Minimal surfaces in symmetric spaces with parallel second fundamental form

In this paper, we study geometry of isometric minimal immersions of Riemannian surfaces in a symmetric space by moving frames and prove that the Gaussian curvature must be constant if the immersion is of parallel second fundamental form. In particular, when the surface is \(S^2\), we discuss the special case and obtain a necessary and sufficient condition such that its second fundamental form is parallel. We also consider isometric minimal two-spheres immersed in complex two-dimensional Kähler symmetric spaces with parallel second fundamental form, and prove that the immersion is totally geodesic with constant Kähler angle if it is neither holomorphic nor anti-holomorphic with Kähler angle \(\alpha \ne 0\) (resp. \(\alpha \ne \pi \)) everywhere on \(S^2\).     

局部凸空间P-自反下的中点局部k-一致凸性(光滑性)

在局部凸空间已有的中点局部kk-一致凸性和中点局部k-一致光滑性这一对对偶概念的基础上,证明了中点局部kk-一致凸性与中点局部(k+1)-一致凸性的关系,给出了在P-自反的条件下它们之间的等价对偶定理.     

On quasi $$\epsilon $$-solution for robust convex optimization problems

This paper devotes to the quasi \(\epsilon \)-solution (one sort of approximate solutions) for a robust convex optimization problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we establish approximate optimality theorem and approximate duality theorems in term of Wolfe type on quasi \(\epsilon \)-solution for the robust convex optimization problem. Moreover, some examples are given to illustrate the obtained results.     

Designing Solid Electrolyte Interfaces towards Homogeneous Na Deposition: Theoretical Guidelines for Electrolyte Additives and Superior High-Rate Cycling Stability

Metallic Na is a promising metal anode for large-scale energy storage. Nevertheless, unstable solid electrolyte interphase (SEI) and uncontrollable Na dendrite growth lead to disastrous short circuit and poor cycle life. Through phase field and ab initio molecular dynamics simulation, we first predict that the sodium bromide (NaBr) with the lowest Na ion diffusion energy barrier among sodium halogen compounds (NaX, X=F, Cl, Br, I) is the ideal SEI composition to induce the spherical Na deposition for suppressing dendrite growth. Then, 1,2-dibromobenzene (1,2-DBB) additive is introduced into the common fluoroethylene carbonate-based carbonate electrolyte (the corresponding SEI has high mechanical stability) to construct a desirable NaBr-rich stable SEI layer. When the Na||Na₃V₂(PO₄)₃ cell utilizes the electrolyte with 1,2-DBB additive, an extraordinary capacity retention of 94 % is achieved after 2000 cycles at a high rate of 10 C. This study provides a design philosophy for dendrite-free Na metal anode and can be expanded to other metal anodes.     

Selective CO2-to-C2H4 Photoconversion Enabled by Oxygen-Mediated Triatomic Sites in Partially Oxidized Bimetallic Sulfide

Selective CO₂ photoreduction into C₂ fuels under mild conditions suffers from low product yield and poor selectivity owing to the kinetic challenge of C−C coupling. Here, triatomic sites are introduced into bimetallic sulfide to promote C−C coupling for selectively forming C₂ products. As an example, FeCoS₂ atomic layers with different oxidation degrees are first synthesized, demonstrated by X-ray photoelectron spectroscopy and X-ray absorption near edge spectroscopy spectra. Both experiment and theoretical calculation verify more charges aggregate around the introduced oxygen atom, which enables the original Co−Fe dual sites to turn into Co−O−Fe triatomic sites, thus promoting C−C coupling of double *COOH intermediates. Accordingly, the mildly oxidized FeCoS₂ atomic layers exhibit C₂H₄ formation rate of 20.1 μmol g⁻¹ h⁻¹, with the product selectivity and electron selectivity of 82.9 % and 96.7 %, outperforming most previously reported photocatalysts under similar conditions.     

Elaborating E/Z-Geometry of Alkenes via Cage-Confined Arylation Catalysis of Terminal Olefins

A visible light photosensitizing metal-organic cage is applied as an artificial supramolecular reactor to control the reaction of aryl radicals with terminal olefins under green light/solvent conditions, which facilitates selective transformation in the confined enzyme-mimicking environment to give a series of geometrically defined E/Z-alkenes. The hydrophobic cage displays good host–guest inclusion with aromatic substrates, promoting Meerwein arylation and protecting E-isomeric products during reaction; while a small amount of benzonitrile can turn on efficient E→Z isomerization. Besides π–π stacking, the hydrogen bonding and halogen bonding interactions also act as control forces for the arylation of aliphatic terminal olefins known as poor acceptors in classic Meerwein arylation. The application of this switchable cage-confined arylation catalysis has been demonstrated by the syntheses of Tapinarof and a marine natural product from the same substrate via controllable E/Z selectivity.     

Unveiling the High-valence Oxygen Degradation Across the Delithiated Cathode Surface

Charge compensation on anionic redox reaction (ARR) has been promising to realize extra capacity beyond transition metal redox in battery cathodes. The practical development of ARR capacity has been hindered by high-valence oxygen instability, particularly at cathode surfaces. However, the direct probe of surface oxygen behavior has been challenging. Here, the electronic states of surface oxygen are investigated by combining mapping of resonant Auger electronic spectroscopy (mRAS) and ambient pressure X-ray photoelectron spectroscopy (APXPS) on a model LiCoO₂ cathode. The mRAS verified that no high-valence oxygen can sustain at cathode surfaces, while APXPS proves that cathode electrolyte interphase (CEI) layer evolves and oxidizes upon oxygen gas contact. This work provides valuable insights into the high-valence oxygen degradation mode across the interface. Oxygen stabilization from surface architecture is proven a prerequisite to the practical development of ARR active cathodes.     

Regulation of Atomic Fe-Spin State by Crystal Field and Magnetic Field for Enhanced Oxygen Electrocatalysis in Rechargeable Zinc-Air Batteries

Highly-active and low-cost bifunctional electrocatalysts for oxygen reduction and evolution are essential in rechargeable metal-air batteries, and single atom catalysts with Fe−N−C are promising candidates. However, the activity still needs to be boosted, and the origination of spin-related oxygen catalytic performance is still uncertain. Herein, an effective strategy to regulate local spin state of Fe−N−C through manipulating crystal field and magnetic field is proposed. The spin state of atomic Fe can be regulated from low spin to intermediate spin and to high spin. The cavitation of d_xz and d_yz orbitals of high spin Fe^III can optimize the O₂ adsorption and promote the rate-determining step (*O₂ to *OOH). Benefiting from these merits, the high spin Fe−N−C electrocatalyst displays the highest oxygen electrocatalytic activities. Furthermore, the high spin Fe−N−C-based rechargeable zinc-air battery displays a high power density of 170 mW cm⁻² and good stability.     

A Polarized Gel Electrolyte for Wide-Temperature Flexible Zinc-Air Batteries

The development of flexible zinc-air batteries (FZABs) has attracted broad attention in the field of wearable electronic devices. Gel electrolyte is one of the most important components in FZABs, which is urgent to be optimized to match with Zn anode and adapt to severe climates. In this work, a polarized gel electrolyte of polyacrylamide-sodium citric (PAM-SC) is designed for FZABs, in which the SC molecules contain large amount of polarized −COO⁻ functional groups. The polarized −COO⁻ groups can form an electrical field between gel electrolyte and Zn anode to suppress Zn dendrite growth. Besides, the −COO⁻ groups in PAM-SC can fix H₂O molecules, which prevents water from freezing and evaporating. The polarized PAM-SC hydrogel delivers a high ionic conductivity of 324.68 mS cm⁻¹ and water retention of 96.85 % after being exposed for 96 h. FZABs with the PAM-SC gel electrolyte exhibit long cycling life of 700 cycles at −40 °C, showing the application prospect under extreme conditions.     

Bis-peri-dinaphtho-rylenes: Facile Synthesis via Radical-Mediated Coupling Reactions and their Distinctive Electronic Structures

Polycyclic aromatic hydrocarbons (PAHs) with a one-dimensional (1D), ribbon-like structure have the potential to serve as both model compounds for corresponding graphene nanoribbons (GNRs) and as materials for optoelectronics applications. However, synthesizing molecules of this type with extended π-conjugation presents a significant challenge. In this study, we present a straightforward synthetic method for a series of bis-peri-dinaphtho-rylene molecules, wherein the peri-positions of perylene, quaterrylene, and hexarylene are fused with naphtho-units. These molecules were efficiently synthesized primarily through intramolecular or intermolecular radical coupling of in situ generated organic radical species. Their structures were confirmed using X-ray crystallographic analysis, which also revealed a slightly bent geometry due to the incorporation of a cyclopentadiene ring at the bay regions of the rylene backbones. Bond lengh analysis and theoretical calculations indicate that their electronic structures resemble pyrenacenes more than quinoidal rylenes. That is, the aromatic sextets are predominantly localized along the long axis of the skeletones. As the chain length increases, these molecules exhibit enhanced electronic absorption with a bathochromic shift, and multiple amphoteric redox waves. This study introduces a novel synthetic approach for generating 1D extended PAHs and GNRs, along with their structure-dependent electronic properties.