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.

Plan poselka "Poltavt︠s︡y"

Digital image

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.

A model for mammalian male determination based on a passive Y chromosome

A model is suggested for mammalian male determination based on interactions postulated to occur among an autosomal repressor gene, an X-linked male-determining gene termed Tdx, and multiple copies of certain DNA sequences on the Y chromosome that do not code for any protein. The repressor, synthesised in limited amounts, has higher affinity for the Y-linked sequences than for Tdx and its affinity for Tdx is greater than that of RNA polymerase. In XY cells the Y effectively binds all available repressor, permitting transcription of Tdx to occur. In XX cells, since competition from the Y-linked high-affinity sequences is absent, the repressor binds to Tdx and prevents transcription. As a result of this competition between Tdx and the Y-linked high-affinity sites for limiting concentrations of the autosomal repressor, the product of the Tdx gene (TDX) is synthesized in the male but not in the female. It is suggested that in determination of the male sex, the role of the Y chromosome is to serve as a sink for the Tdx repressor. The proposed interactions provide a plausible explanation for the genetic properties of several anomalies of sexual development in mouse, man, and other mammals. The model suggests that the postulated multiple, highaffinity sequences on the Y chromosome of the mouse are included among the DNA sequences referred to as the Sxr-Bkm sequences.

Zapys zemelʹnyĭ Na pravo korystovanni︠a︡ zemli︠u︡, shcho znakhoditʹsi︠a︡ v Odeskoï guberni Peryletravenʹsʹkyĭ okruzi Kantakuzenʹsʹy raʹoni pid nazvoi︠u︡ Trudovyshyĭ artilʹ Slava

Digital image

Zapys zemelʹnyĭ Na pravo korystovanni︠a︡ zemli︠u︡, shcho znakhoditʹsi︠a︡ v Odeskoï guberni Peryletravenʹsʹkyĭ okruzi Kantakuzenʹsʹy raʹoni pid nazvoi︠u︡ Trudovyshyĭ artilʹ Slava

Digital image

Sonochemical Acceleration of Conversion of 2-Alkoxytetrahydrofurans to y-Butyrolactones Synthesis of (±)-Quercus Lactone-A

Effect of sonochemical irradiation on the conversion of 2-alkoxytetrahydrofurans to γ-butyro-1actores by Jones reagent, and its extension to the highly stereoselective synthesis of quercus lactone a, is reported.

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.

A comparative molecular dynamics study of diffusion of n-decane and 3-methyl pentane in Y zeolite

Molecular dynamics simulations are reported on the structure and dynamics of n-decane and 3-methylpentane in zeolite NaY. We have calculated several properties such as the center of mass-center of mass rdf, the end-end distance distribution, bond angle distribution and dihedral angle distribution. We have also analysed trajectory to obtain diffusivity and velocity autocorrelation function (VACF). Surprisingly, the diffusivity of 3-methylpentane which is having larger cross-section perpendicular to the long molecular axis is higher than n-decane at 300 K. Activation energies have been obtained from simulations performed at 200 K, 300 K, 350 K, 400 K and 450 K in the NVE ensemble. These results can be understood in terms of the previously known levitation effect. Arrhenious plot has higher value of slope for n-decane (5 center dot 9 kJ/mol) than 3-methylpentane (3 center dot 7 kJ/mol) in agreement with the prediction of levitation effect.

Recent progress on synthesis, multi-scale structure, and properties of Y-Si-O oxides

Yttrium silicates (Y-Si-O oxides), including Y2Si2O7, Y2SiO5, and Y4·67(SiO4)3O apatite, have attracted wide attentions from material scientists and engineers, because of their extensive polymorphisms and important roles as grain boundary phases in improving the high-temperature mechanical/thermal properties of Si3N4and SiC ceramics. Recent interest in these materials has been renewed by their potential applications as high-temperature structural ceramics, oxidation protective coatings, and environmental barrier coatings (EBCs). The salient properties of Y-Si-O oxides are strongly related to their unique chemical bonds and microstructure features. An in-depth understanding on the synthesis - multi-scale structure-property relationships of the Y-Si-O oxides will shine a light on their performance and potential applications. In this review, recent progress of the synthesis, multi-scale structures, and properties of the Y-Si-O oxides are summarised. First, various methods for the synthesis of Y-Si-O ceramics in the forms of powders, bulks, and thin films/coatings are reviewed. Then, the crystal structures, chemical bonds, and atomic microstructures of the polymorphs in the Y-Si-O system are summarised. The third section focuses on the properties of Y-Si-O oxides, involving the mechanical, thermal, dielectric, and tribological properties, their environmental stability, and their structure-property relationships. The outlook for potential applications of Y-Si-O oxides is also highlighted.

A novel ionic diffusion strategy to fabricate high-performance anode-supported solid oxide fuel cells (SOFCs) with proton-conducting Y-doped BaZrO3 films

A stable Y-doped BaZrO3 electrolyte film, which showed a good performance in proton-conducting SOFCs, was successfully fabricated using a novel ionic diffusion strategy.

Thermal properties and thermal shock resistance of γ-Y 2Si2O7

Thermal properties, namely, Debye temperature, thermal expansion coefficient, heat capacity, and thermal conductivity of γ-Y 2Si2O7, a high-temperature polymorph of yttrium disilicate, were investigated. The anisotropic thermal expansions of γ-Y2Si2O7 powders were examined using high-temperature X-ray diffractometer from 300 to 1373 K and the volumetric thermal expansion coefficient is (6.68±0.35) × 10-6 K-1. The linear thermal expansion coefficient of polycrystalline γ-Y2Si2O7 determined by push-rod dilatometer is (3.90±0.4) × 10-6 K-1, being very close to that of silicon nitride and silicon carbide. Besides, γ-Y2Si2O7 displays a low-thermal conductivity, with a κ value measured below 3.0 W·(m·K) -1 at the temperatures above 600 K. The calculated minimum thermal conductivity, κmin, was 1.35 W·(m·K) -1. The unique combination of low thermal expansion coefficient and low-thermal conductivity of γ-Y2Si2O7 renders it a very competitive candidate material for high temperature structural components and environmental/thermal-barrier coatings. The thermal shock resistance of γ-Y2Si2O7 was estimated by quenching dense materials in water from various temperatures and the critical temperature difference, ΔTc, was determined to be 300 K.

Kinetics and mechanism of hot corrosion of γ-Y 2Si 2O 7 in thin-film Na 2SO 4 molten salt

γ-Y 2Si 2O 7 is a promising candidate material both for hightemperature structural applications and as an environmental/thermal barrier coating material due to its unique properties such as high melting point, machinability, thermal stability, low linear thermal expansion coefficient (3.9×10 -6/K, 200°-1300°C), and low thermal conductivity (<3.0 W/ṁK above 300°C). The hot corrosion behavior of γ-Y 2Si 2O 7 in thin-film molten Na 2SO 4 at 850°-1000°C for 20 h in flowing air was investigated using a thermogravimetric analyzer (TGA) and a mass spectrometer (MS). γ-Y 2Si 2O 7 exhibited good resistance against Na 2SO 4 molten salt. The kinetic curves were well fitted by a paralinear equation: the linear part was caused by the evaporation of Na2SO4 and the parabolic part came from gas products evolved from the hotcorrosion reaction. A thin silica film formed under the corrosion scale was the key factor for retarding the hot corrosion. The apparent activation energy for the corrosion of γ-Y 2Si 2O 7 in Na 2SO 4 molten salt with flowing air was evaluated to be 255 kJ/mol.