1-(4-Chloro-3-fluoro­phen­yl)-2-[(3-phenyl­isoquinolin-1-yl)sulfan­yl]ethanone

In the title compound, C23H15ClFNOS, the isoquinoline system and the 4-chloro-3-fluoro­phenyl ring are aligned at 80.4 (1)°. The dihedral angle between the isoquinoline system and the pendant (unsubstituted) phenyl ring is 19.91 (1)°

Effective constructions in plethysms and Weintraub's conjecture

We give a short proof of Weintraub's conjecture by constructing explicit highest weight vectors in the symmetric power of an even exterior power

Multifunctional ZnO nanorod-reduced graphene oxide hybrids nanocomposites for effective water remediation: Effective sunlight driven degradation of organic dyes and rapid heavy metal adsorption

We demonstrate the multi-functionality engineering on nanocomposite by combining one dimensional (1D) ZnO nanorod (NR) and two dimensional (2D) reduced graphene oxide (rGO) for efficient water remediation. Nano-engineered ZnO NR-rGO nanocomposites show efficient water remediation in terms of degradation of organic dyes and removal of heavy metal ions. Herein, we report on the fabrication of ZnO NR-rGO nanocomposite via a facile template-free hydrothermal route with an aim to improve the visible photocatalytic efficiency of the ZnO NR based nanocomposites. The structural and morphological features reveal that the rGO sheets are attached on the ZnO NRs and form a hybrid composite assembly. The surface enabled ZnO NR-rGO nanocomposites were used to degrade organic dye molecules (methylene blue (MB), methyl orange (MO) and rhodamine B (RhB)) under visible irradiation and adsorb Cu (II) and Co (II) ions from water through an adsorption process. The nanocomposite containing 7.5 wt% rGO and ZnO NRs shows a 4-fold enhancement in the visible photocatalytic activity and effective removal of Cu (II) and Co (II) ions from aqueous solution respectively. The photocatalytic performance is discussed in detail with respect to interaction between ZnO NRs and rGO sheets, light-harvesting properties of the nanocomposites. The effective experimental adsorption data also fit very well with the pseudo-second-order model which reveals the surface adsorption of metal ions. The results provide insight into a new method utilize for both visible photo degradation and adsorption for the removal of various wastewater pollutants. Construction of hybrid form of nanostructures delivers the effective catalytic properties with tunable functionalities for the water remediation. © 2017 Elsevier B.V

Extension of holomorphic functions and cohomology classes from non reduced analytic subvarieties

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are generalized versions of the Ohsawa-Takegoshi extension theorem, and borrow many techniques from the long series of papers by T. Ohsawa. The recent achievement that we want to point out is that the surjectivity property holds true for restriction morphisms to non necessarily reduced subvarieties, provided these are defined as zero varieties of multiplier ideal sheaves. The new idea involved to approach the existence problem is to make use of L 2 approximation in the Bochner-Kodaira technique. The extension results hold under curvature conditions that look pretty optimal. However, a major unsolved problem is to obtain natural (and hopefully best possible) L 2 estimates for the extension in the case of non reduced subvarieties -- the case when Y has singularities or several irreducible components is also a substantial issue.Comment: arXiv admin note: text overlap with arXiv:1703.00292, arXiv:1510.0523

1-(3,5-Dimethyl-1H-pyrazol-1-yl)-3-phenyl­isoquinoline

The mol­ecular conformation of the title compound, C20H17N3, is stabilized by an intramolecular C—H⋯N inter­action. The crystal structure shows inter­molecular C—H⋯π inter­actions. The dihedral angle between the isoquinoline unit and the phenyl ring is 11.42 (1)° whereas the isoquinoline unit and the pendent dimethyl pryrazole unit form a dihedral angle of 50.1 (4)°. Furthermore, the angle between the mean plane of the phenyl ring and the dimethyl pyrazole unit is 47.3 (6)°

3-(4-Methoxy­phen­yl)-1H-isochromen-1-one

The asymmetric unit of the title compound, C16H12O3, contains two crystallographically independent mol­ecules. The isochromene ring system is planar (maximum deviation 0.024 Å) and is oriented at dihedral angles of 2.63 (3) and 0.79 (3)° with respect to the methoxy­benzene rings in the two independent mol­ecules

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

3-Acetyl-6-chloro-1-ethyl-4-phenyl­quinolin-2(1H)-one

In the title compound, C19H16ClNO2, the dihedral angle between the plane of the phenyl substituent and 3-acetyl­quinoline unit is 75.44 (5)°. The crystal structure is stabilized by inter­molecular C—H⋯O hydrogen bond

Jordan Pairs, E6 and U-Duality in Five Dimensions

By exploiting the Jordan pair structure of U-duality Lie algebras in D = 3 and the relation to the super-Ehlers symmetry in D = 5, we elucidate the massless multiplet structure of the spectrum of a broad class of D = 5 supergravity theories. Both simple and semi-simple, Euclidean rank-3 Jordan algebras are considered. Theories sharing the same bosonic sector but with different supersymmetrizations are also analyzed.Comment: 1+41 pages, 1 Table; v2 : a Ref. and some comments adde