Reversible C=C Bond Activation by an Intramolecularly Coordinated Antimony(I) Compound

The reaction of N,C,N-chelated stibinidene ArSb ( 1 ) (Ar=C₆H₃-2,6-(CH=NtBu)₂) with selected N-alkyl/aryl-maleimides RN(C(O)CH)₂ (R=Me, tBu, Ph) gave the addition products with bridged bicyclic [2.2.1] structure containing an antimony atom at the bridgehead position, fused with a 6-membered benzene and a 5-membered N-alkyl/aryl-pyrrolidine ring. These compounds were completely characterized. More importantly, additional studies showed that these reactions are reversible in solution, thereby representing an unprecedented reversible activation of a C=C bond by an antimony(I) compound.     

C‐S cross‐coupling reaction using novel and green synthesized CuO nanoparticles assisted by Euphorbia maculata extract

In the present study, biosynthesis of CuO nanoparticles using a rapid, eco‐friendly, cost‐effective and efficient method has been reported employing aqueous Euphorbia maculata extract as mild, renewable and non‐toxic reducing and capping agents without adding any surfactants. The biogenic and green method has some benefits compared to conventional physical and chemical methods. It is simple, cheap and environmentally friendly. The biosynthesized CuO NP displayed a color change pattern (from sky blue to black) on preparation and presented its respective broad peak at 365 nm, which was analyzed by UV–Vis spectroscopy. Using the FT‐IR analysis, biomolecules in E. maculata extract which are responsible for bioreduction activity and synthesize of CuO NP, were identified. The XRD, EDX and FESEM results confirmed the successful synthesis of CuO nanoparticles of 18 nm sizes, with spherical and sponge crystal structure. The catalytic activity of biosynthesized CuO NPs was studied in C‐S cross‐coupling reaction. This method has the advantages of high yields, easy work‐up, and simple reusability. The recovered CuO NP can be reused four times without any considerable loss of its catalytic activity.     

σ2 Hessian方程的Pogorelov型C2 内估计及应用

提出利用拉格朗日乘子法重新证明σ2算子的最优凹性,并定义了一个凸锥Γ3?=λ=(λ1,λ2,?,λn)∈Rn:σ1(λ)>0,σ2(λ|i)>0,1≤i≤n。利用σ2算子的最优凹性，给出了σ2Hessian方程Pogorelov型C2内估计，进而证明了σ2(D2u(x))=1,x∈Rn的满足二次多项式增长条件的Γ3?-凸整解为二次多项式。     

Catalytic C−H/C−F Coupling of Azoles and Acyl Fluorides

A method for the palladium/copper-catalyzed direct acylation of azoles with acyl fluorides is described. This study reports the first examples of acyl fluorides being used as acylation reagents in transition-metal-catalyzed aromatic C−H bond functionalization reactions. Depending on the reaction temperature, decarbonylative coupling may also occur. Mechanistic studies suggest that the cleavage of the aromatic C−H bond, promoted by a copper-phosphine species, is not the rate-limiting step of this acylation.     

On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

An anisotropic area-preserving flow for convex plane curves

This paper will deal with an anisotropic area-preserving flow which keeps the convexity of the evolving curve and the limiting curve converges to a homothety of a symmetric smooth strictly convex plane curve.     

Universal deformation rings and self-injective Nakayama algebras

Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring $R(\mathrm{\Lambda },V)$ and we describe $R(\mathrm{\Lambda },V)$ explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups.     

Direct meta-C−H Perfluoroalkenylation of Arenes Enabled by a Cleavable Pyrimidine-Based Template

The development of efficient and mild methods for the synthesis of organofluorine compounds is of foremost interest in various fields of chemistry. A direct pyrimidine-based selective meta-C−H perfluoroalkenylation of arenes involving several commercially available perfluoroolefins is described. The synthetic versatility of the protocol is demonstrated by an extensive substrate scope including different benzylsulfonyl, alkylarene and phenylacetic acid scaffolds. The generality of this methodology including the meta-C−H perfluoroalkenylation of Ibuprofen, the facile cleavage of the directing group and gram-scale reactions are presented.     

Highly Conjugated π-Systems Arising from Cannibalistic Hexadehydro-Diels–Alder Couplings: Cleavage of C−C Single and Triple Bonds

We have investigated the cannibalistic self-trapping reaction of an ortho-benzyne derivative generated from 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne in an HDDA reaction. Without adding any specific trapping agent, the highly reactive benzyne is trapped by another bisdiyne molecule in at least three different modes. We have isolated and characterized the resulting products and performed high-level calculations concerning the reaction mechanism. During the cannibalistic self-trapping process, either a C≡C triple bond or an sp–sp³ C−C single bond is cleaved. Up to seven rings and nine C−C bonds are formed starting from two 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne molecules. Our experiments and calculations provide considerable insight into the variety of reaction pathways which the ortho-benzyne derivative, generated from a bisdiyne, can take when reacting with another bisdiyne molecule.