A note on dual modules and the transpose

Archiv der Mathematik - It is a classical result in matrix algebra that any square matrix over a field can be conjugated to its transpose by a symmetric matrix. For F a non-Archimedean local field,...     

Copper-Catalyzed Enantioselective Allylic Alkylation with a γ-Butyrolactone-Derived Silyl Ketene Acetal

Herein, we report a Cu-catalyzed enantioselective allylic alkylation using a γ-butyrolactone-derived silyl ketene acetal. Critical to the development of this work was the identification of a novel mono-picolinamide ligand with the appropriate steric and electronic properties to afford the desired products in high yield (up to 96 %) and high ee (up to 95 %). Aryl, aliphatic, and unsubstituted allylic chlorides bearing a broad range of functionality are well-tolerated. Spectroscopic studies reveal that a Cu^I species is likely the active catalyst, and DFT calculations suggest ligand sterics play an important role in determining Cu coordination and thus catalyst geometry.     

Synthesis of High χ–Low N Diblock Copolymers by Polymerization-Induced Self-Assembly

Polymerization-induced self-assembly (PISA) enables the scalable synthesis of functional block copolymer nanoparticles with various morphologies. Herein we exploit this versatile technique to produce so-called “high χ–low N” diblock copolymers that undergo nanoscale phase separation in the solid state to produce sub-10 nm surface features. By varying the degree of polymerization of the stabilizer and core-forming blocks, PISA provides rapid access to a wide range of diblock copolymers, and enables fundamental thermodynamic parameters to be determined. In addition, the pre-organization of copolymer chains within sterically-stabilized nanoparticles that occurs during PISA leads to enhanced phase separation relative to that achieved using solution-cast molecularly-dissolved copolymer chains.     

Reverse Thinking of the Aggregation-Induced Emission Principle: Amplifying Molecular Motions to Boost Photothermal Efficiency of Nanofibers**

Using reverse thinking of the aggregation-induced emission (AIE) principle, we demonstrate an ingenious and universal protocol for amplifying molecular motions to boost photothermal efficiency of fibers. Core–shell nanofibers having the olive oil solution of AIE-active molecules as the core surrounded by PVDF-HFP shell were constructed by coaxial electrospinning. The molecularly dissolved state of AIE-active molecules allows them to freely rotate and/or vibrate in nanofibers upon photoexcitation and thus significantly elevates the proportion of non-radiative energy dissipation, affording impressive heat-generating efficiency. Photothermal evaluation shows that the core–shell nanofibers with excellent durability can reach up to 22.36 % of photothermal conversion efficiency, which is 26-fold as the non-core–shell counterpart. Such a core–shell fiber can be used for photothermal textiles and solar steam generation induced by natural sunlight with green and carbon-zero emission.     

Benchtop NMR analysis of piperazine-based drugs hyperpolarised by SABRE

Piperazine-based drugs, such as N-benzylpiperazine (BZP), became attractive in the 2000s due to possessing effects similar to amphetamines. Herein, BZP, in addition to its pyridyl analogues, 2-, 3-, and 4-pyridylmethylpiperidine (2-PMP, 3-PMP, and 4-PMP respectively) was subjected to the hyperpolarisation technique Signal Amplification By Reversible Exchange (SABRE) in order to demonstrate the use of this technique to detect these piperazine-based drugs. Although BZP was not hyperpolarised via SABRE, 2-PMP, 3-PMP, and 4-PMP were, with the ortho- and meta-pyridyl protons of 4-PMP showing the largest enhancement of 313-fold and 267-fold, respectively, in a 1.4-T detection field, following polarisation transfer at Earth's magnetic field. In addition to the freebase, 4-PMP.3HCl was also appraised by SABRE and was found not to polarise, however, the addition of increasing equivalents of triethylamine (TEA) produced the freebase, with a maximum enhancement observed upon the addition of 3 equivalents of TEA. Further addition of TEA led to a reduction in the observed enhancement. SABRE was also employed to polarise 4-PMP.3HCl (~20% w/w) in a simulated tablet to demonstrate the forensic application of the technique (138-fold enhancement for the ortho-pyridyl protons). The amount of 4-PMP.3HCl present in the simulated tablet was quantified via NMR using D₂O as a solvent and compared well to complimentary gas chromatography–mass spectrometry data. Exchanging D₂O for CD₃OD as the solvent utilised for analysis resulted in a significantly lower amount of 4-PMP.3HCl being determined, thus highlighting safeguarding issues linked to drug abuse in relation to determining the amount of active pharmaceutical ingredient present.     

Cycloaddition Reactions of an Active Cyclic Phosphane/Borane Pair with Alkenes,Alkynes, and Carbon Dioxide

The active six-membered cyclo-FLP 6 undergoes a rapid P/B addition reaction to carbon dioxide. At elevated temperature, the resulting heterobicyclo[2.2.2]octane derived product 7 undergoes ring opening and equilibrates with the cyclotetramer (7)₄ . In the large macrocyclic structure, four monomeric six-membered cyclo-FLP units are connected by four CO₂ molecules to form the supramolecular ring system. The P/B cyclo-FLP 6 undergoes a variety of additional cycloaddition reactions.     

Machine learning identification of symmetrized base states of Rydberg atoms

Studying the complex quantum dynamics of interacting many-body systems is one of the most challenging areas in modern physics. Here, we use machine learning (ML) models to identify the symmetrized base states of interacting Rydberg atoms of various atom numbers (up to six) and geometric configurations. To obtain the data set for training the ML classifiers, we generate Rydberg excitation probability profiles that simulate experimental data by utilizing Lindblad equations that incorporate laser intensities and phase noise. Then, we classify the data sets using support vector machines (SVMs) and random forest classifiers (RFCs). With these ML models, we achieve high accuracy of up to 100% for data sets containing only a few hundred samples, especially for the closed atom configurations such as the pentagonal (five atoms) and hexagonal (six atoms) systems. The results demonstrate that computationally cost-effective ML models can be used in the identification of Rydberg atom configurations.     

Abelian Subgroup Separability of Haken 3-Manifolds and Closed Hyperbolic n-Orbifolds

We prove that abelian subgroups of fundamental groups of Haken3-manifolds and closed hyperbolic n-orbifolds are separable.2000 Mathematical Subject Classification: 20E26, 51M10, 57M05.     

Ionic Liquid Lignosulfonate: Dispersant and Binder for Preparation of Biocomposite Materials

Ionic liquid lignins are prepared from sodium lignosulfonate by a cation exchange reaction and display glass transition temperatures as low as ?13 °C. Diethyleneglycol‐functionalized protic cations inhibit lignin aggregation to produce a free‐flowing “ionic liquid lignin”, despite it being a high‐molecular‐weight polyelectrolyte. Through this approach, the properties of both lignin and ionic liquids are combined to create a dispersant and binder for cellulose+gluten mixtures to produce small microphases. Biocomposite testing pieces are produced by hot‐pressing this mixture, yielding a material with fewer defects and improved toughness in comparison to other lignins. The use of unmodified lignosulfonate, acetylated lignosulfonate, or free ionic liquid for similar materials production yields poorer substances because of their inability to maximize interfacial contact and complexation with cellulose and proteins.