A Frame Work for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to C0C^0 IP methods

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers reliable and efficient a posteriori error estimators. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posed ness of the problem. Subsequently, applications of $C^0$ interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings. Finally, we also discuss the variational discontinuous discretization method (without discretizing the control) and its corresponding error estimates.Comment: 23 pages, 5 figures, 1 tabl

3-(2-Amino-1-methyl-4-oxo-4,5-dihydro-1H-imidazol-5-yl)-3-hydr­oxy-1-phenyl­indolin-2-one ethanol solvate

In the title compound, C18H16N4O3·C2H5OH, mol­ecules are linked into chains by a series of inter­molecular N—H⋯O, N—H⋯N and O—H⋯O hydrogen bonds which stabilize the crystal structure. The indole and creatinine units make a dihedral angle of 56.45 (4)°. The title compound has two chiral centres. The crystal structure indicates the compound is racemic (RR and SS)

3-(2-Amino-1-methyl-4-oxo-4,5-dihydro-1H-imidazol-5-yl)-5-fluoro-3-hydr­oxy-1-methyl­indolin-2-one methanol hemisolvate

In the title compound, C13H13FN4O3·0.5CH3OH, mol­ecules are packed in the crystal structure by a series of O—H⋯N, N—H⋯O, N—H⋯F and O—H⋯O inter­molecular hydrogen bonds. The indole and creatinine units make a dihedral angle of 60.80 (4)°

Near-Infrared Spectroscopy of Carbon-Enhanced Metal-Poor Stars. I. A SOAR/OSIRIS Pilot Study

We report on an abundance analysis for a pilot study of seven Carbon-Enhanced Metal-Poor (CEMP) stars, based on medium-resolution optical and near-infrared spectroscopy. The optical spectra are used to estimate [Fe/H], [C/Fe], [N/Fe], and [Ba/Fe] for our program stars. The near-infrared spectra, obtained during a limited early science run with the new SOAR 4.1m telescope and the Ohio State Infrared Imager and Spectrograph (OSIRIS), are used to obtain estimates of [O/Fe] and 12C/13C. The chemical abundances of CEMP stars are of importance for understanding the origin of CNO in the early Galaxy, as well as for placing constraints on the operation of the astrophysical s-process in very low-metallicity Asymptotic Giant Branch (AGB) stars. This pilot study includes a few stars with previously measured [Fe/H], [C/Fe], [N/Fe],[O/Fe], 12C/13C, and [Ba/Fe], based on high-resolution optical spectra obtained with large-aperture telescopes. Our analysis demonstrates that we are able to achieve reasonably accurate determinations of these quantities for CEMP stars from moderate-resolution optical and near-infrared spectra. This opens the pathway for the study of significantly larger samples of CEMP stars in the near future. Furthermore, the ability to measure [Ba/Fe] for (at least the cooler) CEMP stars should enable one to separate stars that are likely to be associated with s-process enhancements (the CEMP-s stars) from those that do not exhibit neutron-capture enhancements (the CEMP-no stars).Comment: 27 pages, including 5 tables, 6 figures, accepted for publication in The Astronomical Journa

(Z)-Methyl 4-({3-[(2,5-dioxoimidazolidin-4-yl­idene)meth­yl]-1H-indol-1-yl}meth­yl)benzoate

In the title compound, C21H17N3O4, pairs of mol­ecules form a planar[maximum deviation 0.0566 (9) Å] centrosymmetric imidazole dimer via two N—H⋯O hydrogen bonds. These dimeric units are linked by further N—H⋯O hydrogen bonds between the ester carbonyl group and the imidazolidine ring, formiing chains parallel to the c-axis direction. In addition, there are π–π stacking inter­actions between the planar imidazole pairs, with an inter­planar spacing of 3.301 (2) Å. There is a double bond with Z geometry connecting the imidazolidine and indole units

Decoding the compositions of four bright rr-process-enhanced stars

There has been a concerted effort in recent years to identify the astrophysical sites of the $r$-process that can operate early in the Galaxy. The discovery of many $r$-process-enhanced (RPE) stars (especially by the $R$-process Alliance collaboration) has significantly accelerated this effort. However, only limited data exist on the detailed elemental abundances covering the primary neutron-capture peaks. Subtle differences in the structure of the $r$-process pattern, such as the relative abundances of elements in the third peak, in particular, are expected to constrain the $r$-process sites further. Here, we present a detailed elemental-abundance analysis of four bright RPE stars selected from the HESP-GOMPA survey. Observations were carried out with the 10-m class telescope Gran Telescopio Canarias (GTC), Spain. The high spectral signal-to-noise ratios obtained allow us to derive abundances for 20 neutron-capture elements, including the third $r$-process peak element osmium (Os). We detect thorium (Th) in two stars, which we use to estimate their ages. We discuss the metallicity evolution of Mg, Sr, Ba, Eu, Os, and Th in $r$-II and $r$-I stars, based on a compilation of RPE stars from the literature. The strontium (Sr) abundance trend with respect to europium (Eu) suggests the need for an additional production site for Sr (similar to several earlier studies); this requirement could be milder for yttrium (Y) and zirconium (Zr). We also show that there could be some time delay between $r$-II and $r$-I star formation, based on the Mg/Th abundance ratios.Comment: 33 pages, 22 figures, Accepted for publication in MNRA

(E,E)-1-Methyl-2,6-distyrylpyridinium iodide

In the title compound, C22H20N+·I−, the dihedral angles between the central pyridine ring and two outer benzene rings are 15.30 (10) and 11.82 (11)°. There are inter­molecular π–π stacking inter­actions between the nearest phenyl ring over an inversion-related pyridyl ring, the shortest centroid–centroid distance being 3.672 (3) Å. The crystal structure of the compound indicates the 2,6-distyryl substituents have an E configuration