The superexchange mechanism in cobalt phthalocyanine (CoPc) thin films was studied by a low temperature scanning tunneling microscope. The CoPc molecules were found to form one-dimensional antiferromagnetic chains in the film. Collective spin excitations in individual molecular chains were measured with spin-flip associated inelastic electron tunneling spectroscopy. By spatially mapping the spin-flipping channels with submolecular precision, we are able to explicitly identify the specific molecular orbitals that mediate the superexchange interaction between molecules.

An effective and facile fluorescence sensing approach for the determination of 2,4,6-trinitrophenol (TNP) using the chemically oxidized and liquid exfoliated graphitic carbon nitride (g-C3N4) nanosheets was developed. The strong inner filter effect and molecular interactions (electrostatic, π-π, and hydrogen bonding interactions) between TNP and the g-C3N4 nanosheets led to the fluorescence quenching of the g-C3N4 nanosheets with efficient selectivity and sensitivity. Under optimal conditions, the limit of detection for TNP was found to be 8.2 nM. The proposed approach has potential application for visual detection of TNP in natural water samples for public safety and security.

Abstract-The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in infinite time horizon. Examples are presented to illustrate the results established.Index Terms-Asymptotic analysis, generalized Riccati equation, indefinite stochastic linear quadratic (LQ) control, linear matrix inequality, solvability.

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Glutathione (GSH) as a biothiol is an essential peptide related to various diseases. Although multiple strategies for biothiols detection have been developed, there is increasing demand for sensors that can differentiate GSH from cysteine (Cys) and homocysteine (Hcy), owing to the similar structures and thiol groups in these amino acids. Herein, we report a novel Eu/LAPONITE (Lap)-based organic/inorganic hybrid material for selective detection of GSH via an "off-on" process. The fluorescence of Eu(DPA)@Lap-Tris can be quenched by Cu through photoinduced electron transfer (PET). The addition of GSH into the Eu(DPA)@Lap-Tris/Cu system induces the removal of Cu from Eu(DPA)@Lap-Tris and blocks PET, resulting in the recovery of fluorescence. This proposed assay demonstrates higher selectivity toward GSH than Cys and Hcy, and showed a detection limit of 162 nM within a linear range of 0.5-30 μM. Unlike other GSH selective sensors, this platform could be formed into a hydrogel while its sensitivity was maintained. The sensitive response to GSH in serum samples makes this platform an efficient tool for biological applications because of its ease of preparation, high selectivity, good biocompatibility, and low toxicity.

A novel magnetic/fluorometric bimodal sensor was built from carbon dots (CDs) and MnO2. The resulting sensor was sensitive to glutathione (GSH), leading to apparent enhancement of magnetic resonance (MR) and fluorescence signals along with visual changes. The bimodal detection strategy is based on the decomposition of the CDs-MnO2 through a redox reaction between GSH and MnO2. This process causes the transformation from non-MR-active MnO2 to MR-active Mn(2+), and is accompanied by fluorescence restoration of CDs. Compared with a range of other CDs, the polyethylenimine (PEI) passivated CDs (denoted as pCDs) were suitable for detection due to their positive surface potential. Cross-validation between MR and fluorescence provided detailed information regarding the MnO2 reduction process, and revealed the three distinct stages of the redox process. Thus, the design of a CD-based sensor for the magnetic/fluorometric bimodal detection of GSH was emphasized for the first time. This platform showed a detection limit of 0.6 μM with a linear range of 1-200 μM in the fluorescence mode, while the MR mode exhibited a linear range of 5-200 μM and a GSH detection limit of 2.8 μM with a visible change being observed rapidly at 1 μM in the MR images. Furthermore, the introduction of the MR mode allowed the biothiols to be easily identified. The integration of CD fluorescence with an MR response was demonstrated to be promising for providing detailed information and discriminating power, and therefore extend the application of CDs in sensing and imaging.

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