1,235 research outputs found

    Electronic and magnetic properties of V-doped anatase TiO2_{2} from first principles

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    We report a first-principles study on the geometric, electronic and magnetic properties of V-doped anatase TiO2_{2}. The DFT+U (Hubbard coefficient) approach predicts semiconductor band structures for Ti1βˆ’x_{1-x}Vx_{x}O2_{2} (x=6.25 and 12.5%), in good agreement with the poor conductivity of samples, while the standard calculation within generalized gradient approximation fails. Theoretical results show that V atoms tend to stay close and result in strong ferromagnetism through superexchange interactions. Oxygen vacancy induced magnetic polaron could produce long-range ferromagnetic interaction between largely separated magnetic impurities. The experimentally observed ferromagnetism in V-doped anatase TiO2_{2} at room temperature may originate from a combination of short-range superexchange coupling and long-range bound magnetic polaron percolation.Comment: 12 pages and 4 figures (to be appeared in PRB as a brief report

    Defining Urban Boundaries by Characteristic Scales

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    Defining an objective boundary for a city is a difficult problem, which remains to be solved by an effective method. Recent years, new methods for identifying urban boundary have been developed by means of spatial search techniques (e.g. CCA). However, the new algorithms are involved with another problem, that is, how to determine the characteristic radius of spatial search. This paper proposes new approaches to looking for the most advisable spatial searching radius for determining urban boundary. We found that the relationships between the spatial searching radius and the corresponding number of clusters take on an exponential function. In the exponential model, the scale parameter just represents the characteristic length that we can use to define the most objective urban boundary objectively. Two sets of China's cities are employed to test this method, and the results lend support to the judgment that the characteristic parameter can well serve for the spatial searching radius. The research may be revealing for making urban spatial analysis in methodology and implementing identification of urban boundaries in practice.Comment: 26 pages, 5 figures, 7 table

    On the Efficacy and High-Performance Implementation of Quaternion Matrix Multiplication

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    Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also seen many advances in the formal theoretical development of explicitly quaternion linear algebra with promising applications in image processing and machine learning. Despite these advances, there do not currently exist optimized software implementations of quaternion linear algebra. The leverage of optimized linear algebra software is crucial in the achievement of high levels of performance on modern computing architectures, and thus provides a central tool in the development of high-performance scientific software. In this work, a case will be made for the efficacy of high-performance quaternion linear algebra software for appropriate problems. In this pursuit, an optimized software implementation of quaternion matrix multiplication will be presented and will be shown to outperform a vendor tuned implementation for the analogous complex matrix operation. The results of this work pave the path for further development of high-performance quaternion linear algebra software which will improve the performance of the next generation of applicable scientific applications
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