$$L^2_f$$ L f 2 -harmonic 1-forms on smooth metric measure spaces with positive $$\lambda _1(\Delta _f)$$ λ 1 ( Δ f )

In this paper, we study vanishing and splitting results on a complete smooth metric measure space \((M^n,g,\mathrm {e}^{-f}\mathrm {d}v)\) with various negative m-Bakry-Émery Ricci curvature lower bounds in terms of the first eigenvalue \(\lambda _1(\Delta _f)\) of the weighted Laplacian \(\Delta _f\), i.e., \(\mathrm {Ric}_{m,n}\ge -a\lambda _1(\Delta _f)-b\) for \(0<a\le \dfrac{m}{m-1}, b\ge 0\). In particular, we consider three main cases for different a and b with or without conditions on \(\lambda _1(\Delta _f)\). These results are extensions of Dung and Vieira, and weighted generalizations of Li-Wang, Dung-Sung, and Vieira.

     

Large sets with multiplicity

Designs, Codes and Cryptography - Large sets of combinatorial designs has always been a fascinating topic in design theory. These designs form a partition of the whole space into combinatorial...     

Turing patterns induced by self-diffusion in a predator–prey model with schooling behavior in predator and prey

Nonlinear Dynamics - This article considers a reaction–diffusion predator–prey model with schooling behavior both in predator and prey species and subject to the homogeneous Neumann...     

Visible-light-induced,autopromoted nickel-catalyzed three-component arylsulfonation of 1,3-enynes and mechanistic insights

Science China Chemistry - A light-induced, nickel-catalyzed three-component arylsulfonation of 1,3-enynes in the absence of photocatalyst is reported. This methodology exhibited mild conditions,...     

EDITORIAL

The year 2022 marks the 40th anniversary of the Chinese Journal of Polymer Science(CJPS)—a true milestone to be celebrated!In the early stage of the reform and opening,there was an increasing demand for international academic communications.To facilitate these communications.     

Bicomponent Cocatalyst Decoration on Flux-assisted CaTaO2N Single Crystals for Photocatalytic CO2 Reduction under Visible Light

Cubic-like CaTaO₂N photocatalysts with high crystallinity and uniform particle size were successfully prepared by the flux-assisted nitridation method. The growth of CaTaO₂N single crystals under different synthesis conditions was systematically investigated to understand the effects of the crystallinity and optical property on photocatalytic performance of CO₂ reduction. Moreover, the modification of CaTaO₂N single crystals with core-shell Ni−Ag bicomponent cocatalyst by two-step decoration process gave a 2.4 times higher amount of CO evolution than the deposition of sole Ag cocatalyst, because of the synergistic effects of bicomponent cocatalyst on the interfacial electron transfer and surface catalytic process. This study provides a valuable way to construct high-crystalline photocatalysts with effective bicomponent cocatalyst for visible-light-driven CO₂ reduction with H₂O.     

Interaction properties of double-hump solitons in the dispersion decreasing fiber

Nonlinear Dynamics - In this paper, the high-order coupled variable coefficient nonlinear Schrödinger equations is studied. The double-hump soliton solutions for the equations are obtained...     

Isoflavonoids from Astragalus membranaceus Hairy Roots

Chemistry of Natural Compounds -     

Dinuclear Zinc Catalyzed Enantioselective Dearomatization [3+2] Annulation of 2-Nitrobenzofurans and 2-Nitrobenzothiophenes

The application of dinuclear zinc catalysts in a dearomatization reaction has been developed. Catalytic asymmetric dearomatization [3+2] annulations of 2-nitrobenzofurans or 2-nitrobenzothiophenes with CF₃-containing N-unprotected isatin-derived azomethine ylides catalyzed by dinuclear zinc catalysts are realized with excellent diastereomer ratios (dr) of >20 : 1 and enantiomeric excess (ee) of up to 99 %. This protocol provides a practical, straightforward access to structurally diverse pyrrolidinyl spirooxindoles containing a 2,3-fused-dihydrobenzofuran (or dihydrobenzothiphene) moiety, and four contiguous stereocenters. Reactions can be performed on a gram scale. The absolute configuration of products is confirmed by X-ray single crystal structure analysis, and a possible mechanism is proposed.     

Moderate Deviations for Extreme Eigenvalues of Real-Valued Sample Covariance Matrices

Journal of Theoretical Probability - Consider the sample covariance matrices of form $$W=n^{-1}C C^{\top }$$ , where C is a $$k\times n$$ matrix with real-valued, independent and identically...