<p>In case of the PDE's the concept of solving by separation of variables</p><p>has a well defined meaning. One seeks a solution in a form of a</p><p>product or sum and tries to build the general solution out of these</p><p>particular solutions. There are also known systems of second order</p><p>ODE's describing potential motions and certain rigid bodies that are</p><p>considered to be separable. However, in those cases, the concept of</p><p>separation of variables is more elusive; no general definition is</p><p>given.</p><p>In this thesis we study how these systems of equations separate and find that their separation usually can be reduced to sequential separation of single first order ODE´s. However, it appears that other mechanisms of separability are possible.</p>

<p>ICA is the largest general dealer in the Swedish market as well as the largest supplier to the independent ICA-dealers. The principal and one of the biggest stakeholders of this thesis is the department Supply Chain Development who is responsible for the development of ICA’s Supply Chain.</p><p>The purpose of this study is to examine how ICA’s sales are affected by weather and to make recommendations on how ICA should proceed with its work regarding this issue. By leveraging their forecasts by including weather, ICA hopes that their logistical metrics amount of spoilage, service levels and number of inventory days will improve. This thesis describes how ICA is working with weather currently, and furthermore it discusses the existing literature within this area. Extensive statistical surveys have been conducted in order to identify the products that are affected by weather, and to examine how they are affected by different weather variables. Finally, the thesis gives recommendations to ICA on how they can improve their forecasting by taking this study’s results into account.</p><p>Presently ICA has no consistent approach when it comes to considering weather’s impact on sales. Each individual product planner uses his own experience and gut feeling and there is no central guidance or other quantitative information there to help them.</p><p>This thesis is organised around two major statistical studies. First, a correlation study examines the correlation between sales and deviation from mean temperature. The weather parameter was selected following recommendations from earlier studies and from SMHI - the national weather institute in Sweden. The study was conducted on ICA’s entire assortment and identified which items that were affected by weather. These turned out to be about a hundred in number and were affected mainly during the summer; however a few items were also affected in the winter. Most of the affected items were rather logical regarding weather’s effects on sales and have also been pointed out by planners as products that are likely to be affected by weather. Following that, several regression analyses were conducted on the selected weather affected assortment.</p><p>The regression analyses were conducted with various combinations of one or more weather parameters as explanatory variables. Surprisingly, in most cases the deviation from mean temperature alone was the parameter that best explained the variance in sales figures. The result or output of this thesis is a value for the expected change in sales for a selected assortment, given a change in deviation from mean temperature.</p><p>The recommendations given at the end of this thesis explains how ICA in a simple and cost effective way could implement the study's results in their daily work. The proposal is to divide the work by what should be done centrally by the forecasting department, and by what should be done individually by each planner. The forecasting department should regularly collect weather forecasts over different time periods, calculate the deviation from mean temperature and distribute it to the supply planner. After that, it is up to the supply planners on how to best take advantage of this information by taking into account other unique factors affecting each category, such as campaigns, holidays and daily indexes that in many cases have more effect on sales than the weather.</p>

<p>In this paper it is considered the Sircar-Papanicolaou model wich takesinto account a feedback effect of dynamic hedging strategies of pro-gramme traders. Using the Lie group analysis we describe the symmetrygroup of the main equation of the concerned model. We reduce this par-tial differential equation to the ordinary differential equations by usingcorresponding invariants of the subgroups of the main symmetry group.</p>

No description available.

<p>Trots att läroböcker i matematik har en viktig roll i undervisningen, så finns det inte mycket forskning på hur väl de uppfyller sin uppgift. Rapporter om lärobokens roll i skolan förekommer, dock oftast med en negativ klang. Forskning som vi har uppmärksammat tar upp att läroböckerna styr undervisning. Det nationella provet som utfördes för årskurs 3 2009, visade att eleverna har vissa brister i sina matematikkunskaper. Det står i kursplanen för matematik att det är skolans uppgift att utveckla kunskaper som behövs i matematiken för att eleverna ska kunna fatta välgrundade beslut i valsituationer (Skolverket, 2009-11-28). Med ovanstående i åtanke uppkom denna studie med syfte i att ta reda på hur en matematikbok kan se ut och i vilken grad den kan erbjuda eleverna tillfällen att träna de uppsatta målen som finns för årskurs 3.</p><p> </p><p>Resultatet av föreliggande studie visar att de undersökta matematikböckerna inte motsvarar de krav som finns gällande de uppsatta målen för vad eleverna ska uppnå i matematik, till och med årskurs 3. Matematikböckerna tränar ej alla de utsatta målen för matematik. I vår undersökning delade vi upp uppgifterna i kreativa respektive imitativa resonemang. Imitativa resonemang innebär uppgifter som kräver en inövad metod eller ett memorerat svar och dessa uppgifter fanns det betydligt fler av. Kreativa resonemang kräver en ny sorts lösningsmetod för eleverna och var mycket mindre representerade i de båda matematikböckerna vi undersökt. Tidigare forskning har visat på att kreativa resonemang ger eleverna större förståelse för matematik. Med resultatet från nationella provet i åtanke, visade det sig att inte alla elever hade lyckats ta till sig förståelse för de olika räknesätten. Matematikböckernas uppgifter har i studien delats upp i delar som bygger på målen för matematik i årskurs 3. Utifrån delarna har vi sedan kunnat hitta mönster och dragit slutsatser om matematikböckerna som helhet. De undersökta matematikböckerna utger sig ej för att träna alla målen och det är upp till lärarna att kunna ge förutsättningar så att eleverna når alla målen i slutet på årskurs 3. Böckerna utger sig heller inte för att träna imitativa eller kreativa resonemang.</p><p> </p><p>Vi kan genom denna studie rekommendera lärare att uppmärksamma olika matematikböckers innehåll. De bör undersöka vad böckerna kan erbjuda eleverna, för att eleverna ska kunna ha goda förutsättningar för att bli mästare i matematik.</p>

<p>In this work we consider the methods of pricing and hedging an option on the forward commodity market described by the multi-factor diffusion model. In the previous research there were presented explicit valuation formulas for standard European type options and simulation schemes for other types of options. However, hedging strategies were not developed in the available literature. Extending known results this work gives analytical formulas for the price of American, Asian and general European options. Moreover, for all these options hedging strategies are presented. Using these results the dynamics of the portfolio composed of options on futures with different maturities is studied on a commodity market.</p>

Division of labor and division of knowledge are so important andcommon in society today that it is almost impossible to imagine asociety where everyone knows the same things and perform the sametasks. This would be a society where everyone grows, or gathers, andprepares their own food, makes their own tools, builds their ownhouse, and so on. Cultural evolution is the field of research that studies the creationand diffusion of ideas and societies. It is very uncommon for thesestudies to take into account the effects of specialization. Thisthesis will show that specialization is of great importance tocultural evolution. The thesis is divided into three parts: one introduction and two papers. The introduction covers the mathematical models used byeconomists to study the relation between the market and division oflabor. The first paper is an interdisciplinary survey of the researchon division of labor and specialization, including both theoretic andempirical studies. The second paper is a mathematical model of howspecialization of knowledge (i.e. higher education) leads to socialstratification. The model is tested against statistical data fromseveral countries and found to be a good predictor of the differencesin income between people of high and low education.

Boundary-contact problems (BCPs) are studied within the frames of classical mathematical theory of elasticity and plasticity elaborated by Landau, Kupradze, Timoshenko, Goodier, Fichera and many others on the basis of analysis of two- and three-dimensional boundary value problems for linear partial differential equations. A great attention is traditionally paid both to theoretical investigations using variational methods and boundary singular integral equations (Muskhelishvili) and construction of solutions in the form that admit efficient numerical evaluation (Kupradze). A special family of BCPs considered by Shtaerman, Vorovich, Alblas, Nowell, and others arises within the frames of the models of squeezing thin multilayer elastic sheets. We show that mathematical models based on the analysis of BCPs can be also applied to modeling of the clich\'-surface printing contacts and paper surface compressibility in flexographic printing. The main result of this work is formulation and complete investigation of BCPs in layered structures, which includes both the theoretical (statement of the problems, solvability and uniqueness) and applied parts (approximate and numerical solutions, codes, simulation). We elaborate a mathematical model of squeezing a thin elastic sheet placed on a stiff base without friction by weak loads through several openings on one of its boundary surfaces. We formulate and consider the corresponding BCPs in two- and three-dimensional bands, prove the existence and uniqueness of solutions, and investigate their smoothness including the behavior at infinity and in the vicinity of critical points. The BCP in a two-dimensional band is reduced to a Fredholm integral equation (IE) with a logarithmic singularity of the kernel. The theory of logarithmic IEs developed in the study includes the analysis of solvability and development of solution techniques when the set of integration consists of several intervals. The IE associated with the BCP is solved by three methods based on the use of Fourier-Chebyshev series, matrix-algebraic determination of the entries in the resulting infinite system matrix, and semi-inversion. An asymptotic theory for the BCP is developed and the solutions are obtained as asymptotic series in powers of the characteristic small parameter. We propose and justify a technique for the solution of BCPs and boundary value problems with boundary conditions of mixed type called the approximate decomposition method (ADM). The main idea of ADM is simplifying general BCPs and reducing them to a chain of auxiliary problems for 'shifted' Laplacian in long rectangles or parallelepipeds and then to a sequence of iterative problems such that each of them can be solved (explicitly) by the Fourier method. The solution to the initial BCP is then obtained as a limit using a contraction operator, which constitutes in particular an independent proof of the BCP unique solvability. We elaborate a numerical method and algorithms based on the approximate decomposition and the computer codes and perform comprehensive numerical analysis of the BCPs including the simulation for problems of practical interest. A variety of computational results are presented and discussed which form the basis for further applications for the modeling and simulation of printing-plate contact systems and other structures of flexographic printing. A comparison with finite-element solution is performed.

The topic of this thesis is streamline-based integration of dynamic data for porous media systems, particularly in petroleum reservoirs. In the petroleum industry the integration of dynamic data is usually referred to as history matching. The thesis starts out by giving an introduction to streamline-based history-matching methods. Implementations and extensions of two existing methods for streamline-based history matching are then presented. The first method pursued is based on obtaining modifications for streamline-effective properties, which subsequently are propagated to the underlying simulation grid for further iterations. For this method, two improvements are proposed to the original existing method. First, the improved approach involves less approximations, enables matching of porosity, and can account for gravity. Second, a multiscale approach is applied for which the data integration is performed on a hierarchy of coarsened grids. The approach proved robust, and gave a faster and better match to the data. The second method pursued is the so-called generalized travel-time inversion (GTTI) method, which earlier has proven very robust and efficient for history matching. The key to the efficiency of this method is the quasilinear convergence properties and the use of analytic streamline-based sensitivity coefficients. GTTI is applied together with an efficient multiscale-streamline simulator, where the pressure solver is based on a multiscale mixed finite-element method (MsMFEM). To make the history matching more efficient, a selective work-reduction strategy, based on the sensitivities provided by the inversion method, is proposed for the pressure solver. In addition, a method for improved mass conservation in streamline simulation is applied, which requires much fewer streamlines to obtain accurate production-response curves. For a reservoir model with more than one million grid blocks, 69 producers and 32 injectors, the data integration took less than twenty minutes on a standard desktop computer. Finally, we propose an extension of GTTI to fully unstructured grids, where we in particular address issues regarding regularization and computation of sensitivities on unstructured grids with large differences in cell sizes. / Paper I reprinted with kind permission of Elsevier, sciencedirect.com

In this work we consider the methods of pricing and hedging an option on the forward commodity market described by the multi-factor diffusion model. In the previous research there were presented explicit valuation formulas for standard European type options and simulation schemes for other types of options. However, hedging strategies were not developed in the available literature. Extending known results this work gives analytical formulas for the price of American, Asian and general European options. Moreover, for all these options hedging strategies are presented. Using these results the dynamics of the portfolio composed of options on futures with different maturities is studied on a commodity market.