Invertibility of linear maps preserving matrix invariants

There is a noninvertible linear map preserving a given function iff the function is constant on translates of a subspace. Any group preserving the function preserves the subspace. Hence it is often easy to isolate the cases in which such a noninvertible linear map can exist. For similarity invariants of matrices, this happens only for functions of the trace and for fuctions f satisfying f(X + λI) ≡ f(X).     

Facile synthesis of platinum nanoparticle-containing porous carbons,and their application to amperometric glucose biosensing

This study describes the facile synthesis of platinum nanoparticle-containing porous carbons (Pt/C) by carbonization of freeze-dried agarose gels containing potassium tetrachloroplatinate under a nitrogen atmosphere at 800 °C. By adjusting the ratio between agarose and platinate in the freeze-dried gels, the Pt content in the final Pt/C products could be systematically varied from 0–10 wt.%. Transmission electron microscopy, inductively coupled plasma atomic emission spectrometry, X-ray photoelectron spectroscopy, Raman spectroscopy, and nitrogen physisorption measurements revealed that the Pt/C materials obtained by this method possess high surface areas (350–500 m² g^?1), narrow Pt nanoparticle size distributions (6 ± 3 nm) and nanocrystalline graphite –like carbon character. By immobilization of glucose oxidase on the surface of a 4 wt.% Pt/C electrocatalyst prepared by this route, a very sensitive amperometric glucose biosensor was obtained (response time <2 min, sensitivity 1.9 mA M^?1; and a linear response with glucose concentration up to 10 mM). The simplicity and versatility of the described synthetic method suggests its application to the preparation of carbon supported noble metal catalysts including palladium/C and gold/C. Figure

This study describes the facile synthesis of platinum nanoparticle-containing porous carbons (Pt/C) by carbonization of freeze-dried agarose gels containing potassium tetrachloroplatinate. The Pt/C materials exhibited excellent electrocatalytic activities, as demonstrated by their successful integration into amperometric glucose biosensor     

High‐Efficiency Oxygen Reduction to Hydrogen Peroxide Catalyzed by Nickel Single‐Atom Catalysts with Tetradentate N2O2 Coordination in a Three‐Phase Flow Cell

Carbon‐supported Ni^II single‐atom catalysts with a tetradentate Ni‐N₂O₂ coordination formed by a Schiff base ligand‐mediated pyrolysis strategy are presented. A Ni^II complex of the Schiff base ligand (R,R)‐(?)‐N,N′‐bis(3,5‐di‐tert‐butylsalicylidene)‐1,2‐cyclohexanediamine was adsorbed onto a carbon black support, followed by pyrolysis of the modified carbon material at 300 °C in Ar. The Ni‐N₂O₂/C catalyst showed excellent performance for the electrocatalytic reduction of O₂ to H₂O₂ through a two‐electron transfer process in alkaline conditions, with a H₂O₂ selectivity of 96 %. At a current density of 70 mA cm^?2, a H₂O₂ production rate of 5.9 mol g_cat.^?1 h^?1 was achieved using a three‐phase flow cell, with good catalyst stability maintained over 8 h of testing. The Ni‐N₂O₂/C catalyst could electrocatalytically reduce O₂ in air to H₂O₂ at a high current density, still affording a high H₂O₂ selectivity (>90 %). A precise Ni‐N₂O₂ coordination was key to the performance.     

Microwave absorption studies of MgB2 superconductor

Microwave absorption studies have been carried out on MgB₂ superconductor using a standard X-band EPR spectrometer. The modulated low-field microwave absorption signals recorded for polycrystalline (grain size ∼ 10 μm) samples suggested the absence of weak-link character. The field dependent direct microwave absorption has been found to obey a ✓H dependence with two different slopes, which indicated a transition from strongly pinned lattice to flux flow regime.     

Effect of substrate temperature on electrical and magnetic properties of epitaxial La1−x Pb x MnO3 films

Epitaxial La_1−x Pb _x MnO₃ (LPMO) thin films, grown on (100) SrTiO₃ substrates by laser ablation technique at different temperatures between 600 and 850°C, have been characterized for electrical and magnetic properties. The temperature dependence of resistivity showed that the metal-insulator transition temperature (T _MI) decreases with increasing substrate temperature, which has been attributed to decrease in Pb content in the filsm. The YBa₂Cu₃O _x /La_1−x MnO₃ heterostructures, exhibiting both superconductivity and ferromagnetism, have been fabricated.     

Thiolate‐Mediated Photoinduced Synthesis of Ultrafine Ag2S Quantum Dots from Silver Nanoparticles

Photoinduced syntheses offer significant advantages over conventional thermal strategies, including improved control over reaction kinetics and low synthesis temperatures, affording nanoparticles with nontrivial and thermodynamically unstable structures. However, the photoinduced syntheses of non‐metallic nanocrystalline products (such as metal sulfides) have not yet been reported. Herein, we demonstrate the first photoinduced synthesis of ultrafine (sub‐2 nm) Ag₂S quantum dots (QDs) from Ag nanoparticles at 10 °C. By thorough investigation of the mechanism for the transformation, a fundamental link was established between the intrinsic structures of the molecular intermediates and the final Ag₂S products. Our results confirm the viability of low‐temperature photochemical approaches in metal sulfide synthesis, and demonstrate a new rule which could be followed in it.