Sharp Lp estimates for the ∂bequation on the boundaries of real ellipsoids in Cn

In this paper we prove the best possible L^p estimates for the ?-_b -equation on the boundaries of real ellipsoids in Cⁿ, and provide examples to show why they cannot be improved.     

Congruence subgroups in group rings *

For a large class of groups G a precise congruence subgroup of the group generated by the bicyclic units of the integral group ring ZG is determined. As an application an upper bound is calculated for the index in the unit group of ZG for the group generated by the Bass cyclic units and the bicyclic units.     

John Bell and the Identical Twins

I present a biographical profile of John S. Bell based upon extensive interviews I had with him. I present Bell‘s views on the quantum theory along with a simple explanation of his identity. Jeremy Bernstein is Professor Emeritus of Physics at the Stevens Institute of Technology and a former staff writer for The New Yorker.     

Synthesis and Characterization of Bis(methyl-2-pyridylmethylidenedrazinecarbodithioate)manganese(II)

Abstract  Brown crystals of title compound, bis(methyl-2-pyridylmethylidene-drazinecarbodithioate)manganese(II), was formed by reaction of methyl-2-pyridylmethylidenehydrazinecarbodithioate(HNNS) with manganese perchlorate at 323 K temperature and recrystallized from ethanol at room temperature, crystallizing in the monoclinic system, space group P2(1)/n, with a = 11.631(2), b = 14.010(3), c = 13.128(3) ?, β = 105.791(11)°; V = 2058.6(7)  ?³, D _c  = 1.533 g/cm³, Z = 4, C₁₆H₁₆N₆MnS₄, M _r  = 475.53, μ(M₀ K _α ) = 1.060 mm⁻¹, F (000) = 972. The structure was refined to R = 0.0441, wR = 0.1196 for 3,682 (I > 2σ(I)) reflections and S = 1.110. In title complex the coordination geometry about manganese is distorted octahedral and the two ligands in the mer configuration (S and tertiary N atom cis to each other and the iminic N atoms trans). Furthermore, the neutral molecule units Mn^II(NNS)₂ are connected by hydrogen bonds C–H···N and C–H···S and form a three dimensional ordered network structure. Graphical Abstract  The title compound, Mn(NNS)₂, exists as discrete molecules in which the central MnII atom is coordinated by two S atoms and four N atoms from two ligands NNS- molecules in a mer-octahedral configuration. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Sensitivity enhancement in natural-abundance solid-state 33S MAS NMR spectroscopy employing adiabatic inversion pulses to the satellite transitions

The WURST (wideband uniform rate smooth truncation) and hyperbolic secant (HS) pulse elements have each been employed as pairs of inversion pulses to induce population transfer (PT) between the four energy levels in natural abundance solid-state (33)S (spin I=3/2) MAS NMR, thereby leading to a significant gain in intensity for the central transition (CT). The pair of inversion pulses are applied to the satellite transitions for a series of inorganic sulfates, the sulfate ions in the two cementitious materials ettringite and thaumasite, and the two tetrathiometallates (NH(4))(2)WS(4) and (NH(4))(2)MoS(4). These materials all exhibit (33)S quadrupole coupling constants (C(Q)) in the range 0.1-1.0 MHz, with precise C(Q) values being determined from analysis of the PT enhanced (33)S MAS NMR spectra. The enhancement factors for the WURST and HS elements are quite similar and are all in the range 1.74-2.25 for the studied samples, in excellent agreement with earlier reports on HS enhancement factors (1.6-2.4) observed for other spin I=3/2 nuclei with similar C(Q) values (0.3-1.2 MHz). Thus, a time saving in instrument time by a factor up to five has been achieved in natural abundance (33)S MAS NMR, a time saving which is extremely welcome for this important low-gamma nucleus.     

Biocatalysis for C–S bond formation: Porcine pancreatic lipase (PPL) catalysed thiolysis/hydrothiolation reactions in sole water

In this paper, a biocatalytic route is described wherein PPL, lipase from porcine pancreas, in conjunction with water on reaction with different thiophenols and styrene oxides undergo thiolysis with C-S bond formation without the use of any metal catalysts, oxidants, bases, additives or organic solvents towards formation of β-hydroxysulfides in good to excellent yields with high regioselectivity at room temperature. Furthermore, PPL also facilitates thiophenols to undergo hydrothiolation with styrenes or phenylacetylenes in sole water and thus forming linear thioethers or vinylsulfides respectively via C–S bond formation. In addition to the straightforward and atom-efficient protocol, a gram-scale synthesis of β-hydroxysulfide and recyclability for three consecutive cycles without decrease in efficiency of PPL make our biocatalytic protocol for constructing C–S bond highly valuable from both environmental and economic viewpoints than traditional chemical practices.     

A novel and efficient asymmetric synthesis of anti-HIV drug maraviroc

A novel and efficient route to asymmetric synthesis of Maraviroc by using (S)-tert-butanesulfinamide as chiral auxiliary is described. Two interesting impurities of the process are isolated and identified. The synthesis was concise, mild, and easy to operate. The overall yield and stereoselectivity were excellent.     

Modifications of 5,12-dihydroindolo[3,2-a]carbazole scaffold via its regioselective C2,9-formylation and C2,9-acetylation

The effective approaches for regioselective double formylation and acetylation of 5,12-dialkyl-6,7-diaryl-substituted 5,12-dihydroindolo[3,2-a]carbazoles by their treatment with dichloromethyl methyl ether in the presence of SnCl₄ or with acetyl chloride in the presence of AlCl₃ to afford the 2,9-diformyl or 2,9-diacetyl derivatives, respectively, were developed. Furthermore, new 2,9-bis(2,2-dicyanovinyl) derivatives were synthesized by the Knoevenagel condensation of diformyl-containing substrates with malononitrile, when new 2,9-bis(quinoxaline-2-yl)- and 2,9-bis(benzo[g]quinoxaline-2-yl) derivatives were formed via microwave-promoted oxidation of diacetyl-containing substrates with SeO₂ to the corresponding diglyoxals, followed by the reaction of these intermediates with o-phenylendiamine or 2,3-diaminonaphthalene, respectively. The basic optical and electrochemical properties of some 5,12-dihydroindolo[3,2-a]carbazoles were investigated.     

New Transition Metal Oxo‐Thiostannate: Synthesis,Characterization, and Investigation of its Photocatalytic Properties

The new transition metal oxo‐thiostannate {[Ni(cyclen)]₆[Sn₆S₁₂O₂(OH)₆]} · 2(ClO₄) · 19H₂O ( 1 ) was prepared under hydrothermal conditions using Na₄SnS₄ · 14H₂O and [Ni(cyclen)](ClO₄)₂ as reactants. In the crystal structure the rare [Sn₆S₁₂O₂(OH)₆]^10– anion is observed, which is composed of SnS₂O(OH)₃ and SnS₄O₂ octahedra, and SnS₄ tetrahedra sharing edges and corners. The anion is expanded by six Ni²⁺ centered complexes via Ni–S and Ni–OH bonds. The photocatalytic properties for the visible light driven hydrogen evolution reaction shows that 26.6 mmol · g^–1 H₂ were evolved after 3 h.     

A Robust Solid Electrolyte Interphase Layer Augments the Ion Storage Capacity of Bimetallic‐Sulfide‐Containing Potassium‐Ion Batteries

Metal–organic framework‐derived NiCo_2.5S₄ microrods wrapped in reduced graphene oxide (NCS@RGO) were synthesized for potassium‐ion storage. Upon coordination with organic potassium salts, NCS@RGO exhibits an ultrahigh initial reversible specific capacity (602 mAh g^?1 at 50 mA g^?1) and ultralong cycle life (a reversible specific capacity of 495 mAh g^?1 at 200 mA g^?1 after 1 900 cycles over 314 days). Furthermore, the battery demonstrates a high initial Coulombic efficiency of 78 %, outperforming most sulfides reported previously. Advanced ex situ characterization techniques, including atomic force microscopy, were used for evaluation and the results indicate that the organic potassium salt‐containing electrolyte helps to form thin and robust solid electrolyte interphase layers, which reduce the formation of byproducts during the potassiation–depotassiation process and enhance the mechanical stability of electrodes. The excellent conductivity of the RGO in the composites, and the robust interface between the electrodes and electrolytes, imbue the electrode with useful properties; including, ultrafast potassium‐ion storage with a reversible specific capacity of 402 mAh g^?1 even at 2 A g^?1.