An approach to one-dimensional elliptic quasi-exactly solvable models

One-dimensional Jacobian elliptic quasi-exactly solvable second-order differential equations are obtained by introducing the generalized third master functions. It is shown that the solutions of these differential equations are generating functions for a new set of polynomials in terms of energy with factorization property. The roots of these polynomials are the same as the eigenvalues of the differential equations. Some one-dimensional elliptic quasi-exactly quantum solvable models are obtained from these differential equations.      

Developing Novel Fabrication and Optimisation Strategies on Aggregation-Induced Emission Nanoprobe/Polyvinyl Alcohol Hydrogels for Bio-Applications

The current study describes a new technology, effective for readily preparing a fluorescent (FL) nanoprobe-based on hyperbranched polymer (HB) and aggregation-induced emission (AIE) fluorogen with high brightness to ultimately develop FL hydrogels. We prepared the AIE nanoprobe using a microfluidic platform to mix hyperbranched polymers (HB, generations 2, 3, and 4) with AIE (TPE-2BA) under shear stress and different rotation speeds (0–5 K RPM) and explored the FL properties of the AIE nanoprobe. Our results reveal that the use of HB generation 4 exhibits 30-times higher FL intensity compared to the AIE alone and is significantly brighter and more stable compared to those that are prepared using HB generations 3 and 2. In contrast to traditional methods, which are expensive and time-consuming and involve polymerization and post-functionalization to develop FL hyperbranched molecules, our proposed method offers a one-step method to prepare an AIE-HB nanoprobe with excellent FL characteristics. We employed the nanoprobe to fabricate fluorescent injectable bioadhesive gel and a hydrogel microchip based on polyvinyl alcohol (PVA). The addition of borax (50 mM) to the PVA + AIE nanoprobe results in the development of an injectable bioadhesive fluorescent gel with the ability to control AIEgen release for 300 min. When borax concentration increases two times (100 mM), the adhesion stress is more than two times bigger (7.1 mN/mm²) compared to that of gel alone (3.4 mN/mm²). Excellent dimensional stability and cell viability of the fluorescent microchip, along with its enhanced mechanical properties, proposes its potential applications in mechanobiology and understanding the impact of microstructure in cell studies.     

Acet­amidoxime

The oxime of acet­amide, viz. N‐hydroxy­ethanimid­amide, C₂H₆N₂O, has a complex hydrogen‐bonding arrangement in its crystal structure, featuring one strong O—H⋯N hydrogen bond together with weaker hydrogen bonding involving the amide groups. Conjugation effects lead to atypical distances and angles.