Normal families and fixed points of iterates

Let F be a family of holomorphic functions and let K be a constant less than 4. Suppose that for all f in F the second iterate of f does not have fixed points for which the modulus of the multiplier is greater than K. We show that then F is normal. This is deduced from a result about the multipliers of iterated polynomials.Comment: 5 page

Evaluation of LS-DYNA MAT162 for Modeling Composite Fastener Joints for High Rates of Loading

In the present work, the behavior of composite-fastener joints in bearing failure at dynamic stroke rates of 500 in/s, 300 in/s and 100 in/s has been evaluated through progressive damage analysis (PDA) material model in LS-DYNA, namely MAT162. Two joint types: titanium pin and Hi-Lok fastener were analyzed to identify the differences between without and with preload conditions. A meso-level approach where each lamina was modeled separately was employed and a contact definition based on fracture toughness data was defined to represent composite delamination behavior. Test fixture had been modeled in a detailed manner to account for the dynamic effects and the simulation results were validated against experimental data. Preliminary test-analysis correlation indicated that MAT162 predicted results conservatively when compared to tests. Debris accumulation were observed to greatly affect the test results which were not considered in the current modelling strategies

Ordered Carboxylates on TiO (110) Formed at Aqueous Interfaces

As models for probing the interactions between TiO2 surfaces and the dye molecules employed in dye-sensitized solar cells, carboxylic acids are an important class of molecules. In this work we present a scanning tunneling microscopy (STM) and low energy electron diffraction (LEED) study of three small carboxylic acids (formic, acetic, and benzoic) that were reacted with the TiO2(110) surface via a dipping procedure. The three molecules display quite different adsorption behavior, illustrating the different inter-adsorbate interactions that can occur. After exposure to a 10 mM solution, formic acid forms a rather disordered formate overlayer with two distinct binding geometries. Acetic acid forms a well-ordered (2 × 1) acetate overlayer similar to that observed following deposition from vapor. Benzoic acid forms a (2 × 2) overlayer which is stabilized by intermolecular interactions between the phenyl groups

Structure of a model TiO2 photocatalytic interface

The interaction of water with TiO2 is crucial to many of its practical applications, including photocatalytic water splitting. Following the first demonstration of this phenomenon 40 years ago there have been numerous studies of the rutile single-crystal TiO2(110) interface with water. This has provided an atomic-level understanding of the water-TiO2 interaction. However, nearly all of the previous studies of water/TiO2 interfaces involve water in the vapour phase. Here, we explore the interfacial structure between liquid water and a rutile TiO2(110) surface pre-characterized at the atomic level. Scanning tunnelling microscopy and surface X-ray diffraction are used to determine the structure, which is comprised of an ordered array of hydroxyl molecules with molecular water in the second layer. Static and dynamic density functional theory calculations suggest that a possible mechanism for formation of the hydroxyl overlayer involves the mixed adsorption of O2 and H2O on a partially defected surface. The quantitative structural properties derived here provide a basis with which to explore the atomistic properties and hence mechanisms involved in TiO2 photocatalysis

Metropolitan Trends and Challenges in China: The Demographic Dimension

Over the past century China has been transforming from a rural to an urban economy. In the course of this transition, significant regional variations have emerged in urban growth, with a gap forming between coastal and inland areas. This report focuses on Chinas metropolitan regions: Shanghai, Beijing, and Guangdong which are the most socioeconomically advanced regions in China. It is the first outcome of the joint IIASA and Beijing University project on "Regional Urbanization and Human Capital Projections for China," which focuses on demographic matters, and it will analyze the following major issues: What factors have contributed to the growth of Chinas metropolitan areas over the last two decades? What specific urbanization patterns occur in the transformation from a rural to an urban economy? How does demography drive the speed of urbanization, in particular, in the metropolitan areas? How is IIASAs multistate method used for urbanization projections and what are its advantages and disadvantages? What challenges will China face in the near future as a result of rapid metropolitan growth? This paper suggests that the growth of Chinese mega-urban regions will have knock-on effects at the global level in the medium term