A k-space method for nonlinear wave propagation

A k-space method for nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme [Mast et al., IEEE Tran. Ultrason. Ferroelectr. Freq. Control 48, 341-354 (2001)]. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to the finite element method. It is found that, in order to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as small as 0.4. As a result, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient than the conventional finite element method or finite-difference time-domain method for the conditions studied here. However, although the present method is highly accurate for weakly inhomogeneous media, it is found to be less accurate for strongly inhomogeneous media. A possible remedy to this limitation is discussed

Realization of the N(odd)-dimensional Quantum Euclidean Space by Differential Operators

The quantum Euclidean space R_{q}^{N} is a kind of noncommutative space which is obtained from ordinary Euclidean space R^{N} by deformation with parameter q. When N is odd, the structure of this space is similar to R_{q}^{3}. Motivated by realization of R_{q}^{3} by differential operators in R^{3}, we give such realization for R_{q}^{5} and R_{q}^{7} cases and generalize our results to R_{q}^{N} (N odd) in this paper, that is, we show that the algebra of R_{q}^{N} can be realized by differential operators acting on C^{infinite} functions on undeformed space R^{N}.Comment: 10 pages, LaTe

Properties of 2×22\times 2 h-deformed quantum (super)matrices

We investigate the $h$-deformed quantum (super)group of $2\times 2$ matrices and use a kind of contraction procedure to prove that the $n$-th power of this deformed quantum (super)matrix is quantum (super)matrix with the deformation parameter $nh$.Comment: Accepted by International Journal of Theoretical Physic

Decentralized Borrowing and Centralized Default

In the past, foreign borrowing by developing countries was comprised almost entirely of government borrowing. Recently, private firms and individuals in developing countries borrow substantially from foreign lenders. It is not clear whether the observed increase in private sector borrowing leads to overborrowing and frequent defaults by governments in developing countries. In this paper, we develop a tractable quantitative model in which private agents decide how much to borrow but the government decides whether to default. The model with decentralized borrowing increases aggregate credit costs and sovereign default risk, and reduces aggregate welfare, relative to a model with centralized borrowing. Private agents do not internalize the effect of their borrowing on economy-wide credit costs and thus would like to borrow more than the socially efficient level. Depending on the severity of default penalties, decentralized borrowing may lead to either too much or too little debt in equilibrium. The introduction of decentralized borrowing substantially improves the model's empirical fit in terms of matching observed debt levels and default rates.Sovereign Default, Sovereign Debt, Private Borrowing, Capital Flows

The Role of Ecotourism in the Sustainable Development of Qinkou village, Yunnan, China, 2001 to 2013

This study captures evidence of the changes to Qinkou village during the period it was developed as an example of ecotourism in Yunnan province, Southwest China; a process which began in 2001. By examining the aims of the development projects and changes which happened in the village in 2001, 2006 and 2013 respectively, the paper aims to explore how traditions have been understood and deployed with regard to the built environment in Qinkou. It also investigates the shift in focus of academic research into traditional and sustainable development of rural villages over different periods. In 2001, a development project was implemented in Qinkou to demonstrate how tourism could be used as a way to modernise the village. The local government of the Honghe Hani and Yi Autonomous Prefecture, where the village is located, worked with academics in the fields of architecture, planning and anthropology to develop the plan and to obtain funding to transform Qinkou into an ecotourism village. By 2006, the infrastructure of the village had been significantly improved. However, many originally planned activities could not be carried out due to the lack of ongoing funding support and effective management. Tourism alone was unable to bring fundamental changes in Qinkou. Instead, many villagers who worked in the cities returned with savings from the higher incomes enjoyed in the cities and also brought back changed lifestyles that contributed further major transformation. At the same time, the village remained a coherent settlement. The head of the village and management group organised many village co-operative activities. Academic research at the time, on the other hand, focused more on the examination of the cultural symbols of the local families and built environment than providing advice to help the village improve living conditions. In 2013, an application for the spectacular stepped paddy fields in the Prefecture to be listed as a World Heritage Site attracted significant funding from the local government. Qinkou was included in the development master plan; however, the development project for the village focused primarily on the preservation of the traditional forms as cultural symbols. Academic research and local policies discussed needs for sustainable development in order to comply with the requirements of the UNSCO process for World Heritage Site listing. Yet, details of how to achieve social and cultural cohesion remained missing. This paper argues that tourism development in the market-oriented economy now operating in China has worked as the catalyst for the transformation of the village and improvement of living conditions. However, social-cultural sustainable regeneration of rural settlements must create places for the needs of different groups in the local community. The academic research also needs to reinterpret the traditions that were formed and changed by the local communities in a way that is perhaps more diverse and flexible than the previous academic research defined

Twisted vertex operators and unitary Lie algebras

A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac-Moody Lie algebra of type $A_n^{(2)}$ are recovered by the new method.Comment: 26 page