Horizonless,singularity-free,compact shells satisfying NEC

Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition (NEC) collapses to the extent a closed trapped surface is formed, a singularity is inevitable according to Penrose’s singularity theorem. Since positive mass vacuum solutions are generally black holes with trapped surfaces inside the event horizon, matter cannot collapse to an arbitrarily small size without generating a singularity. However, in modified theories of gravity where positive mass vacuum solutions are naked singularities with no trapped surfaces, it is reasonable to expect that matter can collapse to an arbitrarily small size without generating a singularity. Here we examine this possibility in the context of a modified theory of gravity with torsion in an extra dimension. We study singularity-free static shell solutions to evaluate the validity of NEC on the shell. We find that with sufficiently high pressure, matter can be collapsed to arbitrarily small size without violating NEC and without producing a singularity.     

Amino-functionalized MIL-101(Fe) metal-organic framework as a viable fluorescent probe for nitroaromatic compounds

Microchimica Acta - A highly luminescent iron(III)-based amino-functionalized metal-organic framework (MOF) of type NH2-MIL-101(Fe) was synthesized by a solvothermal method. Its structure and...     

Three structures of dispirooxindole derivatives generated in situ through a three‐component one‐pot strategy with complete regio‐ and stereoselectivity

The challenging molecular architecture of spirooxindoles is appealing to chemists because it evokes novel synthetic strategies that address configurational demands and provides platforms for further reaction development. The [3+2] cycloaddition of the carbonyl ylide with arylideneoxindole via a five‐membered cyclic transition state gave a novel class of dispirooxindole derivatives, namely tert‐butyl 4′‐(4‐bromophenyl)‐1′′‐methyl‐2,2′′‐dioxo‐5′‐phenyl‐4′,5′‐dihydrodispiro[indoline‐3,2′‐furan‐3′,3′′‐indoline]‐1‐carboxylate, C₃₆H₃₁BrN₂O, (Ia), 5′‐(4‐bromophenyl)‐1,1′′‐dimethyl‐4′‐phenyl‐4′,5′‐dihydrodispiro[indoline‐3,2′‐furan‐3′,3′′‐indoline]‐2,2′′‐dione, C₃₂H₂₅BrN₂O₃, (Ib), and tert‐butyl 1′′‐methyl‐2,2′′‐dioxo‐4′‐phenyl‐5′‐(p‐tolyl)‐4′,5′‐dihydrodispiro[indoline‐3,2′‐furan‐3′,3′′‐indoline]‐1‐carboxylate, C₃₇H₃₄N₂O₅, (Ic). Crystal structure analyses of these dispirooxindoles revealed the formation of two diastereoisomers selectively and confirmed their relative stereochemistry (SSSR and RRRS). In all three structures, intramolecular C—H...O and π–π interactions between oxindole and dihydrofuran rings are the key factors governing the regio‐ and stereoselectivity, and in the absence of conventional hydrogen bonds, their crystal packings are strengthened by intermolecular C—H...π interactions.     

Mycothiol disulfide reductase: solid phase synthesis and evaluation of alternative substrate analogues

A solid phase synthesis of des-myo-inositol mycothiol disulfide and its alpha-configured methyl- and benzyl-glycoside derivatives has been developed. Kinetic characterisation of these compounds has demonstrated their viability as alternative substrates for use in mycothiol disulfide reductase enzyme assays.     

On reduced semidefinite programs for second order moment bounds with applications

We show that the complexity of computing the second order moment bound on the expected optimal value of a mixed integer linear program with a random objective coefficient vector is closely related to the complexity of characterizing the convex hull of the points \(\{{1 \atopwithdelims (){\varvec{x}}}{1 \atopwithdelims (){\varvec{x}}}' \ | \ {\varvec{x}} \in {\mathcal {X}}\}\) where \({\mathcal {X}}\) is the feasible region. In fact, we can replace the completely positive programming formulation for the moment bound on \({\mathcal {X}}\), with an associated semidefinite program, provided we have a linear or a semidefinite representation of this convex hull. As an application of the result, we identify a new polynomial time solvable semidefinite relaxation of the distributionally robust multi-item newsvendor problem by exploiting results from the Boolean quadric polytope. For \({\mathcal {X}}\) described explicitly by a finite set of points, our formulation leads to a reduction in the size of the semidefinite program. We illustrate the usefulness of the reduced semidefinite programming bounds in estimating the expected range of random variables with two applications arising in random walks and best–worst choice models.     

An end-point global gradient weighted estimate for quasilinear equations in non-smooth domains

A weighted norm inequality involving A₁ weights is obtained at the natural exponent for gradients of solutions to quasilinear elliptic equations in Reifenberg flat domains. Certain gradient estimates in Lorentz–Morrey spaces below the natural exponent are also obtained as a consequence of our analysis.     

Electrochemically promoted Friedel-Crafts acylation of aromatic compounds

Friedel-Crafts acylation is carried out with several aromatic substrates in the presence of an electrochemically active aluminium anode to minimize the inorganic reagents. Only a catalytic amount of AlCl₃ (5 mol %) is required to enable the anodic polarization of the aluminium electrode to promote continuous acylation. This process typically gave products in good yields (70-96%).