Nash multiplicities and isolated points of maximum multiplicity

Let X be an algebraic variety defined over a field of characteristic zero, and let $\xi \in \underset{\_}{\mathrm{Max}}\mathrm{mult}(X)$ be a point in the closed subset of maximum multiplicity of X. We provide a criterion, given in terms of arcs, to determine whether ξ is isolated in $\underset{\_}{\mathrm{Max}}\mathrm{mult}(X)$. More precisely, we use invariants of arcs derived from the Nash multiplicity sequence to characterize when ξ is an isolated point in $\underset{\_}{\mathrm{Max}}\mathrm{mult}(X)$.     

非交换加权Lorentz空间的对偶空间

设μ是一个半有限von Neumann代数.对于0P∞,0q≤∞,定义了非交换加权Lorentz空间Λ_ω~(p,q)(μ)及其associate空间Λ_ω~(p,q)(μ)',给出了空间Λ_ω~(p,q)(μ)'和Λ_ω~(p,q)(μ)'的一些基本性质.应用这些性质,还给出了非交换加权Lorentz空间Λ_ω~p(μ),0P∞的对偶空间.     

LIMITATIONS ON PRESCRIBING THE HOPF DIFFERENTIAL FOR MINIMAL SURFACES IN H3

ABSTRACT

The Hopf map from minimal surfaces in H ³ to holomorphic quadratic differentials on H ² is considered. Whether or not a given quadratic differential is in the image of this map is determined by the global existence/non-existence of solutions to a certain quasi-linear PDE. It is shown that this map is not surjective.     

Free cumulants,Schröder trees,and operads

The functional equation defining the free cumulants in free probability is lifted successively to the noncommutative Faà di Bruno algebra, and then to the group of a free operad over Schröder trees. This leads to new combinatorial expressions, which remain valid for operator-valued free probability. Specializations of these expressions give back Speicher's formula in terms of noncrossing partitions, and its interpretation in terms of characters due to Ebrahimi-Fard and Patras.     

Steady-state and Hopf bifurcations in the Langford ODE and PDE systems

This paper is concerned with the Langford ODE and PDE systems. For the Langford ODE system, the existence of steady-state solutions is firstly obtained by Lyapunov–Schmidt method, and the stability and bifurcation direction of periodic solutions are established. Then for the Langford PDE system, the steady-state bifurcations from simple and double eigenvalues are intensively studied. The techniques of space decomposition and implicit function theorem are adopted to deal with the case of double eigenvalue. Finally, by the center manifold theory and the normal form method, the direction of Hopf bifurcation and the stability of spatially homogeneous and inhomogeneous periodic solutions for the PDE system are investigated.     

Dynamic response of a growing inclusion in a discrete system

The propagation of a semi-infinite line defect, contained in an infinite square-cell lattice is considered. The defect is composed of particles lighter than those in the ambient lattice and it is assumed this defect propagates with constant speed. Dispersion properties of the lattice are related to waves generated by the propagating defect. In order to determine these properties, the Wiener–Hopf technique is applied. Additional features, related to localisation along the defect are also identified. Analysis of the dispersion relations for this lattice, from the kernel function inside the Wiener–Hopf equation, is carried out. The solution of the Wiener–Hopf equation is presented for the case when an external load is applied corresponding to an energy flux at infinity.