On the eigenvalues and eigenfunctions of some integral operators

Some properties of the eigenvalues of the integral operator Kgt defined as Kτf(x) = ∫0τK(x − y) f (y) dy were studied by [1.], 554–566), with some assumptions on the kernel K(x). In this paper the eigenfunctions of the operator Kτ are shown to be continuous functions of τ under certain circumstances. Also, the results of Vittal Rao and the continuity of eigenfunctions are shown to hold for a larger class of kernels.

A Touch of Red : Archaeological and Ethnographic Approaches to Interpreting Finnish Rock Paintings

Approximately 125 prehistoric rock paintings have been found in the modern territory of Finland. The paintings were done with red ochre and are almost without exception located on steep lakeshore cliffs associated with ancient water routes. Most of the sites are found in the central and eastern parts of the country, especially on the shores of Lakes Päijänne and Saimaa. Using shore displacement chronology, the art has been dated to ca. 5000 – 1500 BC. It was thus created mainly during the Stone Age and can be associated with the so-called ‘Comb Ware’ cultures of the Subneolithic period. The range of motifs is rather limited, consisting mainly of schematic depictions of stick-figure humans, elks, boats, handprints and geometric signs. Few paintings include any evidence of narrative scenes, making their interpretation a rather difficult task. In Finnish archaeological literature, the paintings have traditionally been associated with ’sympathetic’ hunting magic, or the belief that the ritual shooting of the painted animals would increase hunting luck. Some writers have also suggested totemistic and shamanistic readings of the art. This dissertation is a critical review of the interpretations offered of Finnish rock art and an exploration of the potentials of archaeological and ethnographic research in increasing our knowledge of its meaning. Methods used include ’formal’ approaches such as archaeological excavation, landscape analysis and the application of neuropsychological research to the study of rock art, as well as ethnographically ’informed’ approaches that make use of Saami and Baltic Finnish ethnohistorical sources in interpretation. In conclusion, it is argued that although North European hunter-gatherer rock art is often thought to lie beyond the reach of ‘informed’ knowledge, the exceptional continuity of prehistoric settlement in Finland validates the informed approach in the interpretation of Finnish rock paintings. The art can be confidently associated with shamanism of the kind still practiced by the Saami of Northern Fennoscandia in the historical period. Evidence of similar shamanistic practices, concepts and cosmology are also found in traditional Finnish-Karelian epic poetry. Previous readings of the art based on ‘hunting magic’ and totemism are rejected. Most of the paintings appear to depict experiences of falling into a trance, of shamanic metamorphosis and trance journeys, and of ‘spirit helper’ beings comparable to those employed by the Saami shaman (noaidi). As demonstrated by the results of an excavation at the rock painting of Valkeisaari, the painted cliffs themselves find a close parallel in the Saami cult of the 'sieidi', or sacred cliffs and boulders worshipped as expressing a supernatural power. Like the Saami, the prehistoric inhabitants of the Finnish Lake Region seem to have believed that certain cliffs were ’alive’ and inhabited by the spirit helpers of the shaman. The rock paintings can thus be associated with shamanic vision quests, and the making of ‘art’ with an effort to socialize the other members of the community, especially the ritual specialists, with trance visions. However, the paintings were not merely to be looked at. The red ochre handprints pressed on images of elks, as well as the fact that many paintings appear ’smeared’, indicate that they were also to be touched – perhaps in order to tap into the supernatural potency inherent in the cliff and in the paintings of spirit animals.

Child temperament and parental personality: continuity and transactional change

Studying the continuity and underlying mechanisms of temperament change from early childhood through adulthood is clinically and theoretically relevant. Knowledge of the continuity and change of temperament from infancy onwards, especially as perceived by both parents is, however, still scanty. Only in recent years have researchers become aware that personality, long considered as stable in adulthood, may also change. Further, studies that focus on the transactional change of child temperament and parental personality also seem to be lacking, as are studies focusing on transactions between child temperament and more transient parental characteristics, like parental stress. Therefore, this longitudinal study examined the degree of continuity of temperament over five years from the infant s age of six months to the child s age of five and a half years, as perceived by both biological parents, and also investigated the bidirectional effects between child temperament and parents personality traits and overall stress experienced during that time. First, moderate to high levels of continuity of temperament from infancy to middle childhood were shown, depicting the developmental links between affectively positive and well-adjusted temperament characteristics, and between characteristics of early and later negative affectivity. The continuity of temperament was quantitatively and qualitatively similar in both parents ratings. The findings also demonstrate that infant and childhood temperament characteristics cluster to form stable temperament types that resemble personality types shown in child and adult personality studies. Second, the parental personality traits of extraversion and neuroticism were shown to be highly stable over five years, but evidence of change in relation to parents views of their child s temperament was also shown: an infant s higher positive affectivity predicted an increase in parental extraversion, while the infant s higher activity level predicted a decrease in parental neuroticism over five years. Furthermore, initially higher parental extraversion predicted higher ratings of the child s effortful control, while initially higher parental neuroticism predicted the child s higher negative affectivity. In terms of changes in parental stress, the infant s higher activity level predicted a decrease in maternal overall stress, while initially higher maternal stress predicted a higher level of child negative affectivity in middle childhood. Together, the results demonstrate that the mother- and father-rated temperament of the child shows continuity during the early years of life, but also support the view that the development of these characteristics is sensitive to important contextual factors such as parental personality and overall stress. While parental personality and experienced stress were shown to have an effect on the child s developing temperament, the reverse was also true: the parents own personality traits and perceived stress seemed to be highly stable, but also susceptible to their experiences of their child s temperament.

Consonance in urban form: The architectural dimension of urban morphology

Consonance in urban form is contingent on the continuity of the fine grain architectural features that are imbued in the commodity of the evolved historic urban fabric. A city's past can be viewed therefore as a repository of urban form characteristics from which concise architectural responses can result in a congruent urban landscape. This thesis proposes new methods to evaluate the interplay of architectural elements that can be traced throughout the lifespan of the particular evolving urban areas under scrutiny, and postulates a theory of how the mapping of historical urban form can correlate with deriving parameters for new buildings.