Aeppli and Bott–Chern cohomology for bi-generalized Hermitian manifolds and d′d″-lemma

We define Aeppli and Bott–Chern cohomology for bi-generalized complex manifolds and show that they are finite dimensional for compact bi-generalized Hermitian manifolds. For totally bounded double complexes $(A,d^{\prime }{d}^{″})$, we show that the validity of $d^{\prime }{d}^{″}$-lemma is equivalent to having the same dimension of several cohomology groups. Some calculations of Bott–Chern cohomology groups of some bi-generalized Hermitian manifolds are given.     

Persistent luminescence and synchrotron radiation study of the Ca2MgSi2O7:Eu2+,R3+ materials

The tetragonal ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+},{\mathrm{R}}^{3+}$ persistent luminescence materials were prepared by a solid state reaction. The UV excited and persistent luminescence was observed in the green region centred at 535 nm. Both luminescence phenomena are due to the same ${\mathrm{Eu}}^{2+}$ ion occupying the single ${\mathrm{Ca}}^{2+}$ site in the host lattice. The ${\mathrm{R}}^{3+}$ codoping usually reduced the persistent luminescence of ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$, which differs from the ${\mathrm{M}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Sr},\mathrm{Ba})$ and ${\mathrm{MAl}}_2{\mathrm{O}}_4$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Ca},\mathrm{Sr})$ materials. Only the ${\mathrm{Tb}}^{3+}$ ion enhanced slightly the persistent luminescence. With the aid of synchrotron radiation, the band gap energy of ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ was found to be about 7 eV that is very similar to those of the ${\mathrm{M}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Sr},\mathrm{Ba})$ materials. Thermoluminescence results suggested that the ${\mathrm{R}}^{3+}$ ions might act as electron traps, but only the TL peaks created by ${\mathrm{Tm}}^{3+}$ and ${\mathrm{Sm}}^{3+}$ can be found in the temperature range accessible. Lattice defects (e.g. oxygen vacancies) are also important, since the same main thermoluminescence peak was observed at about $100{}^{\circ }\mathrm{C}$ with and without ${\mathrm{R}}^{3+}$ codoping.     

Quantum point contact conductance in normal metal/insulator/ metal/dx2−y2+idxy mixed wave superconductor junctions

The tunneling conductance in a normal metal/insulator/metal/$d_{x^2?y^2}+i{d}_{xy}$ mixed wave superconductor (N/I/N/$d_{x^2?y^2}+i{d}_{xy}$) junction is calculated, where the N/I/N region is a quantum wire. It is found in the single-mode case that the magnitude of the tunneling conductance near zero voltage is enhanced due to the Andreev bound state by quasiparticles with perpendicular and horizontal injection, and the zero-bias conductance varies with $L$ ($L$ is the distance from insulating layer to the interface of N/$d_{x^2?y^2}+i{d}_{xy}$ mixed wave superconductor). Splitting of the zero-bias conductance peak appears in the quantum point contact tunneling spectra for an N/I/N/$d_{x^2?y^2}+i{d}_{xy}$ junction, and several subgap peaks can split at the same time. On increasing both $L$ and the magnitude ratio of the two components for the $d_{x^2?y^2}+i{d}_{xy}$ mixed wave, the subgap resonances exhibit an alternately high and low behavior inside the energy gap. These results are different from those in d-wave and p-wave superconductor junctions.     

Pressure dependence of negative thermal expansion in Zr2(WO4)(PO4)2

Negative thermal expansion materials can experience significant stresses when they are used in composites. Under ambient conditions Zr₂(WO₄)(PO₄)₂ displays anisotropic negative thermal expansion (NTE) (${\alpha }_v=?14.0\left(10\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_a=?7.9\left(5\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_b=2.5\left(5\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_c=?8.7\left(2\right)\times 10^{?6}{K}^{?1}$ at 0 GPa). The effect of hydrostatic pressure on its thermal expansion characteristics was investigated by neutron diffraction between 300 and 60 K at pressures up to 0.3 GPa. No phase transitions were observed in the pressure and temperature range examined. The material was found to have a bulk modulus, B₀, of 61.3(8) GPa at ambient temperature, and unlike some other NTE materials, pressure had no detectable effect on thermal expansion (${\alpha }_v=?14.2\left(8\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_a=?7.9\left(3\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_b=2.9\left(5\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_c=?9.2\left(2\right)\times 10^{?6}{K}^{?1}$ at 0.3 GPa).     

Principal and secondary luminescence lifetime components in annealed natural quartz

Time-resolved luminescence spectra from quartz can be separated into components with distinct principal and secondary lifetimes depending on certain combinations of annealing and measurement temperature. The influence of annealing on properties of the lifetimes related to irradiation dose and temperature of measurement has been investigated in sedimentary quartz annealed at various temperatures up to $900{}^{\circ }\mathrm{C}$. Time-resolved luminescence for use in the analysis was pulse stimulated from samples at 470 nm between 20 and $200{}^{\circ }\mathrm{C}$. Luminescence lifetimes decrease with measurement temperature due to increasing thermal effect on the associated luminescence with an activation energy of thermal quenching equal to $0.68\pm 0.01\mathrm{eV}$ for the secondary lifetime but only qualitatively so for the principal lifetime component. Concerning the influence of annealing temperature, luminescence lifetimes measured at $20{}^{\circ }\mathrm{C}$ are constant at about $33\mathrm{\mu }\mathrm{s}$ for annealing temperatures up to $600{}^{\circ }\mathrm{C}$ but decrease to about $29\mathrm{\mu }\mathrm{s}$ when the annealing temperature is increased to $900{}^{\circ }\mathrm{C}$. In addition, it was found that lifetime components in samples annealed at $800{}^{\circ }\mathrm{C}$ are independent of radiation dose in the range 85–1340 Gy investigated. The dependence of lifetimes on both the annealing temperature and magnitude of radiation dose is described as being due to the increasing importance of a particular recombination centre in the luminescence emission process as a result of dynamic hole transfer between non-radiative and radiative luminescence centres.     

Pseudo anti-commuting and Ricci soliton real hypersurfaces in complex two-plane Grassmannians

In this paper, first we introduce a new notion of pseudo anti-commuting for real hypersurfaces in complex two-plane Grassmannians $G_2\left({\mathbb{C}}^{m+2}\right)$ and prove a complete classification theorem, which gives a shrinking Ricci soliton with potential Reeb flow on Hopf real hypersurfaces and a tube over a totally real totally geodesic $\mathbb{Q}{P}^n$, $m=2n$ in $G_2\left({\mathbb{C}}^{m+2}\right)$.