Optimal consumption models in economic growth

We study the optimal consumption problem in the one-sector model of economic growth under uncertainty. We show the existence of a classical solution of the Hamilton-Jacobi-Bellman equation associated with the stochastic optimization problem, and then give an optimal consumption policy in terms of its solution.     

Liquid phase epitaxial growth and optical property of flower-like ZnO nanosheets on Zinc foil

Large scale flower-like ZnO nanosheets have been synthesized on Zinc foil by a simple hydrothermal method. Their morphology and microstructures were characterized and analyzed by X-ray spectroscopy (XRD), field emission scanning electron microscopy (FE-SEM) and high-resolution transmission electron microscopy (HRTEM). The as-synthesized flower-like nanosheets are hexagonal phase single crystal with 200-300 nm in width, 50 nm in thickness. The growth process follows the liquid phase epitaxial growth mechanism. In this approach, the ZnO buffer is used as substrate for the growth of flower-like ZnO nanosheets. The growth direction of the nanosheets is the preferential [0 0 0 1] growth direction of ZnO. The photoluminescence spectrum of the sample exhibits only a sharp and strong UV emission centered at 386 nm, which indicates that the flower-like ZnO nanosheets on Zn foil are of good optical property.     

Anomalous Scaling of Surface Growth Equations with Spatially and Temporally Correlated Noise

Based on the scaling idea of local slopes by Lopez et al. [Phys. Rev. Lett. 94 （2005） 166103], we investigate anomalous dynamic scaling of （d ＋ 1）-dimensional surface growth equations with spatially and temporally correlated noise. The growth equations studied include the Kardar-Parisi-Zhang （KPZ）, Sun-Guo-Grant （SGG）, and Lai-Das Sarma-Villain （LDV） equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively.     

Modelling population growth vialaguerre-type exponentials

We use the Laguerre-type exponentials, i.e., eigenfunctions of the Laguerre-type derivatives, in order to construct new models for population growth. Relevant modifications of the classical exponential, logistic, and Volterra-Lotka models are investigated.     

Strong lateral growth and crystallization via two-dimensional allotropic transformation of semi-metal Bi film

Two-dimensional (2D) nano-objects, such as metallic nanofilms are the most fundamental building blocks for nanoelectronics devices. However, the fabrication of highly ordered nanofilms has been difficult because of well known Stranski-Krastanov growth, which results in rough growth front and high density grains. Here we report on the unusual high-quality film growth of Bi on a Si surface with atomic-level surface/interface smoothness and high film crystallinity. The formation of a newly discovered 2D allotrope was clarified to initiate its strong 2D growth. Above several-monolayer thickness, the 2D allotrope transforms into a single-crystalline film with bulk-like layered structure. Our study unveils the atomistic growth process of nano-sized Bi, and the obtained knowledge here will be generally applicable for the fabrication of various nano-devices using this intriguing material that shows rich thermal, magnetic, electronic properties in nanometer scale.     

Light-induced reversible hydrophilicity of ZnO structures grown by aqueous chemical growth

ZnO wurtzite microrods and flowerlike structures were deposited on glass and ITO substrates by the aqueous chemical growth (ACG) technique at mild temperature (95 °C). Wettability studies revealed that the as-deposited structures are hydrophilic and super-hydrophilic for short and long growth times, respectively. The hydrophilic ZnO surfaces could be reversibly switched to super-hydrophilic by alternation of UV illumination and dark storage. Our results demonstrate that ACG at low temperatures can be efficiently employed to deposit transparent photosensitive ZnO structures exhibiting reversible wettability changes.     

Positive solutions for Schrödinger–Poisson equations with a critical exponent

In this paper we establish the existence of a positive solution of the Schrödinger–Poisson equations with a critical Sobolev exponent. The methods used here are based on the concentration–compactness principle of P. L. Lions and methods of Brezis and Nirenberg.     

Retrieving seasonally adjusted quarterly growth rates from annual growth rates that are reported quarterly

Most macroeconomic time series are reported on a quarterly basis. However, in many cases, official statistical agencies report annual (or ‘year-on-year’) growth rates rather than the quarterly data themselves. In this paper, we demonstrate how to recover seasonally adjusted quarterly growth rates from annual growth rates that are reported quarterly. As an illustration, we apply the technique to the highly seasonal UK Retail Sales series. Using only the annual growth rates calculated from the underlying data, we find that our procedure generates estimated seasonally adjusted quarterly growth rates that are almost indistinguishable from the ‘true’ seasonally adjusted quarterly growth rates.     

Phase Transitions for the Growth Rate of Linear Stochastic Evolutions

We consider a discrete-time stochastic growth model on d-dimensional lattice. The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of binary contact path process and the voter model. We study the phase transition for the growth rate of the “total number of particles” in this framework. The main results are roughly as follows: If d≥3 and the system is “not too random”, then, with positive probability, the growth rate of the total number of particles is of the same order as its expectation. If on the other hand, d=1,2, or the system is “random enough”, then the growth rate is slower than its expectation. We also discuss the above phase transition for the dual processes and its connection to the structure of invariant measures for the model with proper normalization. Supported in part by JSPS Grant-in-Aid for Scientific Research, Kiban (C) 17540112.