Yang-Mills Equation and Bures Metric

It is shown that the connection form (gauge field) related to the generalization of the Berry phase to mixed states proposed by Uhlmann satisfies the source-free Yang–Mills equation * D * D = 0, where the Hodge operator is taken with respect to the Bures metric on the space of finite-dimensional nondegenerate density matrices.     

Synthesis of Functionalized Azobiphenyl- and Azoterphenyl- Ditopic Linkers: Modular Building Blocks for Photoresponsive Smart Materials

Modular synthesis of structurally diverse functionalized azobiphenyls and azoterphenyls for the realization of optically switchable materials has been described. The corresponding synthesis of azobiphenyls and azoterphenyls by stepwise Mills/Suzuki-Miyaura cross-coupling reaction, proceeds with high yields and provides facile access to a library of functionalized building blocks. The synthetic methods described herein allow combining several distinct functional groups within a single unit, each intended for a specific task, such as 1) the −N=N− azobenzene core as a photoswitchable moiety, 2) aryls and heteroaryls, functionalized with carboxylic acids or pyridine at its peripheries, as coordinating moieties and 3) varying substitution, size and length of the backbone for adaptability to specific applications. These specifically designed azobiphenyls and azoterphenyls provide modular bricks, potentially useful for the assembly of a variety of polymers, molecular containers and coordination networks, offering a high degree of molecular functionality. Once integrated into materials, the azobenzene system, as a side group on the organic linker backbone, can be exploited for remotely controlling the structural, mechanical or physical properties, thus being applicable for a broad variety of ‘smart’ applications.     

On bi-skew braces and brace blocks

L. N. Childs defined a bi-skew brace to be a skew brace such that if we swap the role of the two operations, then we find again a skew brace.In this paper, we give a systematic analysis of bi-skew braces. We study nilpotency and solubility, and connections between bi-skew braces and set-theoretic solutions of the Yang–Baxter equation. Further, we deal with Byott's conjecture in the case of bi-skew braces, and we use bi-skew braces as a tool to solve a classification problem proposed by L. Vendramin.In the final part, we investigate brace blocks, defined by A. Koch to be families of group operations on a given set such that any two of them yield a bi-skew brace. We provide a characterisation of brace blocks, illustrate how all known constructions in literature follow in a natural way from our characterisation, and give several new examples.     

Spectral-Parameter Dependent Yang–Baxter Operators and Yang–Baxter Systems From Algebra Structures

For any algebra, two families of colored Yang–Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang–Baxter equation. An open problem about a system of functional equations is stated. The matrix forms of these operators for two and three dimensional algebras are computed. A FRT bialgebra for one of these families is presented. Solutions for the one-parameter quantum Yang–Baxter equation are derived and a Yang–Baxter system constructed.     

杨乐不等式的探微

本文利用分析方法及不等式理论 ,建立了杨乐不等式及其推广与加强的探微形式 .     

A note on the deformed Hermitian Yang-Mills PDE

We prove a priori estimates for a generalised Monge–Ampère PDE with ‘non-constant coefficients’ thus improving a result of Sun in the Kähler case. We apply this result to the deformed Hermitian Yang-Mills (dHYM) equation of Jacob–Yau to obtain an existence result and a priori estimates for some ranges of the phase angle assuming the existence of a subsolution. We then generalise a theorem of Collins–Szèkelyhidi on toric varieties and use it to address a conjecture of Collins–Jacob–Yau.     

杨承宗对中国放射化学的贡献

杨承宗(1911—2011)是我国著名的放射化学家、教育家,我国核燃料工业的开拓者之一,新中国放射化学学科奠基人。目前关于杨承宗的学术贡献多散见于一些回顾和介绍其生平事迹的文献之中,尚乏深入讨论。本文系统梳理了杨承宗不同时期的主要学术工作,认为他对我国放射化学的贡献有二：一是在放射化学学科的建立和长期发展过程中起到了关键作用;二是带领科技人员解决了天然铀生产过程中的各种放射化学及其工艺问题,为我国铀工业的建立提供了重要的技术支撑。最后,结合中国放射化学的发展历程对杨承宗的学术生涯作了简要探讨。     

Lie Bialgebras of Generalized Virasoro-like Type

In this paper, Lie bialgebra structures on generalized Virasoro-like algebras are studied. It is proved that all such Lie bialgebras are triangular coboundary.