Realisation functors in tilting theory

Derived equivalences and t-structures are closely related. We use realisation functors associated to t-structures in triangulated categories to establish a derived Morita theory for abelian categories with a projective generator or an injective cogenerator. For this purpose we develop a theory of (non-compact, or large) tilting and cotilting objects that generalises the preceding notions in the literature. Within the scope of derived Morita theory for rings we show that, under some assumptions, the realisation functor is a derived tensor product. This fact allows us to approach a problem by Rickard on the shape of derived equivalences. Finally, we apply the techniques of this new derived Morita theory to show that a recollement of derived categories is a derived version of a recollement of abelian categories if and only if there are tilting or cotilting t-structures glueing to a tilting or a cotilting t-structure. As a further application, we answer a question by Xi on a standard form for recollements of derived module categories for finite dimensional hereditary algebras

On quiver Grassmannians and orbit closures for representation-finite algebras

We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective-injective; its endomorphism ring is called the projective quotient algebra. For any representation- nite algebra, we use the projective quotient algebra to construct desingularizations of quiver Grassmannians, orbit closures in representation varieties, and their desingularizations. This generalizes results of Cerulli Irelli, Feigin and Reineke

Early diagnosis and better rhythm management to improve outcomes in patients with atrial fibrillation: the 8th AFNET/EHRA consensus conference

Aims Despite marked progress in the management of atrial fibrillation (AF), detecting AF remains difficult and AF-related complications cause unacceptable morbidity and mortality even on optimal current therapy.Methods and results This document summarizes the key outcomes of the 8th AFNET/EHRA Consensus Conference of the Atrial Fibrillation NETwork (AFNET) and the European Heart Rhythm Association (EHRA). Eighty-three international experts met in Hamburg for 2 days in October 2021. Results of the interdisciplinary, hybrid discussions in breakout groups and the plenary based on recently published and unpublished observations are summarized in this consensus paper to support improved care for patients with AF by guiding prevention, individualized management, and research strategies. The main outcomes are (i) new evidence supports a simple, scalable, and pragmatic population-based AF screening pathway; (ii) rhythm management is evolving from therapy aimed at improving symptoms to an integrated domain in the prevention of AF-related outcomes, especially in patients with recently diagnosed AF; (iii) improved characterization of atrial cardiomyopathy may help to identify patients in need for therapy; (iv) standardized assessment of cognitive function in patients with AF could lead to improvement in patient outcomes; and (v) artificial intelligence (AI) can support all of the above aims, but requires advanced interdisciplinary knowledge and collaboration as well as a better medico-legal framework.Conclusions Implementation of new evidence-based approaches to AF screening and rhythm management can improve outcomes in patients with AF. Additional benefits are possible with further efforts to identify and target atrial cardiomyopathy and cognitive impairment, which can be facilitated by AI.</p

Homogeneous catalytic hydrogen formation using a ditungsten cluster and low valency metal ions in aqueous acidic solutions

The formally triply-bonded nonachlorodimetallates [W2(μ-Cl)3Cl6]3- (6) and [Re2(μ-Cl)3Cl6]- (8) undergo a two-electron homogeneous reduction by the chromous or vanadous ions to give the quadruply-bonded species [W2Cl8]4- (4) and [Re2Cl8]2- (7). In aq. HCl solutions complex 6 is an effective catalyst for the anaerobic oxidation of CrII and VII to CrIII and VIII with simultaneous dihydrogen formation. © 1989

Electrochemical reduction of Re3Cl9 in aqueous acidic solutions. Isolation and crystal structure characterization of the one-electron reduced product as the tricaesium-μ3-sulphato-hexachloro-tri-μ-Chloro-triangulo-trirhenium complex, Cs3[Re3Cl9(SO4)]

Electrochemical reduction of the cluster chloride Re3Cl9 (1) containing the Re39+ core, in aqueous hydrochloric acid, gives a purple, oxygen-sensitive but thermally stable solution, from which the singly reduced Re38+ anion, [Re3Cl12-n]4-n (4), has been isolated and structurally characterized as the capped triply-bridging sulphato derivative Cs3[Re3(-μ Cl)3Cl6(μ3-SO4)] (5). © 1991

Redox chemistry of the [Re3(μ-Cl)3X9]3- halides (X = Cl or Br); isolation and structural characterization of the [Re3(μ-Cl)3Br6(H 2O)(μ-O)2]2- cluster anion

The triangulo Re39+ cluster [Re3(μ-Cl)3X9]3- (X = Cl 1a or Br 1b) in concentrated aqueous hydrohalogenic acid solutions underwent a facile one-electron reduction by various reducing agents (VCl2·4H2O, Sn-SnCl2 or Hg) to give the air-sensitive Re38+ anion [Re3(μ-Cl)3X9-n(H2O) n](4-n)- (X = Cl 2a or Br 2b), where n may be 1; the diamagnetism and EPR silence of this compound indicate that it may exist as a dimer with a direct or indirect rhenium-rhenium bond linking two Re38+ trimetal cores. Oxidation of 2 by molecular oxygen in 6 mol dm-3 HX (X = Cl or Br) solutions yielded 1 quantitatively, whereas in the absence of acid and in aprotic solvents oxo-derivatives are formed; from 2b the hexanuclear anion [Re3(μ-Cl)3Br6(H 2O)(μ-O)2]2- 3b was obtained whose structural characterization, as its [PPh4]+ salt 3c, shows that two μ-O ligands bridge two oxidized Re310+ units. The structure of the Re39+ cluster [Co(en)3][Re3(μ-Cl)3Br8(H 2O)]Br has been also determined by X-ray diffraction. The redox couple xRe39+-(Re38+)x, where x = 1 or 2, derived upon mixing 6 mol dm-3 HX (X = Cl or Br) solutions of 1 with an excess of mercury, catalyses efficiently the reduction of molecular oxygen to water

Synthesis, Cyclic Voltammetric and Electrospray Mass Spectrometric Studies of a Series of Tris-Substituted 1,2-Dithiolene Complexes of Tungsten and Molybdenum

Ten new nonsymmetric dithiolenes of the general formula [RR′(C2S2)3M were synthesized, from the corresponding l,3-dithiol-2-ones, or from the corresponding mixed benzoins and tetraphosphorus decasulfide. The redox properties of these ten complexes together with those of the symmetric ones with R = R′ = Ph and M = Mo or W, were investigated by cyclic voltammetry. Two processes were only observed, assigned to C â†&apos; C1− and C1− â†&apos; C2− (C the complex), for which the quasi-reversible E1/2 potentials are highly dependent on the nature of the central metal ion, and for the same metal on the nature of the ligand and on the substituents on the phenyl rings. The ease by which the complexes are reduced is most likely the reason they give ESMS (negative mode) spectra, in spite of the fact they are neutral in solution. The process of this reduction and the parameters affecting it are investigated and discussed. © 1995, American Chemical Society. All rights reserved