Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

Ill-posedness of the Camassa–Holm and related equations in the critical space

We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa–Holm equation, Degasperis–Procesi equation and Novikov equation etc., in the critical Sobolev space $H^{3/2}$ and even in the Besov space $B_{p,r}^{1+1/p}$ for $p\in [1,\infty ],r\in (1,\infty ]$. Our results cover both real-line and torus cases (only real-line case for Novikov), solving an open problem left in the previous works ([5], [14], [16]).     

Two-dimensional coordination polymer-based nanosensor for sensitive and reliable nucleic acids detection in living cells

A reliable and sensitive strategy which can assess nucleic acid levels in living cells would be essential for fundamental research of biomedical applications. Some nanomaterial-based fluorescence biosensors recently developed for detecting nucleic acids, however, are often with expensive, complicated and timeconsuming preparation process. Here, by using a facile bottom-up synthesis method, a two-dimensional(2 D) coordination polymer(CP) nanosheet, [Cu(tz)](Htz = 1,2,4-triazole), was successfully...     

FeOOH Nanocubes Anchored on Carbon Ribbons for Use in Li/O2 Batteries

A composite of FeOOH nanocubes anchored on carbon ribbons has been synthesized and used as a cathode material for Li/O₂ batteries. Fe²⁺ ion-exchanged resin serves as a precursor for both FeOOH nanocubes and carbon ribbons, which are formed simultaneously. The as-prepared FeOOH cubes are proposed to have a core–shell structure, with FeOOH as the shell and Prussian blue as the core, based on information from XPS, TEM, and EDS mapping. As a cathode material for Li/O₂ batteries, FeOOH delivers a specific capacity of 14816 mA h g⁻¹_cathode with a cycling stability of 67 cycles over 400 h. The high performance is related to the low overpotential of the oxygen reduction/evolution reaction on FeOOH. The cube structure, the supporting carbon ribbons, and the -OOH moieties all contribute to the low overpotential. The discharge product Li₂O₂ can be efficiently decomposed in the FeOOH cathode after a charging process, leading to higher cycling stability. Its high activity and stability make FeOOH a good candidate for use in non-aqueous Li/O₂ batteries.     

Pharmacophore features for machine learning in pharmaceutical virtual screening

Molecular Diversity - Methods of three-dimensional molecular alignment generally treat all pharmacophore features equally when superimposing. However, some pharmacophore features can be more...     

Electrochemical synthesis of α,α-dihaloacetophenones from terminal alkyne derivatives

By virtue of electrochemistry, a series of α,α-dihaloacetophenones were easily obtained with good to excellent yields. This electrochemical procedure was taken in a divided cell with constant current in aqueous media. The reaction can be carried out smoothly at room temperature under metal and oxidant free condition, which provides an eco-friendly synthesis for the α,α-dihaloacetophenone derivatives.     

Tween 20-stabilized gold nanoparticles combined with adenosine triphosphate-BODIPY conjugates for the fluorescence detection of adenosine with more than 1000-fold selectivity

This study describes the development of a simple, enzyme-free, label-free, sensitive, and selective system for detecting adenosine based on the use of Tween 20-stabilized gold nanoparticles (Tween 20-AuNPs) as an efficient fluorescence quencher for boron dipyrromethene-conjugated adenosine 5′-triphosphate (BODIPY-ATP) and as a recognition element for adenosine. BODIPY-ATP can interact with Tween 20-AuNPs through the coordination between the adenine group of BODIPY-ATP and Au atoms on the NP surface, thereby causing the fluorescence quenching of BODIPY-ATP through the nanometal surface energy transfer (NSET) effect. When adenosine attaches to the NP surface, the attached adenosine exhibits additional electrostatic attraction to BODIPY-ATP. As a result, the presence of adenosine enhances the efficiency of AuNPs in fluorescence quenching of BODIPY-ATP. The AuNP-induced fluorescence quenching of BODIPY-ATP progressively increased with an increase in the concentration of adenosine; the detection limit at a signal-to-noise ratio of 3 for adenosine was determined to be 60 nM. The selectivity of the proposed system was more than 1000-fold for adenosine over any adenosine analogs and other nucleotides. The proposed system combined with a phenylboronic acid-containing column was successfully applied to the determination of adenosine in urine.