Hållpunkter för lärande : småbarns möten

Developed from human activities, mathematical knowledge is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans’ everyday life, an environment where people reach agreement regarding certain “laws” and principles in mathematics. Through interaction with worldly phenomena and people, children will always gain experience that they can then in turn use to understand future situations. Consequently, the environment in which a child grows up plays an important role in what that child experiences and what possibilities for learning that child has. Variation theory, a branch of phenomenographical research, defines human learning as changes in understanding and acting towards a specific phenomenon. Variation theory implies a focus on that which it is possible to learn in a specific learning situation, since only a limited number of critical aspects of a phenomenon can be simultaneously discerned and focused on. The aim of this study is to discern how toddlers experience and learn mathematics in a daycare environment. The study focuses on what toddlers experience, how their learning experience is formed, and how toddlers use their understanding to master their environment. Twenty-three children were observed videographically during everyday activities. The videographic methodology aims to describe and interpret human actions in natural settings. The children are aged from 1 year, 1 month to 3 years, 9 months. Descriptions of the toddlers’ actions and communication with other children and adults are analyzed phenomenographically in order to discover how the children come to understand the different aspects of mathematics they encounter. The study’s analysis reveals that toddlers encounter various mathematical concepts, similarities and differences, and the relationship between parts and whole. Children form their understanding of such aspects in interaction with other children and adults in their everyday life. The results also show that for a certain type of learning to occur, some critical conditions must exist. Variation, simultaneity, reasonableness and fixed points are critical conditions of learning that appear to be important for toddlers’ learning. These four critical conditions are integral parts of the learning process. How children understand mathematics influences how they use mathematics as a tool to master their surrounding world. The results of the study’s analysis of how children use their understanding of mathematics shows that children use mathematics to uphold societal rules, to describe their surrounding world, and as a tool for problem solving. Accordingly, mathematics can be considered a very important phenomenon that children should come into contact with in different ways and which needs to be recognized as a necessary part of children’s everyday life. Adults working with young children play an important role in setting perimeters for children’s experiences and possibilities to explore mathematical concepts and phenomena. Therefore, this study is significant as regards understanding how children learn mathematics through everyday activities.

Mathematical modeling of level of anaesthesia from EEG measurements

Problem of modeling of anaesthesia depth level is studied in this Master Thesis. It applies analysis of EEG signals with nonlinear dynamics theory and further classification of obtained values. The main stages of this study are the following: data preprocessing; calculation of optimal embedding parameters for phase space reconstruction; obtaining reconstructed phase portraits of each EEG signal; formation of the feature set to characterise obtained phase portraits; classification of four different anaesthesia levels basing on previously estimated features. Classification was performed with: Linear and quadratic Discriminant Analysis, k Nearest Neighbours method and online clustering. In addition, this work provides overview of existing approaches to anaesthesia depth monitoring, description of basic concepts of nonlinear dynamics theory used in this Master Thesis and comparative analysis of several different classification methods.

Long-term fertilizer field trials: comparison of three mathematical response models

Selostus: Lannoituksen pitkäaikaiset kenttäkokeet: kolmen matemaattisen mallin vertailu

Three mathematical models for bucking-to-order

Abstract

Utilisation of Statistics in Intelligent Web Applications

Web-portaalien aiheenmukaista luokittelua voidaan hyödyntää tunnistamaan käyttäjän kiinnostuksen kohteet keräämällä tilastotietoa hänen selaustottumuksistaan eri kategorioissa. Tämä diplomityö käsittelee web-sovelluksien osa-alueita, joissa kerättyä tilastotietoa voidaan hyödyntää personalisoinnissa. Yleisperiaatteet sisällön personalisoinnista, Internet-mainostamisesta ja tiedonhausta selitetään matemaattisia malleja käyttäen. Lisäksi työssä kuvaillaan yleisluontoiset ominaisuudet web-portaaleista sekä tilastotiedon keräämiseen liittyvät seikat.

Selective catalytic reduction of nitrogen oxides with ammonia in forced unsteady state reactors - Case based reasoning and mathematical model simulation reasoning

The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.

A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

BUSINESS CONCEPTS OF MOBILE VALUE-ADDED SERVICES FROM OPERATOR’S POINT OF VIEW

Tämä diplomityö on tehty Lappeenrannassa Telecom Business Research Centerin 5T-projektiin liittyen. Työssä tutkitaan matkaviestinnän lisäarvopalveluiden liiketoimintakonsepteja operaattoreiden näkökulmasta. Lisäarvopalvelut laajentavat operaattoreiden palveluvalikoimaa. Niiden osuuden telekommunikaatioalan yritysten ja erityisesti operaattoreiden tuotoista on ennustettu kasvavan huomattavasti. Työn tärkeimpänä tavoitteena on tuoda uusia näkökulmia ja lisätä ymmärrystä lisäarvopalveluiden liiketoimintakonseptin rakentamisprosessista. Tätä tietämystä käytetään edesauttamaan työn empiirisessä osuudessa tutkitun Content Gateway -tuotteen liiketoimintaa. Tarjoamalla nopean liitynnän ja laskutuskanavan ulkopuolisten palveluntarjoajien ja operaattorin välille tämä tuote mahdollistaa operaattorille ja palveluntarjoajille lisäarvopalveluiden liiketoiminnan käynnistämisen. Lisäarvopalveluiden arvonluontiprosessi vaatii lukuisia yhteistyötä tekeviä osapuolia, joiden yhteistoiminta on dynaamista ja tiedonvälitys avointa, interaktiivista ja nopeaa. Arvonluontiin liittyy myös monia konvergoituvia kehityssuuntia. Perinteinen arvoketjuajattelu on riittämätön uuteen, verkottuneeseen toimintaympäristöön ja sen tilalle on tullut modernimpi arvoverkostomalli. Arvoverkosto luo kilpailuetunsa muita verkostoja vastaan jakamalla resurssit ja kompetenssit optimaalisesti ja liittämällä strategisen ja operationaalisen johtamisen kulttuurit toisiinsa. Tässä työssä verrataan arvoverkoston teoreettisia tavoitteita kahteen lisäarvopalveluiden liiketoimintakonseptiin. Näistä ensimmäinen, i-mode –niminen konsepti on valittu vertailuun edistyksellisyytensä ja tulevaa kehitystä ennakoivien ominaispiirteidensä vuoksi. Toinen esimerkkikonsepti on rakennettu edellä mainitun Content Gateway -tuotteen ympärille. Tutkimus sisältää mm. liikekumppaneiden hankinnan, ansaintalogiikoiden ja verkostojen johtamisen analysoinnin. Työn tuloksena on saatu ohjeita siihen, miten operaattori voi rakentaa tällaista konseptia ja mitä seikkoja tulee ottaa huomioon erityisesti sanomapalveluihin liittyvässä liiketoiminnassa.

Lectio praecursoria: Environmental policy evaluation concepts exemplified in the context of the European Unions strategy for better regulation

Lectio praecursoria 3.2.2006 Tampereen yliopisto

Concepts and Reference. Defending a Dual Theory of Natural Kind Concepts

In this thesis I argue that the psychological study of concepts and categorisation, and the philosophical study of reference are deeply intertwined. I propose that semantic intuitions are a variety of categorisation judgements, determined by concepts, and that because of this, concepts determine reference. I defend a dual theory of natural kind concepts, according to which natural kind concepts have distinct semantic cores and non-semantic identification procedures. Drawing on psychological essentialism, I suggest that the cores consist of externalistic placeholder essence beliefs. The identification procedures, in turn, consist of prototypes, sets of exemplars, or possibly also theory-structured beliefs. I argue that the dual theory is motivated both by experimental data and theoretical considerations. The thesis consists of three interrelated articles. Article I examines philosophical causal and description theories of natural kind term reference, and argues that they involve, or need to involve, certain psychological elements. I propose a unified theory of natural kind term reference, built on the psychology of concepts. Article II presents two semantic adaptations of psychological essentialism, one of which is a strict externalistic Kripkean-Putnamian theory, while the other is a hybrid account, according to which natural kind terms are ambiguous between internalistic and externalistic senses. We present two experiments, the results of which support the strict externalistic theory. Article III examines Fodor’s influential atomistic theory of concepts, according to which no psychological capacities associated with concepts constitute them, or are necessary for reference. I argue, contra Fodor, that the psychological mechanisms are necessary for reference.