An easy-to-use estimate of the energy-release rate for crack arrays

Formation of crack arrays plays an increasing role in several fields of applied physics. The energy-release rate of the cracks controls the development of the array. Therefore, following the concept of configurational forces, a simplified analytical expression is provided for the energy-release rate, which is based both on numerical studies and on a specially adapted beam model. Comparisons of this easy-to-use estimate of the energy-release rate with established results from the literature as well as detailed numerical results are presented. The provided estimate of the energy-release rate can easily be extended to non-equidistant cracks and an anisotropic material.     

Acid-Catalyzed RNA-Oligomerization from 3’,5’-cGMP

The assembly of ancient informational polymers from nucleotide precursors is the central challenge of life's origin on our planet. Among the possible solutions, dry polymerization of 3’,5’-cyclic guanosine monophosphate (3’,5’-cGMP) has been proposed as a candidate to create oligonucleotides of 15–20 units in length. However, the reported sensitivity of the reaction to the presence of cations raised questions of whether this chemistry could be relevant in a geological context. The experiments in this study show that the presence of cations is not restrictive as long as the reaction is conducted in an acidic environment, in contrast to previous reports that suggested optimal conditions at pH 9.     

THE PECULIAR α-AMIDOALKYLATION OF VINYLTRIMETHYLSILANE

Abstract

α-Amidoalkylation of allyttrimethylsilane with methyl-2-chloro-2-(p-chlorobenzoylamino)-ethanoate 1 gave in the presence of Lewis acid racemic methyl-2- (p-chlorobenzoylamino)-4-penteno ate 2. Under the same conditions, vinlytrimethylsilane afforded (±)-trans-2-(p-chlorophenyl)-5,6-dihydro-4-methoxycarbonyl-6-trimethylsilyl-4H-1, 3-oxazine 4 as the major, by n.m.r. data and x-ray crystallography established product.     

A Further Extension of Pnictide Oxide Chemistry – Synthesis and Structure of La2AuP2O

The phosphide oxide La₂AuP₂O was synthesized from lanthanum filings, dried La₂O₃, gold pieces, and ground red phosphorus in the ideal 1.33:0.33:1:2 ratio in an evacuated silica tube at 1473 K. Small single crystals were obtained by recrystallization in a NaCl/KCl flux. The structure was determined on the basis of single‐crystal X‐ray diffractometer data: new type, C2/m, a = 1537.3(3), b = 427.39(8), c = 1009.2(2) pm, β = 131.02(1) °, wR₂ = 0.046, 1102 F² values, 38 variables. La₂AuP₂O contains two striking structural motifs: The oxygen atoms are located in La₄ tetrahedra. The latter are cis‐edge‐shared forming polymeric cationic [La₂O]⁴⁺ chains. These cationic units are separated and charge‐balanced by [AuP₂]^4– polyanions which have monovalent gold in distorted trigonal planar phosphorus coordination. Two crystallographically independent phosphorus sites occur in the polyanion, i.e. isolated P^3– besides dumb‐bells P₂^4– (P2–P2 223 pm). La₂AuP₂O, which crystallizes in the form of ruby red transparent crystals, is an electron precise phosphide oxide (4La³⁺)(2Au⁺)(2P^3–)(P₂^4–)(2O^2–).     

Capital Accumulation and Embodied Technological Progress

This paper combines technology adoption with capital accumulation taking into account technological progress. We model this as a multi-stage optimal control problem and solve it using the corresponding maximum principle. The model with linear revenue can be solved analytically, while the model with market power is solved numerically. We obtain that investment jumps upwards right at the moment that a new technology is adopted. We find that, if the firm has market power, the firm cuts down on investment before a new technology is adopted. Furthermore, we find that larger firms adopt a new technology later.     

Asymmetric,Three‐Component,One‐Pot Synthesis of Spiropyrazolones and 2,5‐Chromenediones from Aldol Condensation/NHC‐Catalyzed Annulation Reactions

A novel one‐pot, three‐component diastereo‐ and enantioselective synthesis of spiropyrazolones has been developed involving the aldol condensation of an enal to generate α,β‐unsaturated pyrazolones, which react with a second equivalent of enal through an N‐heterocyclic carbene (NHC)‐catalyzed [3+2] annulation. The desired spirocyclopentane pyrazolones are obtained in moderate to good yields and good to excellent stereoselectivities. Alternatively, starting from cyclic 1,3‐diketones, 2,5‐chromenediones are available through [2+4] annulation.