Studies in Fuzzy Commutative Algebra

The main objective of this thesis was to extend some basic concepts and results in module theory in algebra to the fuzzy setting.The concepts like simple module, semisimple module and exact sequences of R-modules form an important area of study in crisp module theory. In this thesis generalising these concepts to the fuzzy setting we have introduced concepts of ‘simple and semisimple L-modules’ and proved some results which include results analogous to those in crisp case. Also we have defined and studied the concept of ‘exact sequences of L-modules’.Further extending the concepts in crisp theory, we have introduced the fuzzy analogues ‘projective and injective L-modules’. We have proved many results in this context. Further we have defined and explored notion of ‘essential L-submodules of an L-module’. Still there are results in crisp theory related to the topics covered in this thesis which are to be investigated in the fuzzy setting. There are a lot of ideas still left in algebra, related to the theory of modules, such as the ‘injective hull of a module’, ‘tensor product of modules’ etc. for which the fuzzy analogues are not defined and explored.

Finite domination and Novikov rings. Iterative approach

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ? L R((x)) and C ? L R((x -1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619–632). Here R((x)) = R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.

Finite domination and Novikov homology over strongly Z-graded rings

Let L be a unital Z-graded ring, and let C be a bounded chain complex of finitely generated L-modules. We give a homological characterisation of when C is homotopy equivalent to a bounded complex of finitely generated projective L0-modules, generalising known results for twisted Laurent polynomial rings. The crucial hypothesis is that L is a strongly graded ring. 

Représentations et fusion des algèbres de Temperley-Lieb originale et diluée

Les algèbres de Temperley-Lieb originales, aussi dites régulières, apparaissent dans de nombreux modèles statistiques sur réseau en deux dimensions: les modèles d'Ising, de Potts, des dimères, celui de Fortuin-Kasteleyn, etc. L'espace d'Hilbert de l'hamiltonien quantique correspondant à chacun de ces modèles est un module pour cette algèbre et la théorie de ses représentations peut être utilisée afin de faciliter la décomposition de l'espace en blocs; la diagonalisation de l'hamiltonien s'en trouve alors grandement simplifiée. L'algèbre de Temperley-Lieb diluée joue un rôle similaire pour des modèles statistiques dilués, par exemple un modèle sur réseau où certains sites peuvent être vides; ses représentations peuvent alors être utilisées pour simplifier l'analyse du modèle comme pour le cas original. Or ceci requiert une connaissance des modules de cette algèbre et de leur structure; un premier article donne une liste complète des modules projectifs indécomposables de l'algèbre diluée et un second les utilise afin de construire une liste complète de tous les modules indécomposables des algèbres originale et diluée. La structure des modules est décrite en termes de facteurs de composition et par leurs groupes d'homomorphismes. Le produit de fusion sur l'algèbre de Temperley-Lieb originale permet de «multiplier» ensemble deux modules sur cette algèbre pour en obtenir un autre. Il a été montré que ce produit pouvait servir dans la diagonalisation d'hamiltoniens et, selon certaines conjectures, il pourrait également être utilisé pour étudier le comportement de modèles sur réseaux dans la limite continue. Un troisième article construit une généralisation du produit de fusion pour les algèbres diluées, puis présente une méthode pour le calculer. Le produit de fusion est alors calculé pour les classes de modules indécomposables les plus communes pour les deux familles, originale et diluée, ce qui vient ajouter à la liste incomplète des produits de fusion déjà calculés par d'autres chercheurs pour la famille originale. Finalement, il s'avère que les algèbres de Temperley-Lieb peuvent être associées à une catégorie monoïdale tressée, dont la structure est compatible avec le produit de fusion décrit ci-dessus. Le quatrième article calcule explicitement ce tressage, d'abord sur la catégorie des algèbres, puis sur la catégorie des modules sur ces algèbres. Il montre également comment ce tressage permet d'obtenir des solutions aux équations de Yang-Baxter, qui peuvent alors être utilisées afin de construire des modèles intégrables sur réseaux.

Représentations et fusion des algèbres de Temperley-Lieb originale et diluée

Les algèbres de Temperley-Lieb originales, aussi dites régulières, apparaissent dans de nombreux modèles statistiques sur réseau en deux dimensions: les modèles d'Ising, de Potts, des dimères, celui de Fortuin-Kasteleyn, etc. L'espace d'Hilbert de l'hamiltonien quantique correspondant à chacun de ces modèles est un module pour cette algèbre et la théorie de ses représentations peut être utilisée afin de faciliter la décomposition de l'espace en blocs; la diagonalisation de l'hamiltonien s'en trouve alors grandement simplifiée. L'algèbre de Temperley-Lieb diluée joue un rôle similaire pour des modèles statistiques dilués, par exemple un modèle sur réseau où certains sites peuvent être vides; ses représentations peuvent alors être utilisées pour simplifier l'analyse du modèle comme pour le cas original. Or ceci requiert une connaissance des modules de cette algèbre et de leur structure; un premier article donne une liste complète des modules projectifs indécomposables de l'algèbre diluée et un second les utilise afin de construire une liste complète de tous les modules indécomposables des algèbres originale et diluée. La structure des modules est décrite en termes de facteurs de composition et par leurs groupes d'homomorphismes. Le produit de fusion sur l'algèbre de Temperley-Lieb originale permet de «multiplier» ensemble deux modules sur cette algèbre pour en obtenir un autre. Il a été montré que ce produit pouvait servir dans la diagonalisation d'hamiltoniens et, selon certaines conjectures, il pourrait également être utilisé pour étudier le comportement de modèles sur réseaux dans la limite continue. Un troisième article construit une généralisation du produit de fusion pour les algèbres diluées, puis présente une méthode pour le calculer. Le produit de fusion est alors calculé pour les classes de modules indécomposables les plus communes pour les deux familles, originale et diluée, ce qui vient ajouter à la liste incomplète des produits de fusion déjà calculés par d'autres chercheurs pour la famille originale. Finalement, il s'avère que les algèbres de Temperley-Lieb peuvent être associées à une catégorie monoïdale tressée, dont la structure est compatible avec le produit de fusion décrit ci-dessus. Le quatrième article calcule explicitement ce tressage, d'abord sur la catégorie des algèbres, puis sur la catégorie des modules sur ces algèbres. Il montre également comment ce tressage permet d'obtenir des solutions aux équations de Yang-Baxter, qui peuvent alors être utilisées afin de construire des modèles intégrables sur réseaux.

Les interventions sont-elles modulées par l'intensité du conflit initial chez le macaque crabier (Macaca fascicularis) ?

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Truncated projective spaces, Brown–Gitler spectra and indecomposable A(1)-modules

MSC 19L41; 55S10.

Evaluation of an intervention to promote protective infant feeding practices to prevent childhood obesity : outcomes of the NOURISH RCT at 14 months of age and 6 months post the first of two intervention modules

OBJECTIVE: To evaluate a universal obesity prevention intervention, which commenced at infant age 4-6 months, using outcome data assessed 6-months after completion of the first of two intervention modules and 9 months from baseline. DESIGN: Randomised controlled trial of a community-based early feeding intervention. SUBJECTS AND METHODS: 698 first-time mothers (mean age 30±5 years) with healthy term infants (51% male) aged 4.3±1.0 months at baseline. Mothers and infants were randomly allocated to self-directed access to usual care or to attend two group education modules, each delivered over three months, that provided anticipatory guidance on early feeding practices. Outcome data reported here were assessed at infant age 13.7±1.3 months. Anthropometrics were expressed as z-scores (WHO reference). Rapid weight gain was defined as change in weight-for-age z-score (WAZ) > +0.67. Maternal feeding practices were assessed via self-administered questionnaire. RESULTS: There were no differences according to group allocation on key maternal and infant characteristics. At follow up (n=598 [86%]) the intervention group infants had lower BMIZ (0.42±0.85 vs 0.23±0.93, p=0.009) and infants in the control group were more likely to show rapid weight gain from baseline to follow up (OR=1.5 CI95%1.1-2.1, p=0.014). Mothers in the control group were more likely to report using non- responsive feeding practices that fail to respond to infant satiety cues such as encouraging eating by using food as a reward (15% vs 4%, p=0.001) or using games ( 67% vs 29%, p<0.001). CONCLUSIONS: These results provide early evidence that anticipatory guidance targeting the ‘when, what and how’ of solid feeding can be effective in changing maternal feeding practices and, at least in the short term, reducing anthropometric indicators of childhood obesity risk. Analyses of outcomes at later ages are required to determine if these promising effects can be sustained.

Worldwide outdoor round robin study of organic photovoltaic devices and modules

Accurate characterization and reporting of organic photovoltaic (OPV) device performance remains one of the important challenges in the field. The large spread among the efficiencies of devices with the same structure reported by different groups is significantly caused by different procedures and equipment used during testing. The presented article addresses this issue by offering a new method of device testing using “suitcase sample” approach combined with outdoor testing that limits the diversity of the equipment, and a strict measurement protocol. A round robin outdoor characterization of roll-to-roll coated OPV cells and modules conducted among 46 laboratories worldwide is presented, where the samples and the testing equipment were integrated in a compact suitcase that served both as a sample transportation tool and as a holder and test equipment during testing. In addition, an internet based coordination was used via plasticphotovoltaics.org that allowed fast and efficient communication among participants and provided a controlled reporting format for the results that eased the analysis of the data. The reported deviations among the laboratories were limited to 5% when compared to the Si reference device integrated in the suitcase and were up to 8% when calculated using the local irradiance data. Therefore, this method offers a fast, cheap and efficient tool for sample sharing and testing that allows conducting outdoor measurements of OPV devices in a reproducible manner.

Moduli of equivariant sheaves and Kronecker-McKay modules

We extend Alvarez-Consul and King description of moduli of sheaves over projective schemes to moduli of equivariant sheaves over projective Gamma-schemes, for a finite group Gamma. We introduce the notion of Kronecker-McKay modules and construct the moduli of equivariant sheaves using a natural functor from the category of equivariant sheaves to the category of Kronecker-McKay modules. Following Alvarez-Consul and King, we also study theta functions and homogeneous co-ordinates of moduli of equivariant sheaves.

Semi-automatic generation of learning domain modules for technology supported learning systems

In a time when Technology Supported Learning Systems are being widely used, there is a lack of tools that allows their development in an automatic or semi-automatic way. Technology Supported Learning Systems require an appropriate Domain Module, ie. the pedagogical representation of the domain to be mastered, in order to be effective. However, content authoring is a time and effort consuming task, therefore, efforts in automatising the Domain Module acquisition are necessary.Traditionally, textbooks have been used as the main mechanism to maintain and transmit the knowledge of a certain subject or domain. Textbooks have been authored by domain experts who have organised the contents in a means that facilitate understanding and learning, considering pedagogical issues.Given that textbooks are appropriate sources of information, they can be used to facilitate the development of the Domain Module allowing the identification of the topics to be mastered and the pedagogical relationships among them, as well as the extraction of Learning Objects, ie. meaningful fragments of the textbook with educational purpose.Consequently, in this work DOM-Sortze, a framework for the semi-automatic construction of Domain Modules from electronic textbooks, has been developed. DOM-Sortze uses NLP techniques, heuristic reasoning and ontologies to fulfill its work. DOM-Sortze has been designed and developed with the aim of automatising the development of the Domain Module, regardless of the subject, promoting the knowledge reuse and facilitating the collaboration of the users during the process.

M/V JACQUELYN L Coral Reef Restoration Monitoring Report, Monitoring Events 2004-2005. Florida Keys National Marine Sanctuary Monroe County, Florida

This document presents the results of the monitoring of a repaired coral reef injured by the M/V Jacquelyn L vessel grounding incident of July 7, 1991. This grounding occurred in Florida state waters within the boundaries of the Florida Keys National Marine Sanctuary (FKNMS). The National Oceanic and Atmospheric Administration (NOAA) and the Board of Trustees of the Internal Improvement Trust Fund of the State of Florida, (“State of Florida” or “state”) are the co-trustees for the natural resources within the FKNMS and, thus, are responsible for mediating the restoration of the damaged marine resources and monitoring the outcome of the restoration actions. The restoration monitoring program tracks patterns of biological recovery, determines the success of restoration measures, and assesses the resiliency to environmental and anthropogenic disturbances of the site over time. The monitoring program at the Jacquelyn L site was to have included an assessment of the structural stability of installed restoration modules and biological condition of reattached corals performed on the following schedule: immediately (i.e., baseline), 1, 3, and 6 years after restoration and following a catastrophic event. Restoration of this site was completed on July 20, 2000. Due to unavoidable delays in the settlement of the case, the “baseline” monitoring event for this site occurred in July 2004. The catastrophic monitoring event occurred on August 31, 2004, some 2 ½ weeks after the passage of Hurricane Charley which passed nearby, almost directly over the Dry Tortugas. In September 2005, the year one monitoring event occurred shortly after the passage of Hurricane Katrina, some 70 km to the NW. This report presents the results of all three monitoring events. (PDF contains 31 pages.)

Measurement of small-signal and large-signal responses of packaged laser modules at high temperature

In this paper, the pulsed injection method is extended to measure the chip temperature of various packaged laser modules, such as the DFB laser modules, the FP laser modules, and the EML laser modules. An optimal injection condition is obtained by investigating the dependence of the lasing wavelength on the width and period of the injection pulse in a relatively wide temperature range. The small-signal frequency responses and large-signal performances of packaged laser modules at different chip temperature are measured. The adiabatic small-signal modulation characteristics of packaged LD are first extracted. In the large-signal measurement, the effects of chip temperature, bias current and driving signal on the performances of the laser modules are discussed. It has been found that the large-signal performances of the EML modules depend on the different red-shift speeds of the DFB and EAM sections as chip temperature varying, and the optimal characteristics may be achieved at higher temperature.