Bloch-to-BMOA pullbacks on the disk

For a given holomorphic self map of the unit disk, we consider the Bloch-to- composition property (pullback property) of . Our results are cannot have the pullback property if touches the boundary too smoothly, while has the pullback property if touches the boundary rather sharply. One of these results yields an interesting consequence completely contrary to a higher dimensional result which has been known. These results resemble known results concerning the compactness of composition operators on the Hardy spaces. Some remarks in that direction are included.

     

Arrayed hybrid nanoporous Pt pillars

2D arrayed Pt columns with 3D-nanoporous structure were fabricated by electroplating Pt in reverse micelle (L₂) solution of a nonionic surfactant filled in 1D microchannels of alumina porous membrane. This thin film features a unique hybrid system consisting of nanoporous structure embedded in the secondary microstructure, which is increasingly of great importance in terms of maximal efficacy of the interfacial properties of nanoporous surface. The diameter of the 3D-nanoporous pillars was ～300 nm and the length was precisely controlled by the electroplating condition. This is the first report of the hybrid 3D-nanoporous micro-columnar metal film by one-step electrochemical deposition in a reverse micelle solution.     

Conformal mapping for the Helmholtz equation: acoustic wave scattering by a two dimensional inclusion with irregular shape in an ideal fluid

The complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp/smooth corners in an infinite ideal fluid domain. The improved solutions of Helmholtz equation, shown as Bessel function with mapping function as the argument and fractional order Bessel function, were analytically obtained. Based on the mapping function, the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane. As all the physical vectors are calculated in the mapping plane (η,η), this method can lead to potential vast savings of computational resources and memory. In this work, the results are validated against several published works in the literature. The different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed. The findings show that the variation of angles and frequencies of the incident waves have significant influence on the bistatic scattering pattern and the far-field form factor for the pressure in the fluid.     

Phase changeable silver selenide thin films fabricated by pulse electrodeposition

We have used a simple and direct method to successfully prepare Ag₂Se thin films by pulse electrodeposition from a single aqueous solution of Ag and Se ions. The composition analysis confirms the stoichiometry and the morphological characterization shows that the thin films are dense and smooth. The films have the orthorhombic structure of regular Ag₂Se materials at room temperature, while the electrical measurements reveal an interesting electrical behavior, similar to that of the Ag₂Se nanowire arrays. The Ag₂Se thin films were successfully deposited into polymer templates to form well-defined Ag₂Se nanostructure, which provides a possibility to apply the method to high density, non-volatile memories based on phase change materials.     

Composition Operators on Small Spaces

We show that if a small holomorphic Sobolev space on the unit disk is not just small but very small, then a trivial necessary condition is also sufficient for a composition operator to be bounded. A similar result for holomorphic Lipschitz spaces is also obtained. These results may be viewed as boundedness analogues of Shapiro’s theorem concerning compact composition operators on small spaces. We also prove the converse of Shapiro’s theorem if the symbol function is already contained in the space under consideration. In the course of the proofs we characterize the bounded composition operators on the Zygmund class. Also, as a by-product of our arguments, we show that small holomorphic Sobolev spaces are algebras.     

Development of Co-Sintering Process for Effective Fabrication of Direct-Write Planer Waveguide

We propose a co-sintering process for effective fabrication of three-layered structure for direct-write planar waveguide. Processing parameters and optical properties of the waveguide was investigated.     

Roles of gangliosides in mouse embryogenesis and embryonic stem cell differentiation

Gangliosides have been suggested to play important roles in various functions such as adhesion, cell differentiation, growth control, and signaling. Mouse follicular development, ovulation, and luteinization during the estrous cycle are regulated by several hormones and cell-cell interactions. In addition, spermatogenesis in seminiferous tubules of adult testes is also regulated by several hormones, including follicle-stimulating hormone (FSH) and luteinizing hormone (LH) and cell-cell interactions. The regulation of these processes by hormones and cell-cell interactions provides evidence for the importance of surface membrane components, including gangliosides. During preimplantation embryo development, a mammalian embryo undergoes a series of cleavage divisions whereby a zygote is converted into a blastocyst that is sufficiently competent to be implanted in the ma ternal uterus and continue its development. Mouse embryonic stem (mES) cells are pluripotent cells derived from mouse embryo, specifically, from the inner cell mass of blastocysts. Differentiated neuronal cells are derived from mES cells through the formation of embryonic bodies (EBs). EBs recapitulate many aspects of lineage-specific differentiation and temporal and spatial gene expression patterns during early embryogenesis. Previous studies on ganglioside expression during mouse embryonic development (including during in vitro fertilization, ovulation, spermatogenesis, and embryogenesis) reported that gangliosides were expressed in both undifferentiated and differentiated (or differentiating) mES cells. In this review, we summarize some of the advances in our understanding of the functional roles of gangliosides during the stages of mouse embryonic development, including ovulation, spermatogenesis, and embryogenesis, focusing on undifferentiated and differentiated mES cells (neuronal cells).     

Stereoselective rearrangement of guaianolides to tricyclic δ-valerolactones

An unprecedented, highly stereoselective rearrangement of guaianolides, bearing a double bond at the C-6/C-6a position, to tricyclic δ-valerolactones is described.