Group Ring Research Articles

Density Functional Theory Study of Adhesion Mechanism between Epoxy Resins Cured with 4,4'-Diaminodiphenyl Sulfone and 4,4'-Diaminodiphenylmethane and Carboxyl Functionalized Carbon Fiber.

The molecular mechanism of adhesion of two epoxy resins based on diglycidylether of bisphenol A (DGEBA) cured with 4,4'-diaminodiphenyl sulfone (DDS) and 4,4'-diaminodiphenylmethane (DDM) to the carbon fiber (CF) surface is investigated by employing density functional theory (DFT) calculations. The CF surface was modeled by the armchair-edge structure of graphite functionalized with carboxyl (COOH) groups. Two adhesion interfaces were constructed using the CF surface: one with the DGEBA-DDS molecule (CF/DGEBA-DDS interface) and the other with the DGEBA-DDM molecule (CF/DGEBA-DDM interface). The interfacial properties were analyzed by calculating the maximum adhesion stress (Smax) at the interface. The adhesion stress-displacement curve revealed that Smax is 1160.37 MPa, higher for the CF/DGEBA-DDS interface compared to the CF/DGEBA-DDM interface, which is 1060.48 MPa. The energy decomposition analysis showed a similar DFT contribution to adhesion stress for both interfaces, but the dispersion contribution is more significant at the CF/DGEBA-DDS interface. The crystal orbital Hamilton population (COHP) analysis revealed distinct interfacial interactions despite similar DFT contributions. Hydrogen bonding (H-bonding) between the functional groups at both interfaces including feeble OH-π interactions between the benzene rings of epoxy resins and COOH groups on the CF surface were observed. The orbital interaction energies calculated from integrated COHP, i.e., IpCOHP, revealed that the CF/DGEBA-DDS interface has six H-bonding interactions with large absolute IpCOHP values (>1 eV), whereas the CF/DGEBA-DDM interface has five. The interaction between the amine group of the DGEBA-DDM molecule and the CF surface has a large IpCOHP value among all interactions. The sulfone group being at the center of the DDS molecule and its strong surface interaction positioned the DGEBA-DDS molecule closer to the CF surface than the DGEBA-DDM molecule, enhancing dispersion interaction at the CF/DGEBA-DDS interface. Hence, the CF surface exhibits a stronger affinity toward the DGEBA-DDS molecule than the DGEBA-DDM molecule through dispersion interaction.

Triviality criteria for unbounded complexes

We study properties of modules that appear as syzygies of acyclic complexes of projective, injective, flat or flat-cotorsion modules and obtain criteria for these complexes to be contractible or totally acyclic. Our results illustrate the importance of strongly fp-injective modules in the study of these properties. We examine implications of the existence of complete resolutions (in a certain weak sense) and the finiteness of the Gorenstein projective dimension of pure-projective modules. We also use the orthogonality in the homotopy category between complexes of flat modules and pure acyclic complexes of cotorsion modules, in order to study the syzygies of acyclic complexes of flat modules. Finally, we present some applications of our results to group rings, regarding complete resolutions and cohomological periodicity.

On the twisted group ring isomorphism problem for a class of groups

The twisted group ring isomorphism problem (TGRIP) is a variation of the classical group ring isomorphism problem. It asks whether the ring structure of the twisted group ring determines the group up to isomorphism. In this article, we study the TGRIP for direct product and central product of groups. We provide some criteria to answer the TGRIP for groups by answering the TGRIP for certain associated quotients. As an application of these results, we provide several examples. Finally, we answer the TGRIP for extra-special p-groups, and for all but five groups of order p5, where p≥5 is prime.

Synthesis of New Fluorinated Tubastatin A Derivatives Based on Cyclopentane/Cyclohexane with Good Anti‐tumor Activity in Vitro

AbstractTwo series of novel fluorinated Tubastatin A derivatives based on cyclopentane or cyclohexane substitution were first time synthesized by 5 steps at high yield. The influence of the cycloalkanes substituted N‐methylpiperidine and/or fluorinated group on the cap group of Tubastatin A for the in vitro anti‐tumor activity of seven different tumor cell lines (human hepatoma cells Bel7402 and HepG2, human nasopharyngeal carcinoma cells CNE2 and SUNE1, human breast cancer cells MDA‐MB‐231 and MCF‐7, and human pancreatic cancer cells SW1990) was investigated. Compared with Tubastatin A, these novel derivatives with fluorinated groups on the benzene ring of the cap group enhance activity, and modification of the N‐methylpiperidine to cycloalkanes of the cap group improves solubility. The most promising compound trifluoromethyl and cyclohexane substituted derivative, N‐hydroxy‐4‐((6‐(trifluoromethyl)‐1,2,3,4‐tetrahydro‐9H‐carbazol‐9‐yl)methyl) benza‐mide (6 h), had a wide range of anti‐tumor cell range, the IC50 value for human pancreatic cancer cell line SW1990 was 1.17 μM. Hence, fluorinated groups and cyclohexane result in a wide range of anti‐tumor cell range and good anti‐cancer activity.

Contramodules for algebraic groups: Induction and projective covers

In this paper we investigate contramodules for algebraic groups. Namely, we give contramodule analogs to two 20th century results about comodules. Firstly, we show that induction of contramodules over coordinate rings of algebraic groups is exact if and only if the associated quotient variety is affine. Secondly, we give an inverse limit theorem for constructing projective covers of simple G-modules using G-structures of projective covers of simple modules of the first Frobenius kernel, G1. We conclude by showing that the inverse limit theorem is a special case of a more general phenomenon between injective covers in k[G]-Comod and projective covers in k[G]-Contra.

Insight into evolution characteristics of pyrolysis products of HLH and HL coal with Py-VUVPI-MS and DFT

To achieve a comprehensive understanding of the influence of chemical structure on the evolution characteristics of coal pyrolysis products, pyrolysis reaction of two kinds of low rank coal (Huolinhe and Huangling coal) were investigated with pyrolysis-vacuum ultraviolet photoionization mass spectrometry (Py-VUVPI-MS). The soft ionized mass spectral detection can provide evolved information of original pyrolysis product. The chemical structure of coal samples was characterized by solid-state 13C-NMR, indicating HLH coal with more branched chain and longer aliphatic chain structure. The bond dissociation enthalpies (BDE) of β-Cal-Cal and β-Cal-O within model compounds were obtained with density functional theory. The difference of peak temperature with maximum evolution was collected to investigate the effect of the chemical environment on evolution behavior of pyrolysis products. The results reveal that branched and long aliphatic side-chains can reduces BDE of β-Cal-Cal and β-Cal-O, resulting in the lower peak temperature of pyrolysis products derived from HLH coal. Substituent groups (such as alkyl and hydroxyl groups) attached on the aromatic rings can reduce peak temperatures. Moreover, the effects of the different substituted position on the aromatic ring of the methyl group presented on differences of the BDE. An increase in aromatic ring size correlates with a certain degree of reduction in BDE for β-Cal-Cal; consequently, peak temperature of pyrolysis products with larger aromatic rings is lower. The pyrolysis behavior of coal were discussed based on the experimental observations and theoretical calculation, which are beneficial to understand the reaction route and mechanism of coal pyrolysis.

Application of prophylactic flow restriction in brachiocephalic arteriovenous fistulas

To investigate the effects of prophylactic flow restriction for brachiocephalic arteriovenous fistula on postoperative high-flow-related complications and patency rate in patients undergoing hemodialysis. Clinical data of patients with end-stage renal disease who underwent brachiocephalic arteriovenous fistula surgery for hemodialysis from February 2017 to May 2022 in Department of Nephrology, Sir Run Run Shaw Hospital, Zhejiang University School of Medicine were retrospectively analyzed. During surgery, a 4-5 mm vascular suture loop was placed around the vein near the anastomosis as a flow restriction device in 43 patients (flow restriction group), while 42 patients did not receive the prophylactic flow restriction ring (control group). All patients were followed up for 1 to 5 years. The incidence rates of complications related to the hemodialysis access pathway, including distal ischemia syndrome, the formation of arteriovenous fistula aneurysms, thrombus, high-flow congestive heart failure, anastomosis of the vein within 1 cm of the anastomosis and cephalic arch stenosis, were compared between the two groups. The natural blood flow rate of the arteriovenous fistula, anastomosis size, the internal diameter of the vein near the anastomosis, primary patency rate, assisted primary patency rate, and secondary patency rate of the arteriovenous fistula, were also evaluated and compared between the two groups. Logistic regression analysis was used to investigate the factors affecting arteriovenous fistula patency rates, as well as the impact of the flow-restricting ring on postoperative factors. Ultrasound measurements showed that the internal diameter of the vein at the site of the flow restriction ring in the flow restriction group was (3.7±0.6) mm at three months postoperatively, which was significantly smaller than the internal diameter of the narrowest part of the vein near the anastomosis in the control group [(4.1±1.0) mm, t=－2.416, P<0.01]. The postoperative anastomotic diameter and natural blood flow rate of the arteriovenous fistula in the flow restriction group were both significantly lower than those in the control group (both P<0.05). Furthermore, the incidence rates of various complications in the flow restriction group were significantly lower than those in the control group (all P<0.05). At 6, 12, and 24 months postoperatively, the primary patency rate and assisted primary patency rate in the flow restriction group were significantly higher than those in the control group (both P<0.05), while there was no significant difference in secondary patency rates between the two groups (P>0.05). Binary logistic regression analysis indicated that age, diabetes, and natural blood flow rate of the arteriovenous fistula at 3 months postoperatively were independent risk factors for primary patency rate, while the flow restriction for brachiocephalic arteriovenous fistula was an independent protective factor for primary patency rate (P<0.01 or P<0.05). The application of flow restriction was negatively correlated with anastomotic diameter at 6 and 12 months, natural arteriovenous fistula blood flow, and the incidence rates of cephalic arch stenosis and aneurysm formation (all P<0.05). The prophylactic constriction during brachiocephalic arteriovenous fistula surgery in patients undergoing hemodialysis can limit the size of the anastomosis and postoperative arteriovenous fistula blood flow, reducing complications such as cephalic arch stenosis and high-flow heart failure, and increasing primary patency rates of arteriovenous fistula and delay the reintervention of the fistula.

Effect of taurine on vascular dysfunction in an in vitro ischemia-reperfusion model of rat thoracic aorta.

The primary objective of this study was to evaluate the protective effect of taurine on endothelial dysfunction in a vascular ischemia-reperfusion (IR) model. Thoracic aortas of 9 male Sprague-Dawley rats (350-500g) were cut into rings and randomized into control (n = 7), IR (n = 8), IR + taurine 1mM (n = 7), IR + taurine 10mM (n = 8), IR + taurine 30mM (n = 8), and IR + taurine 100mM (n = 5) groups. Aortic rings in the IR group were stored in 0.9% saline at 4°C for 24h, placed in Krebs-Henseleit solution gassed with 95%O2 + 5%CO2 at 37°C, and exposed to sodium hypochlorite (200μM) for 30min. Responses to KCl (80mM), phenylephrine (10-10-10-4M), acetylcholine (10-10-10-4M), and sodium nitroprusside (SNP, 10-11-10-5M) were recorded. Emax (maximum response) and pD2 (negative logarithm of concentration producing half-maximum response) were calculated. IR decreased KCl contraction (control 1047 ± 176mg, IR 682 ± 128mg, p = 0.0007), which was reversed by 30 and 100mM taurine (960 ± 313mg, p = 0.02 and 1066 ± 488mg, p = 0.02, respectively). IR impaired phenylephrine, acetylcholine, and SNP responses (p < 0.0001). Taurine did not affect IR-impaired phenylephrine contractions. IR decreased both pD2 (control, 7.1 ± 0.1; IR, 6.0 ± 0.2; p < 0.01) and Emax (control, 83.5 ± 2.7%; IR, 26.8 ± 2.5%; p < 0.0001) of acetylcholine relaxation, both of which were reversed by 100mM taurine (pD2, 7.2 ± 0.1; p < 0.001; Emax, 45.4 ± 2.6%; p < 0.0001). For SNP relaxation, IR decreased pD2 (control 8.2 ± 0.1, IR 7.7 ± 0.1, p < 0.01), which was reversed by 100mM taurine (8.5 ± 0.1, p < 0.0001). Taurine protects endothelial function after IR injury. Further studies should explore the mechanism of this effect and the potential of adding taurine to vascular graft storage solutions.

Catalytic oxidation of butylated hydroxytoluene using thermally treated cobalt-copper layered double hydroxides: Synthesis, structural evolution, and mechanistic insights

This study investigates the application of cobalt-copper layered double hydroxides (LDHs) in the oxidation of butylated hydroxytoluene (BHT) and explores their catalytic behavior during thermal treatment. LDHs were synthesized via coprecipitation, and various ratios of Co-Cu hydrotalcite were subjected to thermal treatment. Structural analysis revealed that thermal treatment transforms the LDHs into mixed metal oxides. Among the synthesized catalysts, Co1Cu3-LDHs exhibited superior catalytic activity in the oxidation of BHT. Techniques such as XRD, FT-IR, TGA, N2 adsorption-desorption, SEM, and XPS were employed to investigate the structural changes and surface properties of the LDHs. The Co1Cu3-LDH catalyst, treated at 250 °C, exhibited outstanding catalytic performance, attributed to the synergistic effects between Co and Cu. Upon optimizing the reaction conditions, the conversion of BHT reached 99 %, with a selectivity of 77 % towards 3,5-di‑tert‑butyl‑4-hydroxybenzaldehyde (BHT-CHO). The oxidation mechanism involves the oxidation of the π-electron system on the benzene ring and deep oxidation of the phenolic hydroxyl methyl group, with two potential reaction pathways proposed.

Theoretical study on precise regulation of ESIPT reaction based on ICT effect of o-carborane derivatives

The unique stereocarborane fluorophore design has attracted widespread attention because of its ability to effectively enhance the performance of thin-film fluorescence sensors. This study provides a detailed theoretical investigation of the excited-state intramolecular proton transfer (ESIPT) reactions of three o-carborane derivatives, NaCBO, PaCBO and PyCBO, using density functional theory and time-dependent density functional theory. We found that as the number of benzene rings in the electron donor groups increases, the interaction between the first excited-state electron donor–acceptor fragments is enhanced, weakening the intramolecular hydrogen bonding strength, which in turn inhibits the ESIPT. Notice that the intramolecular charge transfer (ICT) is proportional to the interaction between electron donor and acceptor fragments with the analysis of electron structure. The higher the ICT level of the target system, the more unstable the keto form generated by ESIPT. Therefore, the ESIPT can be precisely manipulated by rationally adjusting the ICT effect. Furthermore, with increasing solvent polarity, the photophysical properties of the chromophores exhibit non-solvatochromism. This is attributed to the rigid o-carborane structure, which serves as a spatial scaffold to increase the adaptability of the molecule to the environment. This study is expected to provide theoretical guidance and new ideas for preparing high-performance thin-film fluorescence sensing.

Unraveling the influence of deposited layers on Ti/RuO2 anodes to define the electroactivity of oxygen evolution and active chlorine reactions

Ti/RuO2 were synthesized using Pechini method with 4, 8 and 16-RuO2 layers, to account for the influence of their physical properties upon their behavior towards reactive oxygen evolution (OER) and active chlorine reaction (CER). Rietveld refinement conducted using X-Ray diffraction (XRD) measurements confirmed the formation of TiO2 (P42/mnm) and RuO2 (P42/mnm, poor rutile-type), which grew on a thin native TiO2 layer forming a solid solution. This analysis corroborated that the smaller RuO2 crystallite size was obtained using 4-layers, unlike the trend of increasing sizes with more layer’s numbers. This situation is not conducive to accessing reactive sites and electronic conduction issues. Interestingly, exchange current densities (j0) in NaCl(aq) presence were higher than Na2SO4(aq) for 4 and 8-layers, evidencing an inhibition of OER to catalyze CER due to RuO2. This behavior is not related to the electroactive area, since this property decreased by rising the number of layers. The 4-layers anode showed the largest production of CER after 20 min of electrolysis, but the lower accelerated lifetime (ALT). Thus, the stacking of more RuO2 layers creates a higher resistance for charge transfer. Likewise, Ti substrate is important to define the CER catalysis, whence a low coverage of RuO2 will be more catalytic than a high coverage of this oxide. The electrode activity was assessed through the removal of 132 µmol L−1 Acetaminophen (ACM), revealing that 93, 80, and 50 % was removed using 4, 8 and 16-layers of RuO2 coating respectively, at 10 mA and 0.1 molL−1 NaCl. Density functional theory (DFT) and high-performance liquid chromatograph coupled to a mass spectrometer (HPLC-MS) were used to propose a reaction mechanism for ACM degradation. Four byproducts with m/z ACM-I-1 (C8H5Cl4NO3) 304, ACM-I-2 (C8H6Cl3NO3) 274, ACM-I-3 (C6H4Cl3NO2) 227, and ACM-I-4 (C6H3Cl3O3) 229 were identified corresponding to the addition of chlorine in the amide group and aromatic ring, as a susceptible site to electrophilic attack.

PCGF2 Acts as an Oncogenic Driver in Colon Cancer through the Upregulation of CENPE.

Colon cancer (CC) is a highly prevalent malignancy that contributes significantly to global morbidity and mortality. The polycomb group ring finger 2 (PCGF2) has been identified as a relevant factor influencing the outcomes of CC. At the same time, the centromere-associated protein E (CENPE) is implicated in promoting carcinogenesis and adversely affecting the survival of tumor patients. The primary objective of this study was to elucidate the precise impact of PCGF2 on CC and unravel the underlying mechanisms associated with CENPE. Human normal colon epithelial cells and CC cells were utilized to investigate the differential expression of PCGF2 and CENPE. CC cell line LOVO was exploited and transfected for PCGF2 regulation. Subsequently, cell viability and proliferation were assessed using the cell counting kit 8 (CCK-8) and colony forming assay. Cell viability and proliferation were assessed using the terminal deoxynucleotidyl transferase (TdT) dUTP nick-end labeling (TUNEL) assay, while cell migration and invasion capabilities were determined using the transwell assay, and mRNA levels of cell cycle-related genes were measured for evaluating cell cycle activation. In addition, mice were used for in vivo experiments to investigate the progression of CC cells with different levels of PCGF2. Moreover, GSK-923295 was used to inhibit CENPE, followed by the evaluation of cell progression. PCGF2 and CENPE were upregulated in CC cell lines (p < 0.001), and upregulation/downregulation of PCGF2 led to the upregulation and downregulation of CENPE (p < 0.001). The upregulation/downregulation of PCGF2 led to an increase/decrease in viability, proliferation, migration, and invasion while suppressing/enhancing apoptosis in LOVO cells (p < 0.001), promoting cell progression. The tumor progression of LOVO cells with PCGF2 knockdown was slower (p < 0.001). The PCGF2-promoting LOVO cell progression was disrupted when CENPE was inhibited, presented by the reversely decreased viability, proliferation, migration, invasion, and cell cycle activation, and increased apoptosis (p < 0.001). PCGF2 promotes CC cell progression by upregulating CENPE, providing PCGF2 inhibition and CENPE inhibition as potential therapeutic targets for treating CC.

Structural characterization of nitazene analogs using electron ionization-mass spectrometry (EI-MS)

Nitazene analogs are among the most recent and potent additions to the novel synthetic opioid (NSO) market, and new analogs continue to emerge. Seized drug analysis commonly utilizes gas chromatography-electron ionization-mass spectrometry (GC-EI-MS), so it is therefore imperative to understand how nitazene analogs behave under EI-MS conditions, and how substitution at various sites on the molecule may impact the resulting EI mass spectra. This study characterizes the EI fragmentation behavior of 20 representative nitazene analogs that contain differing substitutions and proposes rational mechanisms to explain the observed behavior.A general EI fragmentation pathway for nitazene analogs was proposed, with the most common nitazene fragment ions being observed at m/z 86, m/z 107, m/z 58, and m/z 77. Characteristic ions were determined for different substitution groups, enabling the identification of diethyl, desethyl, pyrrolidine, and piperidine substitutions at the amine moiety, and different alkoxy chain lengths at the aromatic ring of the benzyl group. Mechanisms for the formation of these characteristic ions were proposed with the aid of isotopically labeled standards and high-resolution mass spectrometry measurements. To help with the interpretation of EI mass spectra for nitazene analogs, decision trees were developed that encompass the characteristic fragment ions observed for substitutions to the amine moiety and benzyl group, with additional criteria provided for substitutions to the benzimidazole moiety. This study summarizes the fragmentation patterns and characteristic fragment ions in the EI mass spectra of 20 representative nitazene analogs, which will aid the seized drug community in identifying novel nitazene analogs.

Multifunctional cyanoaryl porphyrazine pigments with push-pull structure of macrocycle framing: Photophysics and possible applications

We report the experimental study of fluorescence properties of three porphyrazine derivatives, distinct in the number of fused aromatic rings in aryl groups contained in the macrocycle frame and/or presence of Pd in the macrocycle, in solutions with biological molecules and in methanol-glycerol mixtures. Spectral and lifetime fluorescence analysis has revealed that all three pigments demonstrated two fluorescence transition bands from the first S1 and the second S2 electronic excited states to the ground state S0, and thus followed the anti-Kasha’s rule. Strong dependence of the quantum yield and lifetimes in the S1 → S0 fluorescence band on solution viscosity was observed. A significant increase of the fluorescence decay times and fluorescence intensity with albumin concentration and with presence of other biological molecules in solution was observed as well. A model of the low-laying energy states of porphyrazine derivatives has been developed for elucidation of the fluorescence properties observed, that took into account several radiative and non-radiative relaxation channels in molecular excited states. In particular, the model suggests that the first electronic excited state consists of planar and bent conformations separated by a potential energy barrier and shows a typical molecular-rotor behavior as a function of solution viscosity. Potential applications of the porphyrazine pigments as viscosity sensors and fluorescence probes were considered.

On the coherency of completed group algebras

We investigate coherency properties of certain completed integral group rings.

Schur rings over free Abelian group of rank two

Schur rings are subrings of the group ring of the group G afforded by a partition of G into finite sets. In this paper, Schur rings over a free abelian group of rank two are classified under the assumption that one of the direct factors is a union of some basic sets. There are eight different types, and all but one type of which are traditional.

Synergistic effects of La loading on furfural hydrogenation using wrinkled silica-supported Pd catalysts: Role of partially oxidized Pd and base sites

The catalytic hydrogenation of furfural (FF) to tetrahydrofurfuryl alcohol (THFAL) is complicated by competing hydrogenation reactions involving the carbonyl group and furan ring. To address this challenge, we developed Pd/xLa@wrinkled silica (Pd/xLa@KCC) catalysts exhibiting excellent efficiency via the optimization of La/Si molar ratios, improved Pd dispersion, and stabilization of partially oxidized Pd particles (Pdδ+). These catalysts were designed for the selective hydrogenation of FF to THFAL. Pd/0.2La@KCC, characterized by a high level of oxygen defects, good basicity, and abundant Pdδ+ species, achieved complete conversion and 91.2 % THFAL selectivity at 45 °C within 6 h. Pd/0.2La@KCC exhibited a THFAL formation rate of 100.9 mmol/g/h, 10.8 times higher than that of Pd/0.02La@KCC. Improved Pd dispersion increased the available metallic surface area for H2 dissociations, whereas abundant Lewis-base sites and Pdδ+ species served as adsorption sites for the carbonyl group and furan ring, respectively. The catalyst facilitated the activation and conversion of the furan ring and carbonyl group to THFAL owing to the parallel adsorption geometry of FF. This approach highlights the importance of the surface characteristics of the catalyst for achieving exceptional selectivity and efficiency. Our findings provide valuable insights into the development of advanced catalysts exhibiting excellent selectivity for biomass-derived chemicals.

Invariant rings of the special orthogonal group have nonunimodal h-vectors

For [Formula: see text] an infinite field of characteristic other than two, consider the action of the special orthogonal group [Formula: see text] on a polynomial ring via copies of the regular representation. When [Formula: see text] has characteristic zero, Boutot’s theorem implies that the invariant ring has rational singularities; when [Formula: see text] has positive characteristic, the invariant ring is [Formula: see text]-regular, as proven by Hashimoto using good filtrations. We give a new proof of this, viewing the invariant ring for [Formula: see text] as a cyclic cover of the invariant ring for the corresponding orthogonal group; this point of view has a number of useful consequences, for example, it readily yields the [Formula: see text]-invariant and information on the Hilbert series. Indeed, we use this to show that the [Formula: see text]-vector of the invariant ring for [Formula: see text] need not be unimodal.

Synthesis and crystal structure of (2E)-1-[3,5-bis-(benz-yloxy)phen-yl]-3-(4-eth-oxy-phen-yl)prop-2-en-1-one.

In the title compound, C31H28O4, the phenyl rings of the chalcone unit subtend a dihedral angle of 26.43 (10)°. The phenyl rings of the pendant benz-yloxy groups are orientated at 75.57 (13) and 75.70 (10)° with respect to their attached ring. In the crystal, weak C-H⋯O and C-H⋯π inter-actions link the mol-ecules. The inter-molecular inter-actions were qu-anti-fied and analysed using Hirshfeld surface analysis, which showed a breakdown into H⋯H (49.8%), H⋯C/C⋯H (33.8%) and H⋯O/O⋯H (13.6%) inter-actions with other types making negligible contributions.

(Looking for) the heart of abelian Polish groups

We prove that the category M of abelian groups with a Polish cover introduced in collaboration with Bergfalk and Panagiotopoulos is the left heart of (the derived category of) the quasi-abelian category A of abelian Polish groups in the sense of Beilinson–Bernstein–Deligne and Schneiders. Thus, M is an abelian category containing A as a full subcategory such that the inclusion functor A→M is exact and finitely continuous. Furthermore, M is uniquely characterized up to equivalence by the following universal property: for every abelian category B, a functor A→B is exact and finitely continuous if and only if it extends to an exact and finitely continuous functor M→B. In particular, this provides a description of the left heart of A as a concrete category.We provide similar descriptions of the left heart of a number of categories of algebraic structures endowed with a topology, including: non-Archimedean abelian Polish groups; locally compact abelian Polish groups; totally disconnected locally compact abelian Polish groups; Polish R-modules, for a given Polish group or Polish ring R; and separable Banach spaces and separable Fréchet spaces over a separable complete non-Archimedean valued field.