<p>I studien, Sosialiseringseffekt i skolen: Praksisfellesskapers påvirkning på nyutdannede matematikklæreres identitet, undersøkes ulike praksisfellesskapers påvirkning på nyutdannede matematikklæreres identitet som beskrevet gjennom deres fortellinger. Studien er gjort på bakgrunn av en arbeidsdefinisjon av sosialiseringseffekten. Med utgangspunkt i et situert læringssyn er sosialiseringseffekten definert som praksis¬fellesskapers påvirkning på en lærers identitet. I undersøkelsen gjennomføres narrative intervju med tre nyutdannede matematikk¬lærere. Utgangspunktet for metodevalget er en operasjonalisering av identitetsbegrepet, hvor egenfortelling innlemmes i definisjonen. Narrative intervju gir både en biografisk dybde i de nyutdannede matematikklærernes opplevelser, og en bredde i de historiske, sosiale og kollektive sammenhenger som er forbundet med opplevelsene. Metoden gjør det derfor mulig å tegne læreridentiteter. I tillegg utarbeides det en videreutvikling av begrepet sosialiseringseffekt, som gjøres på bakgrunn av en teoretisk studie av identi¬tets¬begrepet. Videre berikes teoriutviklingen med de nyutdannede matematikk¬lærernes beskrivelser av sin yrkesdebut. Resultatene viser at sosialisering av nyutdannede matematikklære kan foregå gjennom skjulte og synlige praksisfellesskaper, og de rommer både lærer- og elevgrupper, i tillegg til samarbeidsgrupper i lærerutdanningens praksisperioder. Metaforen, den didaktiske kontrakt, har gjort det mulig å skildre elevers reaksjoner på en lærers klasseroms¬praksis, og har derfor bidratt til beskrivelser av læreres sosialisering inn i klasserommets praksisfellesskap. Videre belyses og utdypes det i undersøkelsen at sosialiseringsprosesser er et samspill mellom individets valg og situasjonens begrensende faktorer. Et situert læringssyn koordinerer kognitive og sosiale aspekter i identitetsbegrepet. For å kunne beskrive individers innvirkning på sosialiserings¬prosessen har det i tillegg vist seg hensiktsmessig å sette identitetsbegrepet i sammenheng med habitusteori.</p>

I studien, Sosialiseringseffekt i skolen: Praksisfellesskapers påvirkning på nyutdannede matematikklæreres identitet, undersøkes ulike praksisfellesskapers påvirkning på nyutdannede matematikklæreres identitet som beskrevet gjennom deres fortellinger. Studien er gjort på bakgrunn av en arbeidsdefinisjon av sosialiseringseffekten. Med utgangspunkt i et situert læringssyn er sosialiseringseffekten definert som praksis¬fellesskapers påvirkning på en lærers identitet. I undersøkelsen gjennomføres narrative intervju med tre nyutdannede matematikk¬lærere. Utgangspunktet for metodevalget er en operasjonalisering av identitetsbegrepet, hvor egenfortelling innlemmes i definisjonen. Narrative intervju gir både en biografisk dybde i de nyutdannede matematikklærernes opplevelser, og en bredde i de historiske, sosiale og kollektive sammenhenger som er forbundet med opplevelsene. Metoden gjør det derfor mulig å tegne læreridentiteter. I tillegg utarbeides det en videreutvikling av begrepet sosialiseringseffekt, som gjøres på bakgrunn av en teoretisk studie av identi¬tets¬begrepet. Videre berikes teoriutviklingen med de nyutdannede matematikk¬lærernes beskrivelser av sin yrkesdebut. Resultatene viser at sosialisering av nyutdannede matematikklære kan foregå gjennom skjulte og synlige praksisfellesskaper, og de rommer både lærer- og elevgrupper, i tillegg til samarbeidsgrupper i lærerutdanningens praksisperioder. Metaforen, den didaktiske kontrakt, har gjort det mulig å skildre elevers reaksjoner på en lærers klasseroms¬praksis, og har derfor bidratt til beskrivelser av læreres sosialisering inn i klasserommets praksisfellesskap. Videre belyses og utdypes det i undersøkelsen at sosialiseringsprosesser er et samspill mellom individets valg og situasjonens begrensende faktorer. Et situert læringssyn koordinerer kognitive og sosiale aspekter i identitetsbegrepet. For å kunne beskrive individers innvirkning på sosialiserings¬prosessen har det i tillegg vist seg hensiktsmessig å sette identitetsbegrepet i sammenheng med habitusteori.

Fokuset til denne studien er matematikk i programfaget Tegning og bransjel&#230;re for det yrkesfaglige utdanningsprogrammet Bygg- og anleggsteknikk. M&#229;let er &#229; synliggj&#248;re matematikk som ligger til grunn her, samt &#229; f&#229; en bedre forst&#229;else for hvordan matematikkunnskaper brukes i kombinasjon med kunnskaper knyttet til programfaget. I unders&#248;kelsesperioden ble det arbeidet med et prosjekt i praksisrelatert matematikk for yrkesfaget basert p&#229; arbeidstegninger av en enebolig. Studiens forskningssp&#248;rsm&#229;l er f&#248;lgende: Hvilke matematiske ressurser kan observeres, og hvordan brukes disse av l&#230;reren og elevene i prosjektarbeidet?, Hvilke forbindelser mellom matematikk og programfag fremg&#229;r i elevenes arbeid med prosjektet? og til slutt Hvilken opplevelse har elevene og l&#230;reren av bruken av matematikk i programfaget? I studien er det benyttet kvalitative forskningsmetoder i form av observasjon og intervju av tre elever og deres l&#230;rer i programfaget. Datamaterialet best&#229;r av videoopptak og ble samlet inn i l&#248;pet av prosjekt-periodens to uker. Analyse av data er gjort ved &#229; ta utgangspunkt i et sosiokulturelt l&#230;ringssyn. Det er videre brukt aktivitetsteori og semiotisk teori, i tillegg til teori knyttet til overf&#248;ring av kunnskap mellom kontekster. Resultatene fra studien viser at elevene og l&#230;reren benytter seg av en rekke matematiske ressurser, b&#229;de intellektuelle og fysiske, i arbeidet med prosjektet gitt i programfaget. Flere av de matematiske tegnene og symbolene brukt i arbeidet er knyttet til programfaget og byggebransjen. Det som kjennetegner bruken av matematiske ressurser i prosjektarbeidet er at prosjektoppgavene h&#229;ndteres og l&#248;ses p&#229; en m&#229;lrettet og effektiv m&#229;te, ofte ved hjelp av kalkulatoren som et medierende fysisk redskap. Samtidig indikerer resultatene at det er underforst&#229;tt i kulturen tilh&#248;rende programfaget, hvilke m&#229;leenheter det refereres til, b&#229;de n&#229;r det gjelder arbeidstegningene og dialogene i klasserommet. Videre viser resultatene n&#248;dvendigheten av at elevene behersker samspillet mellom matematikk og programfag, siden arbeidet avhenger av kunnskaper og redskaper knyttet til begge disse kontekstene. Resultatene fra intervjuet med l&#230;reren indikerer at han synes &#229; oppleve at bruken av matematikk i programfaget hovedsakelig best&#229;r i &#229; gj&#248;re utregninger knyttet til problemer og oppgaver innen programfag- og yrkeskontekster. N&#229;r det gjelder elevenes opplevelse til bruken av matematikk i programfaget fremst&#229;r den som at det knytter seg til fysiske reelle ting de kjenner fra kjente yrkessammenhenger, som blant annet boligen som arbeidstegningen representerer. P&#229; denne m&#229;ten kan disse redskapene brukes for &#229; mediere matematiske begreper. Resultatene gjengitt over bidrar til innsikt i hvordan matematikk brukes i programfaget Tegning og bransjel&#230;re, og kan videre benyttes for &#229; tilpasse matematikk-undervisningen ved utdanningsprogrammet Bygg- og anleggsteknikk.

This thesis examines finite dimensional representability of Forward Rate and LIBOR models. A new approach is examined. This approach is more general, elementary, and relevant to finance when compared with existing approaches. This new approach is applied to the following infinite dimensional equations used in finance: ?Gaussian Heath, Jarrow and Morton model; ?Free 1 Heath, Jarrow and Morton model; ?Brace, G?atarek and Musiela???s LIBOR model. Stronger results have been achieved using this approach. The results are as follows: ?The Gaussian HJM model can be represented in finite dimensions if and only if the volatility satisfies a particular differential equation. In which case the finite dimensional representation can be explicitly written; ?The Brace, G?atarek and Musiela???s LIBOR model with one dimensional Wiener process cannot be represented in finite dimensions (other than in a trivial case); ?The Brace, G?atarek and Musiela???s LIBOR model with multidimen-sional Wiener process, and Free HJM have a finite dimensional repre-sentation only if the initial yield curves satisfy a restrictive differential equation. This thesis is arranged as follows ?Chapter 1 is an introduction to this thesis and derivative pricing in general. The reader is referred to section 1.4 titled ???This Thesis?for a more detailed description of the approach of this thesis and its results. ?Chapter 2 contains a brief summary of results from the theory of stochastic processes, stochastic calculus and stochastic equations in infinite dimensions ?Chapter 3 contains an overview of spot market pricing models including the Cox, Ross and Rubinstein and Black and Scholes models. ?Chapter 4 contains an overview of the fixed income market pricing models including the Heath, Jarrow and Morton model; Musiela???s re-formulation of the HJM model; the Goldys, Musiela and Sondermann model; and the Brace, G?atarek and Musiela LIBOR model. ?Chapter 5 contains the primary results of this thesis. Finite Dimen-sional Representability is defined formally and applied to the Musiela reformulated Gaussian HJM model; Musiela reformulated free HJM model; and the Brace, G?atarek and Musiela LIBOR model. This ap-proach and results are compared with the literature.

This thesis presents the results of a computational study on salt transport and accumulation in crop root zone. The main objective of this study is to examine the impacts of past land use on the environment and to examine the effect of irrigation water on the rising of groundwater level and the subsequent salinity problem in rice growing area under given climatic conditions. A special focus has been such impacts in the Wakool irrigation area, NSW, Australia. To this end, a computational model for the assessment and prediction of salinisation in agricultural areas has been developed. This modelling system consists of a land surface scheme (ALSIS) for simulating unsaturated soil moisture and moisture flux, a groundwater flow model (MODFLOW) for estimating the spatial and temporal variations of groundwatertable, a surface flow model (DAFLOW) for calculating water flow in river networks, a module for calculating solute transport at unsaturated zone and a 3-D model (MOC3D) for simulating solute transport in groundwater as well as a module for calculating the spatial and temporal distributions of overland flow depth during wet seasons. The modelling system uses a finite difference linked technique to form a quasi three dimensional model. The land surface scheme is coupled with the groundwater flow model to account for the interactions between the saturated and unsaturated zones. On the land surface, the modelling system incorporates a surface runoff model and detailed treatments of surface energy balance, which is important in es-timating the evapotranspiration, a crucial quantity in calculating the moisture and moisture fluxes in the root zone. Vertical heterogeneity of soil hydraulic properties in the soil profile has been considered. The modelling system has the flexibility of using either Clapp and Hornberger (1978), Broadbridge and White (1988), van Genuchten (1980) or Brooks and Corey (1966) soil water retention models. Deep in the soil, the impact of groundwater table fluctuation on soil moisture and salinity in the unsaturated soil is also included. The calibration and validation for the system have been partially performed with observed groundwater levels in the Wakool irrigation area. The applications of the model to theWakool region are made in two steps. Firstly, a one-dimensional simulation to a selected site in the Wakool irrigation area is carried out to study the possible impact of ponded irrigation on salinisation and the general features of salt movement. Secondly, a more realistic three-dimensional simulation for the entire Wakool region is performed to study the spatial and temporal variations of root zone soil salinity under the influence of past land use from 1975 to 1994. To allow the assessment and prediction of the effects of ponded rice irrigation water (which contains salt) on soil salinity in the area, several hypothetical scenarios using different qualities of water for rice irrigation are tested. To facilitate comparative analysis of different scenarios, a base case is defined, for which irrigation water is assumed to be free of salt. The simulated results show that irrigation increases overall recharge to groundwater in the Wakool irrigation area. The use of ponded irrigation for rice growing has a substantial effect on salt accumulation in the root zone and the rising of groundwater level, indicating that irrigation at rice bay is a major budget item for controlling soil salinity problem in the local area.

This thesis is concerned with stochastic heat equation with memory and nonlinear energy supply. The main motivation to study such systems comes from Thermodynamics, see [85]. The main objective of this work is to study the existence and uniqueness of solutions to such equations and to investigate some fundamental properties of solutions like continuous dependence on initial conditions. In our approach we follow the seminal papers by Da Prato and Clement [10], where the stochastic heat equation with memory is tranformed into an integral equation in a function space and the so-called mild solutions are studied. In the aforementioned papers only linear equations with additive noise were investigated. The main contribution of this work is the extension of this approach to nonlinear equations. Our main tools are the theory of stochastic convolutions as developed in [33] and the theory of resolvent kernels for deterministic linear heat equations with memory, see[10]. Since the solution at time t depends on the whole history of the process up to time t, the resolvent kernel does not define a semigroup of operators in the state space of the process and therefore a ???standard??? theory of stochastic evolution equations as presented in the monograph [33] does not apply. A more delicate analysis of the resolvent kernles and the associated stochastic convolutions is needed. We will describe now content of this thesis in more detail. Introductory Chapters 1 and 2 collect some basic and essentially well known facts about the Wiener process, stochastic integrals, stochastic convolutions and integral kernels. However, some results in Chapter 2 dealing with stochastic convolution with respect to non-homogenous Wiener process are extensions of the existing theory. The main results of this thesis are presented in Chapters 3 and 4. In Chapter 3 we prove the existence and uniqueness of solutions to heat equations with additive noise and either Lipschitz or dissipative nonlinearities. In both cases we prove the continuous dependence of solutions on initial conditions. In Chapter 4 we prove the existence and uniqueness of solutions and continuous dependence on initial conditions for equations with multiplicative noise. The diffusion coefficients defined by unbounded operators are allowed.

Atmosphere-ocean and atmosphere-land interactions are important processes which determine the development of monsoon systems. In this study, a new atmosphere-ocean surface interaction scheme, referred to as AOSIS, is developed and verified with observed data. AOSIS, together with ALSIS (Atmosphere-Land Surface Interaction Scheme), is then coupled into CEMSYS4 (Computational Environmental Modelling System) to investigate the influences of atmosphere-ocean and atmosphere-land surface interactions on the Australian Monsoon, especially the monsoon onset, break and withdrawal. Numerical experiments are carried out and the simulations are compared with the NCEP (National Center for Environmental Prediction, America) data. AOSIS is constructed with three basic components, i.e., a two-layer ocean temperature model, a wind-wave model and a surface flux model. We divide the ocean into a mixed layer and a deep layer. However, the depth of the mixed layer is not constant but varies with time, depending on surface wind shear and buoyancy flux. In AOSIS, we adapted the approach of relating the stages of wave development by wave age and proposed a new expression for calculating the ocean surface roughness length, $z_{0m}$, with consideration of waves. We test AOSIS in a stand along mode against the Moana data and the NCEP data. The comparison with the Moana data shows that AOSIS has considerable skill in simulating SST (sea surface temperature) and energy fluxes, with the simulated values in good agreement with observed data. AOSIS is also successful in simulating the warm and cool effects considered in the COARE (Coupled Ocean-Atmosphere Response Experiment) scheme. Comparison with the NCEP data also confirms that AOSIS simulates SST well. AOSIS and ALSIS are then coupled into CEMSYS4. We apply the system to the simulation of SST and surface energy fluxes over the Australian region and compared the results with the NCEP data. It is found that the simulated SST and energy fluxes are in good agreement with the NCEP data. Further, we study the synoptic events of the Australian Monsoon onset, break and withdrawal and examine the impacts of atmosphere-ocean and atmosphere-land surface interactions on such synoptic events.

We consider conditions under which a continuous functional calculus for a Banach space operator T ?? L(X) may be extended to a bounded Borel functional calculus, and under which a functional calculus for absolutely continuous (AC) functions may be extended to one of for functions of bounded variation (BV). The natural setting for investigating the former case is finitely spectral operators, and for the latter, well-bounded operators. Some such conditions are well-established. If X is a reflexive space, both type of Extensions are assured; in fact if X contains an isomorphic copy of co, then every Operator T ?? L(X) that has a continuous functional calculus necessarily admits a Borel one. We show that if a space X has a predual, then also every operator T ?? L(X) with a continuous functional calculus admits a bounded Borel functional Calculus. In case a Banach space X either contains an isomorphic copy of co, or has a Predual, and T ?? L(X) is an operator with an AC functional calculus, we find that the existence of a decomposition of the identity of bounded variation for T is sufficient to ensure that the AC functional calculus may be extended to a BV functional calculus. We also consider operators defined by a linear map on interpolation families of Banach spaces [Xr, X???] (r???1), where for example Xp = lp, Lp[0,1] or Cp. We show that under certain uniform boundedness conditions, the possession of a BV functional calculus by operators on the spaces Xp, p ?? (r, ???), may be extrapolated to the corresponding operators on the spaces Xr and X???.

The 2-groups of coclass 1 are widely known and James (in 1975) looked at the 2-groups of coclass 2. Development of the p-group generation algorithm implemented by O'Brien at ANU enabled group presentations to be provided for the 2-groups of coclass 3 by Newman and O'Brien for groups of order up to 223. Newman and O'Brien (in 1999) conjectured the number of descendants of 2n for all n. They introduced the concept of a family, with each family related to a different pro-p-group and the concept of a sporadic p-group, a p-group external to any family. They found 1782 sporadic 2-groups with order at most 214. The 70 families of 2-groups of coclass 3 can be further split according to their period, a measure of the repetitive structure of the families. Newman and O'Brien conjectured that these families had periods of 1, 2 or 4. This thesis examines the 2-groups of coclass 3 contained in families with period 1 and shows that the number of descendants conjectured by Newman and O'Brien is correct. Furthermore the presentation of all groups contained in period 1 families is provided and shown to be correct.

The aim of this thesis is to study multi-asset barrier options, where the volatilities of the stocks are assumed to define a matrix-valued bounded stochastic process. The bounds on volatilities may represent, for instance, the extreme values of the volatilities of traded options. As the volatilities are not known exactly, the value of the option can not be determined. Nevertheless, it is possible to calculate extreme values. We show that these values correspond to the best and the worst case scenarios of the future volatilities for short positions and long positions in the portfolio of the options. Our main tool is the equivalence of the option pricing and a certain stochastic control problem and the resulting concept of superhedging. This concept has been well known for some time but never applied to barrier options. First, we prove the dynamic programming principle (DPP) for the control problem. Next, using rather standard arguments we derive the Hamilton-Jacobi-Bellman equation for the value function. We show that the value function is a unique viscosity solution of the Hamilton-Jacobi-Bellman equation. Then we define the super price and superhedging strategy for the barrier options and show equivalence with the control problem studied above. The superprice price can be found by solving the nonlinear Hamilton-Jacobi-Equation studied above. It is called sometimes the Black-Scholes-Barenblatt (BSB) equation. This is the Hamilton-Jacobi-Bellman equation of the exit control problem. The sup term in the BSB equation is determined dynamically: it is either the upper bound or the lower bound of the volatility matrix, according to the convexity or concavity of the value function with respect to the stock prices. By utilizing a probabilistic approach, we show that the value function of the exit control problem is continuous. Then, we also obtain bounds for the first derivative of the value function with respect to the space variable. This derivative has an important financial interpretation. Namely, it allows us to define the superhedging strategy. We include an example: pricing and hedging of a single-asset barrier option and its numerical solution using the finite difference method.