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.

A simulation model of the optimal maintenance strategy: conceptual agent-based approach

In this Master’s thesis agent-based modeling has been used to analyze maintenance strategy related phenomena. The main research question that has been answered was: what does the agent-based model made for this study tell us about how different maintenance strategy decisions affect profitability of equipment owners and maintenance service providers? Thus, the main outcome of this study is an analysis of how profitability can be increased in industrial maintenance context. To answer that question, first, a literature review of maintenance strategy, agent-based modeling and maintenance modeling and optimization was conducted. This review provided the basis for making the agent-based model. Making the model followed a standard simulation modeling procedure. With the simulation results from the agent-based model the research question was answered. Specifically, the results of the modeling and this study are: (1) optimizing the point in which a machine is maintained increases profitability for the owner of the machine and also the maintainer with certain conditions; (2) time-based pricing of maintenance services leads to a zero-sum game between the parties; (3) value-based pricing of maintenance services leads to a win-win game between the parties, if the owners of the machines share a substantial amount of their value to the maintainers; and (4) error in machine condition measurement is a critical parameter to optimizing maintenance strategy, and there is real systemic value in having more accurate machine condition measurement systems.

Spontaneous Focusing on Quantitative Relations and the Development of Rational Number Conceptual Knowledge

The aim of the present set of studies was to explore primary school children’s Spontaneous Focusing On quantitative Relations (SFOR) and its role in the development of rational number conceptual knowledge. The specific goals were to determine if it was possible to identify a spontaneous quantitative focusing tendency that indexes children’s tendency to recognize and utilize quantitative relations in non-explicitly mathematical situations and to determine if this tendency has an impact on the development of rational number conceptual knowledge in late primary school. To this end, we report on six original empirical studies that measure SFOR in children ages five to thirteen years and the development of rational number conceptual knowledge in ten- to thirteen-year-olds. SFOR measures were developed to determine if there are substantial differences in SFOR that are not explained by the ability to use quantitative relations. A measure of children’s conceptual knowledge of the magnitude representations of rational numbers and the density of rational numbers is utilized to capture the process of conceptual change with rational numbers in late primary school students. Finally, SFOR tendency was examined in relation to the development of rational number conceptual knowledge in these students. Study I concerned the first attempts to measure individual differences in children’s spontaneous recognition and use of quantitative relations in 86 Finnish children from the ages of five to seven years. Results revealed that there were substantial inter-individual differences in the spontaneous recognition and use of quantitative relations in these tasks. This was particularly true for the oldest group of participants, who were in grade one (roughly seven years old). However, the study did not control for ability to solve the tasks using quantitative relations, so it was not clear if these differences were due to ability or SFOR. Study II more deeply investigated the nature of the two tasks reported in Study I, through the use of a stimulated-recall procedure examining children’s verbalizations of how they interpreted the tasks. Results reveal that participants were able to verbalize reasoning about their quantitative relational responses, but not their responses based on exact number. Furthermore, participants’ non-mathematical responses revealed a variety of other aspects, beyond quantitative relations and exact number, which participants focused on in completing the tasks. These results suggest that exact number may be more easily perceived than quantitative relations. As well, these tasks were revealed to contain both mathematical and non-mathematical aspects which were interpreted by the participants as relevant. Study III investigated individual differences in SFOR 84 children, ages five to nine, from the US and is the first to report on the connection between SFOR and other mathematical abilities. The cross-sectional data revealed that there were individual differences in SFOR. Importantly, these differences were not entirely explained by the ability to solve the tasks using quantitative relations, suggesting that SFOR is partially independent from the ability to use quantitative relations. In other words, the lack of use of quantitative relations on the SFOR tasks was not solely due to participants being unable to solve the tasks using quantitative relations, but due to a lack of the spontaneous attention to the quantitative relations in the tasks. Furthermore, SFOR tendency was found to be related to arithmetic fluency among these participants. This is the first evidence to suggest that SFOR may be a partially distinct aspect of children’s existing mathematical competences. Study IV presented a follow-up study of the first graders who participated in Studies I and II, examining SFOR tendency as a predictor of their conceptual knowledge of fraction magnitudes in fourth grade. Results revealed that first graders’ SFOR tendency was a unique predictor of fraction conceptual knowledge in fourth grade, even after controlling for general mathematical skills. These results are the first to suggest that SFOR tendency may play a role in the development of rational number conceptual knowledge. Study V presents a longitudinal study of the development of 263 Finnish students’ rational number conceptual knowledge over a one year period. During this time participants completed a measure of conceptual knowledge of the magnitude representations and the density of rational numbers at three time points. First, a Latent Profile Analysis indicated that a four-class model, differentiating between those participants with high magnitude comparison and density knowledge, was the most appropriate. A Latent Transition Analysis reveal that few students display sustained conceptual change with density concepts, though conceptual change with magnitude representations is present in this group. Overall, this study indicated that there were severe deficiencies in conceptual knowledge of rational numbers, especially concepts of density. The longitudinal Study VI presented a synthesis of the previous studies in order to specifically detail the role of SFOR tendency in the development of rational number conceptual knowledge. Thus, the same participants from Study V completed a measure of SFOR, along with the rational number test, including a fourth time point. Results reveal that SFOR tendency was a predictor of rational number conceptual knowledge after two school years, even after taking into consideration prior rational number knowledge (through the use of residualized SFOR scores), arithmetic fluency, and non-verbal intelligence. Furthermore, those participants with higher-than-expected SFOR scores improved significantly more on magnitude representation and density concepts over the four time points. These results indicate that SFOR tendency is a strong predictor of rational number conceptual development in late primary school children. The results of the six studies reveal that within children’s existing mathematical competences there can be identified a spontaneous quantitative focusing tendency named spontaneous focusing on quantitative relations. Furthermore, this tendency is found to play a role in the development of rational number conceptual knowledge in primary school children. Results suggest that conceptual change with the magnitude representations and density of rational numbers is rare among this group of students. However, those children who are more likely to notice and use quantitative relations in situations that are not explicitly mathematical seem to have an advantage in the development of rational number conceptual knowledge. It may be that these students gain quantitative more and qualitatively better self-initiated deliberate practice with quantitative relations in everyday situations due to an increased SFOR tendency. This suggests that it may be important to promote this type of mathematical activity in teaching rational numbers. Furthermore, these results suggest that there may be a series of spontaneous quantitative focusing tendencies that have an impact on mathematical development throughout the learning trajectory.

Microsatellite-dense genetic map: towards genome coverage in a tropical maize (Zea mays L.) population

Dense molecular genetic maps are used for an efficient quantitative trait loci (QTL) mapping and in the marker-assisted selection programs. A dense genetic map was generated with 139 microsatellite markers using 256 F2 plants generated by the crossing of two tropical maize inbred lines (L-02-03D and L-20-01F). This map presented 1,858.61 cM in length, where 10 linkage groups were found spanned, with an average interval of 13.47 cM between adjacent markers. Seventy seven percent of the maize genetic mapping bins were covered, which means an increase of 14% coverage in relation to the previous tropical maize maps. The results provide a more detailed and informative genetic map in a tropical maize population representing the first step to make possible the studies of genetic architecture to identify and map QTL and estimate their effects on the variation of quantitative traits, thus allowing the manipulation and use in tropical maize breeding programs.

A 37-kb restriction map of the human immunoglobulin lambda variable locus, VB cluster, harboring four functional genes and two non-coding Vl sequences

The human immunoglobulin lambda variable locus (IGLV) is mapped at chromosome 22 band q11.1-q11.2. The 30 functional germline v-lambda genes sequenced untill now have been subgrouped into 10 families (Vl1 to Vl10). The number of Vl genes has been estimated at approximately 70. This locus is formed by three gene clusters (VA, VB and VC) that encompass the variable coding genes (V) responsible for the synthesis of lambda-type Ig light chains, and the Jl-Cl cluster with the joining segments and the constant genes. Recently the entire variable lambda gene locus was mapped by contig methodology and its one- megabase DNA totally sequenced. All the known functional V-lambda genes and pseudogenes were located. We screened a human genomic DNA cosmid library and isolated a clone with an insert of 37 kb (cosmid 8.3) encompassing four functional genes (IGLV7S1, IGLV1S1, IGLV1S2 and IGLV5a), a pseudogene (VlA) and a vestigial sequence (vg1) to study in detail the positions of the restriction sites surrounding the Vl genes. We generated a high resolution restriction map, locating 31 restriction sites in 37 kb of the VB cluster, a region rich in functional Vl genes. This mapping information opens the perspective for further RFLP studies and sequencing

Helsingin matkailijakartta = Turistkarta över Helsingfors = Helsinki : Touristenkarte = Helsinki : tourist map = Helsinki : plan touristique

Kartta kääntöpuolella

Map of Helsinki-Helsingfors

Kääntöpuolella kannessa: Finland Travel Bureau Ltd Esplanade 19, Branch Office Stockmanns Department Stores

Helsingin matkailijakartta = Turistkarta över Helsingfors = Helsinki : Touristenkarte = Helsinki : tourist map = Helsinki : plan touristique

Kartta kääntöpuolella

Nieuwe paskaart voor een gedeelte van de Oost-Zee = Nouvelle carte hydrographique d'une partie de la Mer Baltique = Nya pass cort öfwer yen dehl af Oster-Siöön = The new sea map of the second of the East-Sea

Sisältää myös kartakkeet: Pastkaartje van de Noord Bodem, Suomenlahden itäosa ja Laatokka

Nieuwe paskaart voor een gedeelte van de Oost-Zee = Nouvelle carte hydrographique d'une partie de la Mer Baltique = Nya pass cort öfwer yen dehl af Oster-Siöön = The new sea map of the second of the East-Sea

Sisältää myös kartakkeet: Pastkaartje van de Noord Bodem, Suomenlahden itäosa ja Laatokka

A complete map of the southern continent

Nimeketiedot nimiönkehyksissä

A complete map of the southern continent

Nimeketiedot nimiönkehyksissä

A map of Marco Polo's voyages & travels in the 13th century through a great part of Asia, all Tartary, the East India islands & part of Africa

Nimeketiedot nimiönkehyksissä

A map of Russia

Kartta kuuluu A. E. Nordenskiöldin kokoelmaan

A map of the western part of the Roman Empire

Kartta kuuluu A. E. Nordenskiöldin kokoelmaan