Synthesis and Diverse Transformations of a Dinitrogen Dititanium Hydride Complex Bearing Rigid Acridane-Based PNP-Pincer Ligands

Studies on N₂ activation and transformation by transition metal hydride complexes are of particular interest and importance. The synthesis and diverse transformations of a dinitrogen dititanium hydride complex bearing the rigid acridane-based ^acriPNP-pincer ligands {[(^acriPNP)Ti]₂(μ₂-η¹:η²-N₂)(μ₂-H)₂} are presented. This complex enabled N₂ cleavage and hydrogenation even without additional H₂ or other reducing agents. Furthermore, diverse transformations of the N₂ unit with a variety of organometallic compounds such as ZnMe₂, MgMe₂, AlMe₃, B(C₆F₅)₃, PinBH, and PhSiH₃ have been well established at the rigid ^acriPNP-ligated dititanium framework, such as reversible bonding-mode change between the end-on and side-on/end-on fashions, diborylative N=N bond cleavage, the formal insertion of two dimethylaluminum species into the N=N bond, and the formal insertion of two silylene units into the N=N bond. This work has revealed many unprecedented aspects of dinitrogen reaction chemistry.     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

MXene-based composite electrodes for efficient electrochemical sensing of glucose by non-enzymatic method

A recently discovered 2D transition titanium metal carbides also called as MXenes (Ti₃C₂T_x)-based nanocomposite was prepared with Cu₂O through wet precipitation technique, and these materials were further developed as the electrode for sensing glucose by chronoamperometry technique. The prepared MXene-Cu₂O (Ti₃C₂T_x-Cu₂O) nanocomposite was characterized by XRD, FTIR, UV–Vis spectroscopy, FE-SEM, EDAX, and Raman spectroscopy. Morphological studies of the composites revealed that the micro-octahedral shape of Cu₂O is distributed on the surface of MXene with size larger than bare Cu₂O. Further, the prepared composite material was fabricated as a sensing probe, and the electrochemical activities were examined by cyclic voltammetric analysis (CV) and chronoamperometric (CA) methods. From the CV and CA investigation, the current response was higher for the composite than the bare material (Cu₂O & MXene) in the presence of glucose. The amperometric investigation of MXene-Cu₂O composite for the detection of glucose shows a broad linear range (0.01–30 mM) with a sensitivity of 11.061/μAmM cm^?2 and a detection limit of 2.83 μM. Further, the fabricated sensor exhibits good selectivity with interfering species like NaCl, fructose, sucrose, urea, ascorbic acid, lactose, short response time, stability, good reproducibility, and compatibility with human serum sample. From the investigation, the prepared MXene-Cu₂O composite is a good candidate for the direct detection of glucose molecules and is also well suitable for clinical diagnosis.     

Stabilization of the higher order nonlinear Schrödinger equation with constant coefficients

We study the internal stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. Combining multiplier techniques, a fixed point argument and nonlinear interpolation theory, we can obtain the well-posedness. Then, applying compactness arguments and a unique continuation property, we prove that the solution of the higher-order nonlinear Schrödinger equation with a damping term decays exponentially.