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In this note, we prove that minimizers of convex functionals with a convexity constraint and a general class of Lagrangians can be approximated by solutions to fourth-order Abreu-type equations. Our result generalizes that of Le (Twisted Harnack inequality and approximation of variational problems with a convexity constraint by singular Abreu equations.Adv. Math.434(2023)) where the case of quadratically growing Lagrangians was treated. 

Abstract We present a new method for identifying Galactic halo substructures accreted from dwarf galaxies by combining metallicity distribution functions (MDFs) with orbital parameters. Using apogalactic distance–orbital phase space, we assume that the MDF peak of a substructure reflects its progenitor’s chemical signature. We test this approach with two Galactic potentials (St $\ddot{a}$ckel and McMillan) and find consistent results. Our sample consists of retrograde halo stars with low orbital inclinations and intermediate eccentricities (0.5 < e≤ 0.7), drawn from Sloan Digital Sky Survey and Large sky Area Multi-Object Fiber Spectroscopic Telescope spectroscopy combined with Gaia DR3 astrometry. We identify four distinct low-inclination retrograde substructures (LRS 1, LRS 2, LRS 3, LRS 4) with MDF peaks at [Fe/H] = −1.5, −1.7, −1.9, and −2.1, respectively; LRS 3 is newly discovered. Further analysis reveals an additional stream (LRS 2B) with [Fe/H] = −2.3 embedded within LRS 2; the remaining LRS 2 stars (LRS 2A) are associated with Sequoia. LRS 1 is likely linked to Thamnos 2 and Arjuna, and LRS 4 is likely linked to I’itoi. Comparison with the ED-2 stream suggests that LRS 2B is chemically distinct, but high-resolution spectroscopy is required to confirm whether they originate from separate progenitors. Our MDF-based approach demonstrates the utility of chemodynamical space for uncovering halo substructures, while highlighting caveats such as metallicity gradients and redshift evolution of the mass–metallicity relation, which may blur the mapping between MDF peaks and progenitors. 

Abstract We report the discovery of a new subclass of carbon-enhanced metal-poor (CEMP) stars, characterized by high absolute carbon abundances (A(C) > 7.39) and extremely low metallicity ([Fe/H] ≤ –3.1) but notably lacking enhancements in neutron-capture elements, thus falling under the CEMP-no category. This population emerged from a detailed analysis of low-resolution spectroscopic data obtained from the Sloan Digital Sky Survey and the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, where the observed frequency trends with the decreasing metallicity of CEMP-s(s-process-enhanced) and CEMP-no (no neutron-capture enhanced) stars deviated from established expectations. In contrast to earlier findings, we observe a rise in high-A(C) stars below [Fe/H] = −3.1, which we interpret as a distinct group not accounted for in traditional CEMP classifications. Following the Yoon–Beers group classification, we define these stars as Group IV. Statistical modeling confirms their presence as a separate peak in theA(C) distribution, and available radial velocity data suggest that about 30% of Group IV stars may be binaries, indicating possible binary-related formation mechanisms. This discovery challenges the current CEMP-no star formation pathways and implies the existence of alternative or hybrid enrichment scenarios in the early Universe. High-resolution spectroscopic follow-up of Group IV candidates will be crucial for identifying their progenitors and understanding their evolutionary implications. 

Optically anisotropic materials are sought after for tailoring the polarization of light. Recently, colossal optical anisotropy (Δn = 2.1) was reported in a quasi-one-dimensional chalcogenide, Sr9/8TiS3. Compared to SrTiS3, the excess Sr in Sr9/8TiS3 leads to periodic structural modulations and introduces additional electrons, which undergo charge ordering on select Ti atoms to form a highly polarizable cloud oriented along the c-axis, hence resulting in the colossal optical anisotropy. Here, further enhancement of the colossal optical anisotropy to Δn = 2.5 in Sr8/7TiS3 is reported through control over the periodicity of the atomic-scale modulations. The role of structural modulations in tuning the optical properties in a series of SrxTiS3 compounds with x = [1, 9/8, 8/7, 6/5, 5/4, 4/3, 3/2] is investigated using density-functional-theory (DFT) calculations. The structural modulations arise from various stacking sequences of face-sharing TiS6 octahedra and twist-distorted trigonal prisms and are found to be thermodynamically stable for 1 < x < 1.5. As x increases, an indirect-to-direct band gap transition is predicted for x ≥ 8/7 along with an increased occupancy of Ti-dz2 states. Together, these two factors result in a theoretically predicted maximum birefringence of Δn = 2.5 for Sr8/7TiS3. Single crystals of Sr8/7TiS3 were grown using a molten-salt flux method. Single-crystal X-ray diffraction measurements confirm the presence of long-range order with a periodicity corresponding to Sr8/7TiS3, which is further corroborated by atomic-scale observations using scanning transmission electron microscopy. Polarization-resolved Fourier-transform infrared spectroscopy of Sr8/7TiS3 crystals shows Δn ≈ 2.5, in excellent agreement with the theoretical predictions. Overall, these findings demonstrate the compositional tunability of optical properties in SrxTiS3 compounds by control over atomic scale modulations and suggest that similar strategies could be extended to other compounds having modulated structures. 

Tracking activities holds great potential to improve the well-being of older adults, yet the accuracy of activity trackers for this demographic remains in question. Evaluating this accuracy requires ground-truth data directly from older adults, which has largely been gathered in controlled laboratory settings or labeled by researchers. Moreover, considering the diversity in older adults' activity engagement and tracking preferences, personalized activity tracking appears necessary. We demonstrate that older adults can benefit from personalized activity trackers by showing that cadence thresholds for stepping intensities vary within this group. However, collecting ground-truth data from older adults in real-world settings poses unique challenges. This paper examines two sources of ground-truth labels for the smartwatch Inertial Measurement Unit (IMU) data collected with older adults. Using verbal self-reports and a thigh-worn activity tracker, we assess their viability as ground-truth sources in natural settings. Additionally, we evaluate the costs and benefits of triangulating these sources as a ground-truth proxy. Our findings reveal two main costs: data shrinkage and notable effort from both contributors and data stewards. Simultaneously, we observe improved data quality and a greater ability to identify error sources when evaluating a trained model.