Existence and convergence theorems for these equations are proved and conditions ensuring that the corresponding algebraic equations have a stabilizing solution are derived.

Optimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism). In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp's volume and are also investigated.

Este trabalho trata de estimativas inferiores para o primeiro autovalor do problema de Dirichlet para o Laplaciano para domínios relativamente compactos contidos em variedades riemannianas. Essas estimativas são obtidas com hipóteses sobre a curvatura seccional ou a curvatura de Ricci radial e a curvatura do bordo do domínio.
This paper deals of lower estimates for the first eigenvalue of the Dirichlet problem for the Laplacian for relatively compact domains contained in Riemannian manifolds. These estimates are obtained with assumptions on the sectional or Ricci radial curvature and the curvature of the boundary of the domain.

We consider several classes of orthogonal polynomials as well as the Bessel function where we study the convexity of zeros of these polynomials, satisfying either differential or real difference equations, by applying Sturm's comparison and convexity theorems as well as analogues of these theorems. In addition several results are obtained concerning the distances between consecutive zeros of some of these classes of polynomials. Further research possibilities concerning q-polynomials and polynomials satisfying complex difference equations are discussed.
Dissertation (MSc)--University of Pretoria, 2012.
Mathematics and Applied Mathematics
MSc
Unrestricted

This thesis presents a comprehensive study of incidence calculus, a probabilistic logic for reasoning under uncertainty which extends two-value propositional logic to a multiple-value logic. There are three main contributions in this thesis. First of all, the original incidence calculus is extended considerably in three aspects: (a) the original incidence calculus is generalised; (b) an efficient algorithm for incidence assignment based on generalised incidence calculus is developed; (c) a combination rule is proposed for the combination of both independent and some dependent pieces of evidence. Extended incidence calculus has the advantages of representing information flexibly and combining multiple sources of evidence. Secondly, a comprehensive comparison between extended incidence calculus and the Dempster-Shafer (DS) theory of evidence is provided. It is proved that extended incidence calculus is equivalent to DS theory in representing evidence and combining independent evidence but superior to DS theory in combining dependent evidence. Thirdly, the relations between extended incidence calculus and the assumption-based truth maintenance systems are discussed. It is proved that extended incidence calculus is equivalent to the ATMS in calculating labels for nodes. Extended incidence calculus can also be used as a basis for constructing probabilistic ATMSs. The study in this thesis reveals that extended incidence calculus can be regarded as a bridge between numerical and symbolic reasoning mechanisms.

Conceptual Art emerged as an international, avant-garde art movement in the mid-60s. Attacking the prevailing aesthetics of modern art, Conceptual artists claim that art lies not in the object itself but in the artist's idea or intention. Their asserted goals have been to combine theory with art and to eliminate the need for form in artworks. The purpose of this study was to examine and critique the key theoretical writings of three artists whose works have been recognized by the critics as significant and seminal for the Conceptual Art Movement: Joseph Kosuth, Sol LeWitt, and Terry Atkinson.Historical aspects relevant to this study included the following: (i) early twentieth-century antecedents of Conceptual Art; (ii) recent avant-garde movements of the 60s and 70s; (iii) the history and nature of the concept theories of Kosuth, LeWitt, and Atkinson; (ii) a critiqueof t ese theories in terms of their consistency and viabi ity for generating art; (iii) a comparison of Conceptual Art theories with both commonly accepted theories of art and more radical aesthetic theories of contemporary philosophers.Upon completion of this study, it was concluded that despite many ideological differences, Kosuth, LeWitt, and Atkinson agree on two key notions: (i) the locus of the "work of art" is not a physical object; and (ii) it is the artist's idea which alone accounts for the significance of an artwork. Their arguments in support of these notions are unsatisfactory. Longstanding issues in aesthetics, viz., the problems of defining art and evaluating its significance, are not resolved. The critics' acclaim of the writings critiqued in this study must therefore rest on extrinsic features such as the prestige of the artists, the relevance of the content of the writings to dominant trends in contemporary art, and the potential historical significance of their challenges to established views about art and aesthetics.

Thesis (Ph. D.)--University of Cincinnati, 2006.
Advisor: Dr. Michael C. Walker. Title from electronic thesis title page (viewed May 19, 2008). Keywords: IPO; Survey; Going Public; Life-cycle; Market Forces. Includes abstract. Includes bibliographical references.

In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating the first Pontrjagin class for an arbitrary quaternionic toric 8-manifold.

The objective of this dissertation is to study the structure and behavior of the Atmospheric Boundary Layer (ABL) in stable conditions. This type of boundary layer is not completely well understood yet, although it is very important for many practical uses, from forecast modeling to atmospheric dispersion of pollutants. We analyzed data from the SABLES98 experiment (Stable Atmospheric Boundary Layer Experiment in Spain, 1998), and compared the behaviour of this data using Monin-Obukhov's similarity functions for wind speed and potential temperature. Analyzing the vertical profiles of various variables, in particular the thermal and momentum fluxes, we identified two main contrasting structures describing two different states of the SBL, a traditional and an upside-down boundary layer. We were able to determine the main features of these two states of the boundary layer in terms of vertical profiles of potential temperature and wind speed, turbulent kinetic energy and fluxes, studying the time series and vertical structure of the atmosphere for two separate nights in the dataset, taken as case studies. We also developed an original classification of the SBL, in order to separate the influence of mesoscale phenomena from turbulent behavior, using as parameters the wind speed and the gradient Richardson number. We then compared these two formulations, using the SABLES98 dataset, verifying their validity for different variables (wind speed and potential temperature, and their difference, at different heights) and with different stability parameters (zita or Rg). Despite these two classifications having completely different physical origins, we were able to find some common behavior, in particular under weak stability conditions.

Cognitive Load Theory (CLT) and Dual Space Theory (DST) offer differing accounts of learning in complex settings. CLT argues that reducing processing demands on working memory (i.e. reducing cognitive load) will facilitate learning. Conversely, DST suggests that learning is improved by encouraging learners to focus on task rules (rule space search) rather than task instances (instance space search). Despite these differences, CLT researchers have proposed that the theories are complementary, suggesting that rule space search is contingent on low cognitive load. Three studies were conducted to examine this proposal with particular focus on the goal free effect. Study 1 trained participants on a complex task under conditions of high or low rule space search with cognitive load held constant. Results indicated that the high rule space search group acquired greater knowledge despite equivalent cognitive load between the groups. However, results may have been confounded by motivational differences. Study 2 manipulated rule space search and cognitive load in a 2 (goal type) x 2 (information level) between-subjects design. Manipulations were intended to create conditions where cognitive load and rule space search were both high or low, contrary to their proposed dependence. Results however were mixed. Whilst cognitive load and rule space search were unrelated in between-group comparisons, they were negatively related overall, consistent with CLT’s proposal. Study 3 refined the previous 2 x 2 design to clarify these findings. Results indicated that groups encouraged to search rule space did so independently of cognitive load, though results were not entirely consistent with either theory. Taken together, results tentatively suggest that cognitive load does not influence rule space search in all situations. The theories may therefore be independent explanations of learning in complex settings.

In this paper we consider the question of uniqueness of positive solutions for Dirichlet problems of the form - Δ u(x)= g(λ,u(x)) in B, u(x) = 0 on ϑB, where A is the Laplace operator, B is the unit ball in RˆN, and A>0. We show that if g(λ,u)=uˆ(N+2)/(N-2) + λ, that is g has "critical growth", then large positive solutions are unique. We also prove uniqueness of large solutions when g(λ,u)=A f(u) with f(0) < 0, f "superlinear" and monotone. We use a number of methods from nonlinear functional analysis such as variational identities, Sturm comparison theorems and methods of order. We also present a regularity result on linear elliptic equation where a coefficient has critical growth.

This thesis deals with two theories of international trade: the theory of comparative advantage, which is connected to the name David Ricardo and is dominating current trade theory, and Adam Smith’s theory of absolute advantage. Both theories are compared and their assumptions are scrutinised. The former theory is rejected on theoretical and empirical grounds in favour of the latter. On the basis of the theory of absolute advantage, developments of free international trade are examined, whereby the focus is on trade between industrial and underdeveloped countries. The main conclusions are that trade patterns are determined by absolute production cost advantages and that the gap between developed and poor countries is not reduced but rather increased by free trade.
Die vorliegende Publikation vergleicht die zwei zentralen Theorien des internationalen Freihandels: die Theorie der absoluten Kostenvorteile und die Theorie der komparativen Kostenvorteile. Dieser Vergleich führt zu dem Schluss, dass die Theorie der komparativen Kostenvorteile im Gegensatz zu der Theorie der absoluten Kostenvorteile auf unrealistischen und problematischen Annahmen beruht. Im Anschluss werden auf Grundlage der Theorie der absoluten Kostenvorteile zentrale Tendenzen in der Entwicklung des internationalen Handels herausgearbeitet. Im Mittelpunkt steht hierbei die Auswirkung von Freihandel auf entwickelte und unterentwickelte Länder. Die zentralen Schlussfolgerungen dieser Arbeit sind erstens, dass die Richtung des internationalen Handels nicht durch komparative Kostenvorteile, sondern durch absolute Kostenvorteile bestimmt wird und zweitens, dass Freihandel zwar vorteilhaft für unterentwickelte Länder sein kann, aber dass durch Freihandel die Unterschiede zwischen Industrieländern und Entwicklungsländern nicht verkleinert, sondern vergrößert werden.

This study examined the impact that school leaders have on teacher job satisfaction and student achievement. The threefold purpose of this study was to (1) compare transformational and instructional leadership theories, (2) examine the unique impact that school leaders have on student achievement and teacher job satisfaction after controlling for school context and principal demographics, and (3) find which specific leadership practices are associated with increased student achievement and teacher job satisfaction. Participants were 558 teachers from 37 elementary schools in the Intermountain West. Teachers completed the Teachers' Job Satisfaction Scale (TJSS), and were randomly assigned to complete the Multifactor Leadership Questionnaire (MLQ) or the Principal Instructional Management Rating Scale (PIMRS). Student achievement was measured by the Iowa Test of Basic Skills (ITBS) and the Criterion Referenced Test (CRT). Multiple regression and hierarchical linear modeling were used to find the relationships between these measurements. Results indicated that instructional leadership explained more of the variance in student achievement and teacher job satisfaction than transformational leadership. Leadership predicted a meaningful but nonsignificant amount of variance in student achievement, and a large significant amount of the variance in teacher job satisfaction. The control variables of school context and principal demographics tended to explain more of the variance in achievement scores, while leadership explained a majority of the variance in teacher job satisfaction. The leadership functions that were associated with increased student achievement were monitor student progress, protect instructional time, provide incentives for teachers, provide incentives for learning, and contingent reward. The leadership functions that were associated with increased teacher job satisfaction were supervise and evaluate instruction, maintain high visibility, provide incentives for teachers, promote professional development, provide incentives for learning, and individualized consideration. The implications of these findings, as well as the limitations of this research, will be discussed.

Problem:  Triggered by the present emission scandal of Volkswagen, we came across the fact that corporate crises constitute a revenant topic in the business world. They often entail significant consequences for the affected companies such as reputation damages, financial losses and loss of trust from stakeholders. Also the people working at these companies experience exceptional situations, managers as well as employees on all levels. Corporate crises can be influenced by many factors, for instance through internal triggers like power distance, transparency and communication. These factors can influence the development of a corporate crisis in a positive as well as in a negative manner.  Purpose:  With the underlying study our goal was to find fostering and hindering factors for corporate crises that are connected to internal processes within multinational companies. Initially we sought to understand which impact organizational structures have on the crisis management in a company. Later in our study, the impact of corporate culture as well as cultural origin emerged and caught our interest. That resulted in a shift of our focus towards the impact of a company’s cultural origin on corporate crisis management.  Method:  For the underlying master thesis, we conducted 17 semi-structured interviews with 13 companies and investigated the real-life case of Volkswagen through secondary data. Based on that we created 14 case studies. Through a highly explorative iterative process, we further analyzed our collected data going back and forth between our empirical data and emerging theory.  Main Findings:  Our empirical data suggested that corporate crises can be triggered internally, initiated for example by strict governance, hierarchy and insufficient transparency. Moreover, organizational structures are strongly influenced by the corporate culture of a company. Corporate culture, furthermore, seems to be strongly influenced by the cultural origin of a company, regarding decision-making procedures, responsibilities and communication. Finally, in the perception of our respondents within our empirical study there is a link between the cultural origin of a company and its crisis management.  Contribution:  Although crisis management constitutes an exhaustive researched topic, we were able to contribute to the area of crisis management with an empirical indicator of the cultural origin of a company constituting an impacting factor for corporate crisis management. This coherence has not been acknowledged by crisis management literature to a meaningful extent so far.

The challenge of facilitating a shift towards sustainable housing, food and mobility has been taken up by diverse community-based initiatives ranging from "top-down" approaches in low-carbon municipalities to "bottom-up" approaches in intentional communities. This paper compares intervention measures in four case study areas belonging to these two types, focusing on their potential of re-configuring daily housing, food, and mobility practices. Taking up critics on dominant intervention framings of diffusing low-carbon technical innovations and changing individual behavior, we draw on social practice theory for the empirical analysis of four case studies. Framing interventions in relation to re-configuring daily practices, the paper reveals differences and weaknesses of current low-carbon measures of community-based initiatives in Germany and Austria. Low-carbon municipalities mainly focus on introducing technologies and offering additional infrastructure and information to promote low-carbon practices. They avoid interfering into residents¿ daily lives and do not restrict carbon-intensive practices. In contrast, intentional communities base their interventions on the collective creation of shared visions, decisions, and rules and thus provide social and material structures, which foster everyday low-carbon practices and discourage carbon-intensive ones. The paper discusses the relevance of organizational and governance structures for implementing different types of low-carbon measures and points to opportunities for broadening current policy strategies.

Prior research has demonstrated that employees react toward injustice through engaging in sabotage. Most studies on the relationship between injustice and employee sabotage, however, have occurred in North America. It is not known if these findings generalize to other cultural settings. Taking a cross-cultural perspective, I conducted two field studies to (a) examine the role of cultural values and individual difference factors stemming from cultural values and religious beliefs in the link between justice and sabotage (Study 1); (b) explore whether employees in China react differently toward supervisory and customer injustice from employees in North America (Study 2); and (c) to the extent that differences in justice effects exist between countries, examine whether cultural values (e.g., individualism) explain (i.e., mediate) the between-country differences in the injustice-sabotage associations (Study 2). Surveys were administered to 418 front-line employees working in international hotels in China (Study 1) and 203 front-line employees working in one hotel chain in China and Canada (Study 2). Results of Study 1 revealed that the relationship between supervisory justice and sabotage toward supervisor differs as a function of vertical individualism. Moreover, the association between customer injustice and sabotage toward customer occurs as a function of horizontal individualism, negative reciprocity norm, and belief in ultimate justice. Results of Study 2 showed that the strength of the association between customer injustice and sabotage toward customer was significantly weaker among employees in China than in Canada. Three cultural values, namely individualism, uncertainty avoidance, and power distance, accounted for these between-country differences, with individualism as the strongest mediatory factor. Implications and future directions are discussed.

Psychology
Ph.D.
Most life stress literature in bipolar disorder (BD) fails to account for the possibility of a changing relationship between psychosocial context and episode initiation across the course of the disorder. The kindling hypothesis states that over the longitudinal course of recurrent affective disorders, there is a weakening temporal relationship between major life stress and episode initiation (Post, 1992). This process could reflect either a progressive sensitization or a progressive autonomy (i.e., insensitivity) to life stress. The present study aimed to test the kindling model in BD by examining the effect of lifetime mood episodes on the relationship between proximal life events and prospectively assessed mood episodes. Polarity-specific tests of the model were conducted across the continuum of event severity, with respect to both impact and frequency of life events. Moreover, examination of the kindling hypothesis was embedded in the context of two emerging biopsychosocial theories of BD: the expanded Behavioral Approach System Dysregulation Model and the Circadian and Social Rhythm Theory. Data from 278 participants (146 bipolar spectrum participants and 132 normal control participants) were collected as part of the Temple-Wisconsin Longitudinal Investigation of Bipolar Spectrum Project. Hypotheses were polarity- and event-type specific and were in line with a stress sensitization model of bipolar spectrum disorders (BSD), rather than a stress autonomy model. Results partially supported a sensitization model: there was a decreased frequency and an increased impact of major events, and an increased frequency and impact of minor events. However, results for specific polarities and event types were not fully consistent with a stress sensitization model. Implications of these findings are addressed, followed by a discussion of study strengths, limitations, and promising directions for future research.
Temple University--Theses

The aim of this study was to compare practices of assessment with theory. Three teachers on the upper secondary level in English were interviewed. This study contains three research questions, namely, how do teachers work with assessment? To what extent do teachers work with formative assessment in the subject English? In what way do teachers’ perception and experiences of formative assessment relate to current research in the field? The results indicate that formative assessment is an established method in the classroom, which differed from a collegial aspect since most collegial collaborations relate to summative assessment. Teachers used formative assessment to a varied extent and in various ways, which entail a high usage of mapping, defining goals, formal and interactive feedback from teacher to student. The results also indicate small or non-existent usage of peer-assessment, feedback from student to teacher and, self-assessment. The analysis showed that some perceptions between teachers were contradictive, but support from each viewpoint could be found in recent studies. Finally, the results of my study pointed to that formative assessment in practice and theory is a quite ambiguous research field. Some other interesting findings which were not a part of this study’s aim showed that all teachers mention how distance studies due to the coronavirus make summative assessment more challenging. In comparison to summative assessment, formative assessment can somewhat proceed as normal whereas teachers give students formal feedback, but the teachers highlight that the interactive part of feedback disappears. Teachers gave examples of interactive feedback as when students ask for and receive direct feedback in the classroom when working on a written assignment. Teachers reported that students perform better in oral production ever since school had to switch to digital learning, which is also another interesting finding.
Syftet med denna studie är att undersöka lärares bedömningspraktik för att kunna jämföra dessa med forskningsläget. Tre lärare i engelska på gymnasienivå intervjuades. Studien ämnar sig åt att besvara tre frågeställningar: hur arbetar lärare med bedömning? I vilken utsträckning använder engelsklärare sig av formativ bedömning? Vilka kopplingar finns mellan lärares uppfattningar av formativ bedömning och forskningsläget? Resultaten visar på att formativ bedömning är en etablerad metod på klassrumsnivå, däremot tillbringar lärarna ur ett kollegialt perspektiv huvudsakligen åt summativ bedömning. Lärare använde formativ bedömning i varierande grad och på varierande vis, det visade sig att lärare frekvent använder sig av kartläggning av elevers kunskaper, synliggörande av mål och formell samt interaktiv återkoppling från lärare till elev. Resultaten visar på att kamratbedömning, återkoppling från elev till lärare och främjande av egenbedömning används i mycket liten eller ingen utsträckning. Analysen påvisade att lärarnas uppfattningar skiljdes åt sinsemellan men det visade finnas belägg för varje synsätt i forskningen. Slutligen påvisar denna studie på att formativ bedömning i jämförelse av praktik och teori är tvetydig. Några andra intressanta resultat genererades från studien även fast det var en del av studiens syfte. Lärarna beskriver att distansundervisningen som råder på grund av coronaviruset försvårat den summativa bedömningen. I jämförelse med den summativa bedömningen, kan den formativa bedömningen fortsätta som normalt där lärare kan ge elever formell feedback men lärarna understryker att den interaktiva delen av feedback försvinner. Lärarna gav exempel på interaktiv feedback, ett exempel är när elever frågar och får direkt feedback i klassrummet när de arbetar med en skrivuppgift. Lärarna i denna studie beskrev även att elever presterar bättre i muntliga förmågor i engelska sedan undervisningen har skiftat till distansundervisningen, vilket också är en intressant iakttagelse.

Der Historische Institutionalismus und der Evolutorische Institutionalismus - zwei Theorien wie sie unterschiedlicher nicht sein können. Erstaunlicherweise ziehen beide Theorien dennoch am gleichen Strang: Sie verfolgen gleichermaßen das Ziel, Entstehung, Wandel und Funktion von Institutionen zu erklären. Aber gibt es dabei besser und schlechter, stärker und schwächer? Welche Relevanz hat das Thema? Kommen nur erlesene Forscher und Spezialisten in den Genuss der Früchte der Theorien? Oder können sich auch Anwender und „Theorien-Handwerker“ die Vorteile der hier behandelten Denkansätze nutzbar machen? Ziel dieser Arbeit ist es, diesen Fragen nachzugehen. Insbesondere die „Undurchdringbarkeit des Theoriendschungels“ hat es dem Verfasser angetan: Mit der Motivation, dem Leser Vertrautheit im Umgang und in der Anwendung der Theorien zu verschaffen. Ein Bewertungssystem, ein anwendungsorientiertes Modell und die Einbindung eines Hausprojektes sollen dabei helfen. Allerdings soll auch „der Finger auf die eigene Wunde gelegt werden“, indem die eigenen Modelle und Abbildungen kritisch geprüft und Lücken und Widersprüche aufgetan werden. Auch durch eine kritische Würdigung der Arbeit wird ein wichtiger Beitrag geleistet: Sie hilft, etwaigen zukünftigen Forschungsbedarf zu identifizieren. Die einzelnen Schritte zum Ziel setzen zunächst voraus, dass im folgenden Kapitel 2 die zentralen Forschungsfragen dargelegt und Methodik und Untersuchungsrahmen vorgestellt werden. Kapitel 3 und Kapitel 4 gehen mittels Literaturdiskussion und kritisch reflektiertem Zusammenfassen von Vorarbeiten auf die Kernaussagen und Schnittstellen beider Theorien ein. In dem darauf folgenden Theorienvergleich werden die Theorien in Vergleichskategorien auf ihre Stärken und Schwächen hin analysiert und anschließend bewertet. Die Ergebnisse des Theorienvergleichs fließen in Kapitel 5 ein, in welchem ein Modell für die praktische Anwendung entwickelt wird. Zuletzt wird Forschungslücken aufzeigen.

This report is intended to help arbitrate the unsettled matter of when in the course of their early cognitive development children first evidence some "theory-like" understanding of their own and others' mental lives. To this end, this study directly compared results obtained through the administration of two competing assessment procedures, each of which has been used to support conflicting claims regarding the earliest age at which children first evidence an understanding of the possibility of false beliefs. A substantial body of recent research has contributed to a growing, but perhaps premature consensus that children under 4 years of age do not recognize the possibility of counterfactual beliefs in others and consequently lack any early theory of mind. Much of the evidence in support of this late-onset view is based upon the use of an "unexpected change" task developed by Wimmer and Perner (1983) in which children are asked to predict where an inadequately informed story character will search for an object. In contrast to these findings results obtained using a recently developed hide-and-seek task, which directly assessed children's abilities to generate misleading clues in order to produce a false-belief in another, offered strong support for a much earlier-onset position (Chandler, Fritz & Hala, in press). Despite strong methodologic reasons in favour of accepting the results of this investigation the possibility remained that the 3-year-olds in the Chandler et al. study were a special population that might also have succeeded in the unexpected change task had they been given it. To guard against this possibility the present study provided a within-subject comparison of both the unexpected change procedure and the newer hide-and-seek procedure based on the responses of 30 children ages 3.0, 3.5 and 4.0 years. A further test of false-belief understanding was provided by asking subjects to comment directly upon their opponent's belief based on subjects' own misleading actions. As predicted even young 3-year-olds demonstrated the ability to provide misleading clues to their opponent but when faced with the unexpected change task these youngest subjects performed poorly. When responding to the false-belief question based on their own deceptive actions, however, even these youngest subjects showed strong evidence of understanding the possibility of false beliefs in others.
Arts, Faculty of
Psychology, Department of
Graduate

This thesis consists of four parts. In the first part we recall some background theory that will be used throughout the thesis. In the second part, we studied the absolute continuity of the laws of the solutions of some perturbed stochastic differential equaitons(SDEs) and perturbed reflected SDEs using Malliavin calculus. Because the extra terms in the perturbed SDEs involve the maximum of the solution itself, the Malliavin differentiability of the solutions becomes very delicate. In the third part, we studied the absolute continuity of the laws of the solutions of the parabolic stochastic partial differential equations(SPDEs) with two reflecting walls using Malliavin calculus. Our study is based on Yang and Zhang \cite{YZ1}, in which the existence and uniqueness of the solutions of such SPDEs was established. In the fourth part, we gave the existence and uniqueness of the solutions of the elliptic SPDEs with two reflecting walls and general diffusion coefficients.

The present research studies fluvial processes –water and sediment flows – that define the shape of an alluvial channel. The relationship between forms and processes is complex because they are interrelated: the channel shape influences the water flow which drives the sediments movement on the channel bed that modifies the channel form, closing a circle. Although, the objective of the work is a very old question in fluvial studies, to explain the shape of rivers in terms of external controls and internal processes, the problem has not been solved yet and this study provies new elements for its solution. The start of the quest for linking process and forms can be found in the development of regime theories which consists of a set of equations to estimate the width, depth and slope of a stable channel if liquid discharge and sediment supply are known. Regime theories were created in the XIX century within the context of hydraulic engineering in order to design stable irrigation canals (e.g. Kennedy, 1895; Lacey, 1930; Lane, 1955). Leopold and Maddock (1953) introduced the quantitative concept of hydraulic geometry into the context of fluvial geomorphology and showed that alluvial rivers adjust both their slope and channel in order to be in equilibrium for a certain representative discharge. The first studies were eminently empiric, hence there has also been an intense theoretical work focused on explaining regime relations. Parker (1978) demonstrated the importance of bank erodibility, and the need of using improved hydraulic models to calculate the shear stress distribution on irregular cross-sections. Alternative conceptual approaches have been used to explore geometrical channel properties. Langbein & Leopold (1962) took advantage of thermodynamic principles to suggest that the distribution of energy in a river system tends towards the most probable state. After this first pioneering work, further so-called “extremal” hypotheses were proposed such as: minimum unit stream power (Yang and Song, 1979), minimum stream power (Chang, 1980), minimum energy dissipation rate (Brebner and Wilson, 1967; Yang et al., 1981), maximum sediment transport rate (White et al., 1982), maximum friction factor (Davies and Sutherland, 1983) and maximum resistance to flow (Eaton et al, 2004). Millar & Quick (1993) and Millar (2005) proposed models that take into account the bank strength, a distinctive condition not considered in previous works. Because of their lack of physical-based principles, extremal hypothesis approaches have been extensively criticized (Ferguson, 1986; Parker et al., 2007). Defenders claimed their validity based on the principle of least action (Nanson and Huang, 2008) or on the opposed feedback processes acting at the cross-section scale (Eaton et al., 2006). Regime models usually consider three degrees of freedom (width, depth, and slope) and four external control variables (liquid discharge, sediment supply, bed grain size, and bank strength). However, these variables reflect geomorphic processes acting at different temporal and spatial scales (Weichert et al. 2009) a crucial aspect not considered in regime models. The first part of the research was then dedicated to review and discuss theoretical issues inherent to the representation of fluvial systems and to regime theories. As a result, I proposed that a) physical laws and constrains describe the behaviour of a population of river reaches, instead of describing the exact processes within a single river reach; and b) each object contained in the population has uncertain boundaries (width, depth) and uncertain properties (median grain size, slope, bankfull discharge). Regime theories were classified according to the number of dimensions and the way of modeling the fluvial system. In this way, light was shed on the current debate about the validity of extremal hypothesis theories. The second part of the research focus on the study of the river-populations, consisting on the comparison of natural river reaches in Patagonia Region (Argentina) and river reaches disturbed due to human activities in Northern Italy. Extensive field measurements were conducted in Italy and Argentina; five river reaches were surveyed in Italy (belonging to Brenta, Piave and Cordevole rivers, in the Veneto Region) and ten river reaches in Argentina (in the mountain range of Central Patagonia). River reaches were chosen for their morphological homogeneity and for having at least 20 years of continuous flow record. In Argentina systematic measurements began by the middle of twentieth century. For the selected gauge stations records covered a time span ranging from 25 to 63 years. in Italy, water discharge has been measured at the Brenta River since 1924 at the Barzizza station and for the Piave River, flow records are derived from three gauging stations at Segusino, Belluno y Perarolo. Reaches were selected for being completely alluvial and having at least one bank free to evolve. In some cases a thick vegetation was growing in the banks, and in few cases one of the banks was protected with groynes. All selected reaches started and finish at riffles and extended along a whole wave length comprising three riffles and two pools. Then extensive and detailed field information was used to compare natural rivers in Patagonia and disturbed in Italy. The comparison was aimed to assess the stability state of Italian rivers, considering the properties of rivers in Patagonia as a reference of stable state. Then, following the concept of spatial scales and channel response proposed by Weichert et al. (2009), the consequences in regime models of considering the hypothesis that, while channel width and depth adjust quickly to changes in water and sediment supply, reach slope requires longer time spans, was explored. Three models, all of them incorporating a bank stability criterion, were considered in this study. In order to evaluate the performance of models introducing the slope as an independent variable, two modifications to previous models were proposed. The study also used published hydraulic geometry of gravel-bed rivers in other geographical regions (92 streams reaches) and laboratory data (36 small stream). Finally, Millar’s (2005) regime model was used to explain recent morphological changes and potential recovery in the Piave and Brenta rivers. The third and last part of the thesis was dedicated to the development and test of a 2D fully processes-based model, which was named LICAN-LEUFU. This part of the study was based on the assumption that “the channel morphology is driven by and is a consequence of within-channel processes; and a two-spatial-dimensions and depth-averaged model describes best the morphology of the channel”. The first part states that processes are the responsible of observed forms, which is the position hold in this study with regards to the debate on regime models. However, it should not be interpreted that extremal hypotheses are not necessary for predicting the channel shape. Extremal hypotheses express the behaviour at the reach scale while here, reach-scale features are explained by processes acting at a lower spatial scale. The second part means that the 2D model should do better in predicting channel morphology than 1D or aggregated models, i.e, the model is capable of predicting the reach-average form (width and depth) and also within channel morphology (pools and riffles) that are not within the capabilities of 1D or aggregated models. The model was tested in three different ways. The first test was based on flume measurements conducted at the facilities of the University of Hull. The model was used to predict the response of a laboratory flume that developed a static armour under conditions of sediment starvation. The observational consequences consisted on the bed change, surface grain size distribution change, outgoing sediment transport (bulk and grain size distribution). The second test was a middle-term simulation in which the model had to predict the shape of Azul River providing the actual water discharges, bed material, and estimated sediment supply, i.e., it was an application of the 2D model in the context of regime theories. The last test concerned the application of the model to a field case study: the Brenta River. The model was loaded with the initial morphology and surface grain size distribution and a series of runs were performed imposing the recorded discharges. Model predictions were compared against the final DTM (digital terrain model) and then used for assessing the possible evolution of the reach
La presente ricerca studia i processi –i flussi dell’acqua e dei sedimenti- che definiscono la forma dei corsi alluviali. Il rapporto tra forme e processi si presenta molto complesso perché queste aspetti interagiscono mutuamente: la forma dell’alveo influisce il flusso delle acque che guida il moto delle particelle sul fondo ed, a sua volta, modifica la forma del canale. Questo studio riprende un vecchio argomento negli studi fluviali, quello di spiegare la forma dei corsi’acqua come risposta a certi controlli esterni e processi interni. Tuttavia, il problema non è risolto e questo studio apporta nuovi elementi. Il punto di partenza nello studio del rapporto tra forme e processi si trova nelle teorie di regime che consistono in un insieme di equazioni per estimare la larghezza, profondità e pendenza di un corso d’acqua in equilibrio, quando la portata liquida ed il apporto di sedimenti sono conosciuti. Le teorie di regime sono state create nel secolo XIX inquadrate nell’ambito dell’ingegneria idraulica per la progettazione di canali di irrigazioni (Kennedy, 1895; Lacey, 1930; Lane, 1955). Leopold and Maddock (1953) introdussero il concetto di geometria idraulica nella geomorfologia fluviale e dimostrarono che i corsi’acqua modificano la pendenza nonché la sezione trasversale per raggiungere lo stato di equilibrio per una portata rappresentativa. I primi studi sono stati empirici, quindi un intenso lavoro teorico è stato svolto ai fini di spiegare le equazioni di regime. Parker (1978) dimostrò l’importanza di considerare la resistenza delle sponde nelle formulazioni nonché di usare modelli idraulici sofisticati per calcolare correttamente la distribuzione dello sforzo di taglio sul letto dell’alveo. Una strategia alternativa è stata applicata per esplorare le proprietà geometriche dei canali. Langbein e Leopold (1962) considerarono i principi della termodinamica e suggerirono che la distribuzione dell’energia in un fiume tendeva verso lo stato piu probabile. Questo lavoro aprì un cammino teorico e poi altre teorie, chiamate “extremal hypothesis”, sono state proposte: minima potenzia unitaria della corrente (Yang e Song, 1979), minima potenza della corrente (Chang, 1980), minima dissipazione di energia (Brebner and Wilson, 1967; Yang et al., 1981), massimo trasporto di sedimenti (White et al., 1982), massimo fattore di frizione (Davies e Sutherland, 1983) e massima resistenza al flusso (Eaton et al., 2004). Millar e Quick (1993) e piu recentemente Millar (2005) hanno proposto modelli che prendono in considerazione la resistenza delle sponde, un aspetto che non era stato incorporato nei precedenti lavori. Le teorie “extremal hypothesis” sono state criticate per la loro mancanza di base fisica (Ferguson, 1986; Parker et al., 2007). Tra l’altro, i difensori asseriscono la loro validità sulla base del principio di minima azione (Nanson e Huang, 2008), oppure nella esistenza di due feedback opposti che agiscono ad una scala ridota, quella della sezione trasversale (Eaton et al., 2006). Le teorie di regime normalmente considerano tre gradi di libertà (larghezza, profondità e pendenza) e quattro controlli esterni (portata liquida, apporto di sedimenti, diametro dei sedimenti, e resistenza delle sponde). Tuttavia, i parametri geometrici riflettono anche processi che aggiscono ad scale spaziale e temporali differenti (Weichert et al. 2009), un aspetto che non è stato considerato nelle teorie di regime. La prima parte della ricerca è stata orientata alla revisione e discussione dei problemi teorici connessi sia con la rappresentazione dei sistemi fluviali sia con le teorie di regime. Come risultato, ho proposto i seguenti aspetti: a) le leggi della fisica ed i vincoli invocati nelle teorie di regime descrivono il comportamento di una popolazione di fiumi invece di descrivere i processi precisi al interno di un singolo tratto fluviale; b) ogni singolo elemento della popolazione ha dei confini incerti (larghezza e profondità) ed anche delle proprietà incerte (diametro medio delle particelle nell’alveo, pendenza e portata a piene rive). Le teorie di regime sono state classificate secondo il numero di dimensioni ed il modo in cui i fiumi sono modellati. La classificazione è stata applicata alle teorie di regime per comprendere il debattito in torno alla validità delle teorie “extremal hypothesis”. La seconda parte della ricerca è indirizzata verso lo studio delle popolazioni di fiumi. Si presenta un confronto fra fiumi in stato naturale dalla Patagonia Argentina con quelli relativi ai fiumi disturbati dalle attività antropiche localizzati nella regione nordest di Italia. Sono state effettuati rilevamenti intensivi di campo in Italia ed Argentina; cinque tratti sono stati rilevati in Italia (appartenenti ai fiumi Brenta, Piave e Cordevole, tutti localizzati nella Regione del Veneto) e dieci tratti in Argentina (nelle provincie di Chubut e Rio Negro). I tratti scelti per l’indagine hanno omogeneità morfologica lungo tutto il tratto e le stazione di misure delle portate vicine hanno almeno registri di 20 anni di dati. In Argentina le misure sistematiche delle portate iniziarono verso la metà del secolo scorso e quindi ci sono circa tra 23 e 63 anni di datti nelle stazione selezionate. In Italia, le misurazioni per il fiume Brenta si trovano nella stazione di Barzizza vicina a Bassano del Grappa, che ha registri dall’anno 1924. Per quanto riguarda il fiume Piave, dati da tre stazioni sono state analizzati: Belluno, Segusino e Perarolo. I tratti selezionati sono alluviali ed al meno una delle sponde è libera di evolvere. In certi casi la vegetazione copriva una delle sponde e in pochi tratti c’èrano opere di difesa spondale. Tutti i tratti iniziano in un raschio (“riffle”) e finiscono anche in un’altro raschio, estendendosi lungo almeno una lunghezza di onda. La informazione di campo, essendo estesa e dettagliata, è stata utilizzata ai fini di confrontare i corsi naturali e disturbati. Il confronto ha permesso di valutare la stabilità raggiunta dai corsi d’acqua italiani, considerando i fiumi patagonici come riferimento dello stato di equilibrio. Inoltre, seguendo il concetto di rapporto fra scale spaziali e risposta del canale proposta dai ricercatori Weirchert et al. (2009), si valutarono le previsioni delle teorie di regime quando si considera la pendenza come una variabile indipendente. Tre modelli, che incorporano un criterio di stabilità delle sponde, sono stati considerati. Ai fini di valutare la loro performance quando la pendenza è un controllo esterno, due modificazioni a questi modelli sono state proposte. Lo studio utilizza i dati dei fiumi rilevati nonché un database pubblicato composto da 92 tratti fluviali e 36 studi di caso di laboratorio. Alla fine, il modello di Millar (2005) è stato utilizzato per spiegare i cambiamenti recenti nei fiumi Brenta e Piave ed anche per valutare la loro possibile tendenza evolutiva. L’ultima parte della tesi è stata indirizzata allo sviluppo, validazione ed implementazione di un modello bidimensionale basato sui processi, che è stato chiamato LICAN-LEUFU 2D. Questa parte del lavoro si basa sull’ipotesi che “la morfologia del canale è non solo una conseguenza dei processi che aggiscono sul canale ma anche guidata da questi processi; inoltre, due dimensioni spaziali insieme ad un modello “depth-average” permettono di descrivere meglio la morfologia del canale”. La prima parte afferma che i processi sono i responsabili delle forme osservate nel canale, affermazione che costituisce il punto di vista assunto in questo studio per quanto riguarda il dibattito intorno alle teorie di regime. Tuttavia, non deve interpretarsi come un’opposizione alle teorie di “extremal hypothesis”, oppure che non siano utile per prevedere la forma dei canali. Al contrario, come verrà dimostrato nella revisione dello stato dell’arte, le extremalhypotesis esprimono il comportamento del fiume alla scala di tratto, mentre in questo studio, le caratteristiche osservate alla scala di tratto verranno spiegate dai processi che aggiscono ad scale minori. La seconda parte dell’ipotesi significa che un modello bidimensionale dovrebbe prevedere in miglior modo la morfologia di un canale da quanto si ottiene applicando un modello aggregato o unidimensionale, es.., il modello deve essere in grado di prevedere la geometria a scala di tratto (larghezza e profondità) nonchè la morfologia all’interno del tratto (pozze e raschi), che eccedono le capacità dei modelli essistenti. Il modello è stato testato in tre differenti condizioni. Il primo test è stato realizzato sulla base delle misure di canaletta condotte presso l’Università di Hull. Il modello doveva prevedere la risposta di una canaletta di laboratorio, con fondo sabbioso-ghiaioso, che sviluppava una corazza statica in una situazione di apporto nullo di sedimenti. Nel secondo test il modello è stato utilizzato in una simulazione di medio-termine per estimare la forma del Fiume Azul quando vengono fornite come dati di input, le portate, il materiale di fondo ed il apporto de sedimenti. In questo modo, il test costituisce un’applicazione di un modello 2D nel campo delle teorie di regime. L’ultimo test riguarda l’applicazione del modello per lo studio di un caso: il Fiume Brenta. Il modello è stato caricato con una morfologia iniziale dell’alveo corrispondente all’anno 2010, e la granulometria superficiale. Il modello ha simulato il passaggio di tre piene straordinarie che si susseguirono nel periodo 2010-2011. Le previsioni del modello sono state confrontate con il DTM (modello digitale del terreno) che è stato rilevato alla fine del periodo. Inoltre, il modello è stato utilizzato per valutare la possibile tendenza evolutiva del tratto a medio termine.

IN THIS dissertation, we use the Laplacian comparison theorem to prove the comparison of volume Bishop-Gromov s theorem, which assures that if the Ricci curvatures of a complete Riemannian manifold are larger than or equal to (n - 1)k, the volume of a ball with center in p and radius R is smaller than or equal to the volume of a geodesic ball with radius R in the space form of sectional constant curvature k, for all p 2 M and R > 0, where k 2 R. Moreover, equality occurs if all sectional curvature throughout geodesics connecting p and x, for plans which contain the radial vector, is constant and equal to k.
Fundação de Amparo a Pesquisa do Estado de Alagoas
NESTA DISSERTAÇÃO, usamos o teorema de comparação do Laplaciano para demonstrar o teorema de comparação de volume de Bishop-Gromov, o qual assegura que, se as curvaturas de Ricci de uma variedade Riemanniana completa são maiores ou iguais a (n��1)k, k uma constante real, então, para todo p 2 M e para todo R > 0, o volume de uma bola centrada em p e de raio R é menor ou igual que o volume de uma bola geodésica de raio R na forma espacial de curvatura seccional constante k. Ademais, a igualdade ocorre se toda curvatura seccional ao longo de geodésicas ligando p e x, para planos contendo o vetor radial for constante e igual a k.

In this Thesis, we analyze three variational and geometric problems, that extend classical Euclidean issues of the calculus of variations to more general classes of spaces. The results we outline are based on the articles [Ved21; MV21] and on a forthcoming joint work with Nicolussi Golo and Serra Cassano. In the first place, in Chapter 1 we provide a general introduction to metric measure spaces and some of their properties. In Chapter 2 we extend the classical Talenti’s comparison theorem for elliptic equations to the setting of RCD(K,N) spaces: in addition the the generalization of Talenti’s inequality, we will prove that the result is rigid, in the sense that equality forces the space to have a symmetric structure, and stable. Chapter 3 is devoted to the study of the Bernstein problem for intrinsic graphs in the first Heisenberg group H^1: we will show that under mild assumptions on the regularity any stationary and stable solution to the minimal surface equation needs to be intrinsically affine. Finally, in Chapter 4 we study the dimension and structure of the singular set for p-harmonic maps taking values in a Riemannian manifold.

. . . believe in God, believe also in me . . . --John 14.1 "Authoring Authority" analyzes the ways texts function to generate social cohesion while at the same time advancing the power interests of their authors. The study is a comparative, critical, and interdisciplinary/transdisciplinary excavation of the religion-making efforts of the first-century Christian Apostle Paul and the nineteenth-century Mormon Prophet Joseph Smith. This comparison defamiliarizes and recharacterizes the heroes and origin-stories of the dominant (and my own) tradition to force important questions about scholarly perspectives, interests and deferences (protection, exceptionalization), self-reflexivity, and politics. The project's critical orientation deploys insights and models from a range of disciplines to "read" these texts, not for exegetical purposes, but for what they signify and how they function in nascent social formations. The texts of these men were presented as if their contents were other than the products of embedded social actors (e.g. "it really is God's word" 1 Thes 2.13) contending for limited resources such as discursive authority and social power. These charismatic narrators harnessed the authority of pre-existing texts and traditions and integrated them with contemporary perspectives and sentiment. Their texts and performances offered a contingent construal of reality as ultimate reality--which served the power needs of their authors and the existential needs of their communities of subscribers. The dissertation begins with the articulation of an analytical framework appropriate for the critical and comparative academic study of religion. Chapter two contextualizes the lives of these men within cultural settings that provided motivation, made available vocational training and, ultimately provisioned social opportunities for them as adept charismatics. Chapter three directly illuminates the range of techniques embedded in texts, both implicit and explicit, of claiming power and developing a following. The final chapter wrestles with the functional role of deception in social formation and human life.

The goal of this thesis in finance is to combine the use of advanced mathematical methods with a return to foundational economic issues. In that perspective, I study generalized rational expectations and asset pricing in Chapter 2, and a converse comparison principle for backward stochastic differential equations with jumps in Chapter 3. Since the use of stochastic methods in finance is an interesting and complex issue in itself - if only to clarify the difference between the use of mathematical models in finance and in physics or biology - I also present a philosophical reflection on the interpretation of mathematical models in finance (Chapter 4). In Chapter 5, I conclude the thesis with an essay on the history and interpretation of mathematical probability - to be read while keeping in mind the fundamental role of mathematical probability in financial models.
Doctorat en Sciences économiques et de gestion
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