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The set of quasipositive surfaces is closed under incompressible inclusion. We prove that the induced order on fibre surfaces of positive braid links is almost a well-quasi-order. When restricting to quasipositive surfaces containing a…
In this paper we are concerned with numerical methods for nonhomogeneous Helmholtz equations in inhomogeneous media. We design a least squares method for discretization of the considered Helmholtz equations. In this method, an auxiliary…
We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…
By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new…
We prove that for any given compact Riemannian manifold $N$ of dimension $n+1 \geq 3$ and any non-negative Lipschitz function $g$ on $N$, there exists a quasi-embedded, boundaryless hypersurface $M \subset N,$ of class $C^{2, \alpha}$ for…
We study isolated quotient singularities by finite and linearly reductive group schemes (lrq singularities for short) and show that they satisfy many, but not all, of the known properties of finite quotient singularities in characteristic…
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by…
A notion of a split quasi-hereditary algebra has been defined by Cline, Parshall and Scott. Du and Rui describe a based approach to split quasi-hereditary algebras. We develop this approach further to show that over a complete local…
Algebraic structure of a class of differential equations including Heun is shown to be related with the deformations of sl(2) algebra. These include both quadratic and cubic ones. The finite dimensional representation of cubic algebra is…
We develop explicit techniques to investigate algebraic quasi-hyperbolicity of singular surfaces through the constraints imposed by symmetric differentials. We apply these methods to prove that rational curves on Barth's sextic surface,…
Let $Q$ be a quiver with dimension vector $\alpha$ prehomogeneous under the action of the product of general linear groups $\operatorname{GL}(\alpha)$ on the representation variety $\operatorname{Rep}(Q,\alpha)$. We study geometric…
We propose the notion of $E_{2}$-quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the…
A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are…
We study the derived category of the moduli space $SU_C(2)$ of rank $2$ vector bundles on a smooth projective curve $C$ of genus $g\ge 2$ with trivial determinant. This generalizes the recent work by Tevelev and Torres on the case with…
We classify the $O(p)\times O(q)$-invariant constant mean curvature hypersurfaces with singularity at the origin, solving a conjecture of Wu-yi Hsiang.
This is a sequel to \cite{li-qva1} and \cite{li-qva2} in a series to study vertex algebra-like structures arising from various algebras such as quantum affine algebras and Yangians. In this paper, we study two versions of the double Yangian…
We showed the existence of non-radial solutions of the equation $\Delta u -\lambda u + \lambda u^q =0$ on the round sphere $S^m$, for $q<2m/(m-2)$, and study the number of such solutions in terms of $\lambda$. We show that for any…
We classify irreducible representations of finite $W$-algebra of the queer Lie superalgebra $Q(n)$ associated with the principal nilpotent coadjoint orbits. We use this classification and our previous results to obtain a classification of…
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…
Let $X$ be a set of $4$ generic points in $\mathbb{P}^2$ with homogeneous coordinate ring $R$. We classify indecomposable graded MCM modules over $R$ by reducing the classification to the Four Subspace problem solved by Nazarova and…