A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications

We extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound, and apply it to investigate the volume growth, total Betti number, and finite topological type of manifolds with nonasymptotically almost nonnegative Ricci curvature

Finite-dimensionality of attractors for wave equations with degenerate nonlocal damping

In this paper we study the fractal dimension of global attractors for a class of wave equations with (single-point) degenerate nonlocal damping. Both the equation and its linearization degenerate into linear wave equations at the degenerate point and the usual approaches to bound the dimension of the entirety of attractors do not work directly. Instead, we develop a new process concerning the dimension near the degenerate point individually and show the finite dimensionality of the attractor.Comment: 33 page

Culture and capture of fish in Chinese reservoirs

Published in Malaysia by Southbound Sdn. Bhd.Translated from the Chines

CARE: Confidence-rich Autonomous Robot Exploration using Bayesian Kernel Inference and Optimization

In this paper, we consider improving the efficiency of information-based autonomous robot exploration in unknown and complex environments. We first utilize Gaussian process (GP) regression to learn a surrogate model to infer the confidence-rich mutual information (CRMI) of querying control actions, then adopt an objective function consisting of predicted CRMI values and prediction uncertainties to conduct Bayesian optimization (BO), i.e., GP-based BO (GPBO). The trade-off between the best action with the highest CRMI value (exploitation) and the action with high prediction variance (exploration) can be realized. To further improve the efficiency of GPBO, we propose a novel lightweight information gain inference method based on Bayesian kernel inference and optimization (BKIO), achieving an approximate logarithmic complexity without the need for training. BKIO can also infer the CRMI and generate the best action using BO with bounded cumulative regret, which ensures its comparable accuracy to GPBO with much higher efficiency. Extensive numerical and real-world experiments show the desired efficiency of our proposed methods without losing exploration performance in different unstructured, cluttered environments. We also provide our open-source implementation code at https://github.com/Shepherd-Gregory/BKIO-Exploration.Comment: Full version for the paper accepted by IEEE Robotics and Automation Letters (RA-L) 2023. arXiv admin note: text overlap with arXiv:2301.0052

A Coumarin–Hemicyanine Deep Red Dye with a Large Stokes Shift for the Fluorescence Detection and Naked-Eye Recognition of Cyanide

In this study, we synthesized a coumarin–hemicyanine-based deep red fluorescent dye that exhibits an intramolecular charge transfer (ICT). The probe had a large Stokes shift of 287 nm and a large molar absorption coefficient (ε = 7.5 × 105 L·mol−1·cm−1) and is best described as a deep red luminescent fluorescent probe with λem = 667 nm. The color of probe W changed significantly when it encountered cyanide ions (CN−). The absorption peak (585 nm) decreased gradually, and the absorption peak (428 nm) increased gradually, so that cyanide (CN−) could be identified by the naked eye. Moreover, an obvious fluorescence change was evident before and after the reaction under irradiation using 365 nm UV light. The maximum emission peak (667 nm) decreased gradually, whilst the emission peak (495 nm) increased gradually, which allowed for the proportional fluorescence detection of cyanide (CN−). Using fluorescence spectrometry, the fluorescent probe W could linearly detect CN− over the concentration range of 1–9 μM (R2 = 9913, RSD = 0.534) with a detection limit of 0.24 μM. Using UV-Vis spectrophotometry, the linear detection range for CN− was found to be 1–27 μM (R2 = 0.99583, RSD = 0.675) with a detection limit of 0.13 μM. The sensing mechanism was confirmed by 1H NMR spectroscopic titrations, 13C NMR spectroscopy, X-ray crystallographic analysis and HRMS. The recognition and detection of CN− by probe W was characterized by a rapid response, high selectivity, and high sensitivity. Therefore, this probe provides a convenient, effective and economical method for synthesizing and detecting cyanide efficiently and sensitively