Bounds for eigenvalue ratios of the Laplacian

For a bounded domain $\Omega$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian. As an application, we study lower order eigenvalues of the Laplacian and derive the ratios of lower order eigenvalues of the Laplacian.Comment: 14 page

Using fractals and power laws to predict the location of mineral deposits

Around the world the mineral exploration industry is interested in getting that small increase in probability measure on the earth's surface of where the next large undiscovered deposit might be found. In particular WMC Resources Ltd has operations world wide looking for just that edge in the detection of very large deposits of, for example, gold. Since the pioneering work of Mandelbrot, geologists have been familiar with the concept of fractals and self similarity over a few orders of magnitude for geological features. This includes the location and size of deposits within a particular mineral province. Fractal dimensions have been computed for such provinces and similarities of these aggregated measures between provinces have been noted. This paper explores the possibility of making use of known information to attempt the inverse process. That is, from lesser dimensional measures of a mineral province, for example, fractal dimension or more generally multi-fractal measures, is it possible to infer, even with small increase in probability, where the unknown (preferably large) deposits might be located

Experimental and theoretical research on the electrical conductivity of a liquid desiccant for the liquid desiccant air-conditioning system: LiCl aqueous solution

At present, the energy consumption in buildings occupies a large proportion of total energy use, and air-conditionings cost a large proportion of energy in the buildings. The liquid desiccant air-conditioning system has a good energy saving potential and the electrodialysis (ED) regeneration is a reliable choice for the liquid desiccant regeneration. In order to establish the energy consumption model and the performance coefficient model of liquid desiccant air-conditioning system based on ED regeneration using LiCl, experimental and theoretical research on the electrical conductivity of LiCl aqueous solution with a lot of concentrations and temperatures was conducted in this paper. The results show that when polynomial degrees of the mass concentration and the temperature of the LiCl aqueous solution are both 3, the electrical conductivity model for the LiCl aqueous solution is most suitable as its simplicity and high accuracy. Moreover, when the concentration is 36% and the temperature is 22 °C, the liquid desiccant cooling system has the maximum COP of about 5. Finally, a case study of a small office room was conducted, and the result shows that the liquid desiccant cooling system based on electrodialysis regeneration has a good energy-saving potential

Caching and Auditing in the RPPM Model

Crampton and Sellwood recently introduced a variant of relationship-based access control based on the concepts of relationships, paths and principal matching, to which we will refer as the RPPM model. In this paper, we show that the RPPM model can be extended to provide support for caching of authorization decisions and enforcement of separation of duty policies. We show that these extensions are natural and powerful. Indeed, caching provides far greater advantages in RPPM than it does in most other access control models and we are able to support a wide range of separation of duty policies.Comment: Accepted for publication at STM 2014 (without proofs, which are included in this longer version

An analytical study of the modification ability of distribution centers

2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Multi-scale interactions of geological processes during mineralization: cascade dynamics model and multifractal simulation

Relations between mineralization and certain geological processes are established mostly by geologist's knowledge of field observations. However, these relations are descriptive and a quantitative model of how certain geological processes strengthen or hinder mineralization is not clear, that is to say, the mechanism of the interactions between mineralization and the geological framework has not been thoroughly studied. The dynamics behind these interactions are key in the understanding of fractal or multifractal formations caused by mineralization, among which singularities arise due to anomalous concentration of metals in narrow space. From a statistical point of view, we think that cascade dynamics play an important role in mineralization and studying them can reveal the nature of the various interactions throughout the process. We have constructed a multiplicative cascade model to simulate these dynamics. The probabilities of mineral deposit occurrences are used to represent direct results of mineralization. Multifractal simulation of probabilities of mineral potential based on our model is exemplified by a case study dealing with hydrothermal gold deposits in southern Nova Scotia, Canada. The extent of the impacts of certain geological processes on gold mineralization is related to the scale of the cascade process, especially to the maximum cascade division number <i>n</i><sub>max</sub>. Our research helps to understand how the singularity occurs during mineralization, which remains unanswered up to now, and the simulation may provide a more accurate distribution of mineral deposit occurrences that can be used to improve the results of the weights of evidence model in mapping mineral potential