Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Real-time Imaging and Mosaicking of Planar Surfaces

Laajojen pintojen kuvaaminen rajoitetussa työskentelytilassa riittävällä kuvatarkkuudella voi olla vaikeaa. Kuvaaminen on suoritettava osissa ja osat koottava saumattomaksi kokonaisnäkymäksi eli mosaiikkikuvaksi. Kuvauslaitetta käsin siirtelevän käyttäjän on saatava välitöntä palautetta, jotta mosaiikkiin ei jäisi aukkoja ja työ olisi nopeaa. Työn tarkoituksena oli rakentaa pieni, kannettava ja tarkka kuvauslaite paperi- ja painoteollisuuden tarpeisiin sekä kehittää palautteen antamiseen menetelmä, joka koostaaja esittää karkeaa mosaiikkikuvaa tosiajassa. Työssä rakennettiin kaksi kuvauslaitetta: ensimmäinen kuluttajille ja toinen teollisuuteen tarkoitetuista osista. Kuvamateriaali käsiteltiin tavallisella pöytätietokoneella. Videokuvien välinen liike laskettiin yksinkertaisella seurantamenetelmällä ja mosaiikkikuvaa koottiin kameroiden kuvanopeudella. Laskennallista valaistuksenkorjausta tutkittiin ja kehitetty menetelmä otettiin käyttöön. Ensimmäisessä kuvauslaitteessa on ongelmia valaistuksen ja linssivääristymien kanssa tuottaen huonolaatuisia mosaiikkikuvia. Toisessa kuvauslaitteessa nämä ongelmat on korjattu. Seurantamenetelmä toimii hyvin ottaen huomioon sen yksinkertaisuuden ja siihen ehdotetaan monia parannuksia. Työn tulokset osoittavat, että tosiaikainen mosaiikkikuvan koostaminen megapikselin kuvamateriaalista on mahdollista kuluttajille tarkoitetulla tietokonelaitteistolla.

Poisoning effect of s on pd surfaces

In this study we observe the poisoning effect of S to the adsorption and dissociation of 02 molecule on Pd surfaces. To perform this study we used Viennaab initio Simulation Package (VASP) and Spanish Initiative for Electronic structure with thousands of Atoms (SIESTA) ab initio softwares. To describe all Pd surfaces we selected the (100), and (211) surfaces, because we need very reactive and simple surfaces. Before studying the poison¬ing effect of S we had to study the dissociation of 02 on the surfaces. We discovered that on the (100) surface the hollow site is the most reactive site, but at room temperature the steric hinderace effect occurs very easily. If the molecule has enough vibrational energyit will dissociate. On the (211) surface the (100) micro facet's hollow site is the most reactive site and the molecule dissociates in the site without any barrier, and the molecule drifts from the terrace to this site. An S atom sticks on the Pd (100) surface in the hollow site. It affects the d-band density of states of the nearests Pd atoms; It moves the center of the d-band downin energy, when the bond between the Pd atom and the 0 atom is more antibonding. In the hollow site the S atom also blocks the dissociation site of the molecule. On the Pd(211) surface the energetically favourable site of the S atom is the(100) microfacet's hollow site. There it blocks the most reactive site, but its effect to the Pd atoms next to it is not significant.

Distance Transforms on Gray-Level Surfaces

This thesis studies gray-level distance transforms, particularly the Distance Transform on Curved Space (DTOCS). The transform is produced by calculating distances on a gray-level surface. The DTOCS is improved by definingmore accurate local distances, and developing a faster transformation algorithm. The Optimal DTOCS enhances the locally Euclidean Weighted DTOCS (WDTOCS) with local distance coefficients, which minimize the maximum error from the Euclideandistance in the image plane, and produce more accurate global distance values.Convergence properties of the traditional mask operation, or sequential localtransformation, and the ordered propagation approach are analyzed, and compared to the new efficient priority pixel queue algorithm. The Route DTOCS algorithmdeveloped in this work can be used to find and visualize shortest routes between two points, or two point sets, along a varying height surface. In a digital image, there can be several paths sharing the same minimal length, and the Route DTOCS visualizes them all. A single optimal path can be extracted from the route set using a simple backtracking algorithm. A new extension of the priority pixel queue algorithm produces the nearest neighbor transform, or Voronoi or Dirichlet tessellation, simultaneously with the distance map. The transformation divides the image into regions so that each pixel belongs to the region surrounding the reference point, which is nearest according to the distance definition used. Applications and application ideas for the DTOCS and its extensions are presented, including obstacle avoidance, image compression and surface roughness evaluation.

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.

A Large-Sized Multiwire Proportional Counter for Radiological Survey of Large Areas and Surfaces

Työn tavoitteena oli selvittää, miten eri parametrit vaikuttavat monilankaisen verrannollisuuslaskurin laskennallisiin ominaisuuksiin sekä voidaanko suurikokoista monilankaverrannollisuuslaskuria käyttää tehokkaasti suurien pintojen ? - ja ?- kontaminaation mittaamiseen. Ensin selvitettiin EU:n nykyistä clearing-käytäntöä sekä hahmoteltiin tulevia materiaalivirtoja, esiteltiin verrannollisuuslaskurin ja sen monilankamallin toimintaperiaate sekä käytettävien materiaalien ominaisuudet. Kootun teorian pohjalta selvitettiin tärkeimpien parametrien vaikutus ilmaisimen laskennallisiin ominaisuuksiin. Lopuksi suoritettiin rakenteilla olevan monilankaverrannollisuuslaskurin alustava testaus. Tulevien vuosien aikana eri puolilla maailmaa suljettavat erityyppiset ydinlaitokset luovat suuren tarpeen tehokkaiden kontaminaatiomittauslaitteistojen kehittämiselle. Tällä hetkellä mittaukset suoritetaan lähinnä noin 1 dm2 käsi-instrumentein, joten suurikokoinen, automatisoitu mittauslaitteisto sekä tehostaisi mittausprosessia suuresti sekä säästäisi runsaasti miestyötunteja. Jatkotoimenpiteiksi ehdotetaan laitteiston jatkotestausta, liikkeen ja nopeuden testausta sekä lopulta paikkaherkkyystoiminnon toteuttamisperiaatteen valintaa ja testausta.

The initial oxidation of transition metal surfaces

Due to their numerous novel technological applications ranging from the example of exhaust catalysts in the automotive industry to the catalytic production of hydro- gen, surface reactions on transition metal substrates have become to be one of the most essential subjects within the surface science community. Although numerous applications exist, there are many details in the different processes that, after many decades of research, remain unknown. There are perhaps as many applications for the corrosion resistant materials such as stainless steels. A thorough knowledge of the details of the simplest reactions occuring on the surfaces, such as oxidation, play a key role in the design of better catalysts, or corrosion resistant materials in the future. This thesis examines the oxidation of metal surfaces from a computational point of view mostly concentrating on copper as a model material. Oxidation is studied from the initial oxidation to the oxygen precovered surface. Important parameters for the initial sticking and dissociation are obtained. The saturation layer is thoroughly studied and the calculated results arecompared with available experimental results. On the saturated surface, some open questions still remain. The present calculations demonstrate, that the saturated part of the surface is excluded from being chemically reactive towards the oxygen molecules. The results suggest, that the reason for the chemical activity of the saturated surface is due to a strain effect occuring between the saturated areas of the surface.

Many valued algebraic structures as measures of comparison

This thesis studies the properties and usability of operators called t-norms, t-conorms, uninorms, as well as many valued implications and equivalences. Into these operators, weights and a generalized mean are embedded for aggregation, and they are used for comparison tasks and for this reason they are referred to as comparison measures. The thesis illustrates how these operators can be weighted with a differential evolution and aggregated with a generalized mean, and the kinds of measures of comparison that can be achieved from this procedure. New operators suitable for comparison measures are suggested. These operators are combination measures based on the use of t-norms and t-conorms, the generalized 3_-uninorm and pseudo equivalence measures based on S-type implications. The empirical part of this thesis demonstrates how these new comparison measures work in the field of classification, for example, in the classification of medical data. The second application area is from the field of sports medicine and it represents an expert system for defining an athlete's aerobic and anaerobic thresholds. The core of this thesis offers definitions for comparison measures and illustrates that there is no actual difference in the results achieved in comparison tasks, by the use of comparison measures based on distance, versus comparison measures based on many valued logical structures. The approach has been highly practical in this thesis and all usage of the measures has been validated mainly by practical testing. In general, many different types of operators suitable for comparison tasks have been presented in fuzzy logic literature and there has been little or no experimental work with these operators.

First principles modeling of metallic alloys and alloy surfaces

By alloying metals with other materials, one can modify the metal’s characteristics or compose an alloy which has certain desired characteristics that no pure metal has. The field is vast and complex, and phenomena that govern the behaviour of alloys are numerous. Theories cannot penetrate such complexity, and the scope of experiments is also limited. This is why the relatively new field of ab initio computational methods has much to give to this field. With these methods, one can extend the understanding given by theories, predict how some systems might behave, and be able to obtain information that is not there to see in physical experiments. This thesis pursues to contribute to the collective knowledge of this field in the light of two cases. The first part examines the oxidation of Ag/Cu, namely, the adsorption dynamics and oxygen induced segregation of the surface. Our results demonstrate that the presence of Ag on the Cu(100) surface layer strongly inhibits dissociative adsorption. Our results also confirmed that surface reconstruction does happen, as experiments predicted. Our studies indicate that 0.25 ML of oxygen is enough for Ag to diffuse towards the bulk, under the copper oxide layer. The other part elucidates the complex interplay of various energy and entropy contributions to the phase stability of paramagnetic duplex steel alloys. We were able to produce a phase stability map from first principles, and it agrees with experiments rather well. Our results also show that entropy contributions play a very important role on defining the phase stability. This is, to the author’s knowledge, the first ab initio study upon this subject.

Atomic level phenomena on transition metal surfaces

In this study we discuss the atomic level phenomena on transition metal surfaces. Transition metals are widely used as catalysts in industry. Therefore, reactions occuring on transition metal surfaces have large industrial intrest. This study addresses problems in very small size and time scales, which is an important part in the overall understanding of these phenomena. The publications of this study can be roughly divided into two categories: The adsorption of an O2 molecule to a surface, and surface structures of preadsorbed atoms. These two categories complement each other, because in the realistic case there are always some preadsorbed atoms at the catalytically active surfaces. However, all transition metals have an active d-band, and this study is also a study of the in uence of the active d-band on other atoms. At the rst part of this study we discuss the adsorption and dissociation of an O2 molecule on a clean stepped palladium surface and a smooth palladium surface precovered with sulphur and oxygen atoms. We show how the reactivity of the surface against the oxygen molecule varies due to the geometry of the surface and preadsorbed atoms. We also show how the molecular orbitals of the oxygen molecule evolve when it approaches the di erent sites on the surface. In the second part we discuss the surface structures of transition metal surfaces. We study the structures that are intresting on account of the Rashba e ect and charge density waves. We also study the adsorption of suphur on a gold surface, and surface structures of it. In this study we use ab-initio based density functional theory methods to simulate the results. We also compare the results of our methods to the results obtained with the Low-Energy-Electron-Difraction method.

Research and development of III-V semiconductor surfaces for improved device interfaces

This thesis is devoted to understanding and improving technologically important III-V compound semiconductor (e.g. GaAs, InAs, and InSb) surfaces and interfaces for devices. The surfaces and interfaces of crystalline III-V materials have a crucial role in the operation of field-effect-transistors (FET) and highefficiency solar-cells, for instance. However, the surfaces are also the most defective part of the semiconductor material and it is essential to decrease the amount of harmful surface or interface defects for the next-generation III-V semiconductor device applications. Any improvement in the crystal ordering at the semiconductor surface reduces the amount of defects and increases the material homogeneity. This is becoming more and more important when the semiconductor device structures decrease to atomic-scale dimensions. Toward that target, the effects of different adsorbates (i.e., Sn, In, and O) on the III-V surface structures and properties have been investigated in this work. Furthermore, novel thin-films have been synthesized, which show beneficial properties regarding the passivation of the reactive III-V surfaces. The work comprises ultra-high-vacuum (UHV) environment for the controlled fabrication of atomically ordered III-V(100) surfaces. The surface sensitive experimental methods [low energy electron diffraction (LEED), scanning tunneling microscopy/spectroscopy (STM/STS), and synchrotron radiation photoelectron spectroscopy (SRPES)] and computational density-functionaltheory (DFT) calculations are utilized for elucidating the atomic and electronic properties of the crucial III-V surfaces. The basic research results are also transferred to actual device tests by fabricating metal-oxide-semiconductor capacitors and utilizing the interface sensitive measurement techniques [capacitance voltage (CV) profiling, and photoluminescence (PL) spectroscopy] for the characterization. This part of the thesis includes the instrumentation of home-made UHV-compatible atomic-layer-deposition (ALD) reactor for growing good quality insulator layers. The results of this thesis elucidate the atomic structures of technologically promising Sn- and In-stabilized III-V compound semiconductor surfaces. It is shown that the Sn adsorbate induces an atomic structure with (1×2)/(1×4) surface symmetry which is characterized by Sn-group III dimers. Furthermore, the stability of peculiar ζa structure is demonstrated for the GaAs(100)-In surface. The beneficial effects of these surface structures regarding the crucial III-V oxide interface are demonstrated. Namely, it is found that it is possible to passivate the III-V surface by a careful atomic-scale engineering of the III-V surface prior to the gate-dielectric deposition. The thin (1×2)/(1×4)-Sn layer is found to catalyze the removal of harmful amorphous III-V oxides. Also, novel crystalline III-V-oxide structures are synthesized and it is shown that these structures improve the device characteristics. The finding of crystalline oxide structures is exploited by solving the atomic structure of InSb(100)(1×2) and elucidating the electronic structure of oxidized InSb(100) for the first time.

Analysis of Automotive Cybersecurity - Attack surfaces and users’ privacy concerns

Modern automobiles are no longer just mechanical tools. The electronics and computing services they are shipping with are making them not less than a computer. They are massive kinetic devices with sophisticated computing power. Most of the modern vehicles are made with the added connectivity in mind which may be vulnerable to outside attack. Researchers have shown that it is possible to infiltrate into a vehicle’s internal system remotely and control the physical entities such as steering and brakes. It is quite possible to experience such attacks on a moving vehicle and unable to use the controls. These massive connected computers can be life threatening as they are related to everyday lifestyle. First part of this research studied the attack surfaces in the automotive cybersecurity domain. It also illustrated the attack methods and capabilities of the damages. Online survey has been deployed as data collection tool to learn about the consumers’ usage of such vulnerable automotive services. The second part of the research portrayed the consumers’ privacy in automotive world. It has been found that almost hundred percent of modern vehicles has the capabilities to send vehicle diagnostic data as well as user generated data to their manufacturers, and almost thirty five percent automotive companies are collecting them already. Internet privacy has been studies before in many related domain but no privacy scale were matched for automotive consumers. It created the research gap and motivation for this thesis. A study has been performed to use well established consumers privacy scale – IUIPC to match with the automotive consumers’ privacy situation. Hypotheses were developed based on the IUIPC model for internet consumers’ privacy and they were studied by the finding from the data collection methods. Based on the key findings of the research, all the hypotheses were accepted and hence it is found that automotive consumers’ privacy did follow the IUIPC model under certain conditions. It is also found that a majority of automotive consumers use the services and devices that are vulnerable and prone to cyber-attacks. It is also established that there is a market for automotive cybersecurity services and consumers are willing to pay certain fees to avail that.

Analysis of Automotive Cybersecurity - Attack surfaces and users’ privacy concerns

Modern automobiles are no longer just mechanical tools. The electronics and computing services they are shipping with are making them not less than a computer. They are massive kinetic devices with sophisticated computing power. Most of the modern vehicles are made with the added connectivity in mind which may be vulnerable to outside attack. Researchers have shown that it is possible to infiltrate into a vehicle’s internal system remotely and control the physical entities such as steering and brakes. It is quite possible to experience such attacks on a moving vehicle and unable to use the controls. These massive connected computers can be life threatening as they are related to everyday lifestyle. First part of this research studied the attack surfaces in the automotive cybersecurity domain. It also illustrated the attack methods and capabilities of the damages. Online survey has been deployed as data collection tool to learn about the consumers’ usage of such vulnerable automotive services. The second part of the research portrayed the consumers’ privacy in automotive world. It has been found that almost hundred percent of modern vehicles has the capabilities to send vehicle diagnostic data as well as user generated data to their manufacturers, and almost thirty five percent automotive companies are collecting them already. Internet privacy has been studies before in many related domain but no privacy scale were matched for automotive consumers. It created the research gap and motivation for this thesis. A study has been performed to use well established consumers privacy scale – IUIPC to match with the automotive consumers’ privacy situation. Hypotheses were developed based on the IUIPC model for internet consumers’ privacy and they were studied by the finding from the data collection methods. Based on the key findings of the research, all the hypotheses were accepted and hence it is found that automotive consumers’ privacy did follow the IUIPC model under certain conditions. It is also found that a majority of automotive consumers use the services and devices that are vulnerable and prone to cyber-attacks. It is also established that there is a market for automotive cybersecurity services and consumers are willing to pay certain fees to avail that.