In this thesis, capacity-constrained aspects of multi-level, multi-stage productionplanning are investigated. The aim has been to extend Material Requirements Planning Theory (MRP Theory) to cover more general problems dealing with capacity constraints, in particular when non-zero lead times are present and the processes take place in continuous time. MRP Theory deals with multi-level production systems with multiple items taking place either within a discrete or continuous time framework. External demand is considered either deterministic or stochastic. Lead times are assumed to be given constants, and the Net Present Value Principle has been applied as the objective function. The Bill-of-Materials, capturing component as well as capacity requirements, in volume as well as in advanced timing due to lead times, has been described using a generalised input matrix involving Laplace transforms or z transforms. In order to be able to apply Dynamic Programming as a solution method, the system state has been defined and designed in terms of a matrix, in which historical values of cumulative production and cumulative demand are given state variables. A high power computer has been used to calculate solutions to numerical examples. Moreover, this thesis examines the fundamental equations of MRP Theory in order to analyse the possibility to obtain closed-form expressions for the time development of the system, when standard ordering rules of MRP are applied. In addition, capacity-constrained production planning problems and procedures in a paper mill have been surveyed and are presented in the form of a case study.

In this thesis the double exponential jump-diffusion model is considered and the Laplace transform is used as a method for pricing both plain vanilla and path-dependent options. The evolution of the underlying stock prices are assumed to follow a double exponential jump-diffusion model. To invert the Laplace transform, the Euler algorithm is used. The thesis includes the programme code for European options and the application to the real data. The results show how the Kou model performs on the NASDAQ OMX Stockholm Market in the case of the SEB stock.

While great strides have been made in treating many classes of human disease, the late-onset neurodegenerative diseases continue to elude modern medicine. These diseases, which include Alzheimer's disease (AD), Parkinson's disease (PD), Huntington's disease (HD), the transmissible spongiform encephalopathies (TSEs), and amyotrophic lateral sclerosis (ALS), involve accumulation of insoluble aggregates of one or more causative proteins, leading to progressive loss of central nervous system neurons, progressively worsening neurological symptoms, and eventual patient death. All of these diseases are currently incurable and fatal. In the case of ALS, progressive death of upper and lower motor neurons leads to full-body paralysis, respiratory difficulty, and patient death. Of the subset of ALS cases showing familial inheritance, approximately 20% are caused by mutations in the SOD1 gene, encoding the Cu, Zn superoxide dismutase (SOD1). These mutations do not have the common property of impairing SOD1's normal function as a free radical scavenger. Instead, they are thought to increase the protein's likelihood of misfolding and aggregating via a poorly-understood aggregation cascade. It is believed that species populated along the misfolding and aggregation pathway may prove to be good targets for therapies designed to block accumulation of downstream toxic species, or to prevent aberrant protein-protein interactions responsible for neurotoxicity. In this thesis, several new techniques are developed to enable detailed elucidation of the SOD1 unfolding and misfolding pathways. Time-resolved measurements collected during SOD1 unfolding or misfolding of release of bound Cu and Zn, of changes in intrinsic fluorescence, of exposure of hydrophobic surface area, and of alterations in the chemical environment of histidine residues, are presented. A new mathematical analysis technique named the Analytical Laplace Inversion Algorithm is developed for rapid extraction of mechanistic information from these time-resolved signals. These tools are applied to the construction of the most detailed models to date of the unfolding and misfolding mechanisms of WT and ALS-causing mutant SOD1. The models presented identify several well-populated unfolding and misfolding intermediates that could serve as good targets for therapies designed to address the fundamental molecular mechanisms underlying SOD1-associated ALS, and to treat what is currently a devastating and incurable disease.

While great strides have been made in treating many classes of human disease, the late-onset neurodegenerative diseases continue to elude modern medicine. These diseases, which include Alzheimer's disease (AD), Parkinson's disease (PD), Huntington's disease (HD), the transmissible spongiform encephalopathies (TSEs), and amyotrophic lateral sclerosis (ALS), involve accumulation of insoluble aggregates of one or more causative proteins, leading to progressive loss of central nervous system neurons, progressively worsening neurological symptoms, and eventual patient death. All of these diseases are currently incurable and fatal. In the case of ALS, progressive death of upper and lower motor neurons leads to full-body paralysis, respiratory difficulty, and patient death. Of the subset of ALS cases showing familial inheritance, approximately 20% are caused by mutations in the SOD1 gene, encoding the Cu, Zn superoxide dismutase (SOD1). These mutations do not have the common property of impairing SOD1's normal function as a free radical scavenger. Instead, they are thought to increase the protein's likelihood of misfolding and aggregating via a poorly-understood aggregation cascade. It is believed that species populated along the misfolding and aggregation pathway may prove to be good targets for therapies designed to block accumulation of downstream toxic species, or to prevent aberrant protein-protein interactions responsible for neurotoxicity. In this thesis, several new techniques are developed to enable detailed elucidation of the SOD1 unfolding and misfolding pathways. Time-resolved measurements collected during SOD1 unfolding or misfolding of release of bound Cu and Zn, of changes in intrinsic fluorescence, of exposure of hydrophobic surface area, and of alterations in the chemical environment of histidine residues, are presented. A new mathematical analysis technique named the Analytical Laplace Inversion Algorithm is developed for rapid extraction of mechanistic information from these time-resolved signals. These tools are applied to the construction of the most detailed models to date of the unfolding and misfolding mechanisms of WT and ALS-causing mutant SOD1. The models presented identify several well-populated unfolding and misfolding intermediates that could serve as good targets for therapies designed to address the fundamental molecular mechanisms underlying SOD1-associated ALS, and to treat what is currently a devastating and incurable disease.

Nesta contribuição apresentamos uma solução para a equação de transferência radiativa condutiva em geometria cilíndrica. Esta solução é aplicada para simular a radiação e campo de temperatura juntamente com o transporte de energia radiativa e condutiva proveniente do escape liberado em lançamentos de foguetes. Para este fim, discutimos uma abordagem semianalítica reduzindo a equação original, que é contínua nas variáveis angulares, numa equação semelhante ao problema SN da transferência radiativa condutiva. A solução é construída usando um método de composição por transformada de Laplace e o método da decomposição de Adomian. O esquema recursivo ´e apresentado para o sistema de equações de ordenadas duplamente discretas juntamente com as dependências dos parâmetros e suas influências sobre a convergência heurística da solução. A solução obtida, em seguida, permite construir o campo próximo relevante para caracterizar o termo fonte para problemas de dispersão ao ajustar os parâmetros do modelo, tais como, emissividade, refletividade, albedo e outros, em comparação com a observação, que são relevantes para os processos de dispersão de campo distante e podem ser manipulados de forma independente do presente problema. Além do método de solução, também relatamos sobre algumas soluções e simulações numéricas. / In this contribution we present a solution for the radiative conductive transfer equation in cylinder geometry. This solution is applied to simulate the radiation and temperature field together with conductive and radiative energy transport originated from the exhaust released in rocket launches. To this end we discuss a semi-analytical approach reducing the original equation, which is continuous in the angular variables, into an equation similar to the SN radiative conductive transfer problem. The solution is constructed using a composite method by Laplace transform and Adomian decomposition method. The recursive scheme is presented for the doubly discrete ordinate equations system together with parameter dependencies and their influence on heuristic convergence of the solution. The obtained solution allows then to construct the relevant near field to characterize the source term for dispersion problems when adjusting the model parameters such as emissivity, reflectivity, albedo and others in comparison to the observation, that are relevant for far field dispersion processes and may be handled independently from the present problem. In addition to the solution method we also report some solutions and numerical simulations.

Nesta contribuição apresentamos uma solução para a equação de transferência radiativa condutiva em geometria cilíndrica. Esta solução é aplicada para simular a radiação e campo de temperatura juntamente com o transporte de energia radiativa e condutiva proveniente do escape liberado em lançamentos de foguetes. Para este fim, discutimos uma abordagem semianalítica reduzindo a equação original, que é contínua nas variáveis angulares, numa equação semelhante ao problema SN da transferência radiativa condutiva. A solução é construída usando um método de composição por transformada de Laplace e o método da decomposição de Adomian. O esquema recursivo ´e apresentado para o sistema de equações de ordenadas duplamente discretas juntamente com as dependências dos parâmetros e suas influências sobre a convergência heurística da solução. A solução obtida, em seguida, permite construir o campo próximo relevante para caracterizar o termo fonte para problemas de dispersão ao ajustar os parâmetros do modelo, tais como, emissividade, refletividade, albedo e outros, em comparação com a observação, que são relevantes para os processos de dispersão de campo distante e podem ser manipulados de forma independente do presente problema. Além do método de solução, também relatamos sobre algumas soluções e simulações numéricas. / In this contribution we present a solution for the radiative conductive transfer equation in cylinder geometry. This solution is applied to simulate the radiation and temperature field together with conductive and radiative energy transport originated from the exhaust released in rocket launches. To this end we discuss a semi-analytical approach reducing the original equation, which is continuous in the angular variables, into an equation similar to the SN radiative conductive transfer problem. The solution is constructed using a composite method by Laplace transform and Adomian decomposition method. The recursive scheme is presented for the doubly discrete ordinate equations system together with parameter dependencies and their influence on heuristic convergence of the solution. The obtained solution allows then to construct the relevant near field to characterize the source term for dispersion problems when adjusting the model parameters such as emissivity, reflectivity, albedo and others in comparison to the observation, that are relevant for far field dispersion processes and may be handled independently from the present problem. In addition to the solution method we also report some solutions and numerical simulations.

Gas separation with polymer membranes are becoming one of the mainstream separation techniques for a myriad of industrial applications. Membrane technologies are recognized as a viable and economical unit operation compared to more conventional separation processes. The design and material selection of membrane separation processes depends highly on the transport properties of separated gas molecules within the membrane material. Therefore, to use efficient methods for gas membrane characterization is paramount for the proper design of membrane separation processes. A membrane can be typically characterized by three main properties: permeability, solubility and diffusivity. The permeability of a membrane is the product of its diffusivity and solubility, therefore obtaining two of the three parameters is sufficient to fully characterize a membrane. The time-lag method is one of the oldest and most used gas membrane characterization methods. However, it suffers from various limitations that make the method not applicable for many types of membranes. The focus in this study was to develop new gas membrane characterization techniques that are based on extracting the membrane properties from the upstream gas pressure measurements rather than only from the downstream pressure measurements. It is believed that characterizing the membrane based on the upstream pressure measurements would be highly useful in characterizing barrier materials which are usually difficult to characterize using the conventional time-lag method. Moreover, glassy polymers which are widely used in industry exhibit behavior associated with nonlinear sorption isotherms and, therefore, the conventional time-lag method is incapable of obtaining an accurate estimation of glassy polymer properties. As a result, sorption experiments to generate a sorption isotherm are usually required in addition to permeation experiments to fully characterize glassy polymer membranes. To quantify the errors associated with the conventional time-lag assumptions and to fundamentally comprehend the impact of nonlinearities on the time-lag method, a comprehensive numerical investigation has been undertaken using the finite difference method. The investigation has clearly put in evidence the effect of the various Langmuir parameters on the accuracy of the time lag and on the time required to achieve steady state. This investigation also allowed assessing the errors associated with the usual assumptions made on the boundary conditions in determining the time lag. In this study, three novel gas membrane characterization methods were developed and proposed. Two of the proposed methods are concerned with the characterization of membranes that can be represented with a linear sorption isotherm. These two methods are entirely based on the upstream pressure measurements. The third membrane characterization method that is proposed is based on the dynamic monitoring of both upstream and downstream pressure measurements and is applicable to systems that exhibit a nonlinear isotherm sorption behavior. The three proposed methods are promising and further experimental validation is recommended to determine their full range of applicability.

L'application exponentielle duale est une façon d'encoder les matrices de Stokes d'une connexion sur un fibré trivial sur la sphère de Riemann avec deux pôles : un pôle double en 0 et un pôle simple en l'infini.On donne ici une formule pour l'application exponentielle duale comme une série formelle non commutative. D'autres généralisations de cette formule sont données. / The exponential dual map is a way to encode Stokes data of a connection on a trivial vector bundle on the Riemann sphere with two poles: one double pole at 0 and one simple pole at infinity.We give here a formula for the exponential dual map expressed as a non commutative serie. Others generalizations of this formula are given.

Hlavním zájmem diplomové práce je studium zobecněné nabla Laplaceové transformace na časových škálach a její jednoznačnosti, včetně důkazu jednoznačnosti a aplikace jednoznačnosti v zlomkovém kalkulu na časových škálach.

The thesis deals with flexible shaft couplings especially with new category of flexible couplings on the principle of fluid. Mathematical model of gas spring and rotor system with two degrees of freedom are derivated in this work. Last part of the work deals with design modification of flexible coupling with gas springs.