Finite quotients of the automorphism group of a free group

The automorphism group AutF_n of a free group F_n of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group. This gives rise to an antihomomorphism from AutF_nto a permutation group. We determine this antihomomorphic image of AutF_n when G is the semidirect product Z_p x Z_q     

PREFACE

正This special issue of Acta Mathematica Scientia is dedicated to Prof.Boling Guo on the occasion of his 80thbirthday.Prof.Guo was born in Longmen town,Xinluo district,Longyan city,Fujian province,China.After graduating from the Longyan No.1 High School,he was admitted into the Department of Mathematics,Fudan University where he worked after graduation until 1963.In 1963,he moved to Beijing Institute of Applied Physics and     

A General Preparation of Solid Solution-Oxide Heterojunction Photocatalysts through Metal–Organic Framework Transformation Induced Pre-nucleation

Solid solution-oxide heterostructures combine the advantages of solid solution and heterojunction materials to improve electronic structure and optical properties by metal doping, and enhance charge separation and transfer in semiconductor photocatalysts by creating a built-in electric field. Nevertheless, the effective design and synthesis of these materials remains a significant challenge. Here, we develop a generally applicable strategy that leverages the transformable properties of metal–organic frameworks (MOFs) to prepare solid solution-oxide heterojunctions with controllable structural and chemical compositions. The process consists of three main steps. First, MOFs with different topological structures and metal centers are transformed, accompanied by pre-nucleation of a metal oxide. Second, solid solution is prepared through calcination of the transformed MOFs. Finally, a heterojunction is formed by combining solid solution with another metal oxide group through endogenous overflow. DFT calculations and study on carrier dynamics show that the structure of the material effectively prevents electrons from returning to the bulk phase, exhibiting superior photocatalytic reduction performance of CO₂. This study is expected to promote the controllable synthesis and research of MOF-derived heterojunctions.     

Stochastic Simulation of Controlled Radical Polymerization Forming Dendritic Hyperbranched Polymers

Stochastic simulation of the formation process of hyperbranched polymers (HBPs) based on the reversible deactivation radical polymerization (RDRP) using a branch-inducing monomer, evolmer, has been carried out. The simulation program successfully reproduced the change of dispersities (Đs) during the polymerization process. Furthermore, the simulation suggested that the observed Đs (=1.5–2) are due to the distribution of the number of branches instead of undesired side reactions, and that the branch structures are well controlled. In addition, the analysis of the polymer structure reveals that the majority of HBPs have structures close to the ideal one. The simulation also suggested the slight dependence of branch density on molecular weight, which was experimentally confirmed by synthesizing HBPs with an evolmer having phenyl group.     

Enhanced Li+ Diffusion and Lattice oxygen Stability by the High Entropy Effect in Disordered-Rocksalt Cathodes

Cation-disordered Rocksalt oxides (DRXs) are a promising new class of cathode materials for Li-ion batteries due to their natural abundance, low cost and great electrochemical performance. High entropy strategy in Mn-based DRXs appears to be an effective strategy for improving the rate capability, but it suffers from challenges including capacity degradation. The present paper reports a new group of high entropy DRXs (HE DRX) based on Ni²⁺-Nb⁵⁺ pair; the structural and chemical evolution upon cycling of DRXs with an increasing transition metal (TM) species are systematically investigated. An explanation is proposed for how the crystal field stability energy determines that HE DRX could exist in single Rocksalt solid solution structures. We further reveal that the charge compensation mechanism in HE DRX is the result of various TM synergistic effect. More importantly, through various in situ and ex situ techniques and theoretical calculation, the effective integration of more TM cation species within the HE DRX framework promotes better Li⁺ diffusion and improves lattice oxygen stability, consequently increasing capacity upon cycling.     

Ultrasound Treatment Enhanced Semidry-Milled Rice Flour Properties and Gluten-Free Rice Bread Quality

The structural and functional properties of physical modified rice flour, including ultrasound treated rice flour (US), microwave treated rice flour (MW) and hydrothermal treated rice flour (HT) were investigated with wet-milled rice flour (WF) used as a positive control. The results showed the presence of small dents and pores on the rice flour granules of US and MW while more fragments and cracks were showed in HT. XRD and FTIR revealed that moderate ultrasonic treatment promoted the orderly arrangement of starch while hydrothermal treatment destroyed the crystalline structure of rice flour. In addition, the significant decrease of gelatinization enthalpy and the narrowing gelatinization temperature were observed in US. Compared to that of SF, adding physical modified rice flour led to a batter with higher viscoelasticity and lower tan δ. However, the batter added HT exhibited highest G′ and G″ values and lowest tan δ, which led to a harder texture of bread. Texture analysis demonstrated that physical modified rice flour (except HT) reduced the hardness, cohesion, and gumminess of rice bread. Especially, the specific volume of bread with US increased by 15.6% and the hardness decreased by 17.6%. This study suggested that ultrasound treatment of rice flour could improve texture properties and appearance of rice bread.     

Miniaturized matrix solid-phase dispersion and solid-phase clear-up combined with capillary electrophoresis for efficient determination of trace bioactive components in complicated sample matrix: Take Wubi Shanyao Pill as an example

Accurate quantitative analysis of trace analytes in a complicated matrix is a challenge in modern analytical chemistry. An appropriate analytical method is considered to be one of the most common gaps during the whole process. In this study, a green and efficient strategy based on miniaturized matrix solid-phase dispersion and solid-phase extraction combined with capillary electrophoresis was first proposed for extracting, purifying and determining target analytes from complicated matrix, using Wubi Shanyao Pill as an example. In detail, 60 mg of samples were dispersed on MCM-48 to obtain high yields of analytes, then the extract was purified with a solid-phase extraction cartridge. Finally, four analytes in the purified sample solution were determined by capillary electrophoresis. The parameters affecting the extraction efficiency of matrix solid-phase dispersion, purification efficiency of solid-phase extraction and separation effect of capillary electrophoresis were investigated. Under the optimized conditions, all analytes demonstrated satisfactory linearity (R²>0.9983). What's more, the superior green potential of the developed method for the determination of complex samples was confirmed by the Analytical GREEnness Metric Approach. The established method was successfully applied in the accurate determination of target analytes in Wubi Shanyao Pill and thus provided reliable, sensitive, and efficient strategy support for its quality control.     

Synthesis of a new PET/layered niobate hybrid material

A new organic/inorganic hybrid material was prepared by the polymerization of bis(hydroxyethyl) terephthalate (BHET) with a layered niobate compound, H₄Nb₆O₁₇, modified by 11-aminoundecanoic acid (AUA). The hybrid polymer films of BHET with H₄Nb₆O₁₇/AUA exhibited favorable characteristics, particularly of being optically clear, indicating the exfoliation and homogeneous dispersion of H₄Nb₆O₁₇ into the PET/niobate hybrid.     

Layer iteration calculation of low-energy electron-diffraction by Beeby's multiple scattering method

The interlayer structural propagator in Beeby's multiple scattering method is transformed into a reciprocal space representation. Interlayer multiple scattering events can then be summed to convergence in a layer iteration scheme. LEED spectra calculations for general angles of Ni (001) using 8 phase shifts and up to 49 Bloch waves are reported. A 3–5 eV shift in peak positions is found between calculations using 5 and 8 phase shifts, resolving a recent controversy over different inner potential values used for Ni (001).