Gromov–Witten Invariants of Blow-ups Along Surfaces

In this paper, using the gluing formula of Gromov–Witten invariants for symplectic cutting developed by Li and Ruan, we established some relations between Gromov–Witten invariants of a semipositive symplectic manifold M and its blow-ups along a smooth surface.     

Set-theoretic complete intersections in characteristic

We describe a class of toric varieties which are set-theoretic complete intersections only over fields of one positive characteristic .

     

Burghelea-Friedlander-Kappeler's gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion

The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula under an assumption that the product structure is given near the boundary. As applications of this result, we prove the adiabatic decomposition theorems of the zeta-determinant of a Laplacian with respect to the Dirichlet and Neumann boundary conditions and of the analytic torsion with respect to the absolute and relative boundary conditions.

     

Analog of the Gellerstedt problem for a loaded equation of the third order

In this paper, we study an analog of the Gellerstedt problem for the third‐order loaded equation with boundary conditions on nonparallel characteristics in the hyperbolic domain of the equation.     

脚本语言及其应用

介绍了脚本语言的基本组成、主要特征及其与系统编程语言的互补性,给出了使用该类语言开发应用程序的基本方法． 通过分析相关实例数据获得的结论是：脚本语言编程在减少编程工作量、提高组件重用率、缩短开发周期、降低开发费用等方面较系统编程语言具有明显的优势,并具有广阔的应用前景．     

Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations

In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations with two and three lines of changing type.      

From global to local bifurcations in a forced Taylor–Couette flow

The unfolding due to imperfections of a gluing bifurcation occurring in a periodically forced Taylor–Couette system is analyzed numerically. In the absence of imperfections, a temporal glide-reflection Z₂ symmetry exists, and two global bifurcations occur within a small region of parameter space: a heteroclinic bifurcation between two saddle two-tori and a gluing bifurcation of three-tori. As the imperfection parameter increase, these two global bifurcations collide, and all the global bifurcations become local (fold and Hopf bifurcations). This severely restricts the range of validity of the theoretical picture in the neighborhood of the gluing bifurcation considered, and has significant implications for the interpretation of experimental results. PACS 47.20.Ky, 47.20.Lz, 47.20.Ft