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.     

Jet flavor conversions in the quark-gluon plasma

A quark or gluon jet traversing through a quark-gluon plasma can be converted to a gluon or quark jet through scattering with the thermal quarks and gluons in the quark-gluon plasma. Their conversion rates due to two-body elastic and inelastic scattering have recently been evaluated in the lowest order in QCD. Including both energy loss and conversions of quark and gluon jets in the expanding quark-gluon plasma produced in relativistic heavy ion collisions, a net conversion of quark jets to gluon jets has been found. This reduces the difference between the nuclear modification factors for quark and gluon jets in heavy ion collisions and thus enhances the ratios of high transverse momentum protons and antiprotons to pions that are produced from the fragmentation of these jets. To account for the observed similar ratios in central Au + Au and p + p collisions at same energy requires, however, a much larger net quark to gluon jet conversion rate than that given by the lowest-order QCD, indicating the importance of higher-order processes and the strongly coupling properties of the quark-gluon plasma in describing the propagation of jets in the quark-gluon plasma. B.-W. Zhang: On leave from: Institute of Particle Physics, Huazhong Normal University, Wuhan 430079, China Correspondence: C.-M. Ko, Cyclotron Institute and Physics Department, Texas A&M University, College Station, TX 77843-3366, USA     

Determinantal representations of smooth cubic surfaces

For every smooth (irreducible) cubic surface S we give an explicit construction of a representative for each of the 72 equivalence classes of determinantal representations. Equivalence classes (under GL₃ × GL₃ action by left and right multiplication) of determinantal representations are in one to one correspondence with the sets of six mutually skew lines on S and with the 72 (two-dimensional) linear systems of twisted cubic curves on S. Moreover, if a determinantal representation M corresponds to lines (a ₁,...,a ₆) then its transpose M ^t corresponds to lines (b ₁,...,b ₆) which together form a Schläfli’s double-six \(a_1\ldots a_6 \choose b_1\ldots b_6\) . We also discuss the existence of self-adjoint and definite determinantal representation for smooth real cubic surfaces. The number of these representations depends on the Segre type F _i . We show that a surface of type F _i , i = 1,2,3,4 has exactly 2(i?1) nonequivalent self-adjoint determinantal representations none of which is definite, while a surface of type F ₅ has 24 nonequivalent self-adjoint determinantal representations, 16 of which are definite.     

Hyperinvariant subspaces for some subnormal operators

In this article we employ a technique originated by Enflo in 1998 and later modified by the authors to study the hyperinvariant subspace problem for subnormal operators. We show that every ``normalized'subnormal operator such that either does not converge in the SOT to the identity operator or does not converge in the SOT to zero has a nontrivial hyperinvariant subspace.

     

The syn/anti‐Dichotomy in the Palladium‐Catalyzed Addition of Nucleophiles to Alkenes

In this review the stereochemistry of palladium‐catalyzed addition of nucleophiles to alkenes is discussed, and examples of these reactions in organic synthesis are given. Most of the reactions discussed involve oxygen and nitrogen nucleophiles; the Wacker oxidation of ethylene has been reviewed in detail. An anti‐hydroxypalladation in the Wacker oxidation has strong support from both experimental and computational studies. From the reviewed material it is clear that anti‐addition of oxygen and nitrogen nucleophiles is strongly favored in intermolecular addition to olefin–palladium complexes even if the nucleophile is coordinated to the metal. On the other hand, syn‐addition is common in the case of intramolecular oxy‐ and amidopalladation as a result of the initial coordination of the internal nucleophile to the metal.     

Cerium(IV)‐Driven Water Oxidation Catalyzed by a Manganese(V)–Nitrido Complex

The study of manganese complexes as water‐oxidation catalysts (WOCs) is of great interest because they can serve as models for the oxygen‐evolving complex of photosystem II. In most of the reported Mn‐based WOCs, manganese exists in the oxidation states III or IV, and the catalysts generally give low turnovers, especially with one‐electron oxidants such as Ce^IV. Now, a different class of Mn‐based catalysts, namely manganese(V)–nitrido complexes, were explored. The complex [Mn^V(N)(CN)₄]²⁻ turned out to be an active homogeneous WOC using (NH₄)₂[Ce(NO₃)₆] as the terminal oxidant, with a turnover number of higher than 180 and a maximum turnover frequency of 6 min⁻¹. The study suggests that active WOCs may be constructed based on the Mn^V(N) platform.     

Rhodium(II)‐Catalyzed Cycloaddition Reactions of Non‐classical 1,5‐Dipoles for the Formation of Eight‐Membered Heterocycles

A new type of intermolecular rhodium(II)‐catalyzed [5+3] cycloaddition has been developed. This higher‐order cycloaddition between pyridinium zwitterion 1,5‐dipole equivalents and enol diazoacetates enables the formation of eight‐membered heterocyclic skeletons, which are otherwise difficult to construct. The optimized cycloaddition occurs efficiently under mild conditions with a wide range of pyridinium zwitterions and with high functional‐group tolerance.     

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.