Essays in partial identification and applications to treatment effects and policy evaluation.

Dans cette thèse, je me suis interessé à l’identification partielle des effets de traitements dans différents modèles de choix discrets avec traitements endogènes. Les modèles d’effets de traitement ont pour but de mesurer l’impact de certaines interventions sur certaines variables d’intérêt. Le type de traitement et la variable d’intérêt peuvent être défini de manière générale afin de pouvoir être appliqué à plusieurs différents contextes. Il y a plusieurs exemples de traitement en économie du travail, de la santé, de l’éducation, ou en organisation industrielle telle que les programmes de formation à l’emploi, les techniques médicales, l’investissement en recherche et développement, ou l’appartenance à un syndicat. La décision d’être traité ou pas n’est généralement pas aléatoire mais est basée sur des choix et des préférences individuelles. Dans un tel contexte, mesurer l’effet du traitement devient problématique car il faut tenir compte du biais de sélection. Plusieurs versions paramétriques de ces modèles ont été largement étudiées dans la littérature, cependant dans les modèles à variation discrète, la paramétrisation est une source importante d’identification. Dans un tel contexte, il est donc difficile de savoir si les résultats empiriques obtenus sont guidés par les données ou par la paramétrisation imposée au modèle. Etant donné, que les formes paramétriques proposées pour ces types de modèles n’ont généralement pas de fondement économique, je propose dans cette thèse de regarder la version nonparamétrique de ces modèles. Ceci permettra donc de proposer des politiques économiques plus robustes. La principale difficulté dans l’identification nonparamétrique de fonctions structurelles, est le fait que la structure suggérée ne permet pas d’identifier un unique processus générateur des données et ceci peut être du soit à la présence d’équilibres multiples ou soit à des contraintes sur les observables. Dans de telles situations, les méthodes d’identifications traditionnelles deviennent inapplicable d’où le récent développement de la littérature sur l’identification dans les modèles incomplets. Cette littérature porte une attention particuliere à l’identification de l’ensemble des fonctions structurelles d’intérêt qui sont compatibles avec la vraie distribution des données, cet ensemble est appelé : l’ensemble identifié. Par conséquent, dans le premier chapitre de la thèse, je caractérise l’ensemble identifié pour les effets de traitements dans le modèle triangulaire binaire. Dans le second chapitre, je considère le modèle de Roy discret. Je caractérise l’ensemble identifié pour les effets de traitements dans un modèle de choix de secteur lorsque la variable d’intérêt est discrète. Les hypothèses de sélection du secteur comprennent le choix de sélection simple, étendu et généralisé de Roy. Dans le dernier chapitre, je considère un modèle à variable dépendante binaire avec plusieurs dimensions d’hétérogéneité, tels que les jeux d’entrées ou de participation. je caractérise l’ensemble identifié pour les fonctions de profits des firmes dans un jeux avec deux firmes et à information complète. Dans tout les chapitres, l’ensemble identifié des fonctions d’intérêt sont écrites sous formes de bornes et assez simple pour être estimées à partir des méthodes d’inférence existantes.

Fixed point results for multivalued contractions on graphs and their applications

Nous présentons dans cette thèse des théorèmes de point fixe pour des contractions multivoques définies sur des espaces métriques, et, sur des espaces de jauges munis d’un graphe. Nous illustrons également les applications de ces résultats à des inclusions intégrales et à la théorie des fractales. Cette thèse est composée de quatre articles qui sont présentés dans quatre chapitres. Dans le chapitre 1, nous établissons des résultats de point fixe pour des fonctions multivoques, appelées G-contractions faibles. Celles-ci envoient des points connexes dans des points connexes et contractent la longueur des chemins. Les ensembles de points fixes sont étudiés. La propriété d’invariance homotopique d’existence d’un point fixe est également établie pour une famille de Gcontractions multivoques faibles. Dans le chapitre 2, nous établissons l’existence de solutions pour des systèmes d’inclusions intégrales de Hammerstein sous des conditions de type de monotonie mixte. L’existence de solutions pour des systèmes d’inclusions différentielles avec conditions initiales ou conditions aux limites périodiques est également obtenue. Nos résultats s’appuient sur nos théorèmes de point fixe pour des G-contractions multivoques faibles établis au chapitre 1. Dans le chapitre 3, nous appliquons ces mêmes résultats de point fixe aux systèmes de fonctions itérées assujettis à un graphe orienté. Plus précisément, nous construisons un espace métrique muni d’un graphe G et une G-contraction appropriés. En utilisant les points fixes de cette G-contraction, nous obtenons plus d’information sur les attracteurs de ces systèmes de fonctions itérées. Dans le chapitre 4, nous considérons des contractions multivoques définies sur un espace de jauges muni d’un graphe. Nous prouvons un résultat de point fixe pour des fonctions multivoques qui envoient des points connexes dans des points connexes et qui satisfont une condition de contraction généralisée. Ensuite, nous étudions des systèmes infinis de fonctions itérées assujettis à un graphe orienté (H-IIFS). Nous donnons des conditions assurant l’existence d’un attracteur unique à un H-IIFS. Enfin, nous appliquons notre résultat de point fixe pour des contractions multivoques définies sur un espace de jauges muni d’un graphe pour obtenir plus d’information sur l’attracteur d’un H-IIFS. Plus précisément, nous construisons un espace de jauges muni d’un graphe G et une G-contraction appropriés tels que ses points fixes sont des sous-attracteurs du H-IIFS.

Invariant discretizations of partial differential equations

Un algorithme permettant de discrétiser les équations aux dérivées partielles (EDP) tout en préservant leurs symétries de Lie est élaboré. Ceci est rendu possible grâce à l'utilisation de dérivées partielles discrètes se transformant comme les dérivées partielles continues sous l'action de groupes de Lie locaux. Dans les applications, beaucoup d'EDP sont invariantes sous l'action de transformations ponctuelles de Lie de dimension infinie qui font partie de ce que l'on désigne comme des pseudo-groupes de Lie. Afin d'étendre la méthode de discrétisation préservant les symétries à ces équations, une discrétisation des pseudo-groupes est proposée. Cette discrétisation a pour effet de transformer les symétries ponctuelles en symétries généralisées dans l'espace discret. Des schémas invariants sont ensuite créés pour un certain nombre d'EDP. Dans tous les cas, des tests numériques montrent que les schémas invariants approximent mieux leur équivalent continu que les différences finies standard.

Zeolite-encapsulated Co(II), Ni(II) and Cu(II) complexes as catalysts for partial oxidation of benzyl alcohol and ethylbenzene

Co(II), Ni(II) and Cu(II) complexes of dimethylglyoxime and N,N-ethylenebis(7-methylsalicylideneamine) have been synthesized in situ in Y zeolite by the reaction of ion-exchanged metal ions with the flexible ligand molecules that had diffused into the cavities. The hybrid materials obtained have been characterized by elemental analysis, SEM, XRD, surface area, pore volume, magnetic moment, FTIR, UV-Vis and EPR techniques. Analysis of data indicates the formation of complexes in the pores without affecting the zeolite framework structure, the absence of any extraneous species and the geometry of encapsulated complexes. The catalytic activities for hydrogen peroxide decomposition and oxidation of benzyl alcohol and ethylbenzene of zeolite complexes are reported. Zeolite Cu(II) complexes were found to be more active than the corresponding Co(II) and Ni(II) complexes for oxidation reactions. The catalytic properties of the complexes are influenced by their geometry and by the steric environment of the active sites. Zeolite complexes are stable enough to be reused and are suitable to be utilized as partial oxidation catalysts.

Fixed bed reactor performance of invertase immobilized on montmorillonite

Invertase was immobilized on acid activated montmorillonite via two independent procedures, adsorption and covalent binding. The immobilized enzymes were characterized by XRD, NMR and N2 adsorption measurements and their activity was tested in a fixed bed reactor. XRD revealed that the enzyme was situated on the periphery of the clay and the side chains of different amino acid residues were involved in intercalation with the clay matrix. NMR demonstrated that tetrahedral Al was linked to the enzyme during adsorption and the octahedral Al was involved during covalent binding. Secondary interaction of the enzyme with Al was also observed. N2 adsorption studies showed that covalent binding of enzymes caused pore blockage since the highly polymeric species were located at the pore entrance. The fixed bed reactor proved to be efficient for the immobilized invertase. The optimum pH and pH stability improved upon immobilization. The kinetic parameters calculated also showed an enhanced efficiency of the immobilized systems. They could be used continuously for long period. Covalently bound invertase demonstrated greater operational stability.

Glucoamylase immobilized on montmorillonite: Synthesis, characterization and starch hydrolysis activity in a fixed bed reactor

Glucoamylase from Aspergillus Niger was immobilized on montmorillonite clay (K-10) by two procedures, adsorption and covalent binding. The immobilized enzymes were characterized using XRD, surface area measurements and 27Al MAS NMR and the activity of the immobilized enzymes for starch hydrolysis was tested in a fixed bed reactor (FBR). XRD shows that enzyme intercalates into the inter-lamellar space of the clay matrix with a layer expansion up to 2.25 nm. Covalently bound glucoamylase demonstrates a sharp decrease in surface area and pore volume that suggests binding of the enzyme at the pore entrance. NMR studies reveal the involvement of octahedral and tetrahedral Al during immobilization. The performance characteristics in FBR were evaluated. Effectiveness factor (η) for FBR is greater than unity demonstrating that activity of enzyme is more than that of the free enzyme. The Michaelis constant (Km) for covalently bound glucoamylase was lower than that for free enzyme, i.e., the affinity for substrate improves upon immobilization. This shows that diffusional effects are completely eliminated in the FBR. Both immobilized systems showed almost 100% initial activity after 96 h of continuous operation. Covalent binding demonstrated better operational stability.

Production, purification and partial characterization of a novel protease from marine Engyodontium album BTMFS10 under solid state fermentation

Engyodontium album isolated from marine sediment produced protease, which was active at pH 11. Process parameters influencing the production of alkaline protease by marine E. album was optimized. Particle size of <425 mm, 60% initial moisture content and incubation at 25 8C for 120 h were optimal for protease production under solid state fermentation (SSF) using wheat bran. The organism has two optimal pH (5 and 10) for maximal enzyme production. Sucrose as carbon source, ammonium hydrogen carbonate as additional inorganic nitrogen source and amino acid leucine enhanced enzyme production during SSF. The protease was purified and partially characterized. A 16-fold purified enzyme was obtained after ammonium sulphate precipitation and ion-exchange chromatography. Molecular weight of the purified enzyme protein was recorded approximately 38 kDa by SDS-PAGE. The enzyme showed maximum activity at pH 11 and 60 8C. Activity at high temperature and high alkaline pH suggests suitability of the enzyme for its application in detergent industry

Lipase from marine Aspergillus awamori BTMFW032: Production, partial purification and application in oil effluent treatment

Marine fungus BTMFW032, isolated from seawater and identified as Aspergillus awamori, was observed to produce an extracellular lipase, which could reduce 92% fat and oil content in the effluent laden with oil. In this study, medium for lipase production under submerged fermentation was optimized statistically employing response surface method toward maximal enzyme production. Medium with soyabean meal- 0.77% (w/v); (NH4)2SO4-0.1 M; KH2PO4-0.05 M; rice bran oil-2% (v/v); CaCl2-0.05 M; PEG 6000-0.05% (w/v); NaCl-1% (w/v); inoculum-1% (v/v); pH 3.0; incubation temperature 35 8C and incubation period-five days were identified as optimal conditions for maximal lipase production. The time course experiment under optimized condition, after statistical modeling, indicated that enzyme production commenced after 36 hours of incubation and reached a maximum after 96 hours (495.0 U/ml), whereas maximal specific activity of enzyme was recorded at 108 hours (1164.63 U/mg protein). After optimization an overall 4.6- fold increase in lipase production was achieved. Partial purification by (NH4)2SO4 precipitation and ion exchange chromatography resulted in 33.7% final yield. The lipase was noted to have a molecular mass of 90 kDa and optimal activity at pH 7 and 40 8C. Results indicated the scope for potential application of this marine fungal lipase in bioremediation.

Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions

The role of lower partial moments in stochastic modeling

Lower partial moments plays an important role in the analysis of risks and in income/poverty studies. In the present paper, we further investigate its importance in stochastic modeling and prove some characterization theorems arising out of it. We also identify its relationships with other important applied models such as weighted and equilibrium models. Finally, some applications of lower partial moments in poverty studies are also examined

Quantile based reliability aspects of partial moments

Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions

Dominant partial least square factors of consumer purchase behaviour of passenger cars

Globalization and liberalization, with the entry of many prominent foreign manufacturers, changed the automobile scenario in India, since early 1990’s. World Leaders in automobile manufacturing such as Ford, General Motors, Honda, Toyota, Suzuki, Hyundai, Renault, Mitsubishi, Benz, BMW, Volkswagen and Nissan set up their manufacturing units in India in joint venture with their Indian counterpart companies, by making use of the Foreign Direct Investment policy of the Government of India, These manufacturers started capturing the hearts of Indian car customers with their choice of technological and innovative product features, with quality and reliability. With the multiplicity of choices available to the Indian passenger car buyers, it drastically changed the way the car purchase scenario in India and particularly in the State of Kerala. This transformed the automobile scene from a sellers’ market to buyers’ market. Car customers started developing their own personal preferences and purchasing patterns, which were hitherto unknown in the Indian automobile segment. The main purpose of this paper is to develop a model with major variables, which influence the consumer purchase behaviour of passenger car owners in the State of Kerala. Though there are innumerable studies conducted in other countries, there are very few thesis and research work conducted to study the consumer behaviour of the passenger car industry in India and specifically in the State of Kerala. The results of the research contribute to the practical knowledge base of the automobile industry, specifically to the passenger car segment. It has also a great contributory value addition to the manufacturers and dealers for customizing their marketing plans in the State

Nutrient cycling and field-based partial nutrient balances in two mountain oases of Oman

Little is known about nutrient fluxes as a criterion to assess the sustainability of traditional irrigation agriculture in eastern Arabia. In this study GIS-based field research on terraced cropland and groves of date palm (Phoenix dactylifera L.) was conducted over 2 years in two mountain oases of northern Oman to determine their role as hypothesized sinks for nitrogen (N), phosphorus (P) and potassium (K). At Balad Seet 55% of the 385 fields received annual inputs of 100–500 kg N ha^-1 and 26% received 500–1400 kg N ha^-1. No N was applied to 19% of the fields which were under fallow. Phosphorus was applied annually at 1–90 kg ha^-1 on 46% of the fields, whereas 27% received 90–210 kg ha^-1. No K was applied to 27% of the fields, 32% received 1–300 kg K ha^-1, and the remaining fields received up to 1400 kg ha^-1. At Maqta N-inputs were 61–277 kg ha^-1 in palm groves and 112–225 kg ha^-1 in wheat (Triticum spp.) fields, respective P inputs were 9–40 and 14–29 kg ha^-1, and K inputs were 98–421 and 113–227 kg ha^-1. For cropland, partial oasis balances (comprising inputs of manure, mineral fertilizers, N2-fixation and irrigation water, and outputs of harvested products) were similar for both oases, with per hectare surpluses of 131 kg N, 37 kg P, and 84 kg K at Balad Seet and of 136 kg N, 16 kg P and 66 kg K at Maqta. This was despite the fact that N2-fixation by alfalfa (Medicago sativa L.), estimated at up to 480 kg ha^-1 yr^-1 with an average total dry matter of 22 t ha^-1, contributed to the cropland N-balance only at the former site. Respective palm grove surpluses, in contrast were with 303 kg N, 38 kg P, and 173 kg K ha^-1 much higher at Balad Seet than with 84 kg N, 14 kg P, and 91 kg K ha^-1 at Maqta. The data show that both oases presently are large sinks for nutrients. Potential gaseous and leaching losses could at least partly be controlled by a decrease in nutrient input intensity and careful incorporation of manure.

On Vessiot's Theory of Partial Differential Equations

The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.