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.     

Mechanistic Investigation and Conductance Modulation of a Metal-Molecule-Metal Junction via Extra Acid Addition

One important prerequisite for the fabrication of molecular functional device strongly relies on the understanding the conducting behaviors of the metal-molecule-metal junction that can respond to an external stimulus. The model Lewis basic molecule 4,4′-(pyridine-3,5-diyl)dibenzonitrile (DBP), which can react with Lewis acid and protic acid, was synthesized. Then, the molecular conducting behavior of DBP, DBP-B(C₆F₅)₃, and DBP-TfOH (DBP-B(C₆F₅)₃, and DBP-TfOH were produced by Lewis acid and protonic acid treatment of DBP) was researched and compared. Given that their identical physical paths for DBP, DBP-B(C₆F₅)₃, and DBP-TfOH to sustain charge transport, our results indicate that modifying the molecular electronic structure, even not directly changing the conductive physical backbone, can tune the charge transporting ability by nearly one order of magnitude. Furthermore, the addition of another Lewis base triethylamine (of stronger alkaline than DBP), to Lewis acid-base pair reverts the electrical properties back to that of a single DBP junction, that is constructive to propose a useful but simple strategy for the design and construction of reversible and controllable molecular device based on pyridine derived molecule.     

Vacuum-gap-based lumped element Josephson parametric amplifier

We propose a lumped element Josephson parametric amplifier with vacuum-gap-based capacitor.The capacitor is made of quasi-floating aluminum pad and on-chip ground.We take a fabrication process compatible with air-bridge technology,which makes our design adaptable for future on-chip integrated quantum computing system.Further engineering the input impedance,we obtain a gain above 20 dB over 162-MHz bandwidth,along with a quasi quantum-limit noise performance.This work should facilitate the development of quantum information processing and integrated superconducting circuit design.     

Building 2D classification models and 3D CoMSIA models on small-molecule inhibitors of both wild-type and T790M/L858R double-mutant EGFR

Molecular Diversity - Epidermal growth factor receptor (EGFR) has received widespread attention because it is an important target for anticancer drug design. Mutations in the EGFR, especially the...     

The induction of PANoptosis in KRAS-mutant pancreatic ductal adenocarcinoma cells by a multispecific platinum complex

Science China Chemistry - Oncogenic KRAS reprograms pancreatic ductal adenocarcinoma (PDAC) cells to a state that is awfully resistant to apoptosis. An alternative coping strategy is to trigger a...     

The dual form of Beck type identities

The Ramanujan Journal - Inspired by Andrews and Merca’s recent work on the number of even parts over all partitions into distinct parts, we introduce a new kind of Beck type identities, which...     

An AIE-Active probe for detection and bioimaging of pH values based on lactone hydrolysis reaction

Cellular pH homeostasis is essential for many physiological and pathological processes. pH monitoring is helpful for the diagnosis, treatment and prevention of disorders and diseases. Herein, we developed a ratiometric fluorescent pH probe (TCC) based on a coumarin derivative containing a highly active lactone ring. TCC exhibited a typical AIE effect and emitted blue fluorescence under weak acidic condition. When under weak basic condition, the active lactone moiety underwent a hydrolysis reaction to afford a water-soluble product, which gave red-shifted emission. The emission color change from blue through cyan and then to yellow within pH 6.5–9.0 which is approximate to the biological pH range. And the fluorescence color change along with pH value is reversible. Furthermore, TCC was successfully utilized in the detection of the intracellular pH change of live HeLa cells, which indicated that TCC had practical potential in biomedical research.

     

A boundary expansion of solutions to nonlinear singular elliptic equations

In this paper we establish an asymptotic expansion near the boundary for solutions to the Dirichlet problem of elliptic equations with singularities near the boundary.This expansion formula shows the singularity profile of solutions at the boundary.We deal with both linear and nonlinear elliptic equations,including fully nonlinear elliptic equations and equations of Monge-Ampère type.     

Characterizations of $$\sigma$$ -Solvable Finite Groups

Mathematical Notes - All the groups considered in this paper are finite, and $$G$$ always denotes a finite group; $$\sigma$$ is a partition of the set $$\mathbb{P}$$ of all primes, i.e.,...