An sl(2, R) current algebra from AdS_3 gravity

We provide a set of chiral boundary conditions for three-dimensional gravity that allow for asymptotic symmetries identical to those of two-dimensional induced gravity in light-cone gauge considered by Polyakov. These are the most general boundary conditions consistent with the boundary terms introduced by Compere, Song and Strominger recently. We show that the asymptotic symmetry algebra of our boundary conditions is an sl(2,R) current algebra with level given by c/6. The fully non-linear solution in Fefferman--Graham coordinates is also provided along with its charges.Comment: 8 page

Benzyl N-{2-[5-(4-chloro­phen­yl)-1,2,4-oxadiazol-3-yl]propan-2-yl}carbamate

In the title 1,2,4-oxadiazole derivative, C19H18ClN3O3, the 1,2,4-oxadiazole ring makes dihedral angles of 12.83 (8) and 4.89 (8)°, respectively, with the benzyl and 4-chloro­phenyl rings, while the dihedral angle between the benzyl and 4-chloro­phenyl rings is 11.53 (7)°. In the crystal, mol­ecules are linked by N—H⋯N hydrogen bonds into helical chains along the b axis. A weak C—H⋯π inter­action is also present

1-{4-Chloro-2-[2-(2-fluoro­phen­yl)-1,3-dithio­lan-2-yl]phen­yl}-2-methyl-1H-imidazole-5-carbaldehyde

There are two mol­ecules in the asymmetric unit of the title imidazole derivative, C20H16ClFN2OS2. In one mol­ecule, the dithiol­ane ring is disordered over two positions in a 0.849 (9):0.151 (10) ratio. The imidazole ring makes dihedral angles of 79.56 (9) and 18.45 (9)° with the 4-chloro­phenyl and 2-fluoro­phenyl rings, respectively, in one mol­ecule; in the other mol­ecule, the corresponding angles are 82.72 (9) and 17.39 (10)°. In the crystal, mol­ecules are linked by weak C—H⋯O inter­actions and these linked mol­ecules are stacked along the b axis by π–π inter­actions with a centroid–centroid distance of 3.4922 (11) Å. In addition, π–π inter­actions between the imidazole and 2-fluoro­phenyl rings are also observed, with centroid–centroid distances of 3.4867 (11) and 3.4326 (10) Å. The crystal is further consolidated by weak C—H⋯π inter­actions. Cl⋯S [3.5185 (8) Å], C⋯O [3.192 (3) Å] and C⋯C [3.326 (2)–3.393 (3) Å] short contacts are also observed

A recent survey of permutation trinomials over finite fields

Constructing permutation polynomials is a hot topic in the area of finite fields, and permutation polynomials have many applications in different areas. Recently, several classes of permutation trinomials were constructed. In 2015, Hou surveyed the achievements of permutation polynomials and novel methods. But, very few were known at that time. Recently, many permutation binomials and trinomials have been constructed. Here we survey the significant contribution made to the construction of permutation trinomials over finite fields in recent years. Emphasis is placed on significant results and novel methods. The covered material is split into three aspects: the existence of permutation trinomials of the respective forms $x^{r}h(x^{s})$, $\lambda_{1}x^{a}+\lambda_{2}x^{b}+\lambda_{3}x^{c}$ and $x+x^{s(q^{m}-1)+1} +x^{t(q^{m}-1)+1}$, with Niho-type exponents $s, t$

TIRSPEC : TIFR Near Infrared Spectrometer and Imager

We describe the TIFR Near Infrared Spectrometer and Imager (TIRSPEC) designed and built in collaboration with M/s. Mauna Kea Infrared LLC, Hawaii, USA, now in operation on the side port of the 2-m Himalayan Chandra Telescope (HCT), Hanle (Ladakh), India at an altitude of 4500 meters above mean sea level. The TIRSPEC provides for various modes of operation which include photometry with broad and narrow band filters, spectrometry in single order mode with long slits of 300" length and different widths, with order sorter filters in the Y, J, H and K bands and a grism as the dispersing element as well as a cross dispersed mode to give a coverage of 1.0 to 2.5 microns at a resolving power R of ~1200. The TIRSPEC uses a Teledyne 1024 x 1024 pixel Hawaii-1 PACE array detector with a cutoff wavelength of 2.5 microns and on HCT, provides a field of view of 307" x 307" with a plate scale of 0.3"/pixel. The TIRSPEC was successfully commissioned in June 2013 and the subsequent characterization and astronomical observations are presented here. The TIRSPEC has been made available to the worldwide astronomical community for science observations from May 2014.Comment: 20 pages, 21 figures, 2 tables. Accepted for publication in Journal of Astronomical Instrumentatio

N′-(4-Fluoro­benzyl­idene)-2-(4-fluoro­phen­yl)acetohydrazide

In the title compound, C15H12F2N2O, the dihedral angle between the two benzene rings is 48.73 (8)°. The hydrazine group is twisted slightly, with a C—N—N—C torsion angle of 172.48 (12)°. In the crystal, mol­ecules are connected by strong N—H⋯O and weak C—H⋯O hydrogen bonds, forming supra­molecular chains along the c axis. The structure is consolidated by π–π [centroid–centroid separation = 3.6579 (10) Å] and C—H⋯π inter­actions

SYNTHESIS, AB INITIO STRUCTURE DETERMINATION, AND CHARACTERIZATION OF MANGANESE(III) PHENYL PHOSPHONATES

ABSTRACT , space group P1, and Z ϭ 2. The final agreement factors were R WP ϭ 12.8%, R P ϭ 9.1%, and R F ϭ 3.2%. There are 22 non-hydrogen atoms in the asymmetric part of the unit cell, and the positional parameters were refined with the help of soft constraints. The octahedral manganese coordination spheres are distorted due to the Jahn-Teller effect. The structure of this organic-inorganic compound is layered. The thermal behavior of Mn(HO 3 PC 6 H 5 )(O 3 PC 6 H 5 )⅐H 2 O was studied and its thermal decomposition product was identified. © 1998 Elsevier Science Lt