Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted L_p-space. Moreover, we show that a judicious discretization of the representation leads to an atomic decomposition and to Banach frames for these coorbit spaces.     

Accurate Gain Flattening Filters Manufactured by Optical Compensation Monitoring Method

GFFs with less than 0.4 dB peak-to-peak error functions are routinely fabricated using commercially available coating machines by utilizing the natural error compensation mechanism of wavelength variable turning point optical monitoring method.     

Synthesis, crystal structure, and nonlinear optical behavior of beta-unsubstituted meso-meso E-vinylene-linked porphyrin dimers

[structure: see text] A vinylene-linked porphyrin dimer, with no substituents at the beta-positions, has been synthesized by CuI/CsF promoted Stille coupling. In the crystal structure of this dimer, the C(2)H(2) bridge is twisted by 45 degrees relative to the plane of the porphyrins. The absorption, emission spectra, and electrochemistry reveal substantial porphyrin-porphyrin pi-conjugation. The triplet excited-state absorption spectrum of this dimer makes it suitable for reverse saturable absorption at 710-900 nm.     

A twenty-four membered mixed-metal macrocycle; synthesis and structure of cyclo-[(3-Me-1,2-C6H3O2)2SbNa(THF)2]6

The first example of a twenty-four membered mixed p-/s-block macrocycle, cyclo-[(3-Me-1,2-C6H3O2)2SbNa(THF)2]6 1 has been synthesised and structurally characterised from the reaction between 3-Me-1,2-C6H3(OH)(ONa) and (Me2N)2Sb(CH2)3Sb(NMe2)2.     

New Cu(II) complexes with polydentate chelating Schiff base ligands: Synthesis, structures, characterisations and biochemical activity studies

We have reported herein the synthesis of three new Cu(II) complexes of tri- and tetradentate Schiff base ligands containing N₃ or N₄ donor set along with terminal NNN⁻ or SCN⁻ ligands: [L¹Cu(NCS)]ClO₄ (1), [L²Cu(NCS)₂] (2) and [L³Cu(NNN)]ClO₄ (3) [L¹ = NC₅H₄C(CH₃)=N(CH₂)₃N=C(CH₃)C₅H₄N, L²= Me₂N–(CH₂)₃–N=C(CH₃)C₅H₄N and L³ = NC₅H₄CH=N–(CH₂)₄–N=CHC₅H₄N]. The complexes have been systematically characterised by elemental, spectroscopic and electrochemical techniques. Antimicrobial activities of the Schiff base ligands and their metal complexes have been studied using the disc diffusion method on the strains of Candida tropicalis and Bacillus megaterium. Structures of all the complexes have been unequivocally established from single crystal X-ray diffraction analyses that show the monomeric units containing a five-coordinated copper center in highly distorted square pyramidal geometry with thiocyanate or azide anion coordinated as terminal ligand. The complexes 1 and 3 crystallise in monoclinic (P2₁/c) and 2 in triclinic (P-1) space group, respectively.     

Characterisation and cryomagnetic study of a hydrothermally synthesised hydrogen bonded L–M–L type co-ordination polymer

A ligand–metal–ligand type co-ordination polymer [Ni (C₆H₁₂N₄)(NCS)₂(H₂O)₂] _n has been synthesised under controlled hydrothermal conditions. Here 1,3,5,7-tetraazatricyclo[3.3.1]decane [or hexamethylenetetramine (hmt)] has been used as a μ-(N,N′) bidentate spacer molecule. The prepared polymeric complex has been characterised by elemental and spectral analyses. The structure has been confirmed by a single crystal X-ray diffraction study. Magneto-structural correlation has been drawn from cryomagnetic susceptibility measurements (2–300 K) which unequivocally reflects very weak magnetic spin interactions among the long distant octahedral Ni(II) metal centres mediated by hmt and weak hydrogen bonding interactions between the adjacent zigzag one-dimensional polymeric chains carrying into a two-dimensional infinite polymeric framework.     

Reactions of [HOs3(CO)8{µ3-Ph2PCH(R)P(Ph)C6H4}] (R = H,Me) with Bu3SnH: synthesis and structure of bimetallic Os-Sn clusters

Reactions of unsaturated [HOs₃(CO)₈{µ₃-Ph₂PCH(R)P(Ph)C₆H₄}] (R?=?H, Me) with Bu₃SnH are examined. [HOs₃(CO)₈{µ₃-Ph₂PCH(R)P(Ph)C₆H₄}] reacts with Bu₃SnH at room temperature to afford [H₂Os₃(CO)₈(SnBu₃){µ₃-Ph₂PCH(R)P(Ph)C₆H₄}] (1) via oxidative addition of the Sn?H bond to the parent cluster. Heating 1 in refluxing toluene leads to the formation of [H₂Os₃(CO)₇(SnBu₃){µ₃-Ph₂PCH(R)P(Ph)C₆H₄}] (2) through decarbonylation. Cluster 2 exists in two isomeric forms in solution which has been probed by VT NMR spectroscopy. The new Os-Sn bimetallic clusters have been characterized by a combination of analytical and spectroscopic data together with single-crystal X-ray diffraction analysis.

Graphic abstract

     

Oxidative Rearrangement of Substituted Arylalkyl Ketones with Thallium (III) Nitrate: Synthesis of 2,7-Dihydroxycadalene

Synthesis of methyl 2-(3′-methoxy-4′-methylphenyl)-propionate via the T1(NO₃)₃-induced oxidative rearrangement of 3′-methoxy-4′-methylpropiophenone.