On the stability of Riemannian manifold with parallel spinors

Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of the first one, shows that any metric of positive scalar curvature cannot lie too close to a metric with nonzero parallel spinor. We also prove a rigidity result for special holonomy metrics. In the case of SU(m) holonomy, the rigidity result implies that scalar flat deformations of Calabi-Yau metric must be Calabi-Yau. Finally we explore the connection with a positive mass theorem of [D03], which presents another approach to proving these stability and rigidity results. Dedicated to Jeff Cheeger for his sixtieth birthday     

Arithmetic degree and associated graded modules

We prove that the arithmetic degree of a graded or local ring A is bounded above by the arithmetic degree of any of its associated graded rings with respect to ideal I in A. In particular, if Spec(A) is equidimensional and has an embedded component (i.e., A has an embedded associated prime ideal), then the normal cone of Spec(A) along V(I) has an embedded component too. This extends a result of W. M. Ruppert about embedded components of the tangent cone.Mathematics Subject Classification (2000): Primary 13H15, 13A30; Secondary 13D45, 14Q99     

CORBA~( ):一个具有自卫智能体的扩展CORBA

将自卫机制加入OOP成为AOP以提高CORBA中软件的强健性和防卫能力,在CORBA这个异构环境中,一个对象申请服务之后就需等待,如果应答迟迟不到则有可能永远等待下去,为避免这种现象的产生和蔓延,在客户和服务方的行为中加入超时机制(timeout mecha-nism)并采用利己或利他策略,使得对象可独立地根据当前环境和时间决定下一步骤,将这种在协作者失败的情况下仍能生存的对象称为自卫智能体,加入白卫智能体的CORBA称为CORBA~( ),由于智能体可在任何条件下生存,CORBA~( )可为用户提供可靠的服务,也就能实现CORBA~( )中软件构成的强健性。     

Links in a thickened surface

For a given two-dimensional surface μ, we studi invariants for oriented links in μ×[0,1] which generalize the two-variable HOMFLY polynomials when μ is the 2-disk. These invariants are connected to multiparameter quantum groups whose special properties are discussed. Si studiano gli invarianti dei nodi in spazi del tipo μ×[0,1], dove μ è una superficie. Questi invarianti generalizzano gli invarianti di HOMFLY.

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(Conferenza tenuta dal Prof. P. Cotta-Ramusino il 16 maggio 1991)     

Euler characteristics of general linear sections and polynomial Chern classes

We obtain a precise relation between the Chern–Schwartz–MacPherson class of a subvariety of projective space and the Euler characteristics of its general linear sections. In the case of a hypersurface, this leads to simple proofs of formulas of Dimca–Papadima and Huh for the degrees of the polar map of a homogeneous polynomial, extending these formula to any algebraically closed field of characteristic \(0\), and proving a conjecture of Dolgachev on ‘homaloidal’ polynomials in the same context. We generalize these formulas to subschemes of higher codimension in projective space. We also describe a simple approach to a theory of ‘polynomial Chern classes’ for varieties endowed with a morphism to projective space, recovering properties analogous to the Deligne–Grothendieck axioms from basic properties of the Euler characteristic. We prove that the polynomial Chern class defines homomorphisms from suitable relative Grothendieck rings of varieties to \(\mathbb{Z }[t]\).     

Braids on surfaces and finite type invariants

We prove that there is no functorial universal finite type invariant for braids in Σ×I if the genus of Σ is positive. To cite this article: P. Bellingeri, L. Funar, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Investigation on nonradiative decay of I13/2→I15/2 transition of Er-doped oxide glasses

Nonradiative decay of ⁴I_13/2→⁴I_15/2 transition of Er³⁺ has been investigated in a series of oxide glasses. For Er³⁺-doped glass samples, the Judd-Ofelt analysis on absorption spectra was performed and the fluorescence lifetime was determined by extrapolating to zero Er³⁺ concentration limit. Infrared spectra were measured in order to investigate the influence of OH⁻ groups in different glasses. The effects of glass matrix on the decay rate were discussed from the viewpoint of phonon energy, variations of effective fields, and OH⁻ groups. Compared to other glasses, phosphate glass presents low quantum efficiency and large nonradiative decay rate due to its high phonon energy and hygroscopic behavior.