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The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type involving the duration of the dynamic process into optimization. We develop a novel version of the method of discrete approximations of its own qualitative and numerical values with establishing its well-posedness and strong convergence to optimal solutions of the controlled sweeping process. Using advanced tools of first-order and second-order variational analysis and generalized differentiation allows us to derive new necessary conditions for optimal solutions of the discrete-time problems and then, by passing to the limit in the discretization procedure, for designated local minimizers in the original problem of sweeping optimal control. The obtained results are illustrated by a numerical example 

Abstract We present the discovery of 118 new ultracool dwarf candidates, discovered using a new machine-learning tool, namedSMDET, applied to time-series images from the Wide-field Infrared Survey Explorer. We gathered photometric and astrometric data to estimate each candidate’s spectral type, distance, and tangential velocity. This sample has a photometrically estimated spectral class distribution of 28 M dwarfs, 64 L dwarfs, and 18 T dwarfs. We also identify a T-subdwarf candidate, two extreme T-subdwarf candidates, and two candidate young ultracool dwarfs. Five objects did not have enough photometric data for any estimations to be made. To validate our estimated spectral types, spectra were collected for two objects, yielding confirmed spectral types of T5 (estimated T5) and T3 (estimated T4). Demonstrating the effectiveness of machine-learning tools as a new large-scale discovery technique. 

Abstract We present the discovery of 13 new widely separated T dwarf companions to M dwarf primaries, identified using Wide-field Infrared Survey Explorer/NEOWISE data by the CatWISE and Backyard Worlds: Planet 9 projects (hereafter BYW). This sample represents an ∼60% increase in the number of known M + T systems, and allows us to probe the most extreme products of binary/planetary system formation, a discovery space made available by the CatWISE2020 catalog and the BYW effort. Highlights among the sample are WISEP J075108.79-763449.6, a previously known T9 thought to be old due to its spectral energy distribution, which was found by Zhang et al. (2021b) to be part of a common proper motion pair with L34-26 A, a well-studied young M3 V star within 10 pc of the Sun; CWISE J054129.32-745021.5 B and 2MASS J05581644-4501559 B, two T8 dwarfs possibly associated with the very fast-rotating M4 V stars CWISE J054129.32745021.5 A and 2MASS J05581644-4501559 A; and UCAC3 52-1038 B, which is among the widest late-T companions to main-sequence stars, with a projected separation of ∼7100 au. The new benchmarks presented here are prime JWST targets, and can help us place strong constraints on the formation and evolution theory of substellar objects as well as on atmospheric models for these cold exoplanet analogs.