Multi-Eruption Solar Energetic Particle Events Observed by SOHO/ERNE

In the last two decades of studying the Solar Energetic Particle (SEP) phenomenon, intensive emphasis has been put on how and when and where these SEPs are injected into interplanetary space. It is well known that SEPs are related to solar flares and CMEs. However, the role of each in the acceleration of SEPs has been under debate since the major role was taken from flares ascribed to CMEs step by step after the skylab mission, which started the era of CME spaceborn observations. Since then, the shock wave generated by powerful CMEs in between 2-5 solar radii is considered the major accelerator. The current paradigm interprets the prolonged proton intensity-time profile in gradual SEP events as a direct effect of accelerated SEPs by shock wave propagating in the interplanetary medium. Thus the powerful CME is thought of as a starter for the acceleration and its shock wave as a continuing accelerator to result in such an intensity-time profile. Generally it is believed that a single powerful CME which might or might not be associated with a flare is always the reason behind such gradual events.

In this work we use the Energetic and Relativistic Nucleus and Electrons ERNE instrument on board Solar and Heliospheric Observatory SOHO to present an empirical study to show the possibility of multiple accelerations in SEP events. In the beginning we found 18 double-peaked SEP events by examining 88 SEP events. The peaks in the intensity-time profile were separated by 3-24 hours. We divided the SEP events according to possible multiple acceleration into four groups and in one of these groups we find evidence for multiple acceleration in velocity dispersion and change in the abundance ratio associated at transition to the second peak. Then we explored the intensity-time profiles of all SEP events during solar cycle 23 and found that most of the SEP events are associated with multiple eruptions at the Sun and we call those events as Multi-Eruption Solar Energetic Particles (MESEP) events. We use the data available by Large Angle and Spectrometric Coronograph LASCO on board SOHO to determine the CME associated with such events and YOHKOH and GOES satellites data to determine the flare associated with such events. We found four types of MESEP according to the appearance of the peaks in the intensity-time profile in large variation of energy levels. We found that it is not possible to determine whether the peaks are related to an eruption at the Sun or not, only by examining the anisotropy flux, He/p ratio and velocity dispersion. Then we chose a rare event in which there is evidence of SEP acceleration from behind previous CME. This work resulted in a conclusion which is inconsistent with the current SEP paradigm. Then we discovered through examining another MESEP event, that energetic particles accelerated by a second CME can penetrate a previous CME-driven decelerating shock. Finally, we report the previous two MESEP events with new two events and find a common basis for second CME SEPs penetrating previous decelerating shocks. This phenomenon is reported for the first time and expected to have significant impact on modification of the current paradigm of the solar energetic particle events.

Optimization of wind blade design including its energetic characteristics

The goal of the Master’s thesis is to develop and to analyze the optimization method for finding a geometry shape of classical horizontal wind turbine blades based on set of criteria. The thesis develops a technique that allows the designer to determine the weight of such factors as power coefficient, sound pressure level and the cost function in the overall process of blade shape optimization. The optimization technique applies the Desirability function. It was never used before in that kind of technical problems, and in this sense it can claim to originality of research. To do the analysis and the optimization processes more convenient the software application was developed.

Acceleration of Solar Energetic Particles in coronal shocks through self-generated turbulence

The acceleration of solar energetic particles (SEPs) by flares and coronal mass ejections (CMEs) has been a major topic of research for the solar-terrestrial physics and geophysics communities for decades. This thesis discusses theories describing first-order Fermi acceleration of SEPs through repeated crossings at a CME-driven shock. We propose that particle trapping occurs through self-generated Alfvén waves, leading to a turbulent trapping region in front of the shock. Decelerating coronal shocks are shown to be capable of efficient SEP acceleration, provided seed particle injection is sufficient. Quasi-parallel shocks are found to inject thermal particles with good efficiency. The roles of minimum injection velocities, cross-field diffusion, downstream scattering efficiency and cross-shock potential are investigated in detail, with downstream isotropisation timescales having a major effect on injection efficiency. Accelerated spectra of heavier elements up to iron are found to exhibit significantly harder spectra than protons. Accelerated spectra cut-off energies are found to scale proportional to (Q/A)^1.5, which is explained through analysis of the spectral shape of amplified Alfvénic turbulence. Acceleration times to different threshold energies are found to be non-linear, indicating that self-consistent time-dependent simulations are required in order to expose the full extent of acceleration dynamics. The well-established quasilinear theory (QLT) of particle scattering is investigated by comparing QLT scattering coefficients with those found via full-orbit simulations. QLT is found to overemphasise resonance conditions. This finding supports the simplifications implemented in the presented coronal shock acceleration (CSA) simulation software. The CSA software package is used to simulate a range of acceleration scenarios. The results are found to be in agreement with well-established particle acceleration theory. At the same time, new spatial and temporal dynamics of particle population trapping and wave evolution are revealed.

Calibration and simulations of SIXS-P's response to energetic particles

The Solar Intensity X-ray and particle Spectrometer (SIXS) on board BepiColombo's Mercury Planetary Orbiter (MPO) will study solar energetic particles moving towards Mercury and solar X-rays on the dayside of Mercury. The SIXS instrument consists of two detector sub-systems; X-ray detector SIXS-X and particle detector SIXS-P. The SIXS-P subdetector will detect solar energetic electrons and protons in a broad energy range using a particle telescope approach with five outer Si detectors around a central CsI(Tl) scintillator. The measurements made by the SIXS instrument are necessary for other instruments on board the spacecraft. SIXS data will be used to study the Solar X-ray corona, solar flares, solar energetic particles, the Hermean magnetosphere, and solar eruptions. The SIXS-P detector was calibrated by comparing experimental measurement data from the instrument with Geant4 simulation data. Calibration curves were produced for the different side detectors and the core scintillator for electrons and protons, respectively. The side detector energy response was found to be linear for both electrons and protons. The core scintillator energy response to protons was found to be non-linear. The core scintillator calibration for electrons was omitted due to insufficient experimental data. The electron and proton acceptance of the SIXS-P detector was determined with Geant4 simulations. Electron and proton energy channels are clean in the main energy range of the instrument. At higher energies, protons and electrons produce non-ideal response in the energy channels. Due to the limited bandwidth of the spacecraft's telemetry, the particle measurements made by SIXS-P have to be pre-processed in the data processing unit of the SIXS instrument. A lookup table was created for the pre-processing of data with Geant4 simulations, and the ability of the lookup table to provide spectral information from a simulated electron event was analysed. The lookup table produces clean electron and proton channels and is able to separate protons and electrons. Based on a simulated solar energetic electron event, the incident electron spectrum cannot be determined from channel particle counts with a standard analysis method.

Kantavan kehikkorakenteen valmistuksen kehittäminen

Paperikoneen hoitotason muodostaa kantava kehikkorakenne sekä kehikkorakenteiden tuennat. Kantavan kehikkorakenteen valmistuson perinteistä hitsaavaa konepajatuotantoa. Työssä esitetään ratkaisuja valmistuksen kehittämiseen, näiden avulla on tavoitteena pudottaa valmistuksen läpimenoaikaa ja lopullisesti vastata kiristyneeseen kilpailutilanteeseen. Laajempana tavoitteena on osoittaa automaation mahdollisuudet kyseiseen tuotantoon. Alumiinisten rakenteiden toimitukset ovat jatkuvasti kasvaneet. Tähän rakenneryhmään haluttiin panostaa ja tehdä tuotteesta markkinoiden paras sekä kehittää valmistusta, jotta voitaisiin vastata kilpailuun ja lyhyisiin toimitusaikoihin. Työssä esitettävät ratkaisut on suunnattu alumiinisen kantavan kehikon valmistuksen kehittämiseen. Valmistuksen kehittäminen käsittää tuotteen rakennekomponenttien suunnittelemista valmistuksen kannalta, automaation lisäämistä osavalmistukseen sekä hitsauksen kevytmekanisointia.

A support system for evaluating a suitable joining method in the production of sheet metal goods

This report illustrates a comparative study of various joining methods involved in sheet metal production. In this report it shows the selection of joining methods, which includes comparing the advantages and disadvantages of a method over the other ones and choosing the best method for joining. On the basis of various joining process from references, a table is generated containing set of criterion that helps in evaluation of various sheet metal joining processes and in selecting the most suitable process for a particular product. Three products are selected and a comprehensive study of the joining methods is analyzed with the help of various parameters. The table thus is the main part of the analysis process of this study and can be advanced with the beneficial results. It helps in a better and easy understanding and comparing the various methods, which provides the foundation of this study and analysis. The suitability of the joining method for various types of cases of different sheet metal products can be tested with the help of this table. The sections of the created table display the requirements of manufacturing. The important factor has been considered and given focus in the table, as how the usage of these parameters is important in percentages according to particular or individual case. The analysis of the methods can be extended or altered by changing the parameters according to the constraint. The use of this table is demonstrated by pertaining the cases from sheet metal production.

Kokoonpanon kehittäminen tuulivoimalakoneikkojen valmistuksessa

Tämä diplomityö on tehty Hollming Works Oy:n Loviisan yksikölle. Työn tekovaiheessa yrityksessä oltiin aloittamassa tuulivoimalakoneikkojen sarjatyönä tapahtuvaa kokoonpanoa. Työn tavoitteena oli kehittää koneikkojen kokoonpanoverstaan toimintaa. Ennen työn alkua yritykseen oli perustettu tuulivoimalakoneikkojen kokoonpanoon tuoteverstas. Verstaalla kootaan raskaita osakokoonpanoja, jotka lopulta yhdistetään koneikoksi, jota kutsutaan myös naselliksi. Tämän jälkeen varusteluvaiheessa koneikkoon asennetaan mm. erilaisia sähköisiä ja hydraulisia järjestelmiä. Varusteluvaiheen päätteeksi koneikon toiminta testataan. Viimeisenä vaiheenakoneikon päälle asennetaan lasikuitukuori. Työn alkuosassa on käyty läpi tuotannon- ja materiaalinohjauksen perusteita, kokoonpanon kehittämistä ja layout-suunnittelua, jonka pohjalta tuulivoimalaverstaalle tehtiin kokoonpanosoluihin perustuva layoutsuunnitelma. Tuotannonohjaus suunnitelmassa perustuu kapeikko-ohjaukseen. Tuotannon kapeikon muodostava varusteluvaihe imee aiemmista vaiheista osakokoonpanot. Varusteluvaiheen ja testauksen jälkeen koneikko siirtyytyöntöohjatusti lasikuitukuoren asennukseen. Järjestelmässä pyritään tehokkaaseen tilankäyttöön, lyhyeen läpäisyaikaan ja vähäiseen keskeneräisen tuotannon määrään.

Mekanismien dynamiikan simuloinnissa sovellettavia numeerisia- ja mallinnusmenetelmiä

Koneet voidaan usein jakaa osajärjestelmiin, joita ovat ohjaus- ja säätöjärjestelmät, voimaa tuottavat toimilaitteet ja voiman välittävät mekanismit. Eri osajärjestelmiä on simuloitu tietokoneavusteisesti jo usean vuosikymmenen ajan. Osajärjestelmien yhdistäminen on kuitenkin uudempi ilmiö. Usein esimerkiksi mekanismien mallinnuksessa toimilaitteen tuottama voimaon kuvattu vakiona, tai ajan funktiona muuttuvana voimana. Vastaavasti toimilaitteiden analysoinnissa mekanismin toimilaitteeseen välittämä kuormitus on kuvattu vakiovoimana, tai ajan funktiona työkiertoa kuvaavana kuormituksena. Kun osajärjestelmät on erotettu toisistaan, on niiden välistenvuorovaikutuksien tarkastelu erittäin epätarkkaa. Samoin osajärjestelmän vaikutuksen huomioiminen koko järjestelmän käyttäytymissä on hankalaa. Mekanismien dynamiikan mallinnukseen on kehitetty erityisesti tietokoneille soveltuvia numeerisia mallinnusmenetelmiä. Useimmat menetelmistä perustuvat Lagrangen menetelmään, joka mahdollistaa vapaasti valittaviin koordinaattimuuttujiin perustuvan mallinnuksen. Numeerista ratkaisun mahdollistamiseksi menetelmän avulla muodostettua differentiaali-algebraaliyhtälöryhmää joudutaan muokkaamaan esim. derivoimalla rajoiteyhtälöitä kahteen kertaan. Menetelmän alkuperäisessä numeerisissa ratkaisuissa kaikki mekanismia kuvaavat yleistetyt koordinaatit integroidaan jokaisella aika-askeleella. Tästä perusmenetelmästä johdetuissa menetelmissä riippumattomat yleistetyt koordinaatit joko integroidaan ja riippuvat koordinaatit ratkaistaan rajoiteyhtälöiden perusteella tai yhtälöryhmän kokoa pienennetään esim. käyttämällä nopeus- ja kiihtyvyysanalyyseissä eri kiertymäkoordinaatteja kuin asema-analyysissä. Useimmat integrointimenetelmät on alun perin tarkoitettu differentiaaliyhtälöiden (ODE) ratkaisuunjolloin yhtälöryhmään liitetyt niveliä kuvaavat algebraaliset rajoiteyhtälöt saattavat aiheuttaa ongelmia. Nivelrajoitteiden virheiden korjaus, stabilointi, on erittäin tärkeää mekanismien dynamiikan simuloinnin onnistumisen ja tulosten oikeellisuuden kannalta. Mallinnusmenetelmien johtamisessa käytetyn virtuaalisen työn periaatteen oletuksena nimittäin on, etteivät rajoitevoimat tee työtä, eli rajoitteiden vastaista siirtymää ei tapahdu. Varsinkaan monimutkaisten järjestelmien pidemmissä analyyseissä nivelrajoitteet eivät toteudu tarkasti. Tällöin järjestelmän energiatasapainoei toteudu ja järjestelmään muodostuu virtuaalista energiaa, joka rikkoo virtuaalisen työn periaatetta, Tästä syystä tulokset eivät enää pidäpaikkaansa. Tässä raportissa tarkastellaan erityyppisiä mallinnus- ja ratkaisumenetelmiä, ja vertaillaan niiden toimivuutta yksinkertaisten mekanismien numeerisessa ratkaisussa. Menetelmien toimivuutta tarkastellaan ratkaisun tehokkuuden, nivelrajoitteiden toteutumisen ja energiatasapainon säilymisen kannalta.

Automated formulation of optimisation models for steel beam structures

Over 70% of the total costs of an end product are consequences of decisions that are made during the design process. A search for optimal cross-sections will often have only a marginal effect on the amount of material used if the geometry of a structure is fixed and if the cross-sectional characteristics of its elements are property designed by conventional methods. In recent years, optimalgeometry has become a central area of research in the automated design of structures. It is generally accepted that no single optimisation algorithm is suitable for all engineering design problems. An appropriate algorithm, therefore, mustbe selected individually for each optimisation situation. Modelling is the mosttime consuming phase in the optimisation of steel and metal structures. In thisresearch, the goal was to develop a method and computer program, which reduces the modelling and optimisation time for structural design. The program needed anoptimisation algorithm that is suitable for various engineering design problems. Because Finite Element modelling is commonly used in the design of steel and metal structures, the interaction between a finite element tool and optimisation tool needed a practical solution. The developed method and computer programs were tested with standard optimisation tests and practical design optimisation cases. Three generations of computer programs are developed. The programs combine anoptimisation problem modelling tool and FE-modelling program using three alternate methdos. The modelling and optimisation was demonstrated in the design of a new boom construction and steel structures of flat and ridge roofs. This thesis demonstrates that the most time consuming modelling time is significantly reduced. Modelling errors are reduced and the results are more reliable. A new selection rule for the evolution algorithm, which eliminates the need for constraint weight factors is tested with optimisation cases of the steel structures that include hundreds of constraints. It is seen that the tested algorithm can be used nearly as a black box without parameter settings and penalty factors of the constraints.

On Modelling, System Identification and Control of Servo-Systems with a Flexible Load

The present study was done with two different servo-systems. In the first system, a servo-hydraulic system was identified and then controlled by a fuzzy gainscheduling controller. The second servo-system, an electro-magnetic linear motor in suppressing the mechanical vibration and position tracking of a reference model are studied by using a neural network and an adaptive backstepping controller respectively. Followings are some descriptions of research methods. Electro Hydraulic Servo Systems (EHSS) are commonly used in industry. These kinds of systems are nonlinearin nature and their dynamic equations have several unknown parameters.System identification is a prerequisite to analysis of a dynamic system. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) for solving global optimization problems. In the study, the DE algorithm is proposed for handling nonlinear constraint functionswith boundary limits of variables to find the best parameters of a servo-hydraulic system with flexible load. The DE guarantees fast speed convergence and accurate solutions regardless the initial conditions of parameters. The control of hydraulic servo-systems has been the focus ofintense research over the past decades. These kinds of systems are nonlinear in nature and generally difficult to control. Since changing system parameters using the same gains will cause overshoot or even loss of system stability. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. The study is concerned with a second order model reference to positioning control of a flexible load servo-hydraulic system using fuzzy gainscheduling. In the present research, to compensate the lack of dampingin a hydraulic system, an acceleration feedback was used. To compare the results, a pcontroller with feed-forward acceleration and different gains in extension and retraction is used. The design procedure for the controller and experimental results are discussed. The results suggest that using the fuzzy gain-scheduling controller decrease the error of position reference tracking. The second part of research was done on a PermanentMagnet Linear Synchronous Motor (PMLSM). In this study, a recurrent neural network compensator for suppressing mechanical vibration in PMLSM with a flexible load is studied. The linear motor is controlled by a conventional PI velocity controller, and the vibration of the flexible mechanism is suppressed by using a hybrid recurrent neural network. The differential evolution strategy and Kalman filter method are used to avoid the local minimum problem, and estimate the states of system respectively. The proposed control method is firstly designed by using non-linear simulation model built in Matlab Simulink and then implemented in practical test rig. The proposed method works satisfactorily and suppresses the vibration successfully. In the last part of research, a nonlinear load control method is developed and implemented for a PMLSM with a flexible load. The purpose of the controller is to track a flexible load to the desired position reference as fast as possible and without awkward oscillation. The control method is based on an adaptive backstepping algorithm whose stability is ensured by the Lyapunov stability theorem. The states of the system needed in the controller are estimated by using the Kalman filter. The proposed controller is implemented and tested in a linear motor test drive and responses are presented.

Representations of work and worker in the three generations of knowledge management. Critical Discourse Analysis of selected texts.

The thesis studies the representations of different elements of contemporary work as present in Knowledge Management (KM). KM is approached as management discourse that is seen to affect and influence managerial practices in organizations. As representatives of KM discourse four journal articles are analyzed, using the methodology of Critical Discourse Analysis and the framework of Critical Management Studies, with a special emphasis on the question of structure and agency. The results of the analysis reveal that structural elements such as information technology and organizational structures are strongly present in the most influential KM representations, making their improvement also a desirable course of action for managers. In contrast agentic properties are not in a central role, they are subjugated to structural constraints of varying kind and degree. The thesis claims that one such constraint is KM discourse itself, influencing managerial and organizational choices and decision making. The thesis concludes that the way human beings are represented, studied and treated in management studies such as KM needs to be re-examined. Pro gradu-tutkielmassa analysoidaan työhön ja sen tekijään liittyviä representaatioita Tietojohtamisen kirjallisuudessa. Tietojohtamista tarkastellaan liikkeenjohdollisena diskurssina, jolla nähdään olevan vaikutus organisaatioiden päätöksentekoon ja toimintaan. Tutkielmassa analysoidaan neljä Tietojohtamisen tieteellistä artikkelia, käyttäen metodina kriittistä diskurssianalyysiä. Tutkielman viitekehyksenä on kriittinen liikkeenjohdon tutkimus. Lisäksi työssä pohditaan kysymystä rakenteen ja toimijan välisestä vuorovaikutuksesta. Tutkielman analyysi paljastaa, että tietojohtamisen vaikutusvaltaisimmat representaatiot painottavat rakenteellisia tekijöitä, kuten informaatioteknologiaa ja organisaatiorakenteita. Tämän seurauksena mm. panostukset em. tekijöihin nähdään organisaatioissa toivottavana toimintana. Vastaavasti representaatiot jotka painottavat yksilöitä ja toimintaa ovat em. tekijöille alisteisessa asemassa. Tapaa, jolla yksilöitä kuvataan ja käsitellään Tietojohtamisen diskurssissa, tulisikin laajentaa ja monipuolistaa.

Evolution and Stellar Content of AGN Host Galaxies

In this dissertation, Active Galactic Nuclei (AGN) and their host galaxies are discussed. Together with transitional events, such as supernovae and gamma-ray bursts, AGN are the most energetic phenomena in the Universe. The dominant fraction of their luminosity originates from the center of a galaxy, where accreting gas falls into a supermassive black hole, converting gravitational energy to radiation. AGN have a wide range of observed properties: e.g. in their emission lines, radio emission, and variability. Most likely, these properties depend significantly on their orientation to our line-of-sight, and to unify AGN into physical classes it is crucial to observe their orientation-independent properties, such as the host galaxies. Furthermore, host galaxy studies are essential to understand the formation and co-evolution of galactic bulges and supermassive black holes. In this thesis, the main focus is on observationally characterizing AGN host galaxies using optical and near-infrared imaging and spectroscopy. BL Lac objects are a class of AGN characterized by rapidly variable and polarized continuum emission across the electromagnetic spectrum, and coredominated radio emission. The near-infrared properties of intermediate redshift BL Lac host galaxies are studied in Paper I. They are found to be large elliptical galaxies that are more luminous than their low redshift counterparts suggesting a strong luminosity evolution, and a contribution from a recent star formation episode. To analyze the stellar content of galaxies in more detail multicolor data, especially observations at blue wavelengths, are essential. In Paper III, optical - near-infrared colors and color gradients are derived for low redshift BL Lac host galaxies. They show bluer colors and steeper color gradients than inactive ellipticals which, most likely, are caused by a relatively young stellar population indicating a different evolutionary stage between AGN hosts and inactive ellipticals. In Paper II, near-infrared imaging of intermediate redshift radio-quiet quasar hosts is used to study their luminosity evolution. The hosts are large elliptical galaxies, but they are systematically fainter than the hosts of radio-loud quasars at similar redshifts, suggesting a link between the luminosity of the host galaxies and the radio properties of AGN. In Paper IV, the characteristics of near-infrared stellar absorption features of low redshift radio galaxies are compared with those of inactive early-type galaxies. The comparison suggests that early-type galaxies with AGN are in a different evolutionary stage than their inactive counterparts. Moreover, radio galaxies are found to contain stellar populations containing both old and intermediate age components.

Formal Power Analysis of Systems-on-Chip

The design methods and languages targeted to modern System-on-Chip designs are facing tremendous pressure of the ever-increasing complexity, power, and speed requirements. To estimate any of these three metrics, there is a trade-off between accuracy and abstraction level of detail in which a system under design is analyzed. The more detailed the description, the more accurate the simulation will be, but, on the other hand, the more time consuming it will be. Moreover, a designer wants to make decisions as early as possible in the design flow to avoid costly design backtracking. To answer the challenges posed upon System-on-chip designs, this thesis introduces a formal, power aware framework, its development methods, and methods to constraint and analyze power consumption of the system under design. This thesis discusses on power analysis of synchronous and asynchronous systems not forgetting the communication aspects of these systems. The presented framework is built upon the Timed Action System formalism, which offer an environment to analyze and constraint the functional and temporal behavior of the system at high abstraction level. Furthermore, due to the complexity of System-on-Chip designs, the possibility to abstract unnecessary implementation details at higher abstraction levels is an essential part of the introduced design framework. With the encapsulation and abstraction techniques incorporated with the procedure based communication allows a designer to use the presented power aware framework in modeling these large scale systems. The introduced techniques also enable one to subdivide the development of communication and computation into own tasks. This property is taken into account in the power analysis part as well. Furthermore, the presented framework is developed in a way that it can be used throughout the design project. In other words, a designer is able to model and analyze systems from an abstract specification down to an implementable specification.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.