Hyperbolic type metrics and distortion of quasiconformal map pings

This Ph.D. thesis consists of four original papers. The papers cover several topics from geometric function theory, more specifically, hyperbolic type metrics, conformal invariants, and the distortion properties of quasiconformal mappings. The first paper deals mostly with the quasihyperbolic metric. The main result gives the optimal bilipschitz constant with respect to the quasihyperbolic metric for the M¨obius self-mappings of the unit ball. A quasiinvariance property, sharp in a local sense, of the quasihyperbolic metric under quasiconformal mappings is also proved. The second paper studies some distortion estimates for the class of quasiconformal self-mappings fixing the boundary values of the unit ball or convex domains. The distortion is measured by the hyperbolic metric or hyperbolic type metrics. The results provide explicit, asymptotically sharp inequalities when the maximal dilatation of quasiconformal mappings tends to 1. These explicit estimates involve special functions which have a crucial role in this study. In the third paper, we investigate the notion of the quasihyperbolic volume and find the growth estimates for the quasihyperbolic volume of balls in a domain in terms of the radius. It turns out that in the case of domains with Ahlfors regular boundaries, the rate of growth depends not merely on the radius but also on the metric structure of the boundary. The topic of the fourth paper is complete elliptic integrals and inequalities. We derive some functional inequalities and elementary estimates for these special functions. As applications, some functional inequalities and the growth of the exterior modulus of a rectangle are studied.

Värispekrien eron laskenta

Olemassa olevat spektrieromittarit eivät vastaa riittävästi CIEDE2000-värieroa. Tämän työn tavoitteena oli toteuttaa menetelmä, joka laskee värispektrien eron siten, että tulos vastaa CIEDE2000-värieroa. Kehitystyön tuloksena syntyi menetelmä, joka perustuu ennalta laskettuihin eroihin tunnettujen spektrien välillä ja niiden perusteella johdettuihin laskentaparametreihin. menetelmällä pystyy laskemaan spektrieroja vain niiden spektrien välillä, jotka saadaan sekoittamalla tunnettuja spektrejä. Laskentaparametrien laskenta on työläs prosessi ja siksi menetelmään toteutettiin hajautus usealle tietokoneelle. Menetelmä saatiin vastaamaan hyvin CIEDE2000:ia suurimmalle osalle spektrejä harvoja poikkeuksia lukuunottamatta. Ongelmat johtuvat mallissa olevasta matemaattisesta ominaisuudesta. Spektrieromittari näyttää metameerisille spektreille nollasta poikkeavan arvon, vaikka CIEDE2000 näyttää nollaa. Tämä osoittaa spektrieromittarin oikeamman toiminnan CIEDE2000-värieroon verrattuna.

Real-time Image-based RGB-D Camera Motion Tracking and Environment Mapping

In this work, image based estimation methods, also known as direct methods, are studied which avoid feature extraction and matching completely. Cost functions use raw pixels as measurements and the goal is to produce precise 3D pose and structure estimates. The cost functions presented minimize the sensor error, because measurements are not transformed or modified. In photometric camera pose estimation, 3D rotation and translation parameters are estimated by minimizing a sequence of image based cost functions, which are non-linear due to perspective projection and lens distortion. In image based structure refinement, on the other hand, 3D structure is refined using a number of additional views and an image based cost metric. Image based estimation methods are particularly useful in conditions where the Lambertian assumption holds, and the 3D points have constant color despite viewing angle. The goal is to improve image based estimation methods, and to produce computationally efficient methods which can be accomodated into real-time applications. The developed image-based 3D pose and structure estimation methods are finally demonstrated in practise in indoor 3D reconstruction use, and in a live augmented reality application.

Behavior of black liquor nitrogen in combustion : formation of cyanate

The Kraft pulping process is the dominant chemical pulping process in the world. Roughly 195 million metric tons of black liquor are produced annually as a by-product from the Kraft pulping process. Black liquor consists of spent cooking chemicals and dissolved organics from the wood and can contain up to 0.15 wt% nitrogen on dry solids basis. The cooking chemicals from black liquor are recovered in a chemical recovery cycle. Water is evaporated in the first stage of the chemical recovery cycle, so the black liquor has a dry solids content of 65-85% prior to combustion. During combustion of black liquor, a portion of the black liquor nitrogen is volatilized, finally forming N2 or NO. The rest of the nitrogen remains in the char as char nitrogen. During char conversion, fixed carbon is burned off leaving the pulping chemicals as smelt, and the char nitrogen forms mostly smelt nitrogen (cyanate, OCN-). Smelt exits the recovery boiler and is dissolved in water. The cyanate from smelt decomposes in the presence of water, forming NH3, which causes nitrogen emissions from the rest of the chemical recovery cycle. This thesis had two focuses: firstly, to determine how the nitrogen chemistry in the recovery boiler is affected by modification of black liquor; and secondly, to find out what causes cyanate formation during thermal conversion, and which parameters affect cyanate formation and decomposition during thermal conversion of black liquor. The fate of added biosludge nitrogen in chemical recovery was determined in Paper I. The added biosludge increased the nitrogen content of black liquor. At the pulp mill, the added biosludge did not increase the NO formation in the recovery boiler, but instead increased the amount of cyanate in green liquor. The increased cyanate caused more NH3 formation, which increased the NCG boiler’s NO emissions. Laboratory-scale experiments showed an increase in both NO and cyanate formation after biosludge addition. Black liquor can be modified, for example by addition of a solid biomass to increase the energy density of black liquor, or by separation of lignin from black liquor by precipitation. The precipitated lignin can be utilized in the production of green chemicals or as a fuel. In Papers II and III, laboratory-scale experiments were conducted to determine the impact of black liquor modification on NO and cyanate formation. Removal of lignin from black liquor reduced the nitrogen content of the black liquor. In most cases NO and cyanate formation decreased with increasing lignin removal; the exception was NO formation from lignin lean soda liquors. The addition of biomass to black liquor resulted in a higher nitrogen content fuel mixture, due to the higher nitrogen content of biomass compared to black liquor. More NO and cyanate were formed from the fuel mixtures than from pure black liquor. The increased amount of formed cyanate led to the hypothesis that black liquor is catalytically active and converts a portion of the nitrogen in the mixed fuel to cyanate. The mechanism behind cyanate formation during thermal conversion of black liquor was not clear before this thesis. Paper IV studies the cyanate formation of alkali metal loaded fuels during gasification in a CO2 atmosphere. The salts K2CO3, Na2CO3, and K2SO4 all promoted char nitrogen to cyanate conversion during gasification, while KCl and CaCO3 did not. It is now assumed that cyanate is formed when alkali metal carbonate or an active intermediate of alkali metal carbonate (e.g. -CO2K) reacts with the char nitrogen forming cyanate. By testing different fuels (bark, peat, and coal), each of which had a different form of organic nitrogen, it was concluded that the form of organic nitrogen in char also has an impact on cyanate formation. Cyanate can be formed during pyrolysis of black liquor, but at temperatures 900°C or above, the formed cyanate will decompose. Cyanate formation in gasifying conditions with different levels of CO2 in the atmosphere was also studied. Most of the char nitrogen was converted to cyanate during gasification at 800-900°C in 13-50% CO2 in N2, and only 5% of the initial fuel nitrogen was converted to NO during char conversion. The formed smelt cyanate was stable at 800°C 13% CO2, while it decomposed at 900°C 13% CO2. The cyanate decomposition was faster at higher temperatures and in oxygen-containing atmospheres than in an inert atmosphere. The presence of CO2 in oxygencontaining atmospheres slowed down the decomposition of cyanate. This work will provide new information on how modification of black liquor affects the nitrogen chemistry during thermal conversion of black liquor and what causes cyanate formation during thermal conversion of black liquor. The formation and decomposition of cyanate was studied in order to provide new data, which would be useful in modeling of nitrogen chemistry in the recovery boiler.

Tasaisemmin jakaantuneen CIELAB-tyyppisen väriavaruuden määrittäminen värieroellipsien pääakselien eroja minimoimalla

Tässä työssä johdetaan lineaarimuunnoksella CIE x y z-värinsovitusfunktioista uudet värinsovitusfunktiot. Tarvittava muunnosmatriisi etsitään optimoimalla CIE ja BFD-RIT värieroellipsejä Matlab-ympäristössä. Työn tuloksena saatiin muunnosmatriisi, ja sillä muunnetut uudet värinsovitusfunktiot ja CIELAB-tyyppinen väriavaruus. Euklidisella etäisyydellä mitattuna CIE ja BFD-RIT värieroellipsien muoto ja koko paranivat noin kolmanneksen, mikä oli myös tavoitteena.

Numerical Studies of Dark Energy Models and Observations

The cosmological standard view is based on the assumptions of homogeneity, isotropy and general relativistic gravitational interaction. These alone are not sufficient for describing the current cosmological observations of accelerated expansion of space. Although general relativity is extremely accurately tested to describe the local gravitational phenomena, there is a strong demand for modifying either the energy content of the universe or the gravitational interaction itself to account for the accelerated expansion. By adding a non-luminous matter component and a constant energy component with negative pressure, the observations can be explained with general relativity. Gravitation, cosmological models and their observational phenomenology are discussed in this thesis. Several classes of dark energy models that are motivated by theories outside the standard formulation of physics were studied with emphasis on the observational interpretation. All the cosmological models that seek to explain the cosmological observations, must also conform to the local phenomena. This poses stringent conditions for the physically viable cosmological models. Predictions from a supergravity quintessence model was compared to Supernova 1a data and several metric gravity models were studied with local experimental results. Polytropic stellar configurations of solar, white dwarf and neutron stars were numerically studied with modified gravity models. The main interest was to study the spacetime around the stars. The results shed light on the viability of the studied cosmological models.

Metrics for Predicting User Behavior and Experience in an Interactive Storytelling System

In much of the previous research into the field of interactive storytelling, the focus has been on the creation of complete systems, then evaluating the performance of those systems based on user experience. Less focus has been placed on finding general solutions to problems that manifest in many different types of interactive storytelling systems. The goal of this thesis was to identify potential candidates for metrics that a system could use to predict player behavior or how players experience the story they are presented with, and to put these metrics to an empirical test. The three metrics that were used were morality, relationships and conflict. The game used for user testing of the metrics, Regicide is an interactive storytelling experience that was created in conjunction with Eero Itkonen. Data, in the forms of internal system data and survey answers, collected through user testing, was used to evaluate hypotheses for each metric. Out of the three chosen metrics, morality performed the best in this study. Though further research and refinement may be required, the results were promising, and point to the conclusion that user responses to questions of morality are a strong predictor for their choices in similar situations later on in the course of an interactive story. A similar examination for user relationships with other characters in the story did not produce promising results, but several problems were recognized in terms of methodology and further research with a better optimized system may yield different results. On the subject of conflict, several aspects, proposed by Ware et al. (2012), were evaluated separately. Results were inconclusive, with the aspect of directness showing the most promise.

Cohesion Metrics for Improving Software Quality

Abstract Software product metrics aim at measuring the quality of software. Modu- larity is an essential factor in software quality. In this work, metrics related to modularity and especially cohesion of the modules, are considered. The existing metrics are evaluated, and several new alternatives are proposed. The idea of cohesion of modules is that a module or a class should consist of related parts. The closely related principle of coupling says that the relationships between modules should be minimized. First, internal cohesion metrics are considered. The relations that are internal to classes are shown to be useless for quality measurement. Second, we consider external relationships for cohesion. A detailed analysis using design patterns and refactorings confirms that external cohesion is a better quality indicator than internal. Third, motivated by the successes (and problems) of external cohesion metrics, another kind of metric is proposed that represents the quality of modularity of software. This metric can be applied to refactorings related to classes, resulting in a refactoring suggestion system. To describe the metrics formally, a notation for programs is developed. Because of the recursive nature of programming languages, the properties of programs are most compactly represented using grammars and formal lan- guages. Also the tools that were used for metrics calculation are described.