Double degeneration on second-order breather solutions of Maxwell–Bloch equation

The breather solutions of the Maxwell–Bloch equations in a two-level resonant system associated with the self-induced transparency phenomenon are constructed by the Darboux transformation. After constructing the formulas of the second-order breather solutions, the double degeneration and hybrid solutions are studied by the analytical form as well as figures. Our results might be helpful in such application or prevention of the rogue waves from breather solution interactions and degeneration in the nonlinear optical systems associated with the Maxwell–Bloch equations.     

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.     

Concomitant cocrystal and salt: no interconversion in the solid state

A cocrystal and a molecular salt of β‐alanine and dl ‐tartaric acid, C₃H₈NO₂⁺·C₄H₄O₆^?, of the same chemical composition, were studied over a wide temperature range by single‐crystal and powder X‐ray diffraction. Neither the interconversion between the two phases nor any polymorphic transitions were observed in the temperature range from 100 K to the melting points. This contrasts with the solvent‐mediated phase transition from the salt to the cocrystal in a slurry that has been documented earlier.     

Direct through anionic,cationic, and radical active species: Terminal carbon–halogen bond for “controlled”/living polymerizations of styrene

In this work, we examined the synthesis of novel block (co)polymers by mechanistic transformation through anionic, cationic, and radical living polymerizations using terminal carbon–halogen bond as the dormant species. First, the direct halogenation of growing species in the living anionic polymerization of styrene was examined with CCl₄ to form a carbon–halogen terminal, which can be employed as the dormant species for either living cationic or radical polymerization. The mechanistic transformation was then performed from living anionic polymerization into living cationic or radical polymerization using the obtained polymers as the macroinitiator with the SnCl₄/n‐Bu₄NCl or RuCp^*Cl(PPh₃)/Et₃N initiating system, respectively. Finally, the combination of all the polymerizations allowed the synthesis block copolymers including unprecedented gradient block copolymers composed of styrene and p‐methylstyrene. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 465–473     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

单参考态微扰理论发散问题的理论研究

本文对闭壳层和开壳层分子系统由于加入弥散函数导致的单参考态微扰理论的发散问题进行了深入的研究. 发现对开壳层系统，微扰能量的振幅随体系自旋多重度的增加而增加. 本文利用Feenberg变换来处理微扰理论的发散问题. 通过调节Feenberg 变换的参数λ来加速微扰序列的收敛性. 数值计算表明，存在一个λ值，微扰序列收敛最快. 还发现该λ值随着自旋多重度增加而增加.     

Simultaneous Visualization of Endogenous Homocysteine,Cysteine, Glutathione,and their Transformation through Different Fluorescence Channels

Studying numerous biologically important species simultaneously is crucial to understanding cellular functions and the root causes of related diseases. Direct visualization of endogenous biothiols in biological systems is of great value to understanding their biological roles. Herein, a novel multi‐signal fluorescent probe was rationally designed and exploited for the simultaneous sensing of homocysteine (Hcy), cysteine (Cys), and glutathione (GSH) using different emission channels. This probe was successfully applied to the simultaneous discrimination between and visualization of endogenous Hcy, Cys, GSH, and their transformation in living cells.     

On the definition of cavitation intensity

Cavitation intensity has already been used to character the activity or strength of cavitation, and several methods are developed to measure the cavitation intensity. However, the previous definitions of cavitation intensity are often either vague or biased. In this paper, from the point of view of energy, the authors proposed a generalized definition of cavitation intensity, derived an approximate formula to calculate the cavitation intensity and discussed its measure method.