Alkaline Earth–Olefin Complexes with Secondary Interactions

Strontium and calcium (alkaline earth: Ae) olefin complexes stabilised by secondary Ae???F?C and β‐agostic Ae???H?Si interactions are presented. Olefin coordination onto the alkaline earths is plain in the solid state, and it is thermodynamically favoured over the coordination of THF. The existence of the Ae???olefin interactions is corroborated by solution NMR data and DFT computations. The coordination mode of the olefin varies with steric effects and, if enforced, olefin dissociation can be compensated by the other non‐covalent interactions, as supported by DFT computations.     

The B-factor index for the binding site (BFIbs) to prioritize crystal protein structures for docking

Structural Chemistry - In cheminformatics, protein-ligand docking is a powerful tool applied for virtual screening, pose prediction, and binding affinity estimation. However, docking results depend...     

Recovery of Immersions from Their Metric Tensors and Nonlinear Korn Inequalities: A Brief Survey

The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω  R~n→ E~n with prescribed metric tensor field(g ij) : Ω→ S~n, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.     

Abelian and Tauberian results for the one-dimensional modified Stockwell transforms

The aim of this paper is to study the asymptotic behavior of one- dimensional modified Stockwell transform of a tempered distribution signal through the quasiasymptotic behavior at origin or infinity of the signal itself. More precisely, we give some Abelian results which mean that we derive the asymptotic properties of the S-transform of a tempered signal from the quasiasymptotic properties of the signal itself and we do also the opposite. So, we also give some Tauberian results which describe some quasiasymptotic properties of the tempered signal by means of the asymptotic properties of its Stockwell transform.     

Gravitational Field Equations on Fefferman Space–Times

The total space \({\mathfrak M} \approx {\mathbb H}_1 \times S^1\) of the canonical circle bundle over the 3-dimensional Heisenberg group \({\mathbb H}_1\) is a space–time with the Lorentzian metric \(F_{\theta _0}\) (Fefferman’s metric) associated to the canonical Tanaka–Webster flat contact form \(\theta _0\) on \({\mathbb H}_1\). The matter and energy content of \(\mathfrak M\) is described by the energy-momentum tensor \({T}_{\mu \nu }\) (the trace-less Ricci tensor of \(F_{\theta _0}\)) as an effect of the non flat nature of Feferman’s metric \(F_{\theta _0}\). We study the gravitational field equations \(R_{\mu \nu } - (1/2) \, R \, g_{\mu \nu } = {T}_{\mu \nu }\) on \({\mathfrak M}\). We consider the first order perturbation \(g = F_{\theta _0} + \epsilon \, h\), \(\epsilon<< 1\), and linearize the field equations about \(F_{\theta _0}\). We determine a Lorentzian metric g on \({\mathfrak M}\) which solves the linearized field equations corresponding to a diagonal perturbation h.     

Alkoxyallene‐ynes: Selective Preparation of Bicyclo[5.3.0] Ring Systems Including a δ‐Alkoxy Cyclopentadienone

The development of an intramolecular rhodium(I)‐catalyzed Pauson–Khand reaction of alkoxyallene‐ynes with a proximal alkoxy group is reported. This reaction, in the presence of a [Rh(cycloocta‐1,5‐diene)Cl]₂/propane‐1,3‐diylbis(diphenylphosphane) system under a CO atmosphere, constitutes a powerful tool for selectively accessing carbo‐ and heterobicyclo[5.3.0] frameworks featuring an enol ether moiety. Through this procedure, a straightforward access to guaiane skeletons with a tertiary hydroxy group at the C10 position was achieved.     

Approximation by complex szász-durrmeyer operators in compact disks

In the present paper, we deal with the complex Szász-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.