Polar foliations and isoparametric maps

A singular Riemannian foliation $F$ on a complete Riemannian manifold $M$ is called a polar foliation if, for each regular point $p$, there is an immersed submanifold $\Sigma$, called section, that passes through $p$ and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of $M$ into the orbits of a polar action, i.e., an isometric action with sections. In this work we prove that the leaves of $F$ coincide with the level sets of a smooth map $H: M\to \Sigma$ if $M$ is simply connected. In particular, we have that the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.Comment: 9 pages; The final publication is available at springerlink.com http://www.springerlink.com/content/c72g4q5350g513n1

Limitations on the smooth confinement of an unstretchable manifold

We prove that an m-dimensional unit ball D^m in the Euclidean space {\mathbb R}^m cannot be isometrically embedded into a higher-dimensional Euclidean ball B_r^d \subset {\mathbb R}^d of radius r < 1/2 unless one of two conditions is met -- (1)The embedding manifold has dimension d >= 2m. (2) The embedding is not smooth. The proof uses differential geometry to show that if d<2m and the embedding is smooth and isometric, we can construct a line from the center of D^m to the boundary that is geodesic in both D^m and in the embedding manifold {\mathbb R}^d. Since such a line has length 1, the diameter of the embedding ball must exceed 1.Comment: 20 Pages, 3 Figure

A factorization of a super-conformal map

A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a meromorphic function. Analogs of the Liouville theorem, the Schwarz lemma, the Schwarz-Pick theorem, the Weierstrass factorization theorem, the Abel-Jacobi theorem, and a relation between zeros of a minimal surface and branch points of a super-conformal map are obtained.Comment: 21 page

Identifiable Acetylene Features Predicted for Young Earth-like Exoplanets with Reducing Atmospheres Undergoing Heavy Bombardment

The chemical environments of young planets are assumed to be largely influenced by the impacts of bodies lingering on unstable trajectories after the dissolution of the protoplanetary disk. We explore the chemical consequences of impacts within the context of reducing planetary atmospheres dominated by carbon monoxide, methane, and molecular nitrogen. A terawatt high-power laser was selected in order to simulate the airglow plasma and blast wave surrounding the impactor. The chemical results of these experiments are then applied to a theoretical atmospheric model. The impact simulation results in substantial volume mixing ratios within the reactor of 5% hydrogen cyanide (HCN), 8% acetylene (C2H2), 5% cyanoacetylene (HC3N), and 1% ammonia (NH3). These yields are combined with estimated impact rates for the early Earth to predict surface boundary conditions for an atmospheric model. We show that impacts might have served as sources of energy that would have led to steady-state surface quantities of 0.4% C2H2, 400 ppm HCN, and 40 ppm NH3. We provide simulated transit spectra for an Earth-like exoplanet with this reducing atmosphere during and shortly after eras of intense impacts. We predict that acetylene is as observable as other molecular features on exoplanets with reducing atmospheres that have recently gone through their own "heavy bombardments," with prominent features at 3.05 and 10.5 μm

Laser-induced breakdown spectroscopy in space applications: Review and prospects

This review describes the principles and summarizes the challenges of analytical methods based on optical emission spectroscopy (OES) in space applications, with a particular focus on Laser-Induced Breakdown Spectroscopy (LIBS). Over the past decade, LIBS has emerged as a powerful analytical technique for space exploration and In-Situ Resource Utilization (ISRU) of celestial bodies. Its implementation has been suggested for various segments of the Space Resources Value Chain, including prospecting, mining, and beneficiation. Current missions to Mars, including the ChemCam instrument on the Curiosity rover, the SuperCam on the Perseverance rover, and the MarSCoDe on the Zhurong rover, are considered flagship applications of LIBS. Despite neither the Pragyan rover nor the Vikram lander waking from the lunar night, the success of the Chandrayaan-3 mission marks another milestone in the development of LIBS instruments, with further missions, including commercial ones, anticipated. This paper reviews the deployment of LIBS payloads on Mars rovers, upcoming missions prospecting the Moon and asteroids, and LIBS analysis of meteorites. Additionally, it highlights the importance of data processing specific to space applications, emphasizing recent trends in transfer learning. Furthermore, LIBS combined with other spectroscopic techniques (e.g., Raman Spectroscopy, Mass Spectrometry, and Fourier-Transform Infrared Spectroscopy) represents an intriguing platform with comprehensive analytical capabilities. The review concludes by emphasizing the significance of LIBS-based contributions in advancing our understanding of celestial bodies and paving the way for future space exploration endeavor

Risks, benefits, and knowledge gaps of non-native tree species in Europe

Changing ecosystem conditions and diverse socio-economical events have contributed to an ingrained presence of non-native tree species (NNTs) in the natural and cultural European landscapes. Recent research endeavors have focused on different aspects of NNTs such as legislation, benefits, and risks for forestry, emphasizing that large knowledge gaps remain. As an attempt to fulfill part of these gaps, within the PEN-CAFoRR COST Action (CA19128) network, we established an open-access questionnaire that allows both academic experts and practitioners to provide information regarding NNTs from 20 European countries. Then, we integrated the data originating from the questionnaire, related to the country-based assessment of both peer-reviewed and grey literature, with information from available datasets (EUFORGEN and EU-Forest), which gave the main structure to the study and led to a mixed approach review. Finally, our study provided important insights into the current state of knowledge regarding NNTs. In particular, we highlighted NNTs that have shown to be less commonly addressed in research, raising caution about those characterized by an invasive behavior and used for specific purposes (e.g., wood production, soil recultivation, afforestation, and reforestation). NNTs were especially explored in the context of resilient and adaptive forest management. Moreover, we emphasized the assisted and natural northward migration of NNTs as another underscored pressing issue, which needs to be addressed by joint efforts, especially in the context of the hybridization potential. This study represents an additional effort toward the knowledge enhancement of the NNTs situation in Europe, aiming for a continuously active common source deriving from interprofessional collaboration. Copyright © 2022 Dimitrova, Csilléry, Klisz, Lévesque, Heinrichs, Cailleret, Andivia, Madsen, Böhenius, Cvjetkovic, De Cuyper, de Dato, Ferus, Heinze, Ivetić, Köbölkuti, Lazarević, Lazdina, Maaten, Makovskis, Milovanović, Monteiro, Nonić, Place, Puchalka and Montagnoli

Ariel – a window to the origin of life on early earth?

Is there life beyond Earth? An ideal research program would first ascertain how life on Earth began and then use this as a blueprint for its existence elsewhere. But the origin of life on Earth is still not understood, what then could be the way forward? Upcoming observations of terrestrial exoplanets provide a unique opportunity for answering this fundamental question through the study of other planetary systems. If we are able to see how physical and chemical environments similar to the early Earth evolve we open a window into our own Hadean eon, despite all information from this time being long lost from our planet’s geological record. A careful investigation of the chemistry expected on young exoplanets is therefore necessary, and the preparation of reference materials for spectroscopic observations is of paramount importance. In particular, the deduction of chemical markers identifying specific processes and features in exoplanetary environments, ideally “uniquely”. For instance, prebiotic feedstock molecules, in the form of aerosols and vapours, could be observed in transmission spectra in the near future whilst their surface deposits could be observed from reflectance spectra. The same detection methods also promise to identify particular intermediates of chemical and physical processes known to be prebiotically plausible. Is Ariel truly able to open a window to the past and answer questions concerning the origin of life on our planet and the universe? In this paper, we discuss aspects of prebiotic chemistry that will help in formulating future observational and data interpretation strategies for the Ariel mission. This paper is intended to open a discussion and motivate future detailed laboratory studies of prebiotic processes on young exoplanets and their chemical signatures

Ex situ germination of European acorns: data from 93 batches of 12 Quercus species

Key message: We provide data on seedlot germination potential-a key trait related to regeneration-of 12 oak species. Germination was tested at the University of Granada following international protocols with 8985 acorns from 93 batches and 16 countries across Europe. Data on germination probability, acorn origin, mass, and moisture content measured on another 4544 acorns are available at https://doi.org/10.30827/Digibug.87318. Associated metadata are available at https://metadata-afs.nancy.inra.fr/geonetwork/srv/fre/catalog.search#/metadata/a742c6d8-bc37-4ca2-8b81-2447c5a8858d