加权Stepanov伪概自守函数的一些基本性质及其对Volterra积分方程的应用

本文主要研究加权Stepanov伪概自守函数的一些基本性质.首先,本文研究一个加权Stepanov伪概自守函数与它的Stepanov概自守部分的关系.利用这些关系,本文将这类函数的复合定理进行改进.其次,本文研究加权Stepanov伪概自守函数空间中的卷积算子,这里的卷积算子是由绝对可积函数所生成.最后,应用压缩映射原理,本文得到两类Volterra积分方程的加权Stepanov伪概自守解的存在唯一性.本文的结果推广了部分已知结果.     

Design,Synthesis, and Phenotypic Profiling of Pyrano‐Furo‐Pyridone Pseudo Natural Products

Natural products (NPs) inspire the design and synthesis of novel biologically relevant chemical matter, for instance through biology‐oriented synthesis (BIOS). However, BIOS is limited by the partial coverage of NP‐like chemical space by the guiding NPs. The design and synthesis of “pseudo NPs” overcomes these limitations by combining NP‐inspired strategies with fragment‐based compound design through de novo combination of NP‐derived fragments to unprecedented compound classes not accessible through biosynthesis. We describe the development and biological evaluation of pyrano‐furo‐pyridone (PFP) pseudo NPs, which combine pyridone‐ and dihydropyran NP fragments in three isomeric arrangements. Cheminformatic analysis indicates that the PFPs reside in an area of NP‐like chemical space not covered by existing NPs but rather by drugs and related compounds. Phenotypic profiling in a target‐agnostic “cell painting” assay revealed that PFPs induce formation of reactive oxygen species and are structurally novel inhibitors of mitochondrial complex I.     

On a question of Thas on partial 3‐(qn + 1, q + 1, 1) designs

In this note, we answer a question of JA Thas about partial $3$‐ $\left(q^n+1,q+1,1\right)$ designs. We then extend this answer to a result about the embedding of certain partial $3$‐ $\left(q^2+1,q+1,1\right)$ designs into Möbius planes.     

Pseudo Jahn–Teller origin tracking for symmetry breaking in halogenabenzene: How can a bird fly?

The cyclic iodabenzene molecule (CH)₅I was first introduced and characterized as planar configuration and zwitterionic valence structure by Glukhovtsev in 1991. Recently, it caused researchers' great interest due to the theoretical discovery of a stable bird‐like structure by Hoffmann et al. in 2017 which has similar electronic structure and charge distribution as well‐known Meisenheimer complex C₆H. Inspired by this, we continue to tell the halogenabenzene story by revealing the origin of the bird‐like structure and understanding how the electronic behavior affects the geometrical symmetry for a molecule. By combining the Pseudo Jahn–Teller effect (PJTE) theory with the ab initio calculations for halogenabenzenes (CH)₅X (X = F, Cl, Br, I) and C₆H, it is illustrated that the vibronic coupling of ¹A₁ ground state and ¹B₁ excited states with C_2v planar structure along the out‐of‐plane b₁ distortion triggers the symmetry breaking of planar configuration to form a preferred bird‐like structure. This interpretation can be also applied to explain their different stabilization energies by analyzing numerically the energy gaps of coupled electronic states and PJTE vibronic coupling parameters. Taking use of the PJTE formulation above, we also tracked the origin of restoring to be planar for (CH)₅X²⁺ cation, as well as their isoelectronic species (CH)₅O⁺ and (CH)₅N, and suggests an effective strategy to stabilize the planar configuration for halogenabenzenes.     

Characteristic Functions and Symbols in the Theory of Feller Processes

We derive a probabilistic expression for the symbol of the generator of a Feller process.     

Effect of synthesis parameters on the structural,morphological characteristics,and photocatalytic activity of La2O3 nanoparticles

This study investigates the influence of synthesis processes such as sonication, sol-gel, and microwave on the production of highly crystalline Lanthanum oxide nanoparticles (La₂O₃) employing Lanthanum nitrate and Ammonium hydroxide (NH₄OH) as precursors. X-ray diffraction (XRD), particle size analysis (DLS), Field emission scanning electron microscopy (FESEM), Fourier-transform infrared spectroscopy (FTIR), ultraviolet–visible absorption spectroscopy (UV–Vis), and electrochemical impedance spectroscopy (EIS) were used to examine the most effective processing method and its effects on the nanoparticle characteristics, such as structure, morphology, and optical and electrical behavior. Sonication produces La₂O₃ NPs with a smaller crystalline size, an agglomerated nanorod structure, a higher bandgap, and better electrical responsiveness than sol-gel and microwave techniques. Structural and optical characterization tests discovered this. The photocatalytic degradation activity of cationic Safranin and anionic Congo red dye exhibits degradation efficiency of around 90.13% and 89.66%, respectively.     

基于伪类光超曲面奇点分类的教学研究

在微分几何的教学中,曲线,曲面理论是最主要的基础理论知识.欧氏空间中密切曲线在微分几何学中具有重要的研究价值.主要运用具有类光向量的费雷内标架讨论在四维Minkowski空间中与欧氏空间不同的一类特殊密切曲线(伪类光曲线)的一些几何性质,同时通过横截性原理给出了由伪类光曲线生成的伪类光超曲面的局部几何性质与奇点分类.     

Non‐relativistic continuous states in arbitrary dimension for a ring‐shaped pseudo‐Coulomb and energy‐dependent potentials

In this research, the non‐relativistic particle scattering has been investigated for an alternative pseudo‐Coulomb potential plus ring‐shaped and an energy‐dependent potentials in D‐dimensional space. The normalized wave functions of continuous states on the k/2π scale are expressed in terms of the hyper‐geometric series, and formula of phase shifts is presented. Analytical properties of the scattering amplitude and thermodynamics properties are discussed. Some of the numerical results of energy levels have been calculated too. Copyright © 2015 John Wiley & Sons, Ltd.