Utilization of photocatalysts in decarboxylative coupling of carboxylic N-hydroxyphthalimide (NHPI) esters

Recently, the visible-light photoredox decarboxylative couplings of N-(acyloxy)phthalimides (NHPI esters) and its derivatives have become an efficient chemical transformation. Under visible light, the NHPI esters undergo a single-electron transfer (SET) process to afford the corresponding carbon or nitrogen radicals that participate in many chemical transformations. The photoredox decarboxylative couplings have been applied to achieve construction of an array of carbon–carbon and carbon–heteroatom bonds as well as the synthesis of carbocycles and heterocycles. This review categorises photocatalysts, discusses the application and catalysis mechanisms of NHPI esters, and details recent progress in this field.     

Non-integrability vs. integrability in pentagram maps

We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to possess projective duality. We show that in many cases the pentagram map cannot be included into integrable flows as a time-one map, and discuss how the corresponding notion of discrete integrability can be extended to include jumps between invariant tori. We also present a numerical evidence that certain generalizations of the integrable 2D pentagram map are non-integrable and present a conjecture for a necessary condition of their discrete integrability.     

Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: Pro or contra?

The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.     

Non-linear couplings,from the early to the late time universe

Deciphering the mechanisms at play in the formation and evolution of the large-scale structure of the universe is part of the scientific goals of many projects of observational cosmology. In particular, large-scale structure observations can be used to infer mode-coupling effects, whether they come from the physics of the early universe or from its late time evolution. Specificities of such couplings are presented, noting that in principle they can be directly detected through bispectra of the cosmic microwave background temperature anisotropies or density in the local universe. The existence of such couplings have however more far-reaching consequences for the growth of the structure. Those are sketched as well as their possible observational impacts.     

Metal‐Catalyzed Reductive Coupling Reactions of Organic Halides with Carbonyl‐Type Compounds

Metal‐catalyzed reductive coupling reactions of aryl halides and (pseudo)halides with carbonyl‐type compounds have undergone an impressive development within the last years. These methodologies have shown to be a powerful alternate strategy, practicality aside, to the use of stoichiometric, well‐defined, and, in some cases, air‐sensitive organometallic species. In this Minireview, the recent findings in this field are summarized, with particular emphasis on the mechanistic interpretation of the results and future aspects of this area of expertise.     

第一过渡系金属-镝单分子磁体研究进展与展望

第一过渡系中的顺磁性离子Cr^Ⅲ、Mn^Ⅱ/Mn^Ⅲ、Fe^Ⅱ/Fe^Ⅲ、Co^Ⅱ、Ni^Ⅱ和Cu^Ⅱ及抗磁性离子Co^Ⅲ和Zn^Ⅱ均可与Dy^Ⅲ在多齿螯合配体配位下形成单分子磁体配合物。在本文中,我们阐述或汇总了几乎所有的第一过渡系金属-镝单分子磁体。对于由顺磁性第一过渡金属离子和Dy^Ⅲ离子形成的配合物,有2个有趣的现象需要引起人们的注意：一是一些Cr-Dy配合物具有较高的阻塞温度和较大的矫顽场,这可归功于配合物内Cr^Ⅲ离子和Dy^Ⅲ离子之间较强的磁耦合作用（|J|>10 cm^-1）。二是报道的Fe^Ⅱ₂-Dy配合物的能垒可达到319 cm^-1（459 K）,这在第一过渡系金属-镝单分子磁体中也是比较高的。这可能与Fe^Ⅱ₂-Dy中Dy^Ⅲ具有较高的轴向对称性（D_5h）有关,且从头计算表明该配合物中Dy的第一激发态也具有较高的轴向对称性。除了部分Cr-Dy和Fe^Ⅱ-Dy配合物外,其他顺磁性第一过渡金属-Dy的能垒较低,这可能由配合物内顺磁离子间弱的磁耦合造成的。为了消除磁耦合对磁弛豫行为影响,近年来人们关注于使用抗磁性第一过渡金属离子与Dy^Ⅲ构建单分子磁体配合物。相比其他核数的Zn-Dy配合物,三核Zn₂Dy配合物被报道的数目最多且研究得最为深入,这可能与较易调控Zn₂Dy中Dy配位几何对称性有关。最后,我们提出了几点关于进一步提升第一过渡系金属-镝单分子磁体的磁性能的建议,其中最为重要的是控制Dy配位几何的轴向对称性及Dy的基态m_J的电荷分布。对于第一过渡系金属-镝单分子磁体中的Dy^Ⅲ离子,Dy^Ⅲ基态m_J的电荷与配体的电荷之间的静电排斥应该降到最低。     

GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS OF SOLITON HIERARCHY

Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.     

一族离散的可积Hamilton方程与可积的辛映射

该文讨论一个新的离散特征值问题，导出了相应的离散的Hamilton系统的保谱族，并且证明了它们是Liouville可积系。通过谱问题的双非线性化，导出一个新的可积的辛映射 。      

A cohomological obstruction for global quasi-bi-Hamiltonian fields

We introduce the notion of integrating factor for a 1-form which is an inner product of a vector fields and a 2-form, and the notion of weakly bi-Hamiltonian field also, which is locally quasi-bi-Hamiltonian. A cohomological class in some first cohomology space is associated to such vector fields when this is weakly bi-Hamiltonian and defined relatively to the above 1-form. This class is a cohomological obstruction to the existence of a global integrating factor for the 1-form.