Value distribution of the hyperbolic Gauss maps for flat fronts in hyperbolic three-space

We give an effective estimate for the totally ramified value number of the hyperbolic Gauss maps of complete flat fronts in the hyperbolic three-space. As a corollary, we give the upper bound of the number of exceptional values of them for some topological cases. Moreover, we obtain some new examples for this class.Comment: 14 pages, to appear in Houston Journal of Mathematic

Anyon Basis of c=1 Conformal Field Theory

We study the $c=1$ conformal field theory of a free compactified boson with radius $r=\sqrt{\beta}$ ($\beta$ is an integer). The Fock space of this boson is constructed in terms of anyon vertex operators and each state is labeled by an infinite set of pseudo-momenta of filled particles in pseudo-Dirac sea. Wave function of multi anyon state is described by an eigenfunction of the Calogero-Sutherland (CS) model. The $c=1$ conformal field theory at $r=\sqrt{\beta}$ gives a field theory of CS model. This is a natural generalization of the boson-fermion correspondence in one dimension to boson-anyon correspondence. There is also an interesting duality between anyon with statistics $\theta=\pi/\beta$ and particle with statistics $\theta=\beta \pi$.Comment: 17 page

Ramification estimates for the hyperbolic Gauss map

We give the best possible upper bound on the number of exceptional values and the totally ramified value number of the hyperbolic Gauss map for pseudo-algebraic constant mean curvature one surfaces in the hyperbolic three-space and some partial results on the Osserman problem for algebraic case. Moreover, we study the value distribution of the hyperbolic Gauss map for complete constant mean curvature one faces in de Sitter three-space.Comment: 16 pages, corrected some typos. OCAMI Preprint Series 08-1, to appear in Osaka Journal of Mathematic

Four-Dimensional Painlev\'e-Type Equations Associated with Ramified Linear Equations III: Garnier Systems and Fuji-Suzuki Systems

This is the last part of a series of three papers entitled "Four-dimensional Painlev\'e-type equations associated with ramified linear equations". In this series of papers we aim to construct the complete degeneration scheme of four-dimensional Painlev\'e-type equations. In the present paper, we consider the degeneration of the Garnier system in two variables and the Fuji-Suzuki system

Topological edge Mott insulating state in two dimensions at finite temperatures -bulk and edge analysis-

We study a bilayer Kane-Mele-Hubbard model with lattice distortion and inter-layer spin exchange interaction under cylinder geometry. Our analysis based on real-space dynamical mean field theory with continuous-time quantum Monte Carlo demonstrates the emergence of a topological edge Mott insulating (TEMI) state which hosts gapless edge modes only in collective spin excitations. This is confirmed by the numerical calculations at finite temperatures for the spin-Hall conductivity and the single-particle excitation spectrum; the spin Hall conductivity is almost quantized, $\sigma^{xy}_\mathrm{spin}\sim2(e/2\pi)$, predicting gapless edge modes carrying the spin current, while the helical edge modes in the single-particle spectrum are gapped out with respecting symmetry. It is clarified how the TEMI state evolves from the ordinary spin Hall insulating state with increasing the Hubbard interaction at a given temperature and then undergoes a phase transition to a trivial Mott insulating state. With a bosonization approach at zero temperature, we further address which collective modes host gapless edge modes in the TEMI state.Comment: 9 pages, 6 figure

Innovating global value chains : creation of the netbook market by Taiwanese firms

This paper explores the process of creation of the netbook market by Taiwanese firms as an example of a disruptive innovation by latecomer firms. As an analytical framework, I employ the global value chain perspective to capture the dynamics of vertical inter-firm relationships that drive some firms in the chain to change the status quo of the industry. I then divide the process of the emergence of the netbook market into three consecutive stages, i.e. (1) the launch of the first-generation netbook by a Taiwanese firm named ASUSTeK, (2) the response of the two powerful platform leaders of the industry, Intel and Microsoft Intel, to ASUSTeK’s innovation, and (3) the market entry by another powerful Taiwanese firm, Acer, and explain how Taiwanese firms broke the Intel-centric market and tapped into the market-creating innovation opportunities that had been suppressed by the two powerful platform leaders. I also show that the creation of the netbook industry was an evolutionary process in which a series of responses by different industry players led to changes in the status quo of the industry.Taiwan, Information services industry, Computer, Industrial technology, Marketing, Market share, Industrial management, Disruptive innovation, Latecomer firms, Global value chains, The PC industry