The first essay constitutes a theory which lends truth to the Kuznets hypothesis. The attention is centered on the role of financial markets in defining the process of knowledge accumulation, and ultimately the distribution of income earning capabilities in a population of ex ante heterogeneous individuals. The provision of credit is hindered by one-sided lack of commitment embedded in the area of educational investment. Adaptation in the legislative system to accommodate a punishment scheme conditional on default is the critical requirement for the economy to be carried on a dynamic growth path, albeit one of higher and worsening inequality. Owing to the accumulation of human capital and the associated externality on future generations’ knowledge productivity, the economy ultimately makes its transition to a state of lower income differentials. The second essay is an enquiry on the role of monetary policy in determining the growth dynamics of a small open economy. We postulate that the possibility of intermediated credit does not exist, the intention of the assumption being to uncover the role of inflation as tax on private spending. The analysis brings a valid argument of the superneutrality of money. Inflation when operating as consumption tax has no impact on the growth rate of output. This is established irrespective of the labor supply be held fixed, or incorporated as endogenous decision. When imitating the role of capital taxation, inflationary policy has a negative effect on capital accumulation in a framework of fixed labor supply. However, the validity of the superneutrality result is once again reestablished in an environment accommodating the endogeneity of labor supply. The third essay is a theoretical investigation of the long-run effects of tax and expenditure policies in an open economy framework. The aim is to establish an analytic basis for the factual evidence associated with the non-monotonic response of the current account to fiscal shocks. To this endeavor we sought two sources of time non-separability in the preference structure, habit-forming consumption in consumer durable goods. Optimal private choices induce non-monotonic dynamics on consumption behavior that are exactly consistent with the evidence on the current account.

We formalize and analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuoustime but not in discrete-time.

We first introduce some coupling of a finite number of Probabilistic Cellular Automata dynamics (PCA), preserving the stochastic ordering. Using this tool, for a general attractive probabilistic cellular automata on SZd, where S is finite, we prove that a condition (A) is equivalent to the (time-) convergence towards equilibrium of this Markovian parallel dynamics, in the uniform norm, exponentially fast. This condition (A) means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite ‘box’-volume. For a class of reversible PCA dynamics on {−1, +1}Zd / with a naturally associated Gibbsian potential ϕ, we prove that a Weak Mixing condition for ϕ implies the validity of the assumption (A); thus the ‘exponential ergodicity’ of the dynamics towards the unique Gibbs measure associated to ϕ holds. On some particular examples of this PCA class, we verify that our assumption (A) is weaker than the Dobrushin-Vasershtein ergodicity condition. For some special PCA, the ‘exponential ergodicity’ holds as soon as there is no phase transition.

We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.

The applications of magnetic materials are related to their magnetic and crystal structure as well as electronic properties. In this thesis, mainly experimental methods have been focussed on novel materials and bulk materials. A selection of materials were studied by several techniques like Mössbauer spectroscopy, X-ray and neutron diffraction and magnetisation measurements. New technology allow us to prepare artificial materials with unic magnetic properties. Magnetic multilayers are very interesting not only from phenomenological point of view but also as good applications materials. In this work will be shown some results from Fe/V and Fe/Co multilayer system The (Fe1-xMnx)3P system has been studied at both ends of the composition range. At the Fe-rich end, compounds exhibiting ferromagnetic ordering are formed, while at the Mn-rich end, an antiferromagnetic coupling was discovered. The experimental results are supported by theoretical calculations. Rare-earth compounds with focus on Fe0.65Er0.2B0.15 were studied by means of traditional Mössbauer spectroscopy, Monochromatic Circular Polarized Mössbauer Spectroscopy, X-ray diffraction and magnetic mesurements. This compound shows interesting behaviour of Fe magnetic moment at low and room temperature. The first magnetic studies on rhombohedral Li3Fe2(PO4)3 at low temperature has also been made and an antiferromagnetic structure was revealed.

Context represents any knowledge obtained from Wireless Sensor Networks (WSNs) about the object being monitored (such as time and location of the sensed events). Time and location are important constituents of context as the information about the events sensed in WSNs is comprehensive when it includes spatio-temporal knowledge. In this thesis, we first concentrate on the development of a suite of lightweight algorithms on temporal event ordering and time synchronization as well as localization for WSNs. Then, we propose an energy-efficient clustering routing protocol for WSNs that is used for message delivery in the former algorithm. The two problems - temporal event ordering and synchronization - are dealt with together as both are concerned with preserving temporal relationships of events in WSNs. The messages needed for synchronization are piggybacked onto the messages exchanged in underlying algorithms. The synchronization algorithm is tailored to the clustered topology in order to reduce the overhead of keeping WSNs synchronized. The proposed localization algorithm has an objective of lowering the overhead of DV-hop based algorithms by reducing the number of floods in the initial position estimation phase. It also randomizes iterative refinement phase to overcome the synchronicity of DV-hop based algorithms. The position estimates with higher confidences are emphasized to reduce the impact of erroneous estimates on the neighbouring nodes. The proposed clustering routing protocol is used for message delivery in the proposed temporal algorithm. Nearest neighbour nodes are employed for inter-cluster communication. The algorithm provides Quality of Service by forwarding high priority messages via the paths with the least cost. The algorithm is also extended for multiple Sink scenario. The suite of algorithms proposed in this thesis provides the necessary tool for providing spatio-temporal context for context-aware WSNs. The algorithms are lightweight as they aim at satisfying WSN's requirements primarily in terms of energy-efficiency, low latency and fault tolerance. This makes them suitable for emergency response applications and ubiquitous computing.

Context represents any knowledge obtained from Wireless Sensor Networks (WSNs) about the object being monitored (such as time and location of the sensed events). Time and location are important constituents of context as the information about the events sensed in WSNs is comprehensive when it includes spatio-temporal knowledge. In this thesis, we first concentrate on the development of a suite of lightweight algorithms on temporal event ordering and time synchronization as well as localization for WSNs. Then, we propose an energy-efficient clustering routing protocol for WSNs that is used for message delivery in the former algorithm. The two problems - temporal event ordering and synchronization - are dealt with together as both are concerned with preserving temporal relationships of events in WSNs. The messages needed for synchronization are piggybacked onto the messages exchanged in underlying algorithms. The synchronization algorithm is tailored to the clustered topology in order to reduce the overhead of keeping WSNs synchronized. The proposed localization algorithm has an objective of lowering the overhead of DV-hop based algorithms by reducing the number of floods in the initial position estimation phase. It also randomizes iterative refinement phase to overcome the synchronicity of DV-hop based algorithms. The position estimates with higher confidences are emphasized to reduce the impact of erroneous estimates on the neighbouring nodes. The proposed clustering routing protocol is used for message delivery in the proposed temporal algorithm. Nearest neighbour nodes are employed for inter-cluster communication. The algorithm provides Quality of Service by forwarding high priority messages via the paths with the least cost. The algorithm is also extended for multiple Sink scenario. The suite of algorithms proposed in this thesis provides the necessary tool for providing spatio-temporal context for context-aware WSNs. The algorithms are lightweight as they aim at satisfying WSN's requirements primarily in terms of energy-efficiency, low latency and fault tolerance. This makes them suitable for emergency response applications and ubiquitous computing.

This thesis presents several algorithms that update the vertex separation of a tree after the tree is modified; the vertex separation of a graph measures the largest number of vertices to the left of and including a vertex that are adjacent to vertices to the right of the vertex, when the vertices in the graph are arranged in the best possible linear ordering. Vertex separation was introduced by Lipton and Tarjan and has since been applied mainly in VLSI design. The tree is modified by either attaching another tree or removing a subtree. The first algorithm handles the special case when another tree is attached to the root, and the second algorithm updates the vertex separation after a subtree of the root is removed. The last two algorithms solve the more general problem when subtrees are attached to or removed from arbitrary vertices; they have good running time performance only in the amortized sense. The running time of all our algorithms is sublinear in the number of vertices in the tree, assuming certain information is precomputed for the tree. This improves upon current algorithms by Skodinis and Ellis, Sudborough, and Turner, both of which have linear running time for this problem. Lower and upper bounds on the vertex separation of a general graph are also derived. Furthermore, analogous bounds are presented for the cutwidth of a general graph, where the cutwidth of a graph equals the maximum number of edges that cross over a vertex, when the vertices in the graph are arranged in the best possible linear ordering.

Hybrid Make-To-Stock (MTS)-Make-To-Order (MTO) manufacturing is a well known policy that captures the benefits of both MTS and MTO policies. This manufacturing policy is adopted by many manufacturing firms because it allows for production based on customer specifications while keeping short response times. We study a hybrid MTS-MTO manufacturing system which consists of two processing stages and an intermediate buffer between these two stages. We propose two separate scenarios for ordering and replenishment of components from the first stage which will give more realistic guidance for practitioners. The first scenario is batching customer orders before being released to the first stage. The second scenario is batch replenishment of common components from the first stage. Most existing MTS-MTO models focus on one-for-one ordering and replenishment strategies. We enhance these models by introducing a batch ordering policy to account for economies of scale in ordering when there is an ordering cost associated with each order placed for common components. We use queueing theory to model the system behavior and use the matrix-geometric method to evaluate system performance under the new ordering policy. Afterwards, we develop an optimization model with the objective to minimize the system overall costs. The purpose of our optimization model is to find the optimal intermediate buffer size and the optimal order quantity for the system. In the second scenario, we introduce the batch replenishment policy from stage 1. This policy is suitable when stage 1 and stage 2 are physically distant and there is a shipping cost incurred when components are transferred from stage 1 to stage 2. The decision variables in this model are the intermediate buffer size and the shipping quantity. We show that the base stock policy is sub-optimal when there is an ordering cost incurred for ordering components. The savings from adopting the batch ordering policy are high and the response time for most customer orders is not affected. When there are shipping costs and shipping time between the two stages, we show that the right selection of the system decision variables can have a large impact on the total cost incurred by the system.

This thesis presents several algorithms that update the vertex separation of a tree after the tree is modified; the vertex separation of a graph measures the largest number of vertices to the left of and including a vertex that are adjacent to vertices to the right of the vertex, when the vertices in the graph are arranged in the best possible linear ordering. Vertex separation was introduced by Lipton and Tarjan and has since been applied mainly in VLSI design. The tree is modified by either attaching another tree or removing a subtree. The first algorithm handles the special case when another tree is attached to the root, and the second algorithm updates the vertex separation after a subtree of the root is removed. The last two algorithms solve the more general problem when subtrees are attached to or removed from arbitrary vertices; they have good running time performance only in the amortized sense. The running time of all our algorithms is sublinear in the number of vertices in the tree, assuming certain information is precomputed for the tree. This improves upon current algorithms by Skodinis and Ellis, Sudborough, and Turner, both of which have linear running time for this problem. Lower and upper bounds on the vertex separation of a general graph are also derived. Furthermore, analogous bounds are presented for the cutwidth of a general graph, where the cutwidth of a graph equals the maximum number of edges that cross over a vertex, when the vertices in the graph are arranged in the best possible linear ordering.