An isochore versal deformation theorem

We introduce a cohomological approach to isochore deformation problems. We use this formulation in order to prove an isochore versal deformation theorem for holomorphic function germs.     

Tangent circle bundles admit positive open book decompositions along arbitrary links

In the present paper we generalize the divide lying in the unit disk, introduced by A'Campo, to compact, oriented, smooth surfaces, and prove a fibration theorem for generalized divides. As a consequence, we will show that, for any link L in the tangent circle bundle Y to the compact surface, there exists an additional knot K such that the link L∪K is the binding of a “positive” open book decomposition of Y.     

Relative morsification theory

In this paper we develop a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known morsification results for non-isolated singularities and generalise them to a much wider context. We also show that deforming functions of finite codimension with respect to an ideal within the same ideal respects the Milnor fibration. Furthermore we present some applications of the theory: we introduce new numerical invariants for non-isolated singularities, which explain various aspects of the deformation of functions within an ideal; we define generalisations of the bifurcation variety in the versal unfolding of isolated singularities; applications of the theory to the topological study of the Milnor fibration of non-isolated singularities are presented. Using intersection theory in a generalised jet-space we show how to interpret the newly defined invariants as certain intersection multiplicities; finally, we characterise which invariants can be interpreted as intersection multiplicities in the above mentioned generalised jet space.     

First measurement of the helicity-dependent γ p?pη differential cross-section

The helicity dependence of the γ p↦pη reaction has been measured for the first time at a center-of-mass angle θ^* _η = 70^° in the photon energy range from 780 MeV to 790 MeV. The experiment, performed at the Mainz microtron MAMI, used a 4π-detector system, a circularly polarized, tagged photon beam, and a longitudinally polarized frozen-spin target. The helicity 3/2 cross-section is found to be small and the results for helicity 1/2 agree with predictions from the MAID analysis. Received: 19 December 2002 / Accepted: 10 March 2003 / Published online: 20 May 2003     

A SAXS study of the nanostructural characteristics of TEOS-derived sonogels upon heat treatment up to 1100 °C

Xerogels obtained from the acid-catalyzed and ultrasound stimulated hydrolysis of TEOS were submitted to heat treatment at temperatures ranging from 60 to 1100 °C and studied by small-angle X-ray scattering (SAXS). The SAXS intensity as a function of the modulus of the scattering vector q was obtained in the range from q₀=0.19 to q_m=4.4 nm⁻¹. At 60 °C the xerogels exhibit an apparent surface fractal structure with a fractal dimension D_S∼2.5 in a length scale ranging from 1/q₁∼1 to 1/q_m∼0.22 nm. This structure becomes extremely rough at 120 °C (D_S∼3) and at 150 °C, it apparently converts to a mass fractal with a fractal dimension D∼2.4. This may mean an emptying of the pores with preservation of a share of the original mass fractal structure of the wet aged gel, for it had presented a mass fractal dimension D∼2.2. A well characterized porous structure formed by 2.0 nm mean size pores with smooth surface of about 380 m²/g is formed at 300 °C and remains stable until approximately 800 °C. At 900 °C the SAXS intensity vanishes indicating the disappearance of the pores in the probed length scale. The elimination of the nanopores occurs by a mechanism in which the number of pores diminishes keeping constant their mean size. The xerogels exhibit a foaming phenomenon above 900 °C and scatter following Porod's law as does a surface formed by a coarse structure.     

混合序列加权和的完全收敛性和强收敛性

讨论了 ρ混合序列加权和的完全收敛性和强收敛性 ,推广了Stout和Thrum定理     

Non-trivial simple poles at negative integers and mass concentration at singularity

Let (X,0) be the germ of a normal space of dimension n+1 and let f be the germ at 0 of a holomorphic function on X. Assume both X and f have an isolated singularity at 0. Denote by J the image of the restriction map , where F is the Milnor fibre of f at 0. We prove that the canonical Hermitian form on , given by poles of order at in the meromorphic extension of , passes to the quotient by J and is non-degenerate on . We show that any non-zero element in J produces a “mass concentration” at the singularity which is related to a simple pole concentrated at for (in a non-na?ve sense). We conclude with an application to the asymptotic expansion of oscillatory integrals , for , when . Received: 28 May 2001 / Published online: 26 April 2002     

Finite Abelian actions on surfaces

Edmonds showed that two free orientation preserving smooth actions φ₁ and φ₂ of a finite Abelian group G on a closed connected oriented smooth surface M are equivalent by an equivariant orientation preserving diffeomorphism iff they have the same bordism class [M,φ₁]=[M,φ₂] in the oriented bordism group Ω₂(G) of the group G. In this paper, we compute the bordism class [M,φ] for any such action of G on M and we determine for a given M, the bordism classes in Ω₂(G) that are representable by such actions of G on M. This will enable us to obtain a formula for the number of inequivalent such actions of G on M. We also determine the “weak” equivalence classes of such actions of G on M when all the p-Sylow subgroups of G are homocyclic (i.e. of the form n(Z/pαZ)).     

Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem

In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders.