A remark on rational isochronous potentials

一个由2个非线性耦合的ODE组成的系统，在系数受到适当限制的情况下，它是显式可解的且可能是等时的

A system of 2 nonlinearly coupled ODEs which is explicitly solvable and possibly isochronous provided its coefficients are suitably restricted

本文研究了一个包含2个非线性耦合一阶ODE的系统，该系统由多项式之比构成，含23个系数。作者发现通过15个参数的公式限制这些系数可使初值问题显式可解，并借助Mathematica找出12个约束保证系统属性，展示了多个可解及等时解的实例。

Remarks on rational solutions of Yang-Baxter equations

In this article, we study unitary rational solutions of the associative Yang-Baxter equation with three spectral parameters. We explain how such solutions arise from the geometry of vector bundles on a cuspidal cubic curve. Moreover, we investigate how these solutions are related to the quantum and classical Yang-Baxter equations.

关于切比雪夫有理函数、多点Padé逼近和噪声的一个注记

A remark on Chebyshev rational functions, multipoint Padé approximants and Noise

受多点Padé逼近在物理学界兴趣的启发，讨论切比雪夫有理函数如何产生多点Padé逼近，给出递推关系和连分数，并数值展示噪声对插值方案的影响。

An update on PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally-extended supersymmetric partners

The $\cal PT$-symmetric complexified Scarf II potential $V(x)= - V_1 \sech^{2}x + {\rm i} V_2 \sech x \tanh x$, $V_1>0$ , $V_{2}\neq 0$ is revisited to study the interplay among its coupling parameters. The existence of an isolated real and positive energy level that has been recently identified as a spectral singularity or zero-width resonance is here demonstrated through the behaviour of the corresponding wavefunctions and some property of the associated pseudo-norms is pointed out. We also construct four different rationally-extended supersymmetric partners to $V(x)$, which are $\cal PT$-sy…

Rational Hadamard products via Quantum Diagonal Operators

We use the remark that, through Bargmann-Fock representation, diagonal operators of the Heisenberg-Weyl algebra are scalars for the Hadamard product to give some properties (like the stability of periodic fonctions) of the Hadamard product by a rational fraction. In particular, we provide through this way explicit formulas for the multiplication table of the Hadamard product in the algebra of rational functions in $\C[[z]]$.

A Remark on CFT Realization of Quantum Doubles of Subfactors. Case Index < 4

It is well-known that the quantum double $D(N\subset M)$ of a finite depth subfactor $N\subset M$, or equivalently the Drinfeld center of the even part fusion category, is a unitary modular tensor category. Thus should arise in conformal field theory. We show that for every subfactor $N\subset M$ with index $[M:N]<4$ the quantum double $D(N\subset M)$ is realized as the representation category of a completely rational conformal net. In particular, the quantum double of $E_6$ can be realized as a $\mathbb Z_2$-simple current extension of $\mathrm{SU}(2)_{10}\times \mathrm{Spin}(11)_1$ and thus …