The Simple Connectedness of Tame Algebras with Separating Almost Cyclic Coherent Auslander–Reiten Components

We study the simple connectedness of the class of finite-dimensional algebras over an algebraically closed field for which the Auslander–Reiten quiver admits a separating family of almost cyclic coherent components. We show that a tame algebra in this class is simply connected if and only if its first Hochschild cohomology space vanishes.

     

On amenability of two-generator groups

A discrete group G is amenable if there exists a finitely additive probability measure on G which is invariant under left translations and is defined on all subsets of G. It is proved that if the group is generated by two elements and is amenable then there are words being relators whose most of the consecutive pairs of the letters belong to a certain four-element set of pairs. This fact is applied to reproving non-amenability of a braid group. The same group provides an example showing that such type of condition is not su?cient for amenabilty.     

Aromatic and Antiaromatic Pathways in Triphyrin(2.1.1) Annelated with Benzo[b]heterocycles

Understanding of the aromatic properties and magnetically induced current densities of highly conjugated chromophores is important when designing molecules with strongly delocalized electronic structure. Linear extension of the triphyrin(2.1.1) skeleton with an annelated benzo[b]heterocycle fragment modifies the aromatic character by extending the electron delocalization pathway. Two-electron reduction leads to an antiaromatic triphyrin(2.1.1) ring and an aromatic benzo[b]heterocycle subunit. Current-density calculations provide detailed information about the observed pathways and their strengths.     

Ground State of the Conformal Flow on 𝕊3

We consider the conformal flow model derived in Bizoń et al. (2017) as a normal form for the conformally invariant cubic wave equation on 𝕊³. We prove that the energy attains a global constrained maximum at a family of particular stationary solutions that we call the ground state family. Using this fact and spectral properties of the linearized flow (which are interesting in their own right due to a supersymmetric structure), we prove nonlinear orbital stability of the ground state family. The main difficulty in the proof is due to the degeneracy of the ground state family as a constrained maximizer of the energy. © 2019 Wiley Periodicals, Inc.     

Mono-Aryl/Alkylthio-Substituted (Hetero)acenes of Exceptional Thermal and Photochemical Stability by the Thio-Friedel–Crafts/Bradsher Cyclization Reaction

The highly substituted mono-aryl/alkylthio-(hetero)acenes prepared in this study have been found to be thermally more stable (T_decomp.=331–354 °C) than the known di-aryl/alkylthio-substituted acenes by an average of 25 °C. They are also much more photostable at 254 and 365 nm (in both argon and air) than the parent anthracene and other reported anthracenes. The most photostable aryl/alkylthio-anthracenes at 254 nm were found to be 60–70 (in air) and 130 (in argon) times more stable in solution than the unsubstituted anthracene, and much more stable than known EDG/EWG-substituted anthracenes (EDG=electron-donating group, EWG=electron-withdrawing group) with an extended aromatic core. Furthermore, the acenes showed significantly higher photostability at 365 nm in both air and argon. The anthracenes were obtained by the novel thio-Friedel–Crafts/Bradsher cyclization reaction of hitherto unknown [o-(1,3-dithian-2-yl)aryl](aryl)methyl thioethers. The developed approach provides a general access to mono-aryl/alkylthio-substituted (hetero)acene frameworks containing at least three fused (hetero)aromatic rings. The characteristic feature of this approach, which leads to highly substituted acenes, is that the substituents, unlike in other methods, may be introduced at an early stage of the synthesis. DFT and TD-DFT calculations confirmed the stabilizing role of the aryl/alkylthio substituent in the mono-aryl/alkylthio-substituted anthracenes, which are the most stable anthracenes prepared to date. Their high photostability is mainly due to the quenching of singlet oxygen by the acene and the quenching of the acene S₁ state by molecular oxygen.     

N → Sn coordination in the complexes of tin halides with pyridine: A comparison between Sn(II) and Sn(IV)

The experimentally well‐known complexation of tin(II) and tin(IV) halides with pyridine (py) leads to structures showing N → Sn coordination. In the present work, the complexes SnX_n·mpy (where X = F, Cl, Br, I; n = 2, 4; m = 1, 2) possessing this kind of coordination were studied using a computational quantum chemical approach. Various aspects in the theoretical picture of these complexes were examined to find similarities and differences in their N → Sn coordination. The aspects included, among others, the physical nature of intermolecular interactions, and their role in establishing the structure and energetic stabilization of the complexes. In this context, the effect of tin valency was inspected in great detail. As proven by several theoretical methods, a largely ionic character with a certain covalent component can be attributed to the studied N → Sn coordination, irrespective of tin valency. All complexes are destabilized by py‐py and three‐body interactions, but the Sn(II) complexes experience it to a greater extent. Marked differences are observed in the structural behavior of N → Sn and SnX_n during complex formation. This affects the energetics of complexation and, in consequence, the penta‐coordinated Sn(IV) center shows a higher propensity to expand its coordination number, compared with the tri‐coordinated Sn(II) center. The present study supplements the experimental characterization of SnX_n·mpy and, in general, it sheds light on the coordination of heteroaromatic nitrogen to tin. The survey of the Cambridge Structural Database revealed that such coordination occurred in a number of crystal structures.     

Shape morphing and topology optimization of fluid channels by explicit boundary tracking

An integrated shape morphing and topology optimization approach based on the deformable simplicial complex methodology is developed to address Stokes and Navier‐Stokes flow problems. The optimized geometry is interpreted by a set of piecewise linear curves embedded in a well‐formed triangular mesh, resulting in a physically well‐defined interface between fluid and impermeable regions. The shape evolution is realized by deforming the curves while maintaining a high‐quality mesh through adaption of the mesh near the structural boundary, rather than performing global remeshing. Topological changes are allowed through hole merging or splitting of islands. The finite element discretization used provides smooth and stable optimized boundaries for simple energy dissipation objectives. However, for more advanced problems, boundary oscillations are observed due to conflicts between the objective function and the minimum length scale imposed by the meshing algorithm. A surface regularization scheme is introduced to circumvent this issue, which is specifically tailored for the deformable simplicial complex approach. In contrast to other filter‐based regularization techniques, the scheme does not introduce additional control variables, and at the same time, it is based on a rigorous sensitivity analysis. Several numerical examples are presented to demonstrate the applicability of the approach.     

A Mechanistic Study on the Oxidative Degradation of Dibenzazepine Derivatives by Manganese(III) Complexes in Acidic Sulfate Media

The oxidative degradation of tricyclic antidepressants (TCA) was studied in the presence of a large excess of the oxidizing agent manganese(III) and its reduced form manganese(II) sulfate in acidic media. The products were detected and identified using UV–vis, ESI‐MS, IR, and EPR methods. The mechanism of the reaction was studied for the following two classes of TCA: 10,11‐dihydro‐5H‐dibenz[b, f]azepines and dibenz[b, f]azepines. The oxidative degradation between dibenz[b, f]azepines and the manganese(III) ions resulted in the formation of substituted acridine with the same substituent as in the origin dibenz[b, f]azepine derivative. The pseudo–first‐order rate constants (k_obs) were determined for the degradation process. The dependences of the observed rate constants on the [Mn^III] with a zero intercept were linear. The reaction between 10,11‐dihydro‐5H‐dibenz[b, f]azepines, and the manganese(III) sulfate ion resulted in oxidative dehydrogenation, which proceeded via the formation of the following two intermediates: a free organic radical and a dimer. Further oxidation of the second intermediate led to a positively charged radical dimer as the single final product. Linear dependences of the pseudo–first‐order rate constants (k_obs) on the [Mn^III] with a zero intercept were established for the degradation of 10,11‐dihydro‐5H‐dibenz[b, f]azepines. The observed rate constants were dependent on the [H⁺] and independent of the [TCA] within the excess concentration range of the manganese(III) complexes used in the isolation method. The radical product of the degradation of 10,11‐dihydro‐5H‐dibenz[b, f]azepines was not stable in the aqueous solution and was subsequently transformed to a nonradical dimer in the next slower step. The observed rate constants were independent of the [Mn^III], independent of the [H⁺] and increased slightly with increasing TCA concentrations when TCA was used in excess. The mechanistic consequences of all of these results are discussed.     

Bis(N‐Confused Porphyrin) as a Semirigid Receptor with a Chirality Memory: A Two‐Way Host Enantiomerization through Point‐to‐Axial Chirality Transfer

The adduct formation of protonated bis(N‐confused porphyrin) (BNCP, 3,3′‐bis(meso‐tetratolyl‐2‐aza‐21‐carbaporphyrin) with chiral anions, carboxylic acids, and alcohols was studied in solution by means of ¹H NMR and circular dichroism (CD) spectroscopic analysis and DFT methods. The addition of enantiopure guests to the acidified BNCP resulted in optical activity that vanished after neutralization. Pairs of the ¹H NMR‐distinguishable diastereomers were formed when enantiopure guests were applied, although a single form was observed upon the addition of the racemic mixtures in each case. Unidirectional configuration change that led to diastereomeric excess was observed in several instances. Such an excess was memorized by metalation of the adducts with AgBF₄, thus resulting in optically active silver(III) complexes of BNCP with some enantiomeric excess. Absolute configurations of BNCP cations and bis(zinc) and bis(silver(III)) complexes were determined on the basis of time‐dependent (TD)‐DFT calculations of their CD spectra. It was shown that some of the chiral carboxylates induced opposite directions of enantiomerization of di‐ and tetracations or di‐/tetracation and bis(zinc) complexes. The source of the optical activity of the equimolar diastereomeric mixture of adducts is discussed.