Tilings of the sphere by congruent quadrilaterals II: edge combination a3ba^3 b with rational angles

Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of $a^3b$-quadrilaterals with all angles being rational degrees. There are $12$ sporadic and $3$ infinite sequences of quadrilaterals admitting the $2$-layer earth map tilings together with their modifications, and $3$ sporadic quadrilaterals admitting $4$ exceptional tilings. Among them only $3$ quadrilaterals are convex. New interesting non-edge-to-edge triangular tilings are obtained as a byproduct.Comment: 36 pages, 36 figures, 10 table

Uniaxial and hydrostatic pressure effects in alpha-RuCl3 single crystals via thermal-expansion measurements

We present high-resolution thermal-expansion and specific-heat measurements of single crystalline alpha-RuCl3. An extremely hysteretic structural transition expanding over 100 K is observed by thermal- expansion along both crystallographic axes, which we attribute to a change of stacking sequence of the RuCl3 layers. Three magnetic transitions are observed, which we link to the different stacking sequences. Using our data and thermodynamic relations, we derive the uniaxial and hydrostatic pressure derivatives of all three magnetic transitions. Our results demonstrate that magnetic order should be totally suppressed by very moderate pressures of 0.3 GPa to 0.9 GPa. Finally, we discuss why our results differ from recent hydrostatic pressure measurements and suggest a possible route to reaching the spin-liquid state in alpha-RuCl3.Comment: 6 pages, 3 figure

Tilings of the sphere by congruent quadrilaterals III: edge combination a3ba^3b with general angles

Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of $a^3b$-quadrilaterals with some irrational angle: there are a sequence of $1$-parameter families of quadrilaterals admitting $2$-layer earth map tilings together with their basic flip modifications under extra condition, and $5$ sporadic quadrilaterals each admitting a special tiling. A summary of the full classification is presented in the end.Comment: 29 pages, 22 figures, 12 tabl

Real estate rental market: a 10-year bibliometricbased review

The real estate rental market (RERM) is considered to have an important role in the entire real estate market. It refers to a property composed of land and its buildings, including the natural resources that can be rented or leased. Previous researches show that most developed countries have experienced the historical process of passively renting, actively buying, and actively renting. Moreover, academic interest in the impact of different sectors of the RERM has been reviewed increasingly over the past decade. However, previous studies provide limited insights into a comprehensive review of the RERM. Based on a 10-year database of 790 articles collected from the Web of Science, a comprehensive literature review is presented to discover the knowledge structure of RERM using CiteSpace software. First, this study recognizes the cluster of the articles, and discusses six major clusters in detail. Next, this study has identified four research trends that emerged during the past decade. To reveal the differences between the studies in the United States (US), China and the United Kingdom (UK), this study compares their publication scales and co-word networks. Finally, this study suggests six meaningful future research directions

Magnetic anisotropy in hole-doped superconducting Ba 0.67K 0.33Fe 2As2 probed by polarized inelastic neutron scattering

We use polarized inelastic neutron scattering (INS) to study spin excitations of optimally hole-doped superconductor Ba$_{0.67}$K$_{0.33}$Fe$_2$As$_{2}$ ($T_c=38$ K). In the normal state, the imaginary part of the dynamic susceptibility, $\chi^{\prime\prime}(Q,\omega)$, shows magnetic anisotropy for energies below $\sim$7 meV with c-axis polarized spin excitations larger than that of the in-plane component. Upon entering into the superconducting state, previous unpolarized INS experiments have shown that spin gaps at $\sim$5 and 0.75 meV open at wave vectors $Q=(0.5,0.5,0)$ and $(0.5,0.5,1)$, respectively, with a broad neutron spin resonance at $E_r=15$ meV. Our neutron polarization analysis reveals that the large difference in spin gaps is purely due to different spin gaps in the c-axis and in-plane polarized spin excitations, resulting resonance with different energy widths for the c-axis and in-plane spin excitations. The observation of spin anisotropy in both opitmally electron and hole-doped BaFe$_2$As$_2$ is due to their proximity to the AF ordered BaFe$_2$As$_2$ where spin anisotropy exists below $T_N$.Comment: 5 pages, 4 figure

Expression and function of ATP-dependent potassium channels in zebrafish islet β-cells

ATP-sensitive potassium channels (K(ATP) channels) are critical nutrient sensors in many mammalian tissues. In the pancreas, K(ATP) channels are essential for coupling glucose metabolism to insulin secretion. While orthologous genes for many components of metabolism–secretion coupling in mammals are present in lower vertebrates, their expression, functionality and ultimate impact on body glucose homeostasis are unclear. In this paper, we demonstrate that zebrafish islet β-cells express functional K(ATP) channels of similar subunit composition, structure and metabolic sensitivity to their mammalian counterparts. We further show that pharmacological activation of native zebrafish K(ATP) using diazoxide, a specific K(ATP) channel opener, is sufficient to disturb glucose tolerance in adult zebrafish. That β-cell K(ATP) channel expression and function are conserved between zebrafish and mammals illustrates the evolutionary conservation of islet metabolic sensing from fish to humans, and lends relevance to the use of zebrafish to model islet glucose sensing and diseases of membrane excitability such as neonatal diabetes