Denna fallstudie undersöker hur glesbygdsskolan utformar och organiserar stödinsatser för elever ibehov av särskilda utbildningsinsatser i matematik (SUM-elever). Det som studien fokuserar på är hurSUM-elever identifieras och kartläggs, vilka extra anpassningar och vilket särskilt stöd som utformasoch organiseras i matematik, arbetet med inkludering samt vilka arbetsuppgifter specialpedagogenhar i arbetet med matematiska stödinsatser. Studien bygger på intervjuer med lärare, specialpedagogoch rektor från två olika glesbygdsskolor i samma kommun samt deras kvalitetsredovisningar. Denteoretiska utgångspunkt som denna studie har är den fenomenologiska. Resultatet visar att skolornaupptäcker eleven i det dagliga arbetet. Lärarna anpassar den ordinarie undervisningen till SUMelevernavilket gör att särskilt stöd är ovanligt och stor andel av eleverna klarar nationella proven imatematik. Det råder en inkluderande miljö i glesbygdsskolan och specialpedagogensarbetsuppgifter är i till stor del att handleda och stötta lärarna.

I den här studien deltar två blivande speciallärare i en aktionsstudie i syfte att genomsamverkan med matematiklärare stärka elevers möjligheter till lärande i matematik hoselever i behov av anpassningar. Två aktioner på olika grundskolor presenteras, på den enaskolan i årskurs 3 och på den andra i årskurs 5. Professionella strukturerade samtal och nogavalda samverkansformer har visat sig resultera i en ökning av såväl generella anpassningarsom anpassningar på individnivå för både SUM-elever och elever i behov av utmaningar. Istudien presenteras en mängd anpassningar som genomförts och slutligen förs en intressantdiskussion om hur detta sätt att arbeta kan bli verklighet i vår kommande yrkesroll.

Abstract Advanced multiple-input multiple-output (MIMO) transceiver structures which utilize the knowledge of channel state information (CSI) at the transmitter side to optimize certain link parameters (e.g., throughput, fairness, spectral efficiency, etc.) under different constraints (e.g., maximum transmitted power, minimum quality of services (QoS), etc.) are considered in this thesis. Adaptive transmission schemes for point-to-point MIMO systems are considered first. A robust link adaptation method for time-division duplex systems employing MIMO-OFDM channel eigenmode based transmission is developed. A low complexity bit and power loading algorithm which requires low signaling overhead is proposed. Two algorithms for computing the sum-capacity of MIMO downlink channels with full CSI knowledge are derived. The first one is based on the iterative waterfilling method. The convergence of the algorithm is proved analytically and the computer simulations show that the algorithm converges faster than the earlier variants of sum power constrained iterative waterfilling algorithms. The second algorithm is based on the dual decomposition method. By tracking the instantaneous error in the inner loop, a faster version is developed. The problem of linear transceiver design in MIMO downlink channels is considered for a case when the full CSI of scheduled users only is available at the transmitter. General methods for joint power control and linear transmit and receive beamformers design are provided. The proposed algorithms can handle multiple antennas at the base station and at the mobile terminals with an arbitrary number of data streams per scheduled user. The optimization criteria are fairly general and include sum power minimization under the minimum signal-to-interference-plus-noise ratio (SINR) constraint per data stream, the balancing of SINR values among data streams, minimum SINR maximization, weighted sum-rate maximization, and weighted sum mean square error minimization. Besides the traditional sum power constraint on the transmit beamformers, multiple sum power constraints can be imposed on arbitrary subsets of the transmit antennas.This extends the applicability of the results to novel system architectures, such as cooperative base station transmission using distributed MIMO antennas. By imposing per antenna power constraints, issues related to the linearity of the power amplifiers can be handled as well. The original linear transceiver design problems are decomposed as a series of remarkably simpler optimization problems which can be efficiently solved by using standard convex optimization techniques. The advantage of this approach is that it can be easily extended to accommodate various supplementary constraints such as upper and/or lower bounds for the SINR values and guaranteed QoS for different subsets of users. The ability to handle transceiver optimization problems where a network-centric objective (e.g., aggregate throughput or transmitted power) is optimized subject to user-centric constraints (e.g., minimum QoS requirements) is an important feature which must be supported by future broadband communication systems.

Ces deux dernières décennies, les techniques de somme connexe essentiellement basées sur des outils d'analyse ont permis de faire des progrès importants dans la compréhension de nombreux problèmes non linéaires issus de la géométrie (étude des métriques à courbure scalaire constante en géométrie Riemannienne, métriques auto-duales, métrique ayant des groupes d'holonomie spéciaux, métriques extrémales en géométrie Kaehlerienne, équations de Yang-Mills, étude des surfaces minimales et des surfaces à courbure moyenne constante, métriques d'Einstein, etc.). Ces techniques se sont avérées être un outil puissant pour démontrer l'existence de solutions à des problèmes hautement non linéaires. Si les techniques permettant d'effectuer des sommes connexes en des points isolés sont bien comprises et fréquemment utilisées, les techniques permettant d'effectuer des sommes connexes le long de sous-variétés ne sont pas encore bien maîtrisées. Le principal objectif de cette thèse est de combler (partiellement) cette lacune en développant de telles techniques applicables dans le cadre de l'étude des métriques à courbure scalaire constante et aussi dans le cadre de l'étude des équations de comptabilité d'Einstein en relativité générale / These last two decades the connected sum techniques, essentially based on analytical tools, are revealed to be a powerful instrument to understand solutions of several nonlinear problem issued from the geometry (constant scalar curvature metrics in Riemannian geometry, self-dual metrics, metrics with special holonomy group, extremal Kaehler metrics, Yang-Mills equations, minimal and constant mean curvature surfaces, Einstein metrics, etc.). Even tough the techniques which allows one to consider the connected sum at points for solutions of nonlinear PDE's are frequently used and deeply understood, the analogous techniques for connected sums along sub-manifolds have not been mastered yet. The main purpose of this thesis is to (partially) plug this gap by developing such techniques in the context of the constant scalar curvature metrics and the Einstein constraint equations in general relativity

Femtosecond time-resolved photoelectron spectroscopy (fsTRPES) experiments have been used to study the photoelectron energy spectra of simple molecules since the 1980’s. Analysis of these spectra provides information about the ultrafast internal conversion dynamics of the parent ions. However, ultraviolet pulses must be used for these pump-probe experiments in order to ionize the molecules. Since current solid state lasers, such as the Ti:sapphire laser, typically produce pulses centered at 800nm, it is necessary to generate UV pulses with nonlinear frequency mixing techniques. I therefore constructed an optical setup to generate the 3rd and 4th harmonics, at 266.7nm and 200nm, respectively, of a Ti:sapphire (Ti:sa) chirped-pulse amplified (CPA) laser system that produces 35fs pulses centered at 800nm. Thin Beta-Barium Borate (β-BaB2O4 or BBO) crystals were chosen to achieve a compromise between short pulse durations and reasonable conversion efficiencies, since ultrashort pulses are quite susceptible to broadening from group velocity dispersion (GVD). Output energies of around 11μJ and 230nJ were measured for the 266.7nm and 200nm pulses, respectively. The transform limits of the 3rd and 4th harmonic pulse lengths were calculated from their measured spectral widths. We found that the 266.7nm bandwidth was large enough to support sub-30fs pulses, and due to cutting at the lower-wavelength end of the 200nm spectrum, we calculated an upper limit of 38fs. The pulses were compressed with pairs of CaF2 prisms to compensate for dispersion introduced by transmissive optics. Two-photon absorption (TPA) intensity autocorrelations revealed fully compressed pulse lengths of 36 ± 2 fs and 42 ± 4 fs for the 3rd and 4th harmonics, respectively.

This thesis introduces normal factor graphs under a new semantics, namely, the exterior function semantics. Initially, this work was motivated by two distinct lines of research. One line is ``holographic algorithms,'' a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is ``normal graphs,'' an elegant framework proposed by Forney for representing codes defined on graphs. The nonrestrictive normality constraint enables the notion of holographic transformations for normal factor graphs. We establish a theorem, called the generalized Holant theorem, which relates a normal factor graph to its holographic transformation. We show that the generalized Holant theorem on one hand underlies the principle of holographic algorithms, and on the other reduces to a general duality theorem for normal factor graphs, a special case of which was first proved by Forney. As an application beyond Forney's duality, we show that the normal factor graphs duality facilitates the approximation of the partition function for the two-dimensional nearest-neighbor Potts model. In the course of our development, we formalize a new semantics for normal factor graphs, which highlights various linear algebraic properties that enables the use of normal factor graphs as a linear algebraic tool. Indeed, we demonstrate the ability of normal factor graphs to encode several concepts from linear algebra and present normal factor graphs as a generalization of ``trace diagrams.'' We illustrate, with examples, the workings of this framework and how several identities from linear algebra may be obtained using a simple graphical manipulation procedure called ``vertex merging/splitting.'' We also discuss translation association schemes with the aid of normal factor graphs, which we believe provides a simple approach to understanding the subject. Further, under the new semantics, normal factor graphs provide a probabilistic model that unifies several graphical models such as factor graphs, convolutional factor graphs, and cumulative distribution networks.

The diploma thesis deals with the impact of a possible introduction of the employee cost lump sum and of cancelling the tax exemption of some tax fringe benefits on the tax liability of the employee. In the first part the fringe benefits taxation system is described, in the second part the fringe benefits taxation system in some OECD countries is described; the third final part shows calculations of the rate of the employee cost lump sum and the analyses of the impact of the modified tax legislation on the tax liability of the model tax payers.

Early efforts in order to be able to detect and remedy mathematical difficulties are of great importance for students mathematical knowledge development. Students in need of special education in mathematics (SEM) all have the same right to, based on their ability, receive the right guidance and stimulus for optimal development.   The purpose of this study is to investigate which changes in the basic number sense comprehension of students in SEM can be detected after an intervention with Vektor and how this change manifests itself.   A group of students age 6-7 and educators participated in the study. The study was conducted through both student interviews and an intervention. Before and after the intervention, the students were interviewed in order to discover whether the intervention has contributed to any changes in the students basic number sense comprehension.   The results of the study show that the change in the understanding of number sense has been predominantly positive for the students who participated in the study. The semiconcrete representations that are in the application have been supportive during the work. Both for the students who need to consolidate their knowledge and the students who with the help oft the support have been able to generalize their previous knowledge.   The conclusion that can be drawn from the study is that Vektor, as a complement to good teacher-led teaching, can contribute to SEM students mathematical development. From a special educational perspective, Vektor, through its adaptive ability, is a good tool for stimulating and motivating students in SEM. This means that the combination of Vektor and teacher-led teaching can create increased accessibility to mathematics for all students.

Practical control problems are subject to dealing with instrumentation noise and inaccurate models. These can be modelled as measurement and state noise, respectively. Nonlinear state estimators, for example a particle filter, can be used to mitigate these effects. However, they are usually computationally expensive which makes them impractical for industrial use. This text investigates using General Purpose Graphics Processing Units (GPGPU) to improve the performance particle and Gaussian sum filters by parallelizing their prediction, update and resampling steps. GPGPU accelerated filters are found to outperform non-accelerated filters as the number of particle increases. GPGPU acceleration also allows particle filters with 2^19.5 particles to be used on systems with dynamic time constants on the order of 0.1 second and for Gaussian sum filters with 2^18.5 particles to be used with time constants on the order of 1 second. The filters are applied to a bioreactor system containing R. Oryzae, where MPC control is applied to the production phase fumaric acid and glucose concentrations. The bioreactor is modelled using results from Iplik (2017) and Swart (2019). It is found that the GPGPU filters improved run times allow for more particles to be used which provides increased filter accuracy and thus better performance. This improved performance comes at the cost of consuming more energy. Thus, it is believed that the GPGPU implementations should be used for applications with complex dynamics/noise that require large numbers of particles and/or high sampling rates. / Dissertation (MEng (Control Engineering))--University of Pretoria, 2021. / Chemical Engineering / MEng (Control Engineering) / Unrestricted

En betydelsefull faktor för att kunna förebygga eller minska elevers svårigheter i matematik är att de upptäcks tidigt. Det är viktigt att ha kunskap om vilka signaler som ska betraktas som avvikande och kräver en särskild utredning (Butterworth, 2011; Malmer, 2006). Syftet med denna rapport är att undersöka och analysera lärares,speciallärares och specialpedagogers strategier att identifiera SUM-elever, årskurs 1-3 via deras beskrivningar. Studien har en kvalitativ ansats med vissa kvantitativa delar. Metoderna har varit dels semistrukturerade intervjuer med specialpedagoger och speciallärare och dels enkäter med många öppna frågor till lärarna. Undersökningen visar bland annat att pedagogerna ofta använder sig av olika kartläggningsmaterial för att upptäcka SUM-elever. De upptäcker även SUM-eleverna i det dagliga arbetet och i olika former av dialoger med andra pedagoger, elever och vårdnadshavare. Kartläggningsmaterial används olika, på vissa skolor genomförs kartläggning regelbundet efter en viss plan och på andra skolor används kartläggning vid behov. Vidare varierar det hur specialpedagogen och specialläraren använder sin tid för att hitta SUM-elever. Vissa bedömer det som betydelsefullt att observera och vara i klassen, andra bedömer det som mer verkningsfullt att handleda personal och jobba enskilt med elever för att upptäcka elever i behov av särskilt stöd i matematik. I undersökningen framkom att pedagogerna inte är konsekventa i sina åsikter när det gäller hur de är grundade de specialpedagogiska perspektiven. De olika tankar som pedagogerna ger uttryck för kan sägas spegla hela skalan av specialpedagogiska perspektiv. Avslutningsvis kan man säga att pedagogerna anser att lärarnas behörighet och kompetens är det mest avgörande för om SUM-eleverna ska upptäckas. Även klasstorleken har viss betydelse för möjligheter att upptäcka SUM-elever. Speciallärarna och specialpedagogerna anser utöver detta att ett bra kartläggningsmaterial och att erfarenhet har betydelse då det gäller att upptäcka SUM-elever. Det framkom även att pedagogerna tyckte att det saknades tydlig ledning och engagemang från rektor i arbetet att upptäcka SUM-elever. Nyckelord: dialog, kartläggning, specialpedagogiska perspektiv, SUM-elev, särskilt undervisningsbehov i matematik.