Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis

Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a generic wavelet frame based image restoration model, called the "general model", which includes most of the existing wavelet frame based models as special cases. Moreover, the general model also includes examples that are new to the literature. Motivated by our earlier studies [1-3], We provide an asymptotic analysis of the general model as image resolution goes to infinity, which establishes a connection between the general model in discrete setting and a new variatonal model in continuum setting. The variational model also includes some of the existing variational models as special cases, such as the total generalized variational model proposed by [4]. In the end, we introduce an algorithm solving the general model and present one numerical simulation as an example

Environmental Sustainability and Economic Development: A World View

Sustainability, especially environmental sustainability, has obtained more and more attention globally.  However, many questions remain unclear.  For example, how economic development and environmental sustainability are correlated with each other?  How economically developed a country needs to be when environmental sustainability becomes necessary?  Does environmental sustainability require certain degree of economic development?  The purposes of this study are: (1) to investigate the relationship between environmental sustainability and economic development; (2) to examine the current status of environmental sustainability in both developed and developing countries; and (3) to develop a world view of environmental sustainability.  By applying well-developed theories (Maslow’s Hierarchy of Needs and the Environmental Kuznets Curve) and analyzing reliable statistical data (Environmental Performance Index, Environmental Performance Index, CO2 emission, energy consumption, ecological footprint, and waste generation), two correlated relationships (positive vs. negative) between environmental sustainability and economic development were identified, followed by the development of two types of environmental sustainability (proactive vs. passive).  When both correlated relationship were combined, the Environmental Sustainability Curve was developed and supported by the Environmental Kuznets Curve.  Then by following product life cycle, the current status of environmental sustainability in both developed countries and developing countries were examined.  At the end, when the world was examined as a whole by combining the developing countries and developed countries together, a world view of environmental sustainability was formed.  Even though developed countries have a low environmental impact from production stage and disposal stage and developing countries have a low environmental impact from consumption stage, the world view combined with both types of countries is very troublesome and serious due to high environmental impact from production, consumption and disposal.   Therefore, immediate response to address all the environmental damages is necessary from all countries. Keywords: Environmental, Sustainability, World, Econom

Nonlinear analysis of dynamical complex networks

Copyright © 2013 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics. Examples of such complex networks include the Internet, that is, a network of routers or domains, the World Wide Web (WWW), that is, a network of websites, the brain, that is, a network of neurons, and an organization, that is, a network of people. Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural properties of complex networks. It has been found out that the general structure of the interaction network may play a crucial role in the emergence of synchronization phenomena in various fields such as physics, technology, and the life sciences