Wavelet Galerkin method for fractional elliptic differential equations

Under the guidance of the general theory developed for classical partial differential equations (PDEs), we investigate the Riesz bases of wavelets in the spaces where fractional PDEs usually work, and their applications in numerically solving fractional elliptic differential equations (FEDEs). The technique issues are solved and the detailed algorithm descriptions are provided. Compared with the ordinary Galerkin methods, the wavelet Galerkin method we propose for FEDEs has the striking benefit of efficiency, since the condition numbers of the corresponding stiffness matrixes are small and uniformly bounded; and the Toeplitz structure of the matrix still can be used to reduce cost. Numerical results and comparison with the ordinary Galerkin methods are presented to demonstrate the advantages of the wavelet Galerkin method we provide.Comment: 20 pages, 0 figure

Tuning Optical Properties of Transparent Conducting Barium Stannate by Dimensional Reduction

We report calculations of the electronic structure and optical properties of doped $n$-type perovskite BaSnO3 and layered perovskites. While doped BaSnO$_3$ retains its transparency for energies below the valence to conduction band onset, the doped layered compounds exhibit below band edge optical conductivity due to transitions from the lowest conduction band. This gives absorption in the visible for Ba2SnO4. Thus it is important to minimize this phase in transparent conducting oxide (TCO) films. Ba3Sn2O7 and Ba4Sn3O10 have strong transitions only in the red and infrared, respectively. Thus there may be opportunities for using these as wavelength filtering TCO

An investigation on China’s NGOs in urban heritage preservation

As for China’s urban heritage preservation, besides the top-down actors, some non-governmental organizations have emerged and started to play increasingly noticeable parts. The paper accordingly explores China's increasingly pluralistic situation in urban heritage preservation, and reveals the roles of these non-governmental players. The paper selects Tianjin Memory as a specific case, and elucidates its developments and transformations from 2006 to the present via documental research, in-depth interviews and internet big data analyses. Informed by internal ecological relationship analyses, the paper divides its development process into four main stages: start, rapid development, differentiation and reorganization. Each stage is examined from six factors, i.e. human resources, structure and management, finance, social resources, products and achievements, based on NGOs’ influence evaluation in sociology. The research further identifies the main limitations and challenges for Tianjin Memory. As a part of the discussions about China’s current pluralistic urbanism, this paper brings forwards some suggestions for a healthy and sustainable future of Tianjin Memory and other similar NGOs in China

Sn(II)-containing phosphates as optoelectronic materials

We theoretically investigate Sn(II) phosphates as optoelectronic materials using first principles calculations. We focus on known prototype materials Sn$_n$P$_2$O$_{5+n}$ (n=2, 3, 4, 5) and a previously unreported compound, SnP$_2$O$_6$ (n=1), which we find using global optimization structure prediction. The electronic structure calculations indicate that these compounds all have large band gaps above 3.2 eV, meaning their transparency to visible light. Several of these compounds show relatively low hole effective masses ($\sim$2-3 m$_0$), comparable the electron masses. This suggests potential bipolar conductivity depending on doping. The dispersive valence band-edges underlying the low hole masses, originate from the anti-bonding hybridization between the Sn 5s orbitals and the phosphate groups. Analysis of structure-property relationships for the metastable structures generated during structure search shows considerable variation in combinations of band gap and carrier effective masses, implying chemical tunability of these properties. The unusual combinations of relatively high band gap, low carrier masses and high chemical stability suggests possible optoelectronic applications of these Sn(II) phosphates, including p-type transparent conductors. Related to this, calculations for doped material indicate low visible light absorption, combined with high plasma frequencies.Comment: 10 pages, 10 figures, Supplementary informatio