Riesz potential estimates for a class of double phase problems

A double phase problem with a bounded Borel measure on the right hand side is studied. We prove an optimal pointwise gradient estimate for such a measure data problem via Riesz potentials of the measure under log-Dini continuity assumption on the modulating coefficients. As a consequence, we find an optimized $C^1$ regularity criterion.     

Display of Potassium Channel–Blocking Tertiapin‐Q Peptides on Gold Nanoparticles Enhances Depolarization of Cellular Membrane Potential

The use of nanoparticle (NP) systems to control cellular physiology, including membrane potential, can facilitate furthered understanding of many disparate cellular processes ranging from cellular proliferation to tissue regeneration. A gold NP (AuNP) bioconjugate system based on the honeybee venom peptide, tertiapin‐Q (AuNP‐TPN‐Q), that depolarizes membrane potential by targeting inward rectifier potassium channels (Kir), is developed. The conjugate elicits, in a peptide concentration–dependent manner, a greater and more rapid depolarization response compared to the free peptide alone. The specificity of the interaction of the AuNP‐TPN‐Q conjugate with the Kir channel using immunocytochemistry and competition binding assays is confirmed. It is further shown that membrane depolarization is photothermally reversible via the laser‐induced plasmonic heating of the AuNP, providing a level of control over Kir channels not afforded by currently available drugs. The functional nanobioconjugate described herein provides a new research tool for understanding the intricacies of ion channel activity and the modulation of cellular membrane potential.     

玻色-爱因斯坦凝聚体中的怪波操控

利用Darboux变换法, 解析地研究了玻色-爱因斯坦凝聚体(BEC)中的怪波. 结果表明: 当谱参数等于非线性系数时, BEC中形成一种新型的单洞怪波; 而当谱参数小于非线性系数时, BEC中出现双洞怪波. 进一步地, 怪波的出现位置可通过调节周期性势阱的驱动频率和强度来控制. 此外, 随着原子间相互作用的减小, 怪波的最高幅度也随之降低. 相关结果可为预防怪波的危害提供帮助.     

Evaluation of Ionic Liquids Based on Amino Acid Anions for Use in Liquid‐junction Free Reference Electrodes

In this paper we report on the novel polymeric membranes for the liquid junction‐free reference electrodes. The membranes contain the ionic liquids (ILs) based on the amino acid anions, namely valine‐, leucine‐, lysine‐ and histidine‐anions, and 1‐butyl‐3‐methylimidazolium cation. Addition of the ILs, and especially of the valine‐based one, to the polymeric plasticized membranes allows significant stabilization of the electrode potential and makes it insensitive to the solution composition. A simple criterion based on the calculated lipophilicities of the cation and anion of the IL is proposed for a priori estimation of its applicability for potential stabilization. The addition of the IL as a microcomponent is found to be advantageous over plasticizing the membrane with the IL due to better potential stability, higher dissociation degree and mobility of the species. The resistance of the novel reference membranes can be tuned by addition of the lipophilic membrane electrolytes, e. g. ETH500. The applicability of the developed reference electrodes is verified in the potentiometric calibration of the indicator K⁺‐ and Ca²⁺‐selective electrodes. Implementation of the amino acid‐based ionic liquids with low environmental toxicity can make a significant contribution to the development of nature‐friendly potentiometry.     

Ground state solutions for Klein–Gordon–Maxwell system with steep potential well

In this paper, we study the following Klein–Gordon–Maxwell system $\left\{\begin{array}{c}-\Delta u+(\lambda a\left(x\right)+1)u-(2\omega +\varphi )\varphi u=f(x,u),\mathrm{in}{\mathbb{R}}^3,\hfill \\ -\Delta \varphi =-(\omega +\varphi )u^2,\mathrm{in}{\mathbb{R}}^3.\hfill \end{array}\right.$Using variational methods, we obtain the existence of ground state solutions under some appropriate assumptions on $a$ and $f$.     

An ab initio-based global potential energy surface for the SH3 system and full-dimensional state-to-state quantum dynamics study for the H2 + HS → H2S + H reaction

An accurate potential energy surface for the ground electronic state of SH₃ system has been constructed with 41,882 high level ab initio energy points and the neural network fitting method. The time-dependent wave packet method has been used to calculate the first state-to-state differential cross sections for the title reaction up to 1.2 eV in full dimensions, based on the reactant–product decoupling scheme. It is found that the majority of H₂S are produced in the ground vibrational state, with a large fraction of available energy for the reaction ending up as product translational motion. The differential cross sections at the threshold energy are dominated by a very narrow peak in the backward direction. With the increase of collision energy, the width of the angular distribution increases considerably, which is a typical feature of a direct reaction via abstract mechanism, similar to the H₂ + OH → H₂O + H reaction. © 2018 Wiley Periodicals, Inc.     

Ab initio structure and vibration-rotation dynamics of germylene,GeH2

Accurate structure and potential energy surface of germylene, GeH₂, in its ground electronic state ¹A₁ were determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to sextuple-zeta quality. The Born-Oppenheimer equilibrium structural parameters for the ¹A₁ state are estimated to be r_e(GeH) = 1.5793 Å and ∠_e(HGeH) = 91.19^∘. The term value T_e for the lowest excited electronic state ã³B₁ of GeH₂ is predicted to be 9140 cm^–1. The vibration-rotation energy levels for the ¹A₁ state of the ⁷⁴GeH₂, ⁷⁴GeD₂, ⁷²GeH₂, and ⁷⁰GeH₂ isotopologues were determined using a variational approach and compared with the experimental data. The role of the core-electron correlation, higher-order valence-electron correlation, scalar relativistic, spin-orbit, and adiabatic effects for prediction of the structure and vibration-rotation dynamics of the GeH₂ molecule is discussed. © 2019 Wiley Periodicals, Inc.     

Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.