Review on ionization and quenching mechanisms of Trichel pulse

Trichel pulse is a kind of pulsed mode in negative DC corona discharge, which has attracted significant attention because of its considerable applications in industry. Over eighty years, plenty of effort including simulations and experiments has been spent to reveal the ionization and quenching mechanisms of Trichel pulse. By revisiting and summarizing the basic characteristics and well-accepted ionization and quenching mechanisms, this review provides a basic understanding and the current status of Trichel pulse.     

Negative thermal expansion in NbF_3 and NbOF_2:A comparative theoretical study

Thermal expansion control is always an obstructive factor and challenging in high precision engineering field. Here,the negative thermal expansion of Nb F_3 and Nb OF_2 was predicted by first-principles calculation with density functional theory and the quasi-harmonic approximation(QHA). We studied the total charge density, thermal vibration, and lattice dynamic to investigate the thermal expansion mechanism. We found that the presence of O induced the relatively strong covalent bond in Nb OF_2, thus weakening the transverse vibration of F and O in Nb OF_2, compared with the case of Nb F_3.In this study, we proposed a way to tailor negative thermal expansion of metal fluorides by introducing the oxygen atoms.The present work not only predicts two NTE compounds, but also provides an insight on thermal expansion control by designing chemical bond type.     

Homogeneous variable exponent Besov and Triebel–Lizorkin spaces

We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.     

Multiple positive solutions for Schrödinger‐Poisson system involving singularity and critical exponent

In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form where 0 ∈ Ω is a smooth bounded domain in , , and λ > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained.     

Stripped Charge of Ag Less than Deposited one Owing to Negative Capacitance Caused by Redox Reactions

Anodic stripping voltammetry was made in AgNO₃ solution, here Ag was deposited under long term potentiostatic conditions to evaluate the reduction charge, q_r, and then was stripped by linear sweep voltammetry to determine the oxidation charge, q_o. The charges were unbalanced, satisfying ca. q_o=0.7|q_r|, where other possible reduction charge such as by dioxygen and dichlorosilver were subtracted. The 30 % loss of the anodic charge can be ascribed to the negative capacitance by the potential sweep generation of Ag⁺. The generated Ag⁺ forms a dipole with a counter ion, of which orientation is the same as the direction of the externally applied electric field and opposite to the dipoles of solvent. The redox dipole decreases the conventional double layer capacitance caused by solvent dipoles, and high concentrations of Ag⁺ takes the capacitance to be negative values. The unbalanced charge, however, has no influence on quantitative determination of concentrations Ag⁺ by use of a calibration line.     

关于负超几何分布期望与方差算法的注记

研究了非还原取样模型中负超几何随机变量的联合分布,得到了若干有用的推论.据此给出了负超几何分布的期望和方差的一种分解算法.     

Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether $\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}$ takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range $0?\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}?1$. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.