Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Karnaugh map analysis and synthesis of threshold functions

A unate function can easily be identified on a Karnaugh map from the well-known property that it cons ist s only ofess en ti al prime implicante which intersect at a common implicant. The additional property that the plot of a unate function F(x, ... XII) on a Karnaugh map should possess in order that F may also be Ivrealizable (n';:; 6) has been found. It has been sh own that the I- realizability of a unate function F corresponds to the ' compac tness' of the plot of F. No resort to tho inequalities is made, and no pre-processing such as positivizing and ordering of the given function is required.

A Note on Easily Testable Realizations for Logic Functions

It is shown that at most, n + 3 tests are required to detect any single stuck-at fault in an AND gate or a single faulty EXCLUSIVE OR (EOR) gate in a Reed-Muller canonical form realization of a switching function.

Pyrrolidine ring conformations in prolyl peptides from 13C spin-lattice relaxation times

A method was developed in the framework of a bistable jump model to obtain the pyrrolidine ring conformations in proline peptides from 13C spin-lattice relaxation times. Equations are presented expressing the ring torsions in terms of the 13C spin-lattice relaxation times of the ring carbons. This method was applied to 26 pyrrolidine ring systems and acceptable conformations were obtained.

ORP1L, a new Rab7 effector and regulator of late endosome functions

Oxysterol binding protein (OSBP) homologues have been found in eukaryotic organisms ranging from yeast to humans. These evolutionary conserved proteins have in common the presence of an OSBP-related domain (ORD) which contains the fully conserved EQVSHHPP sequence motif. The ORD forms a barrel structure that binds sterols in its interior. Other domains and sequence elements found in OSBP-homologues include pleckstrin homology domains, ankyrin repeats and two phenylalanines in an acidic tract (FFAT) motifs, which target the proteins to distinct subcellular compartments. OSBP homologues have been implicated in a wide range of intracellular processes, including vesicle trafficking, lipid metabolism and cell signaling, but little is known about the functional mechanisms of these proteins. The human family of OSBP homologues consists of twelve OSBP-related proteins (ORP). This thesis work is focused on one of the family members, ORP1, of which two variants were found to be expressed tissue-specifically in humans. The shorter variant, ORP1S contains an ORD only. The N-terminally extended variant, ORP1L, comprises a pleckstrin homology domain and three ankyrin repeats in addition to the ORD. The two ORP1 variants differ in intracellular localization. ORP1S is cytosolic, while the ankyrin repeat region of ORP1L targets the protein to late endosomes/lysosomes. This part of ORP1L also has profound effects on late endosomal morphology, inducing perinuclear clustering of late endosomes. A central aim of this study was to identify molecular interactions of ORP1L on late endosomes. The morphological changes of late endosomes induced by overexpressed ORP1L implies involvement of small Rab GTPases, regulators of organelle motility, tethering, docking and/or fusion, in generation of the phenotype. A direct interaction was demonstrated between ORP1L and active Rab7. ORP1L prolongs the active state of Rab7 by stabilizing its GTP-bound form. The clustering of late endosomes/lysosomes was also shown to be linked to the minus end-directed microtubule-based dynein-dynactin motor complex through the ankyrin repeat region of ORP1L. ORP1L, Rab7 and the Rab7-interacting lysosomal protein (RILP) were found to be part of the same effector complex recruiting the dynein-dynactin complex to late endosomes, thereby promoting minus end-directed movement. The proteins were found to be physically close to each other on late endosomes and RILP was found to stabilize the ORP1L-Rab7 interaction. It is possible that ORP1L and RILP bind to each other through their C-terminal and N-terminal regions, respectively, when they are bridged by Rab7. With the results of this study we have been able to place a member of the uncharacterized OSBP-family, ORP1L, in the endocytic pathway, where it regulates motility and possibly fusion of late endosomes through interaction with the small GTPase Rab7.

A Note on Minimal Reed-Muller Canonical Forms of Switching Functions

A nonexhaustive procedure for obtaining minimal Reed-Muller canonical (RMC) forms of switching functions is presented. This procedure is a modification of a procedure presented earlier in the literature and enables derivation of an upper bound on the number of RMC forms to be derived to choose a minimal one. It is shown that the task of obtaining minimal RMC forms is simplified in the case of symmetric functions and self-dual functions.

The biological functions of mouse twinfilin isoforms

The actin cytoskeleton is essential for many cellular processes, including motility, morphogenesis, endocytosis and signal transduction. Actin can exist in monomeric (G-actin) or filamentous (F-actin) form. Actin filaments are considered to be the functional form of actin, generating the protrusive forces characteristic for the actin cytoskeleton. The structure and dynamics of the actin filament and monomer pools are regulated by a large number of actin-binding proteins in eukaryotic cells. Twinfilin is an evolutionarily conserved small actin monomer binding protein. Twinfilin is composed of two ADF/cofilin-like domains, separated by a short linker and followed by a C-terminal tail. Twinfilin forms a stable, high affinity complex with ADP-G-actin, inhibits the nucleotide exchange on actin monomers, and prevents their assembly into filament ends. Twinfilin was originally identified from yeast and has since then been found from all organisms studied except plants. Not much was known about the role of twinfilin in the actin dynamics in mammalian cells before this study. We set out to unravel the mysteries still covering twinfilins functions using biochemistry, cell biology, and genetics. We identified and characterized two mouse isoforms for the previously identified mouse twinfilin-1. The new isoforms, twinfilin-2a and -2b, are generated from the same gene through alternative promoter usage. The three isoforms have distinctive expression patterns, but are similar biochemically. Twinfilin-1 is the major isoform during development and is expressed in high levels in almost all tissues examined. Twinfilin-2a is also expressed almost ubiquitously, but at lower levels. Twinfilin-2b turned out to be a muscle-specific isoform, with very high expression in heart and skeletal muscle. It seems all mouse tissues express at least two twinfilin isoforms, indicating that twinfilins are important regulators of actin dynamics in all cell and tissue types. A knockout mouse line was generated for twinfilin-2a. The mice homozygous for this knockout were viable and developed normally, indicating that twinfilin-2a is dispensable for mouse development. However, it is important to note that twinfilin-2a shows similar expression pattern to twinfilin-1, suggesting that these proteins play redundant roles in mice. All mouse isoforms were shown to be able to sequester actin filaments and have higher affinity for ADP-G-actin than ATP-G-actin. They are also able to directly interact with heterodimeric capping protein and PI(4,5)P2 similar to yeast twinfilin. In this study we also uncovered a novel function for mouse twinfilins; capping actin filament barbed ends. All mouse twinfilin isoforms were shown to possess this function, while yeast and Drosophila twinfilin were not able to cap filament barbed ends. Twinfilins localize to the cytoplasm but also to actin-rich regions in mammalian cells. The subcellular localizations of the isoforms are regulated differently, indicating that even though twinfilins biochemical functions in vitro are very similar, in vivo they can play different roles through different regulatory pathways. Together, this study show that twinfilins regulate actin filament assembly both by sequestering actin monomers and by capping filament barbed ends, and that mammals have three biochemically similar twinfilin isoforms with partially overlapping expression patterns.

Large Low-Frequency Fluctuations in the Velocity of a Driven Vortex Lattice in a Single Crystal of 2H-NbSe2 Superconductor

The driven state of a well-ordered flux line lattice in a single crystal of 2H-NbSe2 in the time domain has revealed the presence of substantial fluctuations in velocity, with large and distinct time periods (similar to seconds). A superposition of a periodic drive in the driven vortex lattice causes distinct changes in these fluctuations. We propose that prior to the onset of the peak effect there exists a heretofore unexplored regime of coherent dynamics, with unexpected behavior in velocity fluctuations.

Origin of activation of Lattice Oxygen and Synergistic Interaction in Bimetal-Ionic Ce0.89Fe0.1Pd0.01O2-delta Catalyst

Flourite-type nanocrystalline Ce0.9Fe0.1O2-delta and Ce0.89Fe0.1Pd0.01O2-delta solid solutions have been synthesized by solution combustion method,'.which show higher oxygen storage/release property (OSC) compared to CeO2 and Ce0.8Zr0.2O2. Temperature programmed reduction an XPS study reveal that the presence of Pd ion in Ce0.9Fe0.1O2-delta facilitates complete reduction of Fe3+ to Fe2+ state and partial reduction of Ce4+ to Ce3+ state at.temperatures as low as 105 degrees C compared to 400 degrees C for monometal-ionic Ce0.9Fe0.1O2-delta. Fe3+ ion is reduced to Fe2+ and not to Feo due to favorable redox potential for Ce4+ + Fe2+ -> Ce3+ + Fe3+ reaction. Using first-principles density functional theory calculation we determine M-O (M = Pd, Fe, Ce) bond lengths, and find that bond lengths vary from shorter (2.16 angstrom) to longer (2.9 angstrom) bond distances compared to mean Ce-O bond distance of 2.34 angstrom. for CeO2. Using these results in bond valence analysis, we show that oxygen with bond valences as low as -1.55 are created, leading to activation of lattice oxygen in the bimetal ionic catalyst. Temperatures of CO oxidation and NO reduction by CO/H-2 are lower with the bimetalionic Ce0.89Fe0.1Pd0.01O2-delta catalyst compared to monometal-ionic Ce0.9Fe0.1O2-delta and Ce0.99Pd0.01O2-delta catalysts. From XPS studies of Pd impregnated on CeO2 and Fe2O3 oxides, we show that the synergism leading to low temperature activation of lattice oxygen in bimetal-ionic catalyst Ce0.89Fe0.1Pd0.01O2-delta is due to low-temperature reduction of Pd2+ to Pd-0, followed by Pd-0 + 2Fe(3+) -> Pd2+ + 2Fe(2+), Pd-0 + 2Ce(4+) -> Pd2+ + 2Ce(3+) redox reaction.

Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.

Automata and logics over finitely varying functions

We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or “signals”. In particular, we introduce a natural class of automata for generating finitely varying functions called View the MathML source’s, and show that it coincides in terms of language definability with a natural monadic second-order logic interpreted over finitely varying functions Rabinovich (2002) [15]. We also identify a “counter-free” subclass of View the MathML source’s which characterise the first-order definable languages of finitely varying functions. Our proofs mainly factor through the classical results for word languages. These results have applications in automata characterisations for continuously interpreted real-time logics like Metric Temporal Logic (MTL) Chevalier et al. (2006, 2007) [6] and [7].