Paleontology provides insights into the history of the planet, from the origins of life billions of years ago to the biotic changes of the Recent. The scope of paleontological research is as vast as it is varied, and the field is constantly evolving. In an effort to identify “Big Questions” in paleontology, experts from around the world came together to build a list of priority questions the field can address in the years ahead. The 89 questions presented herein (grouped within 11 themes) represent contributions from nearly 200 international scientists. These questions touch on common themes including biodiversity drivers and patterns, integrating data types across spatiotemporal scales, applying paleontological data to contemporary biodiversity and climate issues, and effectively utilizing innovative methods and technology for new paleontological insights. In addition to these theoretical questions, discussions touch upon structural concerns within the field, advocating for an increased valuation of specimen-based research, protection of natural heritage sites, and the importance of collections infrastructure, along with a stronger emphasis on human diversity, equity, and inclusion. These questions offer a starting point—an initial nucleus of consensus that paleontologists can expand on—for engaging in discussions, securing funding, advocating for museums, and fostering continued growth in shared research directions.

In this paper, we investigate Kolmogorov-type theorems for small perturbations of degenerate Hamiltonian systems. These systems are index by a parameter ξ as $ H(y,x,\xi) = \langle\omega(\xi),y\rangle {+ \bar h(y,\xi)}+\varepsilon P(y,x,\xi,\varepsilon) $, where ɛ > 0. We assume that the frequency mapping $\omega(\cdot)$, $\bar h(y,\cdot)=O(|y|^2)$ and the perturbation $\varepsilon P(y,x,\cdot, \varepsilon)$ maintain Hölder continuity about ξ. We prove that the persistent invariant tori retain the same frequency as those of the unperturbed tori, under a certain topological degree condition and a weak convexity condition for the frequency mapping. Notably, this paper presents, to our understanding, pioneering results on the KAM theorem under such conditions with only assumption of Hölder continuous dependence of frequency mapping ω on the parameter.

The discovery that blazars dominate the extra-galactic $\gamma$-ray sky is a triumph in the Fermi era. However, the exact location of $\gamma$-ray emission region still remains in debate. Low-synchrotron-peaked blazars (LSPs) are estimated to produce high-energy radiation through the external Compton process, thus their emission regions are closely related to the external photon fields. We employed the seed factor approach proposed by Georganopoulos et al. It directly matches the observed seed factor of each LSP with the characteristic seed factors of external photon fields to locate the $\gamma$-ray emission region. A sample of 1 138 LSPs with peak frequencies and peak luminosities was adopted to plot a histogram distribution of observed seed factors. We also collected some spectral energy distributions (SEDs) of historical flare states to investigate the variation of $\gamma$-ray emission region. Those SEDs were fitted by both quadratic and cubic functions using the Markov-chain Monte Carlo method. Furthermore, we derived some physical parameters of blazars and compared them with the constraint of internal $\gamma\gamma$-absorption. We find that dusty torus dominates the soft photon fields of LSPs and most $\gamma$-ray emission regions of LSPs are located at 1–10 pc. The soft photon fields could also transition from dusty torus to broad line region and cosmic microwave background in different flare states. Our results suggest that the cubic function is better than the quadratic function to fit the SEDs.

We introduce the notion of completed $F$-crystals on the absolute prismatic site of a smooth $p$-adic formal scheme. We define a functor from the category of completed prismatic $F$-crystals to that of crystalline étale $\mathbf {Z}_p$-local systems on the generic fiber of the formal scheme and show that it gives an equivalence of categories. This generalizes the work of Bhatt and Scholze, which treats the case of a mixed characteristic complete discrete valuation ring with perfect residue field.

Creating an environmentally friendly precursor to form a kaolinite intercalation compound is important for promoting the applications of nanohybrid kaolinite in electrochemical sensors, low- or zero-toxicity drug carriers, and clay-polymer nanocompounds. In the present study, a stable hydrated kaolinite pre-cursor with d001= 0.84 nm was prepared successfully by heating the transition phase, the as-prepared kaolinite-hydrazine intercalate, at temperatures between 40 and 70ºC. The structure of the hydrated kaolinite was characterized by X-ray diffraction and infrared spectroscopy. The morphology was examined using scanning electron microscopy. The results showed that the hydrated hydrazine of the transition phase was easy to decompose to hydrazines and water molecules in the interlayer at 40-70ºC. Hydrazine molecules de-intercalated gradually, and water molecules remained in the ditrigonal holes of the silicate layer with sufficient stability, finally forming the stable 0.84 nm hydrated kaolinite in the system with a success rate of 80–90%. The 0.84 nm hydrated kaolinite may become an excellent precursor for the preparation of other kaolinite intercalates. A degree of intercalation of ~100% was obtained for the kaolinite-ethylene glycol intercalate, and a degree of intercalation of ~80% was obtained for the kaolinite-glycine intercalate from the 0.84 nm hydrated kaolinite precursor.

This paper studies the synchronization control of the blanket remote maintenance robot (BRMR) of the China fusion engineering test reactor (CFETR). First, the general state space mathematical model of BRMR was established by using a physical-based method. Second, based on the receding horizon optimization of model predictive control (MPC) and cross-coupling error reduction in cross-coupling control (CCC), the innovative MPC-CCC controller was proposed to realize the single-system and multisystem error convergence and high accuracy transportation of blanket through the high accuracy synchronization control of BRMR. Third, to verify the control effectiveness of the MPC-CCC controller, two types of simulations and experiments were implied compared with the original proportional-integral (PI) controller in Mover. Results showed that simulation and experiments were highly consistent. It is found that the use of an MPC-CCC controller can result in up to a 70% reduction in displacement error and up to a 59% reduction in synchronization error compared to the PI controller. And the accuracy of the MPC-CCC controller satisfies the real requirement of the maintenance process of the blanket. This work provides the theoretical basis and practical experience for the highly stable, safe, and efficient maintenance of blankets in the future.

In this paper, we provide a new approach to prove some weighted-blowup formulae for genus zero orbifold Gromov–Witten invariants. As a consequence, we show the invariance of symplectically rational connectedness with respect to weighted-blowup along positive centers. Furthermore, we use this method to give a new proof to the genus zero relative-orbifold correspondence of Gromov–Witten invariants.