There are many types of bioreactors used for producing bacteria populations in commercial, medical and research applications. This report presents a systematic discussion of some of the most important models corresponding to the well known reproduction kinetics such as the Michaelis-Menten kinetics, competitive substrate inhibition and competitive product inhibition. We propose a modification of a known model, analyze it in the same manner as known models and discuss the most popular types of bioreactors and ways of controlling them. This work summarises much of the known results and may serve as an aid in attempts to design new models.

We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.

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

<p>Studie är baserad på Siegler & Ramani (2008) “Playing linear numerical board games promotes low-income child­ren´s numerical development”<em>. </em>Syfte är att undersöka om det med intensivträning (i form av ett linjärt tärningsspel) går att stimulera sexåriga barns talförståelse inom talområdet 1-10. Metoderna som valts är fältexperiment och observation. Fält­experimentet påvisar att intensivträning med ett tärningsspel, utfört under 4 stycken 15 minuters lektioner under en tvåveckors period, tydligt kan förbättra barns talförståelse medan observationen visar att utfallet påverkas av pedagogens olika yrkesverktyg samt undervis­ningens organisation (en-till-en undervisning)<em>. </em>Slutsatsen är att tidig pedagogisk matematik­stimulans kan förbättra elevers förutsättningar inför skolstart. <em></em></p> / <p>This study is based on Siegler & Ramani (2008) “Playing linear numerical board games promotes low-income children's numerical development.” The purpose is to examine to which extent intensive training of a linear boardgame may stimulate the number concept 1-10 among six-year-olds and the factors conducive to such results. The chosen methods are experiment and  observation. The experiment shows that intensive training with a linear boardgame, done during four 15-minute lessons over a two week period clearly can improve the childrens numerical understanding. The observation also indicate the importance for outcome of the  teacher, her professional tools and the teaching organization (one-to-one teaching). The conclusion is that early maths teaching can improve the conditions for pupils beginning school</p>

<p>Syftet med uppsatsen har varit att undersöka hur elever ser på ämnet matematik och matematikundervisning. Vår ambition har även varit att få syn på vad elever finner lustfyllt och mindre lustfyllt med matematiken och matematikundervisning.</p><p>Utgångspunkten till det valda ämnet är att många elever som slutar grundskolan inte når upp till betyget Godkänd i matematik (SOU, 2004). Med hjälp av enkätfrågor ställda till 30 stycken elever i år 4, varav 7 elever som ingår i en mindre undervisningsgrupp under matematiklektioner, försökte vi finna svar på våra frågor. De 7 elever som ingår i den mindre undervisningsgruppen har även svarat på enkäten utifrån hur de upplevde matematiklektionerna när de var integrerade i den stora undervisningsgruppen. Vårt syfte med detta har varit att göra en jämförelse mellan de olika gruppernas upplevelse.</p><p>Resultatet av enkätundersökningen visade att majoriteten av eleverna i den mindre undervisningsgruppen tycker att matematik är "så där", vilket handlar om att eleverna upplevde matematik både som roligt och tråkigt. Hälften av dessa elever tyckte inte om matematikundervisningen när de ingick i stor undervisningsgrupp, men som de däremot gör när de ingår i liten undervisningsgrupp. Drygt hälften av eleverna i stor undervisningsgrupp tycker om matematik och hälften av dessa elever gav svaret att de tycker om matematiklektionerna, andra hälften tyckte ”så där” om matematiklektionerna.</p><p>I litteraturstudien kom vi bland annat i kontakt med Sjöbergs studie (2006) där 13 elever som efter avslutad grundskola inte nått upp till betyget godkänd i matematik, fick ge sin syn på varför de ansåg att de hamnat i matematiksvårigheter. En annan studie som också visade intresse var Engström (2006) som i sin avhandling har tittat på hur datorn kan användas som redskap i matematikundervisning.</p><p>Det framkom även i litteraturstudien att orsakerna till elevers matematiksvårigheter kan orsakas av vilken förmåga som läraren har att förmedla matematikkunskaper till elever. Vi alla är olika och lär oss på olika sätt. Samt att miljön har en stor inverkan.</p><p> </p>

<p>In this paper the Heath, Jarrow and Morton (HJM) framework is applied in the programming language Java for the estimation of the future spot rate. The subcase of an exponential model for the diffusion coefficient (volatility) is used for the pricing of interest rate derivatives (caps).</p>

<p>Forecasting the stock market is a complex task, partly because of the random walk behavior of the stock price series. The task is further complicated by the noise, outliers and missing values that are common in financial time series. Despite of this, the subject receives a fair amount of attention, which probably can be attributed to the potential rewards that follows from being able to forecast the stock market.</p><p>Since artificial neural networks are capable of exploiting non-linear relations in the data, they are suitable to use when forecasting the stock market. In addition to this, they are able to outperform the classic autoregressive linear models.</p><p>The objective of this thesis is to investigate if the stock market can be forecasted, using the so called error correction neural network. This is accomplished through the development of a method aimed at finding the optimum forecast model.</p><p>The results of this thesis indicates that the developed method can be applied successfully when forecasting the stock market. Of the five stocks that were forecasted in this thesis using forecast models based on the developed method, all generated positive returns. This suggests that the stock market can be forecasted using neural networks.</p>

<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.</p><p>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.</p><p>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.</p>

<p>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.</p><p>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.</p><p>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.</p> / Paper I reprinted with kind permission of Elsevier, sciencedirect.com

<p>This report consider a system describing three competing species with populations <em>x</em>, <em>y</em> and <em>z</em>. Sufficient conditions for every positive equilibrium to be asymptotically stable have been found. First it is shown that conditions on the pairwise competitive interaction between the populations are needed. Actually, these conditions are equivalent to asymptotic stability for any two-dimensional competing system of the three species. It is also shown that these alone are not enough, and that a condition on the competitive interaction between all three populations is also needed. If all conditions are fulfilled, each population will survive on a long-term basis and there will be a stable coexistence.</p>