Weakly automorphism invariant modules and essential tightness

While a module is pseudo-injective if and only if it is automorphism-invariant, it was not known whether automorphism-invariant modules are tight. It is shown that weakly automorphism-invariant modules are precisely essentially tight. We give various examples of weakly automorphism-invariant and essentially tight modules and study their properties. Some particular results: (1) R is a semiprime right and left Goldie ring if and only if every right (left) ideal is weakly injective if and only if every right (left) ideal is weakly automorphism invariant; (2) R is a CEP-ring if and only if R is right artinian and every indecomposable projective right R-module is uniform and essentially R-tight.     

Anchored Mediator Enabling Shuttle-Free Redox Mediation in Lithium-Oxygen Batteries

Redox mediators (RMs) are considered an effective countermeasure to reduce the large polarization in lithium-oxygen batteries. Nevertheless, achieving sufficient enhancement of the cyclability is limited by the trade-offs of freely mobile RMs, which are beneficial for charge transport but also trigger the shuttling phenomenon. Here, we successfully decoupled the charge-carrying redox property of RMs and shuttling phenomenon by anchoring the RMs in polymer form, where physical RM migration was replaced by charge transfer along polymer chains. Using PTMA (poly(2,2,6,6-tetramethyl-1-piperidinyloxy-4-yl methacrylate)) as a polymer model system based on the well-known RM tetramethylpiperidinyloxyl (TEMPO), it is demonstrated that PTMA can function as stationary RM, preserving the redox activity of TEMPO. The efficiency of RM-mediated Li₂O₂ decomposition remains remarkably stable without the consumption of oxidized RMs or degradation of the lithium anode, resulting in an improved performance of the lithium-oxygen cell.     

Asymmetric reactions based on 1,3-oxathianes3̄: Secondary α-hydroxyacids,RCHOHCO2H and glycols RCHOHCH2OH

Reduction of the previously prepared¹ chiral 2-acyl-l,3-oxathianes derived from (+)-pulegone with various metal hydride combinations proceeds stereoselectively, with diastereomer excess (d.e.) of as much as 97% in the case of reduction of phenyl ketones with lithium tri-sec.butylborohydride. Lesser selectivity (maximum 82% d.e.) is achieved with primary or tertiary alkyl ketones: the predominant diastereomer is readily purified by chromatography. The major product in these cases is that predicted by Cram's chelate rule. The product ratio is reversed with diiasobutylaluminum hydride and also in the reduction of secondary alkyl ketones with lithium sec. butylborohydride, where stereoselectivity is low. The 2-hydroxyalkyl-l,3-oxathianes are cleaved to α-hydroxyaldehydes with N-chlorosuccinimide-silver nitrate and the aldehydes reduced to glycols, RCHOHCH₂OH with sodium borohydride with little or no racemization. Esters, RCHOHCO₂CH₃, are obtained in high enantiomeric purity by O-benzylating the 2-hydroxyalkyl-l,3-oxathianes prior to cleavage, oxidizing with sodium chlorite following cleavage, esterifying and debenzylating. A method for measuring the enantiomeric purity of glycols RCHOHCH₂OH by conversion to 2-phenyl-l,3-dioxolanes with benzaldehyde, followed by proton NMR analysis of the resulting 2-phenyl-4-alkyl-l,3-dioxolane diastereomer pair in the presence of a chiral europium shift reagent is described.     

Microbiological transformations—XII: Microbiological reduction of racemic 1-(2',2',3'-trimethyl-cyclopent-3'-en-1'-yl)propan-2-one and 1-(2',2',3'-trimethyl-cyclopent-3'-en-1'-yl)butan-2-one by rhodotorula mucilaginosa

The microbiological reduction of (±)-l-(2',2',3'-trimethylcyclopent-3'-en-l'-yl)-propan-2-one (4) and (±)-1-(2',2',3'-trimethylcyclopent-3'-en-l'-yl)-butan-2-one (5) by Rhodotorula mucilaginosa was investigated. Both enantiomers of 4 are reduced stereospecifically to corresponding alcohols; (+)-(2S, l'R)-(2',2',3'-trimethylcyclopent-3'-en-l'-yl)-propan-2-ol (6) and (-)-(2S,l'S)-(2',2',3'-trimethylcyclopent-3'-en-l'-yl)-propan-2-ol (7). p ]The substrate selectivity in the reduction of 5 was observed: R enantiomer of 5 yields stereospecifically (+)-(2S,1'R)-(2',2',3'-trimethylcyclopent-3'-en-l'-yl)-butan-2-ol (8) while S(-)5 remains unchanged.     

Rosen-Morse potentials for relativistic spinless particles; approximate solutions

We deal with the D-dimensional radial Klein-Gordon equation for Rosen-Morse type potential with unequal scalar and vector potentials. We apply a proper approximation to the centrifugal term and, by proposing an ansatz solution to the resulting equation, we obtain the bound-state solution. To check the accuracy of our results, we compare our obtained quasi-analytical energies with the exact numerical ones.     

Efficiency enhancement of flexible dye-sensitized solar cell with sol–gel formed Nb2O5 blocking layer

We investigated the effect of a Nb₂O₅ blocking layer formed through the sol–gel method introduced to a titanium metal foil electrode in a flexible dye sensitized solar cell. The blocking layer formed directly on the working electrode physically separates the working electrode from the electrolyte, and prevents back transfer of electrons from the electrode to the electrolyte. The gel processing conditions (sol reaction time) and heat treatment temperature used in formation of the Nb₂O₅ blocking layer have been shown to affect the performance of the dye sensitized solar cell and optimal values of these parameters have been determined. A sol reaction time of 45 min and heat treatment temperature of 550 °C has been observed to result in optimal cell performance (η = 6.185%, J_sc = 13.233 mA/cm², V_oc = 0.672 V, ff = 0.694). Introduction of an Nb₂O₅ blocking layer enhances solar cell efficiency by 39.7%, which is much greater than the increase of 24.6% observed in a similar cell containing a TiO₂ blocking layer under standard illumination conditions. The results obtained via Nb₂O₅ have been observed to be superior to those obtained via a TiO₂ blocking layer.     

Pyrrole-based scaffolds for turn mimics

Two amino acid derived synthons were combined to give homopropargylic amines 2. Platinum dichloride was used to cyclize these intermediates into pyrroles 3 which collapsed to the target secondary structure mimics 1 on treatment with base. Side chains of these compounds overlay with an idealized type 1 β-turn and with an inverse γ-turn.