Matemaattis-luonnontieteellinen tiedekunta


Recent Submissions

  • Karppinen, Sini (2016)
    The theory of transformations groups is the theory of symmetries of a set. Formally, a symmetry of a set is a bijective map from the set to itself. If the set has some kind of mathematical structure, then we are naturally interested in those symmetries which preserve the given structure. For example, the symmetries of a topological space are homeomorphisms. When the transformations of a set form a group, we call the group a transformation group and the set a G-set. We also say that the group G acts on the set X. The study of these groups will reveal a lot about the set itself. In this thesis we are interested in topological transformation groups i.e. the transformation groups of topological spaces.We will, in particular, study the case where the topological space X is completely regular and where the transformation group G is a Lie group. The theory of Lie groups is vast and they have a well-understood structure. Our main goal is to present and prove the so-called slice theorem which is one of the most important results in the theory of transformation groups. A slice in a G-space X characterizes the action of G locally in an invariant neighbourhood of an orbit of X. The slice theorem i.e. the fact that there exists a slice at every point in a G-space X was first proved in the case where G is a compact Lie group. This was done in the 1950s by Gleason, Koszul, Montgomery and Yang and in full generality by Mostow. In order to prove the existence of slices in the case of non-compact Lie groups, the way that G acts needs to somehow be restricted. It turns out that proper action is the right way to do this. The existence of slices for proper actions of noncompact Lie groups was firsst proved by Palais in 1961. Abels and Lütkepohl presented a different kind of proof in 1977. We will present these two proofs in detail and compare them. We will present the machinery needed for the two proofs. The first four chapters are dedicated to the general theory of topological transformation groups, Lie groups and their representations and infinite-dimensional manifolds. Chapter five is dedicated to proper actions. Then in chapter six the two different proofs for the existence of slices for proper actions of non-compact Lie groups arepresented. After the detailed presentations of the proofs, we will compare them in a more general level. We will also present some applications of the slice theorem and consider possible ways to generalize the slice theorem for non-Lie groups.
  • Tiala, Heidi (Helsingin yliopisto, 2017)
    The starting point for the work was to develop a method for covalent binding of phospholipids on fused silica capillaries for capillary electrochromatography (CEC). The method consists of three steps. First, the silanol groups in the fused silica capillary were aminopropylsilylated with 3-(aminopropyl)-triethoxy silane (APTES). Secondly, the product of aminopropylsilylation was allowed to react with glutaraldehyde giving an imidoaldehyde, which further reacted with the primary amino group of phospholipids. The stability of the coating was verified by measuring the electroosmotic flow (EOF) mobility after aminopropylsilylation with APTES and liposome coating. The highest stability of the EOF was obtained using coatings made of liposomes comprising 1-palmitoyl-2-oleyl-sn-glycero-3-phosphocholine (POPC) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine (POPS). The EOF remained stable even after injection of a large number of analytes. The tested phospholipids were selected to mimic biological membranes. In the coating procedure the following phospholipids were used: POPC, 1,2-didodecanoyl-sn-glycero-3-phosphate (DLPA), 1,2-didodecanoyl-sn-glycero-3-phosphoethanolamine (DLPE), and POPS. Primary amino groups were needed for stable covalent binding of liposomes to the fused silica capillary wall. The phospholipids POPC and POPS contained primary amino groups. The highest stability of the covalent binding was achieved using liposome dispersions of 3 mM POPC/POPS 80/20 mol-% but the retention factors for aldosterone, testosterone, and progesterone were higher using a 2 mM POPC/POPS 80/20 mol-% dispersion. The thickness of the liposome layers was measured with quartz crystal microbalance (QCM). The mass of the adsorbed liposomes was higher for the 2 mM POPC/POPS 80/20 mol-% dispersion than for the 3 mM POPC/POPS 80/20 mol-% dispersion, which explained the higher retention factors for the analytes studied. The developed coating method was used to the separation of model steroids by on-line open-tubular CEC mass spectrometry (OT-CEC-MS). The steroids, which are poorly visible or non-visible by UV-detection, could be separated and detected by on-line OT-CEC-MS. Six different type of steroids were separated and detected by this method. There was no ion suppression in the MS due to lipid leakage. The effect of reducing the formed Schiff’s base with sodium borohydride and the impact of liposome composition on the stability of the coating were investigated. NaBH4 treatment did not improve the stability of the EOF, but rather decreased it. The effect of NaBH4 reduction on 40/40/20 mol % POPC/POPS/cholesterol-coated capillaries was also investigated, and the results were similar to those obtained with the 80/20 mol % POPC/POPS-coated capillaries: the stability of the coating was better without NaBH4 treatment. The effect of cholesterol in the phospholipid coating was studied and the results show that cholesterol can well be included in phospholipid coatings covalently attached to silica. 2 mM 40/40/20 mol% POPC/POPS/cholesterol showed greater stability than 2 mM 80/20 mol% POPC/POPS. However, much higher retention factors of aldosterone, testosterone, and progesterone were obtained with 2 mM 80/20 mol % POPC/POPS liposome coatings than with 2 mM 40/40/20 mol% POPC/POPS/cholesterol coatings. This may be due to the fact that cholesterol is likely to increase the rigidity of lipid membranes. Also the stability and robustness of the capillary column was tested by individual injections of a large amount of analytes into the capillary: almost 400 injections were made into the 40/40/20 mol% POPC/POPS/cholesterol coated capillary (different type of drugs). The EOF was stable for over 200 injections.
  • Gilmore, Clifford (Helsingin yliopisto, 2014)
    Linear dynamics is a rapidly evolving area of operator theory, however the only results related to the dynamics of the commutator operators have hitherto been on the characterisation of the hypercyclicity of the left and right multiplication operators. This text introduces the requisite background theory of hypercyclicity before surveying the hypercyclicity of the left and right multiplication operators. It expands on this to prove sufficient conditions for the hypercyclicity of the two-sided multiplication operator. Conditions are established under which the general class of elementary operators are never hypercyclic on Banach algebras and notably it is shown that elementary operators are never hypercyclic on the space of bounded linear operators of the Argyros-Haydon Banach space. In the first main result of this text, large classes of operators for which the induced commutator operators are never hypercyclic on separable Banach ideals are identified. In particular it is proven that commutator operators induced by compact and Riesz operators are never hypercyclic on the ideal of compact operators and that commutator operators are also never hypercyclic on the ideal of compact operators of the Argyros-Haydon Banach space. In the Hilbert space setting it is demonstrated that commutator operators induced by hyponormal operators are never hypercyclic on the ideal of Hilbert-Schmidt operators. In the second main result, nonzero scalar multiples of the backward shift operator on the Hilbert space H is identified as a strong candidate to induce a hypercyclic commutator operator on the separable ideal of compact operators on the separable Hilbert space H. However it is proven that it cannot have a dense orbit and hence is never hypercyclic. This study indicates that the commutator operator typically behaves in a non-hypercyclic fashion and that if they exist, instances of hypercyclic commutator operators are rare.
  • Luisto, Rami (Helsingin yliopisto, 2014)
    The work focuses on the basic properties of BLD-mappings between geometric manifolds. We are especially interested in the limit properties of sequences of BLD-mappings and the regularity properties of the branch sets of BLD-mappings induced by these limit properties. The main result of the thesis shows via topological-metric tools that the locally uniform limit of L-BLD-mappings is an L-BLD-mapping.
  • Tuomisto, Maiju (Helsingin yliopisto, 2015)
    Interest in studying chemistry has decreased among lower secondary school students in Finland. Learning chemistry is challenging: one must move between the macro, sub-micro and symbolic levels of chemistry knowledge and construct models of abstract concepts that cannot be seen. The periodic table is one of these complicated yet useful models. How can we motivate students to learn the periodic table and to use the related skills? Adolescents like to play during their free time. In research literature, educational games are mentioned as one motivational teaching method that improves learning results. The main objectives of this research project were 1) To develop a framework for designing and evaluating chemistry-related educational games to support both learning and teaching at the lower secondary level ; and 2) To develop games for chemistry education to support the learning of the periodic table and the use of related skills. Three different design research projects are included in this licentiate thesis. The theoretical framework for these projects consisted of the theory of design research, the theory of educational games and the theory of the periodic table as a teaching model. Problem analyses conducted as part of the design research projects broadened the theory framework to also cover misconceptions about the contents of the periodic table and quality criteria for educational games. In design challenge 1, a design and evaluation framework for chemistry-related educational card and board games on the lower secondary level was developed. Based on an integrative literature review, the features of high-quality digital and non-digital games were uncovered. The design result was further developed based on these features and the new Finnish National Curriculum Framework 2014. The inter-rater agreement of the developed framework was tested with two educational card games. The calculated Cohen s kappa values (κ = 0.718 and κ = 0.756) indicate that the framework is concordant and working well. In design challenges 2 and 3, two novel card games for teaching the periodic table were developed. These games were called Jaksollisuusdomino (Periodic Table Dominoes) and Kerää kolmikko (Collect the Triad). The games were tested on chemistry teachers. Based on the results, the games were developed further and subjected to the novel design and evaluation framework developed in design challenge 1. The games were found to be of good quality, but some improvements should be made at least in the categories of pre- and post-game evaluation and connection to the macroscopic level. As results of this research, three design solutions were developed. The created design and evaluation framework for educational games works both as a descriptive theory and a prescriptive model for teachers and game developers. Both of the developed card games work as prescriptive models for teachers. All three of the design solutions may also be adapted to other teaching and learning purposes. Keywords: board game, card game, chemistry, design research, education, educational game, elements, evaluation, games, learning game, lower-secondary level, periodic table, teaching method
  • Astuti, Davide Nicola (Helsingin yliopisto, 2014)
    The provision of wireless access to voice and data services experienced an impressive growth of importance during the last 20 years. Most of the Internet applications employ the TCP/IP protocol suite to deliver their services. TCP has been developed to operate in a terrestrial network environment. However, with the rapid rise in wireless communication in recent years, it has become important to adapt TCP to heterogeneous environments that include both wireline networks and Wireless Wide-Area Networks (W-WANs), such as satellite and terrestrial wireless networks, in order to optimize performance. The specific link characteristics of wireless and satellite links, in particular high latencies and frequent frame losses due to bit-corruption, affect performance of transport protocols. TCP suffers because of low bandwidth, long connection set-up times, high latency and error rate, inefficient use of air link capacity. Most of next generation satellite systems utilizes Bandwidth-on-Demand (BoD) mechanisms to efficiently share radio resources among a large number of users. BoD mechanisms often causes additional link delay, which has a detrimental effect on TCP performance. In this thesis, we propose a new TCP/IP-friendly link level protocol, namely Satellite Link Aware Communication Protocol (SLACP) which incorporates a novel error-recovery mechanism aimed at drastically reduce the residual Packet Error Rate (PER) as seen by higher layers without producing significant extra delay. The protocol has been validated with experimental evaluations conducted in a Digital Video Broadcasting-Return Channel System (DVB-RCS) satellite environment, where the BoD technique Demand Assignment Multiple Access (DAMA) is employed to regulate the access to the satellite channel. Cross-layer interactions between link layer and transport layer as well as the impact of BoD mechanisms on TCP dynamics are investigated. Furthermore, experiments using a selected set of state-of-the-art TCP enhancements in conjunction with our TCP/IP-friendly link-level protocol have been carried out. The proposed mechanisms and improvements of the link and transport layer would be relevant for many wireless WAN systems.
  • Kangas, Kaisa (2014)
    We study quasiminimal classes, i.e. abstract elementary classes (AECs) that arise from a quasiminimal pregeometry structure. For these classes, we develop an independence notion, and in particular, a theory of independence in $M^{eq}$. We then generalize Hrushovski's Group Configuration Theorem to our setting. In an attempt to generalize Zariski geometries to the context of quasiminimal classes, we give the axiomatization for Zariski-like structures, and as an application of our group configuration theorem, show that groups can be found in them assuming that the pregeometry obtained from the bounded closure operator is non-trivial. Finally, we study the cover of the multiplicative group of an algebraically closed field and show that it provides an example of a Zariski-like structure.
  • Juntunen, Marianne (2014)
    Kemia tieteenalana on suuressa roolissa kestävämmän tulevaisuuden tekijänä ja globaalien ongelmien ratkaisijana. Kestävää kehitystä ja eettiseen vastuullisuuteen kasvattamista painotetaan opetussuunnitelmien perusteissa, kansallisissa ja kansainvälisissä opetusalan strategioissa, kemian opetuksen tutkimuskirjallisuudessa ja Suomen kemianteollisuudessa. Tarvitaan lisää ympäristötietoisia kemistejä, kemian opettajia ja oppilaita – tulevia kansalaisia lukuisten koko maapalloa koskettavien ympäristöhaasteiden ratkaisemiseen. Lisensiaattitutkielman päätavoitteena oli kehittää kestävään kehitykseen liittyvää tutkimuksellista kemian opetusta, joka vahvistaa oppilaiden ympäristötietoisuutta sekä positiivista kemiakuvaa. Kestävä kehitys kemian opetuksessa liittyy yhteiskuntaperustaisiin kemian aiheisiin, esimerkiksi elinkaariajatteluun ja vihreään kemiaan. Kehittämistutkimuksen teoreettisessa ongelma-analyysissä tarkasteltiin tutkimuksen näkökulmasta keskeisiä lähestymistapoja: kestävää kehitystä ja kemiaa, vihreää kemiaa, elinkaarianalyysiä ja -ajattelua, ympäristötietoisuutta, yhteiskuntaperustaisuutta ja tutkimuksellista opiskelua. Empiirisessä kehittämisosassa etsittiin vastauksia seuraaviin tutkimuskysymyksiin: 1) Minkälaista on kestävää kehitystä edistävä elinkaariajattelun tutkimuksellinen kemian opetus? 2) Miten yhteisöllisesti kehitetty kehittämistuotos elinkaariaiheen kemian opetukseen vaikuttaa oppilaiden ympäristötietoisuuteen ja kemiakuvaan? Tutkimus toteutettiin kemian opettajien täydennyskoulutusten yhteydessä, joissa aiheina olivat tutkielmassa käsitellyt asiat: kestävä kehitys, vihreä kemia, erilaisten tuotteiden elinkaaret, ympäristötietoisuus, yhteiskuntaperustaisuus ja tutkimuksellinen opiskelu. Täydennyskoulutuksissa luotiin yhteisöllisesti elinkaariaiheisia tutkimuksellisia kemian opetusmalleja. Kemian tieto kytkettiin tuotteen tai materiaalin elinkaareen. Tutkimuksen kohteena olivat kemian opettajien opetusmallit, niistä yhteisöllisesti kehitetty kehittämistuotos ja sen avulla opiskelevien yläkoulun oppilaiden kokemukset. Yhteisölliseen kehittämisprosessiin osallistuivat 21 kemian opettajaa ja aineistoa analysoineet kaksi tutkijaa vuosina 2010–2012. Opetusmallien kehittäminen pohjautui teoreettiseen ongelma-analyysiin. Tutkimuksessa yhteisöllisesti kehitetyn opetusmallin vaikuttavuustarkasteluun osallistui 105 peruskoulun yhdeksäsluokkalaista. Tutkimusmenetelminä kehittämistutkimuksessa käytettiin tekstimuotoisen aineiston ja puolistrukturoitujen haastattelujen sisällönanalyysiä sekä kvantitatiivisia kyselyitä. Kehittämistutkimuksen empiirisen kehittämisosan tuloksena saatiin: 1) kestävän kehityksen opetukseen uusia elinkaariaiheisia tutkimuksellisia kemian opetusmalleja ja niistä yhteisöllisesti kehitetty kehittämistuotos, ja 2) tietoa elinkaariaiheisen tutkimuksellisen kemian opetuksen vaikutuksista oppilaiden ympäristötietoisuuteen ja kemiakuvaan. Tutkimustulosten luotettavuutta tarkasteltiin tutkija- ja menetelmätriangulaatiolla. Opettajat toteuttivat kestävää kehitystä edistävää elinkaariajattelun tutkimuksellista kemian opetusta usealla eri tavalla. He kehittivät yhteensä 20 uutta opetusmallia. Opettajien eniten käyttämä lähestymistapa oli pienryhmissä toteutettava avoin projektityö. Siinä oppilaat saivat tutkia itse valitsemansa tuotteen elinkaarta. Tästä lähestymistavasta kehitettiin yhteisöllisesti kehittämistuotos elinkaariajattelun kemian opetukseen. Osa opettajista valitsi tutkimuskohteen oppilaille valmiiksi, jolloin tutkimustehtävät liittyivät raaka-aineisiin, kulutustavaroihin, ruoka-aineisiin tai veteen. Opetusmenetelminä opetusmalleissa käytettiin pienryhmissä tapahtuvaa kysymysten tekoa, tiedon etsintää ja arviointia, tulosten muodostamista ja esittämistä, laboratoriokokeita, videoita, opintovierailuita, väittelyä, uusien tuotteiden suunnittelua, draamaa ja oppimispäiväkirjoja. Kehittämistuotoksena saatu elinkaariaiheinen tutkimuksellinen projektityö lisäsi oppilaiden yhteiskunnallista ja ympäristötietoista pohdintaa. Oppilaat korostivat erityisesti luonnonsuojelun ja kierrätyksen merkitystä. Enemmistö oppilaista uskoi vastaavien projektien vaikuttavan positiivisesti nuorten ympäristötietoisuuteen. Projektityö vaikutti positiivisesti oppilaiden kemiakuvaan. He huomasivat, että kemiassa oppii arkeen ja yhteiskuntaan liittyviä hyödyllisiä asioita. Oppilaat arvostivat uudenlaista kemian opiskelutapaa, joka oli itsenäinen ja sosiaalinen. Lisensiaattitutkielmassa esitetty opetusmalli elinkaariajattelun tutkimukselliseen kemian opetukseen on uudenlainen esimerkki tutkimuksellisesta työtavasta, joka tukee monipuolisia opiskelu- ja kansalaistaitoja, motivoi oppilasta kemian opiskeluun sekä ohjaa häntä pohtimaan kestävää kehitystä. Elinkaariaiheinen tutkimuksellinen kemian opetus sopii perusopetukseen, mutta sitä voi soveltaa myös kaikille kouluasteille. Tämän lisensiaattitutkielman teoreettisen ongelma- analyysin havaintoja ja empiirisen kehittämisosan tutkimustuloksia voidaan käyttää kemian opetuksen suunnittelussa ja kemian opettajien koulutuksessa kestävän kehityksen aiheisiin liittyen.
  • Tuovinen, Riikka (Helsingin yliopisto, 2012)
    Kuuluisa, edelleen avoin, invariantin aliavaruuden ongelma kysyy onko jokaisella rajoitetulla lineaarisella operaattorilla (separoituvassa, ääretönulotteisessa) Hilbertin avaruudessa olemassa ei-triviaalia invarianttia aliavaruutta. Erään lähestymistavan kyseisen ongelman ratkaisuun tarjoavat niin sanotut universaalit operaattorit. Nimittäin, positiivinen vastaus invariantin aliavaruuden ongelmaan on yhtäpitävää sen kanssa, että jonkin universaalin operaattorin kaikki minimaaliset invariantit aliavaruudet ovat yksiulotteisia. Nordgren et al. löysivät artikkelissaan Invertible composition operators on H^p (J. Funct. Anal. 73, 1987, 324--344) klassisessa Hardyn avaruudessa H^2 erään konkreettisen universaalin operaattorin, joka on hyperbolisen kompositio-operaattorin ja sen pistespektriin kuuluvalla luvulla kerrotun identiteettioperaattorin erotus. Näin invariantin aliavaruuden ongelma voitaisiin ratkaista selvittämällä hyperbolisen kompositio-operaattorin invarianttien aliavaruuksien muodostama hila Hardyn avaruudessa H^2 tarpeeksi hyvin. Lisensiaatintutkielmani on yksityiskohtainen selvitys edellä mainitun hyperbolisen kompositio-operaattorin avulla muodostetun operaattorin universaalisuudesta. Tähän tarvitaan laajaa matemaattista koneistoa liittyen mm. sisäfunktioihin (mukaan lukien yksikkökiekon Möbius-kuvaukset ja Blaschken tulot), interpoloiviin jonoihin, spektraali- ja operaattoriteoriaan sekä Rieszin kantoihin.
  • Ojala, Heikki (Helsingin yliopisto, 2011)
    A single molecule is enough to initiate a biological function. Therefore methods to study single biomolecules are important. By measuring one biomolecule at a time it is possible to reveal the differences from molecule to molecule. Moreover, with these methods one can measure short-lived non-equilibrium states of the molecules. An optical tweezers instrument for single molecule experiments was modified to permit constant force experiments. The resulting force-clamp control was then used to measure enzymatic activity of the molecular motor lambda exonuclease at different temperatures. The force-clamp experiments were performed in a dumbbell geometry where two polystyrene spheres are connected by a DNA molecule. A single continuous wave laser source created the dual trap optical tweezers with one stationary and one steerable trap. Acousto-optic deflectors steered the trap according to a digital feedback control from a field programmable gate array. Using the feedback control, at 1.3±0.3 pN force, the lambda exonuclease reaction rate was measured to be 23±16 nt/s at 25±1°C and 54±15 nt/s at 37±1°C. The most important achievement in this thesis was the detected increase in the reaction rate of lambda exonuclease due to the increased temperature. Thus, the real-time force- clamp control opens up new possibilities to study the molecular machinery that generates forces and movements in living organisms.
  • Rosberg, Eira (Helsingin yliopisto, 2012)
    This study examined the field of Finnish Environmental Impact Assessment procedures from years 2000-2008 in Finland. In addition two case studies of critical cases revealed insights into projects and their context. The theoretical background of the research included Popper s philosophy of three worlds: knowledge can be absolute, relative and symbolic. In addition the theory of values and process thinking was utilized. One of the most important findings was that Finnish Environmental Impact Assessment procedures display large regional variation. This variation was obvious in the amount and types of projects in different regions. Furthermore, the duration of procedures as well as the types of competent authorities statements showed regional variation. Variation in the competent authorities opinions indicates that the quality of procedures in Finland also had regional variation. The study also found the EIA process is inconsistent and has regional variation. The knowledge of some key EIA personnel expanded during the procedure, yet for some there can be a conflict in their environmental values. Some practices inhibited learning, which prevented deliberative planning practice and caused a quality risk to planning. Variation in the EIA process complicates the process predictability and can harm trust creation in the temporary project network which causes another quality risk to urban and regional planning. Environmental Impact Assessment procedure is a steering method for society. But it has not developed from a ´toolbox´ level to a systemic level to promote sustainable development in a region. The effects of environmental impact assessments on decision-making, such as land-use planning, environmental permits, the responsible developer s plans and municipal decision-making are guiding, at best. But worse, it can almost paralyze the decision-making process. The weak link between EIA in projects and other processes of urban and regional planning complicates the way in which procedures operate. To conclude, it is important to understand how EIA can better respond to its demands. Rather than following strict protocols, one should focus on the ultimate purpose of the procedure and how the procedure and its results may systemically advance sustainable development in the region. By applying similar protocols one can enhance sustainable development in other regional planning processes in our project-intensive society. Strengthening process and quality thinking does not mean that the procedure should be a mechanistic tool or a strict recipe for implementation. In urban and regional planning one needs communicative and methodical participation and context sensitivity. It is possible to strengthen the quality of planning in a changing context and in project networks, which are of limited duration and temporary organization.
  • Lindén, Greger (Helsingin yliopisto, 1993)
  • Daniel, Laila (Helsingin yliopisto, 2008)
    With the proliferation of wireless and mobile devices equipped with multiple radio interfaces to connect to the Internet, vertical handoff involving different wireless access technologies will enable users to get the best of connectivity and service quality during the lifetime of a TCP connection. A vertical handoff may introduce an abrupt, significant change in the access link characteristics and as a result the end-to-end path characteristics such as the bandwidth and the round-trip time (RTT) of a TCP connection may change considerably. TCP may take several RTTs to adapt to these changes in path characteristics and during this interval there may be packet losses and / or inefficient utilization of the available bandwidth. In this thesis we study the behaviour and performance of TCP in the presence of a vertical handoff. We identify the different handoff scenarios that adversely affect TCP performance. We propose several enhancements to the TCP sender algorithm that are specific to the different handoff scenarios to adapt TCP better to a vertical handoff. Our algorithms are conservative in nature and make use of cross-layer information obtained from the lower layers regarding the characteristics of the access links involved in a handoff. We evaluate the proposed algorithms by extensive simulation of the various handoff scenarios involving access links with a wide range of bandwidth and delay. We show that the proposed algorithms are effective in improving the TCP behaviour in various handoff scenarios and do not adversely affect the performance of TCP in the absence of cross-layer information.
  • Kangasharju, Jaakko (Helsingin yliopisto, 2006)
    In recent years, XML has been accepted as the format of messages for several applications. Prominent examples include SOAP for Web services, XMPP for instant messaging, and RSS and Atom for content syndication. This XML usage is understandable, as the format itself is a well-accepted standard for structured data, and it has excellent support for many popular programming languages, so inventing an application-specific format no longer seems worth the effort. Simultaneously with this XML's rise to prominence there has been an upsurge in the number and capabilities of various mobile devices. These devices are connected through various wireless technologies to larger networks, and a goal of current research is to integrate them seamlessly into these networks. These two developments seem to be at odds with each other. XML as a fully text-based format takes up more processing power and network bandwidth than binary formats would, whereas the battery-powered nature of mobile devices dictates that energy, both in processing and transmitting, be utilized efficiently. This thesis presents the work we have performed to reconcile these two worlds. We present a message transfer service that we have developed to address what we have identified as the three key issues: XML processing at the application level, a more efficient XML serialization format, and the protocol used to transfer messages. Our presentation includes both a high-level architectural view of the whole message transfer service, as well as detailed descriptions of the three new components. These components consist of an API, and an associated data model, for XML processing designed for messaging applications, a binary serialization format for the data model of the API, and a message transfer protocol providing two-way messaging capability with support for client mobility. We also present relevant performance measurements for the service and its components. As a result of this work, we do not consider XML to be inherently incompatible with mobile devices. As the fixed networking world moves toward XML for interoperable data representation, so should the wireless world also do to provide a better-integrated networking infrastructure. However, the problems that XML adoption has touch all of the higher layers of application programming, so instead of concentrating simply on the serialization format we conclude that improvements need to be made in an integrated fashion in all of these layers.
  • Kemppainen, Mikko (Helsingin yliopisto, 2010)
    Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.