New neighborhood based rough sets

Neighborhood based rough sets are important generalizations of the classical rough sets of Pawlak, as neighborhood operators generalize equivalence classes. In this article, we introduce nine neighborhood based operators and we study the partial order relations between twenty-two different neighborhood operators obtained from one covering. Seven neighborhood operators result in new rough set approximation operators. We study how these operators are related to the other fifteen neighborhood based approximation operators in terms of partial order relations, as well as to seven non-neighborhood-based rough set approximation operators

Assessment of crystallographic influence on material properties of calcite brachiopods

Calcium carbonate biominerals are frequently analysed in materials science due to their abundance, diversity and unique material properties. Aragonite nacre is intensively studied, but less information is available about the material properties of biogenic calcite, despite its occurrence in a wide range of structures in different organisms. In particular, there is insufficient knowledge about how preferential crystallographic orientations influence these material properties. Here, we study the influence of crystallography on material properties in calcite semi-nacre and fibres of brachiopod shells using nano-indentation and electron backscatter diffraction (EBSD). The nano-indentation results show that calcite semi-nacre is a harder and stiffer (H {approx} 3–5 GPa; E = 50–85 GPa) biomineral structure than calcite fibres (H = 0.4–3 GPa; E = 30–60 GPa). The integration of EBSD to these studies has revealed a relationship between the crystallography and material properties at high spatial resolution for calcite semi-nacre. The presence of crystals with the c-axis perpendicular to the plane-of-view in longitudinal section increases hardness and stiffness. The present study determines how nano-indentation and EBSD can be combined to provide a detailed understanding of biomineral structures and their analysis for application in materials science

Phonon-phason coupling in icosahedral quasicrystals

From relaxation simulations of decoration-based quasicrystal structure models using microscopically based interatomic pair potentials, we have calculated the (usually neglected) phonon-phason coupling constant. Its sign is opposite for the two alloys studied, i-AlMn and i-(Al,Cu)Li; a dimensionless measure of its magnitude relative to the phonon and phason elastic constants is of order 1/10, suggesting its effects are small but detectable. We also give a criterion for when phonon-phason effects are noticeable in diffuse tails of Bragg peaks.Comment: 7 pages, LaTeX, uses Europhys Lett macros (included

Positivity and strong ellipticity

We consider second-order partial differential operators $H$ in divergence form on \Ri^d with a positive-semidefinite, symmetric, matrix $C$ of real $L_\infty$-coefficients and establish that $H$ is strongly elliptic if and only if the associated semigroup kernel satisfies local lower bounds, or, if and only if the kernel satisfies Gaussian upper and lower bounds.Comment: 9 page

Topological Superfluid Transition Induced by Periodically Driven Optical Lattice

We propose a scenario to create topological superfluid in a periodically driven two-dimensional square optical lattice. We study the phase diagram of a spin-orbit coupled s-wave pairing superfluid in a periodically driven two-dimensional square optical lattice. We find that a phase transition from a trivial superfluid to a topological superfluid occurs when the potentials of the optical lattices are periodically changed. The topological phase is called Floquet topological superfluid and can host Majorana fermions.Comment: 6 pages, 1 figure

An investigation of pulsar searching techniques with the Fast Folding Algorithm

Here we present an in-depth study of the behaviour of the Fast Folding Algorithm, an alternative pulsar searching technique to the Fast Fourier Transform. Weaknesses in the Fast Fourier Transform, including a susceptibility to red noise, leave it insensitive to pulsars with long rotational periods (P > 1 s). This sensitivity gap has the potential to bias our understanding of the period distribution of the pulsar population. The Fast Folding Algorithm, a time-domain based pulsar searching technique, has the potential to overcome some of these biases. Modern distributed-computing frameworks now allow for the application of this algorithm to all-sky blind pulsar surveys for the first time. However, many aspects of the behaviour of this search technique remain poorly understood, including its responsiveness to variations in pulse shape and the presence of red noise. Using a custom CPU-based implementation of the Fast Folding Algorithm, ffancy, we have conducted an in-depth study into the behaviour of the Fast Folding Algorithm in both an ideal, white noise regime as well as a trial on observational data from the HTRU-S Low Latitude pulsar survey, including a comparison to the behaviour of the Fast Fourier Transform. We are able to both confirm and expand upon earlier studies that demonstrate the ability of the Fast Folding Algorithm to outperform the Fast Fourier Transform under ideal white noise conditions, and demonstrate a significant improvement in sensitivity to long-period pulsars in real observational data through the use of the Fast Folding Algorithm.Comment: 19 pages, 15 figures, 3 table

China's building stock estimation and energy intensity analysis

Reliable and objective data regarding building stock is essential for predicting and analyzing energy demand and carbon emission. However, China's building stock data is lacking. This study proposes a set of China building floor space estimation method (CBFSM) based on the improved building stock turnover model. Then it measures China's building stocks by vintage and type from 2000 to 2015, as well as building energy intensity (national level and provincial level) and energy-efficient buildings. Results showed that total building stocks increased significantly, rising from 35.2 billion m2 in 2000 to 63.6 billion m2 in 2015, with the average growth rate 4.0%. The deviations were well below 10% by comparing with China Population Census, which validated the reliability of CBFSM and the results. As for energy intensity, urban dwellings and rural dwellings showed relatively stable and increasing trend respectively. The commercial building energy intensity saw a downward trend during “12th Five Year Plan” period. This indicated the effectiveness of building energy efficiency work for commercial buildings since 2005.38.6 billion m2 residential dwellings and 5.7 billion m2 commercial buildings still need to be retrofitted in future. CBFSM can overcome shortages in previous studies. It can also provide Chinese government with technical support and data evidence to promote the building energy efficiency work

Second-order operators with degenerate coefficients

We consider properties of second-order operators $H = -\sum^d_{i,j=1} \partial_i \, c_{ij} \, \partial_j$ on \Ri^d with bounded real symmetric measurable coefficients. We assume that $C = (c_{ij}) \geq 0$ almost everywhere, but allow for the possibility that $C$ is singular. We associate with $H$ a canonical self-adjoint viscosity operator $H_0$ and examine properties of the viscosity semigroup $S^{(0)}$ generated by $H_0$. The semigroup extends to a positive contraction semigroup on the $L_p$-spaces with $p \in [1,\infty]$. We establish that it conserves probability, satisfies $L_2$~off-diagonal bounds and that the wave equation associated with $H_0$ has finite speed of propagation. Nevertheless $S^{(0)}$ is not always strictly positive because separation of the system can occur even for subelliptic operators. This demonstrates that subelliptic semigroups are not ergodic in general and their kernels are neither strictly positive nor H\"older continuous. In particular one can construct examples for which both upper and lower Gaussian bounds fail even with coefficients in C^{2-\varepsilon}(\Ri^d) with $\varepsilon > 0$.Comment: 44 page