Boussinesq方程行波解的存在性

利用平面动力系统方法的分支理论，研究了Boussinesq方程，通过对Boussinesq方程进行行波变换，得到了相应行波系统的首次积分和平衡点，给出了不同参数条件下的相图，证实了Boussinesq方程存在孤立波解和周期波解。     

Asymmetric nonlinear-mode-conversion in an optical waveguide withPT symmetry

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.     

Synthesis and Diverse Transformations of a Dinitrogen Dititanium Hydride Complex Bearing Rigid Acridane-Based PNP-Pincer Ligands

Studies on N₂ activation and transformation by transition metal hydride complexes are of particular interest and importance. The synthesis and diverse transformations of a dinitrogen dititanium hydride complex bearing the rigid acridane-based ^acriPNP-pincer ligands {[(^acriPNP)Ti]₂(μ₂-η¹:η²-N₂)(μ₂-H)₂} are presented. This complex enabled N₂ cleavage and hydrogenation even without additional H₂ or other reducing agents. Furthermore, diverse transformations of the N₂ unit with a variety of organometallic compounds such as ZnMe₂, MgMe₂, AlMe₃, B(C₆F₅)₃, PinBH, and PhSiH₃ have been well established at the rigid ^acriPNP-ligated dititanium framework, such as reversible bonding-mode change between the end-on and side-on/end-on fashions, diborylative N=N bond cleavage, the formal insertion of two dimethylaluminum species into the N=N bond, and the formal insertion of two silylene units into the N=N bond. This work has revealed many unprecedented aspects of dinitrogen reaction chemistry.     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Modulating Charge Carrier Efficient Separation Enabled by Lewis Base Modification in Paper-based Photoelectrochemical Sensor

The separation efficiency of charge carriers determines the analytical sensitivity of the paper-based photoelectrochemical sensor. Herein, the Lewis base modification strategy is proposed to promote the carrier separation through an in-situ ion exchange method. Firstly, three-dimensional paper-based hierarchically TiO₂ (PHT) arrays are prepared with the one-step hydrothermal method. With the aid of Lewis base, the photo-induced charge separation efficiency and the photocurrent signal are obviously increased. Ultimately, sensitive sensing of prostate specific antigen (PSA) is achieved and the linear range is 1 pg/mL–100 ng/mL with the detection limitation of 0.3 pg/mL.     

Stabilization of the higher order nonlinear Schrödinger equation with constant coefficients

We study the internal stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. Combining multiplier techniques, a fixed point argument and nonlinear interpolation theory, we can obtain the well-posedness. Then, applying compactness arguments and a unique continuation property, we prove that the solution of the higher-order nonlinear Schrödinger equation with a damping term decays exponentially.     

Synchronizing Substrate Activation Rates in Multicomponent Reactions with Metal–Organic Framework Catalysts

A study on the influence of the cation coordination number, number of Lewis acid centers, concurrent existence of Lewis base sites, and structure topology on the catalytic activity of six new indium MOFs, has been carried out for multicomponent reactions (MCRs). The new indium polymeric frameworks, namely [In₈(OH)₆(popha)₆(H₂O)₄]?3 H₂O ( InPF‐16 ), [In(popha)(2,2′‐bipy)]?3 H₂O ( InPF‐17 ), [In₃(OH)₃(popha)₂(4,4′‐bipy)]?4 H₂O ( InPF‐18 ), [In₂(popha)₂(4,4′‐bipy)₂]?3 H₂O ( InPF‐19 ), [In(OH)(Hpopha)]?0.5 (1,7‐phen) ( InPF‐20 ), and [In(popha)(1,10‐phen)]?4 H₂O ( InPF‐21 ) (InPF=indium polymeric framework, H₃popha=5‐(4‐carboxy‐2‐nitrophenoxy)isophthalic acid, phen=phenanthroline, bipy=bipyridine), have been hydrothermally obtained by using both conventional heating (CH) and microwave (MW) procedures. These indium frameworks show efficient Lewis acid behavior for the solvent‐free cyanosilylation of carbonyl compounds, the one pot Passerini 3‐component (P‐3CR) and the Ugi 4‐component (U‐4CR) reactions. In addition, InPF‐17 was found to be a highly reactive, recyclable, and environmentally benign catalyst, which allows the efficient synthesis of α‐aminoacyl amides. The relationship between the Lewis base/acid active site and the catalytic performance is explained by the 2D seven‐coordinated indium framework of the catalyst InPF‐17 . This study is an attempt to highlight the main structural and synthetic factors that have to be taken into account when planning a new, effective MOF‐based heterogeneous catalyst for multicomponent reactions.