Let $F$ be a totally real field in which $p$ is unramified and let $B$ be a quaternion algebra over $F$ which splits at at most one infinite place. Let $\overline {r}:\operatorname {{\mathrm {Gal}}}(\overline {F}/F)\rightarrow \mathrm {GL}_2(\overline {\mathbb {F}}_p)$ be a modular Galois representation which satisfies the Taylor–Wiles hypotheses. Assume that for some fixed place $v|p$, $B$ ramifies at $v$ and $F_v$ is isomorphic to $\mathbb {Q}_p$ and $\overline {r}$ is generic at $v$. We prove that the admissible smooth representations of the quaternion algebra over $\mathbb {Q}_p$ coming from mod $p$ cohomology of Shimura varieties associated to $B$ have Gelfand–Kirillov dimension $1$. As an application we prove that the degree-two Scholze's functor (which is defined by Scholze [On the $p$-adic cohomology of the Lubin–Tate tower, Ann. Sci. Éc. Norm. Supér. (4) 51 (2018), 811–863]) vanishes on generic supersingular representations of $\mathrm {GL}_2(\mathbb {Q}_p)$. We also prove some finer structure theorems about the image of Scholze's functor in the reducible case.

Power scaling in conventional broad-area (BA) lasers often leads to the operation of higher-order lateral modes, resulting in a multiple-lobe far-field profile with large divergence. Here, we report an advanced sawtooth waveguide (ASW) structure integrated onto a wide ridge waveguide. It strategically enhances the loss difference between higher-order modes and the fundamental mode, thereby facilitating high-power narrow-beam emission. Both optical simulations and experimental results illustrate the significant increase in additional scattering loss of the higher-order modes. The optimized ASW lasers achieve an impressive output power of 1.1 W at 4.6 A at room temperature, accompanied by a minimal full width at half maximum lateral divergence angle of 4.91°. Notably, the far-field divergence is reduced from 19.61° to 11.39° at the saturation current, showcasing a remarkable 42% improvement compared to conventional BA lasers. Moreover, the current dependence of divergence has been effectively improved by 38%, further confirming the consistent and effective lateral mode control capability offered by our design.

The integration of camera and LiDAR technologies has the potential to significantly enhance construction robots’ perception capabilities by providing complementary construction information. Structured light cameras (SLCs) are a desirable alternative as they provide comprehensive information on construction defects. However, fusing these two types of information depends largely on the sensors’ relative positions, which can only be established through extrinsic calibration. This paper introduces a novel calibration algorithm considering a customized board for SLCs and repetitive LiDARs, which are designed to facilitate the automation of construction robots. The calibration board is equipped with four symmetrically distributed hemispheres, whose centers are obtained by fitting the spheres and adoption with the geometric constraints. Subsequently, the spherical centers serve as reference features to estimate the relationship between the sensors. These distinctive features enable our proposed method to only require one calibration board pose and minimize human intervention. We conducted both simulation and real-world experiments to assess the performance of our algorithm. And the results demonstrate that our method exhibits enhanced accuracy and robustness.

Dispersive and Strichartz estimates are obtained for solutions to the wave equation with a Laguerre potential in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the Schrödinger operator involved, we subsequently prove the dispersive estimate for the corresponding Schrödinger semigroup, obtain a Gaussian-type upper bound, establish Bernstein-type inequalities, and finally pass to the Müller–Seeger’s subordination formula. The desired Strichartz estimates follow by the established dispersive estimate and the standard argument of Keel–Tao.

Mineral-microbe interactions are widespread in a number of environmental processes such as mineral weathering, decomposition, and transformation. Both clay minerals and silicate-weathering bacteria are widely distributed in nature, and the latter contribute to weathering, diagenesis, and mineralization of major rock-forming minerals. The purpose of this study was to observe changes in the chemical composition and structure, especially the phase transformation, of smectite after processing by a silicate-weathering bacterium. The interaction between Bacillus mucilaginosus and bentonite was studied using custom culture media. Results from Inductively Coupled Plasma-Atomic Emission Spectrometry revealed that the bacterium promoted release of Si and Al from solid bentonite to solution. Concomitantly, the Ka nd Fe contents of the mineral increased as shown by X-ray photoelectron spectroscopy results. After interaction with the bacterium, the montmorillonite underwent a possible structure transformation to smectite, as indicated by the emergence of a new weak peak (d = 9.08 Å) shown by X-ray diffraction patterns. The mineralogical changes were also demonstrated by the decrease in the specific surface area of the mineral from 33.0 to 24.0 m2/g (these lower values for SSA of bentonite are related to the particle size of the smectite examined (120-160 mesh) and the weakened absorption bands in Al-O-H and Si-O-Si vibrations by Micro Fourier-transform infrared spectroscopy. The morphology changes in the bacteria observed by environmental scanning electron microscopy and atomic force microscopy revealed an obvious growth of the flagella in the presence of bentonite.

This article examines the earliest examples of replication of bronze objects of complicated structure in China. It uses four quadrupeds from the Freer Gallery (National Museum of Asian Art, Smithsonian Institution), the Asian Art Museum of San Francisco, the British Museum, and the Yūrinkan Museum in Kyōto as examples to illustrate the complex technology required in replicating bronzes. It provides evidence to define identical bronzes and proves that the four quadrupeds shared the same decorated model. The application of section-mold casting, spacers, clay cores, and mold section assemblage will be examined using 3D scanning, X-ray photography, computerized tomography (CT) scanning, and alloy composition analysis.

ZrO2:Eu3+ hollow spheres were successfully fabricated with the resin microspheres as the template. The sample characterizations were carried out by means of x-ray diffraction (XRD), scanning electron microscope (SEM), and photoluminescence spectra. XRD results revealed that Eu3+-doped samples were pure t-ZrO2 phase after being calcined at 873 K. SEM results exhibited that this Eu3+ doped ZrO2 was hollow spheres; the diameter and thickness of which were about 450 and 50 nm, respectively. Upon excitation at 394 nm, the orange-red emission bands at the wave length longer than 570 nm were from 5D0 → 7FJ (J = 1, 2) transitions. The asymmetry ratio of (5D0 → 7F2)/(5D0 → 7F1) intensity is about 1.61, 1.26, 1.42, 1.42, 1.40, and 1.38 for the Eu3+ concentration 0.4, 0.7, 1.0, 1.5, 2.0, and 2.5 mol%, respectively. These values suggest that the asymmetry ratio of Eu3+ ions is independent of the doping concentration. The optimal doping concentration of Eu3+ ions in ZrO2 is 1.5 mol%. According to Dexter's theory, the critical distance between Eu3+ ions for energy transfer was determined to be 16 Å.