Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players'' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented.

Genetic studies of the PRP17 gene of Saccharomyces cerevisiae: a domain essential for function maps to a nonconserved region of the protein

The PRP17 gene product is required for the second step of pre-mRNA splicing reactions. The C-terminal half of this protein bears four repeat units with homology to the beta transducin repeat. Missense mutations in three temperature-sensitive prp17 mutants map to a region in the N-terminal half of the protein. We have generated, in vitro, 11 missense alleles at the beta transducin repeat units and find that only one affects function in vivo. A phenotypically silent missense allele at the fourth repeat unit enhances the slow-growing phenotype conferred by an allele at the third repeat, suggesting an interaction between these domains. Although many missense mutations in highly conserved amino acids lack phenotypic effects, deletion analysis suggests an essential role for these units. Only mutations in the N-terminal nonconserved domain of PRP17 are synthetically lethal in combination with mutations in PRP16 and PRP18, two other gene products required for the second splicing reaction. A mutually allele-specific interaction between Prp17 and snr7, with mutations in U5 snRNA, was observed. We therefore suggest that the functional region of Prp17p that interacts with Prp18p, Prp16p, and U5 snRNA is the N terminal region of the protein.

Subspace intersection method of high-resolution bearing estimation in shallow ocean using acoustic vector sensors

The subspace intersection method (SIM) provides unbiased bearing estimates of multiple acoustic sources in a range-independent shallow ocean using a one-dimensional search without prior knowledge of source ranges and depths. The original formulation of this method is based on deployment of a horizontal linear array of hydrophones which measure acoustic pressure. In this paper, we extend SIM to an array of acoustic vector sensors which measure pressure as well as all components of particle velocity. Use of vector sensors reduces the minimum number of sensors required by a factor of 4, and also eliminates the constraint that the intersensor spacing should not exceed half wavelength. The additional information provided by the vector sensors leads to performance enhancement in the form of lower estimation error and higher resolution.

Indian Ocean response to anomalous conditions in 2006

[1] The equatorial Indian Ocean (EIO) exhibited anomalous conditions characteristic of an Indian Ocean dipole (IOD) during 2006. The eastern EIO had cold sea surface temperature anomalies (SSTA), lower sea level, shallow thermocline and higher chlorophyll than normal. The anomalies in the east, restricted to the south of the equator, were highest off Sumatra. The western pole of the IOD was marked by warm SSTA and deeper thermocline with maxima on either side of the equator. An ocean general circulation model of the Indian Ocean forced by QuikSCAT winds reproduces the IOD of 2006 remarkably well. The switch over to cooling in the east and warming in the west happened during May and July respectively. In the east, airsea heat flux initiated cold SSTA in the model which were sustained later by oceanic processes. In the west, surface heat fluxes and horizontal advection caused warm SSTA and contribution by the latter decreased after August. Citation: Vinayachandran, P. N., J. Kurian, and C. P. Neema (2007), Indian Ocean response to anomalous conditions in 2006, Geophys. Res. Lett., 34, L15602, doi:10.1029/2007GL030194.

Indian Ocean response to anomalous conditions in 2006

The equatorial Indian Ocean (EIO) exhibited anomalous conditions characteristic of an Indian Ocean dipole (IOD) during 2006. The eastern EIO had cold sea surface temperature anomalies (SSTA), lower sea level, shallow thermocline and higher chlorophyll than normal. The anomalies in the east, restricted to the south of the equator, were highest off Sumatra. The western pole of the IOD was marked by warm SSTA and deeper thermocline with maxima on either side of the equator. An ocean general circulation model of the Indian Ocean forced by QuikSCAT winds reproduces the IOD of 2006 remarkably well. The switch over to cooling in the east and warming in the west happened during May and July respectively. In the east, air-sea heat flux initiated cold SSTA in the model which were sustained later by oceanic processes. In the west, surface heat fluxes and horizontal advection caused warm SSTA and contribution by the latter decreased after August.

Mechanisms of formation of the Arabian Sea mini warm pool in a high-resolution Ocean General Circulation Model

An Ocean General Circulation Model of the Indian Ocean with high horizontal (0.25 degrees x 0.25 degrees) and vertical (40 levels) resolutions is used to study the dynamics and thermodynamics of the Arabian Sea mini warm pool (ASMWP), the warmest region in the northern Indian Ocean during January-April. The model simulates the seasonal cycle of temperature, salinity and currents as well as the winter time temperature inversions in the southeastern Arabian Sea (SEAS) quite realistically with climatological forcing. An experiment which maintained uniform salinity of 35 psu over the entire model domain reproduces the ASMWP similar to the control run with realistic salinity and this is contrary to the existing theories that stratification caused by the intrusion of low-salinity water from the Bay of Bengal into the SEAS is crucial for the formation of ASMWP. The contribution from temperature inversions to the warming of the SEAS is found to be negligible. Experiments with modified atmospheric forcing over the SEAS show that the low latent heat loss over the SEAS compared to the surroundings, resulting from the low winds due to the orographic effect of Western Ghats, plays an important role in setting up the sea surface temperature (SST) distribution over the SEAS during November March. During March-May, the SEAS responds quickly to the air-sea fluxes and the peak SST during April-May is independent of the SST evolution during previous months. The SEAS behaves as a low wind, heat-dominated regime during November-May and, therefore, the formation and maintenance of the ASMWP is not dependent on the near surface stratification.

On the roles of the northeast cold surge, the Borneo vortex, the Madden-Julian Oscillation, and the Indian Ocean Dipole during the extreme 2006/2007 flood in southern Peninsular Malaysia

The mid-December 2006 to late January 2007 flood in southern Peninsular Malaysia was the worst flood in a century and was caused by three extreme precipitation episodes. These extreme precipitation events were mainly associated with strong northeasterly winds over the South China Sea. In all cases, the northeasterlies penetrated anomalously far south and followed almost a straight trajectory. The elevated terrain over Sumatra and southern Peninsular Malaysia caused low-level convergence. The strong easterly winds near Java associated with the Rossby wave-type response to Madden-Julian Oscillation (MJO) inhibited the counter-clockwise turning of the northeasterlies and the formation of the Borneo vortex, which, in turn, enhanced the low-level convergence over the region. The abrupt termination of the Indian Ocean Dipole (IOD) in December 2006 played a secondary role as warmer equatorial Indian Ocean helped in the MJO formation.

Semi-supervised learning of WLAN radio maps

In this thesis a manifold learning method is applied to the problem of WLAN positioning and automatic radio map creation. Due to the nature of WLAN signal strength measurements, a signal map created from raw measurements results in non-linear distance relations between measurement points. These signal strength vectors reside in a high-dimensioned coordinate system. With the help of the so called Isomap-algorithm the dimensionality of this map can be reduced, and thus more easily processed. By embedding position-labeled strategic key points, we can automatically adjust the mapping to match the surveyed environment. The environment is thus learned in a semi-supervised way; gathering training points and embedding them in a two-dimensional manifold gives us a rough mapping of the measured environment. After a calibration phase, where the labeled key points in the training data are used to associate coordinates in the manifold representation with geographical locations, we can perform positioning using the adjusted map. This can be achieved through a traditional supervised learning process, which in our case is a simple nearest neighbors matching of a sampled signal strength vector. We deployed this system in two locations in the Kumpula campus in Helsinki, Finland. Results indicate that positioning based on the learned radio map can achieve good accuracy, especially in hallways or other areas in the environment where the WLAN signal is constrained by obstacles such as walls.

Future chemistry teachers use of knowledge dimensions and high-order cognitive skills in pre-laboratory concept maps

This poster describes a pilot case study, which aim is to study how future chemistry teachers use knowledge dimensions and high-order cognitive skills (HOCS) in their pre-laboratory concept maps to support chemistry laboratory work. The research data consisted of 168 pre-laboratory concept maps that 29 students constructed as a part of their chemistry laboratory studies. Concept maps were analyzed by using a theory based content analysis through Anderson & Krathwohls' learning taxonomy (2001). This study implicates that novice concept mapper students use all knowledge dimensions and applying, analyzing and evaluating HOCS to support the pre-laboratory work.

Surface freshwater from Bay of Bengal runoff and Indonesian Throughflow in the Tropical Indian Ocean

According to recent estimates, the annual total continental runoff into the Bay of Bengal (BoB) is about 2950 km 3, which is more than half that into the entire tropical Indian Ocean (IO). Here we use climatological observations to trace the seasonal pathways of near surface freshwater from BoB runoff and Indonesian Throughflow (ITF) by removing the net contribution from precipitation minus evaporation. North of 20 degrees S, the amount of freshwater from BoB runoff and ITF changes with season in a manner consistent with surface currents from drifters. BoB runoff reaches remote regions of the Arabian Sea; it also crosses the equator in the east to join the ITF. This freshwater subsequently flows west across the southern tropical IO in the South Equatorial Current.

Enhancement of workability in AZ31 alloy-processing maps: Part I,castmaterial

Processing maps developed on the basis of the Dynamic Materials Model provide valuable information that might help the metal working industry in solving problems related to workability and microstructural control in commercial alloys. In this research, the processing maps for an as-cast AZ31 magnesium alloy are presented. The results are validated via microstructural observations, clearly delineating safe and unsafe regimes for further process design of this alloy.

Narrowband Detection of Acoustic Source in Shallow Ocean using Vector Sensor Array

The problem of narrowband CFAR (constant false alarm rate) detection of an acoustic source at an unknown location in a range-independent shallow ocean is considered. If a target is present, the received signal vector at an array of N sensors belongs to an M-dimensional subspace if N exceeds the number of propagating modes M in the ocean. A subspace detection method which utilises the knowledge of the signal subspace to enhance the detector performance is presented in thisMpaper. It is shown that, for a given number of sensors N, the performance of a detector using a vector sensor array is significantly better than that using a scalar sensor array. If a target is detected, the detector using a vector sensor array also provides a concurrent coarse estimate of the bearing of the target.