极大3限制边连通二部图的充分条件

设G=(V,E)是一个连通图.称一个边集合S■E是一个k限制边割,如果G-S的每个连通分支至少有k个顶点.称G的所有k限制边割中所含边数最少的边割的基数为G的k限制边连通度,记为λ_k(G).定义ξ_k(G)=min{[X,■]:|X|=k,G[X]连通,■=V(G)\X}.称图G是极大k限制边连通的,如果λ_k(G)=ξ_k(G).本文给出了围长为g>6的极大3限制边连通二部图的充分条件.     

A Structurally Robust Chiral Borate Ion: Molecular Design,Synthesis, and Asymmetric Catalysis

Catalysis by chiral weakly‐coordinating anions (WCAs) remains underdeveloped due to the lack of a molecular design strategy for exploiting their characteristics, such as the non‐nucleophilic nature. Here, we report the development of a chiral borate ion comprising an O,N,N,O‐tetradentate backbone, which ensures hitherto unattainable structural robustness. Upon pairing with a proton, the hydrogen borate acts as an effective catalyst for the asymmetric Prins‐type cyclization of vinyl ethers, providing access to structurally and stereochemically defined dihydropyrans. The key to selectivity control is the distinct ability of the borate ion to discriminate the prochiral faces of the acyclic oxonium ion intermediate and dictate the regiochemical outcome. We anticipate that this study paves the way for exploring the untapped potential of WCA catalysis for selective chemical synthesis.     

一类Weingarten曲面的基本方程和LAX对

研究三维欧氏空间中两个主曲率满足一类有理函数关系的Weingarten曲面的Gauss-Codazzi方程的分类,并给出它们的Lax对.     

Functionalized Silver-Ion-Mediated α-dC/β-dC Hybrid Base Pairs with Exceptional Stability: α-d-5-Iodo-2′-Deoxycytidine and Its Octadiynyl Derivative in Metal DNA

Silver-mediated α-dC–Ag⁺–β-dC hybrid base pairs decorated with 5-iodo- or 5-octadiynyl residues are well accommodated in duplex DNA. A strong T_m increase and favorable thermodynamic data for duplex DNA were observed after addition of silver ions. The phenomenon is particularly obvious when both nucleobases of the base pairs are functionalized. Neither the position of the base pair, nor the type of 5-substituent had a negative influence. On the contrary, functionalization of conventional silver-mediated β-dC–Ag⁺–β-dC homo base pairs showed a negative impact induced by the bulky substituents. To this end, cytosine modified 12-mer oligodeoxynucleotides were prepared by solid-phase synthesis employing new α-anomeric 2′-deoxycytidine phosphoramidites. A multigram scale synthesis was developed for 5-iodo-α-d -2′-deoxycytidine ( 1 ) employing the direct glycosylation of cytosine with Hoffer's α-d -halogenose followed by separation of anomeric DMT nucleosides. Regarding base-pair stability and functionalization silver-mediated α/β-dC hybrid base pairs were found to be superior to β/β-dC homo pairs. According to their extraordinary properties, they might find applications in DNA diagnostics, material science, or nanotechnology.     

Rapid and Scalable Access to Sequence-Controlled DHDM Multiblock Copolymers by FLP Polymerization

An immortal N-(diphenylphosphanyl)-1,3-diisopropyl-4,5-dimethyl-1,3-dihydro-2H-imidazol-2-imine/diisobutyl (2,6-di-tert-butyl-4-methylphenoxy) aluminum (P(NIⁱPr)Ph₂/(BHT)AlⁱBu₂)-based frustrated Lewis pair (FLP) polymerization strategy is presented for rapid and scalable synthesis of the sequence-controlled multiblock copolymers at room temperature. Without addition of extra initiator or catalyst and complex synthetic procedure, this method enabled a tripentacontablock copolymer (n=53, k=4, dp_n=50) to be achieved with the highest reported block number (n=53) and molecular weight (M_n=310 kg mol⁻¹) within 30 min. More importantly, this FLP polymerization strategy provided access to the multiblock copolymers with tailored properties by precisely adjusting the monomer sequence and block numbers.     

Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

Unprecedented Oxidative Addition and Metal‐Only Lewis Pair Chemistry of Antimony Trihalides

Reaction of the zero‐valent platinum complex [Pt(PCy₃)₂] with SbF₃ generates the cationic diplatinum stibenium complex [{(Cy₃P)₂Pt}₂(μ‐SbF₂)]⁺, the first unsupported metal‐only Lewis pair containing an antimony‐centered Lewis acid. In contrast, SbCl₃ undergoes oxidative addition to [Pt(PCy₃)₂], resulting in the dihalostibanyl complex trans‐[PtCl(SbCl₂)(PCy₃)₂], the first example of oxidative addition of an antimony–halide bond to a transition metal.     

Effects of Ionic Liquids on the Thermodynamics of Hydrogen Activation by Frustrated Lewis Pairs: A Density Functional Theory Study**

Nowadays, hydrogen activation by frustrated Lewis pairs (FLPs) and their applications are one of the emerging research topics in the field of catalysis. Previous studies have shown that the thermodynamics of this reaction is determined by electronic structures of FLPs and solvents. Herein, we investigated systems consisting of typical FLPs and ionic liquids (ILs), which are well known by their large number of types and excellent solvent effects. The density functional theory (DFT) calculations were performed to study the thermodynamics for H₂ activation by both inter- and intra-molecular FLPs, as well as the individual components. The results show that the computed overall Gibbs free energies in ILs are more negative than that computed in toluene. Through the thermodynamics partitioning, we find that ILs favor the H−H cleavage elemental step over the elemental steps of proton attachment, hydride attachment and zwitterionic stabilization. Moreover, the results show that these effects are strongly dependent on the type of FLPs, where intra-molecular FLPs are more affected compared to the inter-molecular FLPs.     

Triple Frustrated Lewis Pair-Type Reactivity on a Single Rare-Earth Metal Center

Rare-earth metal cations have been used rarely as Lewis-acidic components in the chemistry of frustrated Lewis pairs (FLPs). Herein, we report the first cerium/phosphorus system ( 2 ) employing a heptadentate N₄P₃ ligand, which exhibits triple FLP-type reactivity towards a series of organic substrates, including isocyanates, isothiocyanates, diazomethane, and azides on a single rare-earth Lewis acidic Ce center. This result shows that the Ce center and three P atoms in 2 could simultaneously activate three equivalents of small molecules under mild conditions. This study broadens the diversity of FLPs and demonstrates that rare earth based FLP exhibit unique properties compared with other FLP systems.     

Reversible Activation of Water by an Air- and Moisture-Stable Frustrated Rhodium Nitrogen Lewis Pair

[Cp*Rh(κ³N,N′,P- L )][SbF₆] (Cp*=C₅Me₅), bearing a guanidine-derived phosphano ligand L , behaves as a “dormant” frustrated Lewis pair and activates H₂ and H₂O in a reversible manner. When D₂O is employed, a facile H/D exchange at the Cp* ring takes place through sequential C(sp³)−H bond activation.