Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Functional regulation of the Neurofibromatosis 2 tumor suppressor merlin

Neurofibromatosis 2 (NF2) is an autosomal dominant disorder manifested by the formation of multiple benign tumors of the nervous system. Affected individuals typically develop bilateral vestibular schwannomas which lead to deafness and balance disorders. The syndrome is caused by inactivation of the NF2 tumor suppressor gene, and mutation or loss of the NF2 product, merlin, is sufficient for tumorigenesis in both hereditary and sporadic NF2-associated tumors. Merlin belongs to the band 4.1 superfamily of cytoskeletal proteins, which also contain the related ezrin, radixin, and moesin (ERM) proteins. The ERM members provide a link between the cell cytoskeleton and membrane by connecting membrane-associated proteins to actin filaments. By stabilizing complexes in the cell cortex, the ERMs modulate morphology, growth, and migration of cells. Despite their structural homology, overlapping subcellular distribution, direct molecular association, and partial overlap of molecular interactions, merlin and ezrin exert opposite effects on cell proliferation. Merlin suppresses cell proliferation, whereas ezrin expression is linked to oncogenic activity. We hypothesized that the regions which differ between the proteins might explain merlin s specificity as a tumor suppressor. We therefore analyzed the regions, which are most diverse between merlin and ezrin; the N-terminal tail and the C-terminus. To determine the properties of the C-terminal region, we studied the two most predominant merlin isoforms together with truncation variants similar to those found in patients. We also focused on the evolutionally conserved C-terminal residues, E545-E547, that harbor disease causing mutations in its corresponding DNA sequence. In addition to inhibiting cell proliferation, merlin regulates cytoskeletal organization. The morphogenic properties of merlin may play a role in tumor suppression, since patient-derived tumor cells demonstrate cytoskeletal abnormalities. We analyzed the mechanisms of merlin-induced extension formation and determined that the C-terminal region of amino acids 538-568 is particularly important for the morphogenic activity. We also characterized the role of C-terminal merlin residues in the regulation of proliferation, phosphorylation, and intramolecular associations. In contrast to previous reports, we demonstrated that both merlin isoforms are able to suppress cell proliferation, whereas C-terminally mutated merlin constructs showed reduced growth inhibition. Phosphorylation serves as a mechanism to regulate the tumor suppressive activity of merlin. The C-terminal serine 518 is phosphorylated in response to both p21-activated kinase (PAK) and protein kinase A (PKA), which inactivates the growth inhibitory function of merlin. However, at least three differentially phosphorylated forms of the protein exist. In this study we demonstrated that also the N-terminus of merlin is phosphorylated by AGC kinases, and that both PKA and Akt phosphorylate merlin at serine 10 (S10). We evaluated the impact of this N-terminal tail phosphorylation, and showed that the phosphorylation state of S10 is an important regulator of merlin s ability to modulate cytoskeletal organization but also regulates the stability of the protein. In summary, this study describes the functional effect of merlin specific regions. We demonstrate that both S10 in the N-terminal tail and residues E545-E547 in the C-terminus are essential for merlin activity and function.

Ecology of the Asian Elephant in Southern India. II. Feeding Habits and Crop Raiding Patterns

The Asian elephant's foraging strategy in its natural habitat and in cultivation was studied in southern India during 1981-83. Though elephants consumed at least 112 plant species in the study area, about 85% of their diet consisted of only 25 species from the order Malvales and the families Leguminosae, Palmae, Cyperaceae and Gramineae. Alteration between a predominantly browse diet during the dry season with a grass diet during the early wet season was related to the seasonally changing protein content of grasses. Crop raiding, which was sporadic during the dry season, gradually increased with more area being cultivated with the onset of rains. Raiding frequency reached a peak during October-December, with some villages being raided almost every night, when finger millet (Eleusine coracana) was cultivated by most farmers. The monthly frequency of raiding was related to the seasonal movement of elephant herds and to the size of the enclave. Of their total annual food requirement, adult bull elephants derived an estimated 9.3% and family herds 1.7% in quantity from cultivated land. Cultivated cereal and millet crops provided significantly more protein, calcium and sodium than the wild grasses. Ultimately, crop raiding can be thought of as an extension of the elephant's optimal foraging strategy.

Interest in university studies : Its role and relation to other motivational variables

This dissertation empirically explored interest as a motivational force in university studies, including the role it currently plays and possible ways of enhancing this role as a student motivator. The general research questions were as follows: 1) What role does interest play in university studies? 2) What explains academic success if studying is not based on interest? 3) How do different learning environments support or impede interest-based studying? Four empirical studies addressed these questions. Study 1 (n=536) compared first-year students explanations of their disciplinary choices in three fields: veterinary medicine, humanities and law. Study 2 (n=28) focused on the role of individual interest in the humanities and veterinary medicine, fields which are very different from each other as regards their nature of studying. Study 3 (n=52) explored veterinary students motivation and study practices in relation to their study success. Study 4 (n=16) explored veterinary students interest experience in individual lectures on a daily basis. By comparing different fields and focusing on one study field in more detail, it was possible to obtain a many-sided picture of the role of interest in different learning environments. Questionnaires and quantitative methods have often been used to measure interest in academic learning. The present work is based mostly on qualitative data, and qualitative methods were applied to add to the previous research. Study 1 explored students open-ended answers, and these provided a basis for the interviews in Study 2. Study 3 explored veterinary students portfolios in a longitudinal setting. For Study 4, a diary including both qualitative and quantitative measures was designed to capture veterinary students interest experience. Qualitative content analysis was applied in all four studies, but quantitative analyses were also added. The thesis showed that university students often explain their disciplinary choices in terms of interest. Because interest is related to high-quality learning, the students seemed to have a good foundation for successful studies. However, the learning environments did not always support interest-based studying; Time-management and coping skills were found to be more important than interest in terms of study success. The results also indicated that interest is not the only motivational variable behind university studies. For example, future goals are needed in order to complete a degree. Even so, the results clearly indicated that it would be worth supporting interest-based studying both in professionally and generally oriented study fields. This support is important not only to promote high-quality learning but also meaningful studying, student well-being, and life-long learning.

Asukkaan Helsinki? : Tapaustutkimus vuorovaikutteisuudesta kaupunkisuunnittelussa

This study examines the interaction between inhabitants and urban planning. In addition to traditional methods of participation there can be seen an increasing need to find new channels and means to influence on one´s environment. Hearing of inhabitants during planning is hoped to decrease the amount of claims and this way to speed up the planning process. Discussion that emphasizes competitiveness and innovativeness in planning has brought out the role of inhabitants as selective consumers and end users. This extension of civil perspective completes the thought of participation in city planning and adds the pressure on developing the interaction and user orientation. The aim of the study is to point out the present situation of inhabitant´s participation and influencing in Helsinki. Helsinki City Planning Department opened a new information and exhibiotion hall called Laituri in 2008. Laituri provides the latest information about planning projects in Helsinki and temporary exhibitions as well as it operates as communication channel and information point for the department. In this study Laituri is examined as a case study of interaction between citizen and planner. The study is divided into two principal themes. The aim is to research action and interactivity at Laituri from the inhabitants´and planners´point of view. The qualitative study has inquiries, interview surveys and observation as research methods. Empiricial data of the study consists of three parts which complement each other: Laituri operational reseach, inquiry directed to the members of Laituri team and interviews of three experts. The aim is to find answers to questions like, does Laituri reach the citizens and will the opportunities to participate improve along Laituri. The study examines also how the local knowledge of inhabitants will come across to planners and further to planning. The study combines discussions of inhabitants´ influencing in Finnish society and science community. Cornerstones of the study are inhabitant participation, interaction and local knowledge in urban planning. The theory behind the study is communicative planning theory. In addition the theory consists of key concepts. The study introduces a concept of Inhabitant´s Helsinki, which reflects the inhabitant as customer-citizen who is an active product developer in participative urban planning. According to the research results the experts of Laituri and majority of inhabitants in Helsinki experience that the inhabitant´s possibilities to participate will improve along Laituri. However half of the citizens in Helsinki believe that local knowledge and ideas will only have minor impact on the final plan. According to city dwellers the present practise used by Helsinki City Planning Department supports only partially adequate interaction. The experts of Laituri experience that the role of Laituri is first of all forum of communication and discussion channel instead of effective local data collector. Based on the results the study introduces a model of inhabitant´s participation field. According to the model Laituri can be seen as phenomenom in Helsinki urban planning which has the elements of network municipality. The planner is more like diplomatic trend-setter and visionary. The inhabitant of Helsinki is an expert in city living and participative producer of local knowledge. Participation methods are increasingly segmented and tailored in every plan and project. The study argues that Inhabitant´s Helsinki is a pluralistic milieu in constant pressure for change. Therefore reaching the everyday life experiencies of inhabintants should be at higher degree in Helsinki City Planning Department´s operations.

Metastable extension of the fluorite phase field in Y2O3---ZrO2 and its effect on grain growth

Pure Y2O3 and Y2O3---ZrO2 solid solutions have been prepared by melt atomization and by pyrolysis of nitrate solutions. Extended solubility is readily achieved in both techniques for the entire composition range investigated: melts with 0–30% ZrO2 and precursors with 0–50% ZrO2. However, solidification of under cooled droplets yields almost exclusively single phase powders with the structure of cubic yttria (D53). In contrast, the pyrolysis route leads to a sequence of metastable microstructures beginning with a nanocrystalline disordered fluorite-based (C1) solid solution. Further heating leads to the evolution of much larger (micron size) flake crystals with a {001} texture, concurrent with partial ordering of the oxygen ions to the sites occupied in the D53 structure. The driving force for ordering and the rate of grain growth decrease with increasing ZrO2 addition. Abrupt heating to high temperatures or electron irradiation can induce ordering without substantial grain growth. There is no significant reduction in porosity during the recrystallization, which with the other observations suggests that grain growth is driven by the free energy available for the ordering transformation from fluorite to the yttria structure. This route offers opportunities for single crystal thin film development at relatively low processing temperatures.

Metastable extension of the fluorite phase field in Y2O3---ZrO2 and its effect on grain growth

Pure Y2O3 and Y2O3-ZrO2 solid solutions have been prepared by melt atomization and by pyrolysis of nitrate solutions. Extended solubility is readily achieved in both techniques for the entire composition range investigated: melts with 0-30% ZrO2 and precursors with 0-50% ZrO2. However, solidification of under cooled droplets yields almost exclusively single phase powders with the structure of cubic yttria (D5(3)). In contrast, the pyrolysis route leads to a sequence of metastable microstructures beginning with a nanocrystalline disordered fluorite-based (C1) solid solution. Further heating leads to the evolution of much larger (micron size) flake crystals with a {001} texture, concurrent with partial ordering of the oxygen ions to the sites occupied in the D5(3) structure. The driving force for ordering and the rate of grain growth decrease with increasing ZrO2 addition. Abrupt heating to high temperatures or electron irradiation can induce ordering without substantial grain growth. There is no significant reduction in porosity during the recrystallization, which with the other observations suggests that grain growth is driven by the free energy available for the ordering transformation from fluorite to the yttria structure. This route offers opportunities for single crystal thin film development at relatively low processing temperatures.

Probabilistic extension to realistic abductive reasoning model

In this paper, we give a method for probabilistic assignment to the Realistic Abductive Reasoning Model, The knowledge is assumed to be represented in the form of causal chaining, namely, hyper-bipartite network. Hyper-bipartite network is the most generalized form of knowledge representation for which, so far, there has been no way of assigning probability to the explanations, First, the inference mechanism using realistic abductive reasoning model is briefly described and then probability is assigned to each of the explanations so as to pick up the explanations in the decreasing order of plausibility.

Stability of spatially developing boundary layers in pressure gradients

A new formulation of the stability of boundary-layer flows in pressure gradients is presented, taking into account the spatial development of the flow and utilizing a special coordinate transformation. The formulation assumes that disturbance wavelength and eigenfunction vary downstream no more rapidly than the boundary-layer thickness, and includes all terms nominally of order R(-1) in the boundary-layer Reynolds number R. In Blasius flow, the present approach is consistent with that of Bertolotti et al. (1992) to O(R(-1)) but simpler (i.e. has fewer terms), and may best be seen as providing a parametric differential equation which can be solved without having to march in space. The computed neutral boundaries depend strongly on distance from the surface, but the one corresponding to the inner maximum of the streamwise velocity perturbation happens to be close to the parallel flow (Orr-Sommerfeld) boundary. For this quantity, solutions for the Falkner-Skan flows show the effects of spatial growth to be striking only in the presence of strong adverse pressure gradients. As a rational analysis to O(R(-1)) demands inclusion of higher-order corrections on the mean flow, an illustrative calculation of one such correction, due to the displacement effect of the boundary layer, is made, and shown to have a significant destabilizing influence on the stability boundary in strong adverse pressure gradients. The effect of non-parallelism on the growth of relatively high frequencies can be significant at low Reynolds numbers, but is marginal in other cases. As an extension of the present approach, a method of dealing with non-similar flows is also presented and illustrated. However, inherent in the transformation underlying the present approach is a lower-order non-parallel theory, which is obtained by dropping all terms of nominal order R(-1) except those required for obtaining the lowest-order solution in the critical and wall layers. It is shown that a reduced Orr-Sommerfeld equation (in transformed coordinates) already contains the major effects of non-parallelism.

The absolute orientation of a molecule in space: Extension of the 'CIP' system

A scheme for denoting the absolute spatial orientation of molecules and molecular fragments is presented; this is based on three angular deviations - one for each spatial dimension - with respect to a reference orientation, which is itself defined with the help of certain features of the Cahn-Ingold-Prelog stereochemical notation. The new scheme helps in reconstructing the three-dimensional characteristics of molecules from purely verbal descriptors, and may thus find application in various information storage and retrieval processes (e.,-. encrypting holograms, etc.).

On the dynamics of activation of mammalian X chromosomes

We have investigated a mathematical model of the process of activation of the X chromosomes in eutherian mammals. The model assumes that the activation is brought about over some definite time interval T by the complete saturation of N receptor sites on an X chromosome by M activating molecules (or multiples of M). The probability λ of a first hit on the receptor site is considered to be very much lower than that of subsequent hits; that is, we assume strong co-operative binding. Assuming further that an incomplete saturation of receptor sites is malfunctional, we can show that for proper activation of X chromosomes in normal diploid males and females, we must have λMT ≥ 3 and 0·96 ≤ N/M ≤ 1. An extension of this analysis for the triploid cases shows that under these conditions, we cannot explain the activation of two X's if the number of activating molecules is fixed at M. This suggests that there must be two classes of triploid embryos differing from each other in a step-wise manner in the number of activating molecules. In other words, triploids with two active X chromosomes would require 2M activating molecules as opposed to M molecules in triploids with a single active X. This interpretation of the two classes of triploids would be consistent with differing imprinting histories of the parental contributions to the triploid zygote.

Influence of matrix characteristics on fracture toughness of high volume fraction Al2O3/Al–AlN composites

The role of matrix microstructure on the fracture of Al-alloy composites with 60 vol% alumina particulates was studied. The matrix composition and microstructure were systematically varied by changing the infiltration temperature and heat treatment. Characterization was carried out by a combination of metallography, hardness measurements, and fracture studies conducted on compact tension specimens to study the fracture toughness and crack growth in the composites. The composites showed a rise in crack resistance with crack extension (R curves) due to bridges of intact matrix ligaments formed in the crack wake. The steady-state or plateau toughness reached upon stable crack growth was observed to be more sensitive to the process temperature rather than to the heat treatment. Fracture in the composites was predominantly by particle fracture, extensive deformation, and void nucleation in the matrix. Void nucleation occurred in the matrix in the as-solutionized and peak-aged conditions and preferentially near the interface in the underaged and overaged conditions. Micromechanical models based on crack bridging by intact ductile ligaments were modified by a plastic constraint factor from estimates of the plastic zone formed under indentations, and are shown to be adequate in predicting the steady-state toughness of the composite.