Regularity of solutions to stochastic Volterra equations with infinite delay

In this article we give necessary and sufficient conditions providing regularity of solutions to stochastic Volterra equations with infinite delay on a -dimensional torus. The harmonic analysis techniques and stochastic integration in function spaces are used. The work applies to both the stochastic heat and wave equations.

     

球环型产氚聚变堆中子学分析

对球环型产氚聚变堆概念设计中的中子学设计进行了计算分析。此设计利用了球形环的先进等离子体物理性能和紧凑的结构特征,并尽量利用真空室内的空间安置氚生产包层以减少氚泄漏而提高氚增殖率,达到年产氚量1kg的目标。2D中子学计算得到的氚增殖率高于1．68的设计是其它类似设计没有达到的,进一步体现出球环型产氚聚变堆的先进性。     

G 2-manifolds and coassociative torus fibration

Let (φ ₀, g ₀) be a flat G ₂-structure on the torus T ⁷. For a certain finite group Γ-action on T ⁷ preserving the G ₂-structure, Joyce constructed a closed G ₂-manifold M from the resolution of the orbifold T ⁷/Γ. The main purpose of this paper is to prove that there exist global coassociative fibrations on open submanifolds of certain Joyce manifolds.      

Rigid isotopy classification of real algebraic curves of bidegree (3,3) on quadrics

A rigid isotopy of nonsingular real algebraic curves on a quadric is a path in the space of such curves of a given bidegree. We obtain the rigid isotopy classification of nonsingular real algebraic curves of bidegree (3, 3) on a hyperboloid and on an ellipsoid. We also study of the space of real algebraic curves of bidegree (3, 3) with a single node or cusp. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 810–815, December, 1999.     

R^4中的伪脐曲面及Gauss映射

本文研究了伪脐曲面M的一些性质,基于它并利用M的Ganuss映射,给出了M作为R^4中平坦环面的一个充分条件。     

Global analytic and Gevrey hypoellipticity of sublaplacians under Diophantine conditions

In this paper we consider the problem of global Gevrey and analytic regularity for a class of partial differential operators on a torus in the form of a sum of squares of vector fields, which may not satisfy the bracket condition. We show that these operators are globally Gevrey or analytic hypoelliptic on the torus if and only if the coefficients satisfy certain Diophantine approximation properties.

     

Experiments on fall of open tori

Fall of open tori horizontally dropped in quiescent water is experimentally investigated. The fall is controlled by the Galileo number, the torus aspect ratio and the solid to fluid density ratio. The dependence of the descent velocity and of the drag coefficient on the control parameters is first analyzed. As the control parameters are varied, vertical translation, zigzagging and spiraling descent are observed. These different descent modes are characterized and a phase diagram of the falling tori are presented as function of the three control parameters.     

Discrete accidental symmetry for a particle in a constant magnetic field on a torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the 1/r and r² potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the θ-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters θ_x and θ_y explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.     

加厚环面中标架环链的约化多项式

研究加厚环面中的标架环链.给出标架环链在Kauffman尖括号拆接代数中的表达式.利用Gro\"{o}bner基理论,我们从上述表达式中得到标架环链的约化多项式,该多项式是标架环链的同痕不变量且可计算.     

一类量子环面李代数的单性(英文)

令C_q:=C_q[t₁^±1,t₂^±1,t₃^±1]为量子环面结合代数,L_q=C_q/C为量子环面李代数。本文定义了一个与q=（qij）_i,j=1³相关的指数方程体系,称之为C_q的特征方程组。通过这个特征方程组,证明了L_q是非单的当且仅当特征方程组在Z³中有非零解。对于|q|=0,证明了在C_q中存在一个极大交换子代数I,并且I严格包含中心Z（C_q）。同时文中也指出,对于|q|≠0,在C_q中不存在这样的子代数。