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     

Structure–electrical property study of anisotropic polyaniline films

The relationships of the structure and electrical properties of anisotropic HCl‐doped polyaniline (PANI) films cast from N,N′‐dimethylpropylene urea (DMPU) solutions and stretched to different draw ratios were studied. The anisotropic structure of the stretched PANI films was examined by X‐ray diffraction, near‐infrared wave‐guide coupling, and polarized infrared measurements. The PANI emeraldine base (EB) films cast from DMPU solutions had a single‐phase noncrystalline structure, and stretching of the films did not cause crystallization to occur. The transition moment angles of two weakly absorbing infrared bands were determined, and the Hermans' orientation functions for the PANI EB films were calculated. The PANI films were then doped with HCl, and the electrical properties were determined by impedance spectroscopy. With a specially designed test fixture, the in‐plane and through‐plane impedance was obtained. The conductivity along the stretch direction increased with orientation. The in‐plane conductivity was significantly higher than the through‐plane conductivity. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 823–841, 2003     

Existence for a degenerate diffusion problem with a nonlinear operator

We study a degenerate nonlinear variational inequality which can be reduced to a multivalued inclusion by an appropriate change of the unknown function. We establish existence, uniqueness and regularity results. An application arising in the theory of water diffusion in porous media is discussed as an example.      

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.     

k连通图可缩边导出子图的连通性

引进S1 3边形的概念 .证明了 ,对于k(k =3或 4)连通图G ,若G无S1 3边形 ,则 是 2连通的 ;另外也得到 ,设G是k(k≥ 2 )连通图 ,若对G的任一断片F ,有｜F｜ >[k/2 ]+ 1 ,则 是 2连通的 .从而改进并推广了N .Dean的结论 .     

The nature of phase separation in binary oxide melts and glasses. III. Borate and germanate systems

A review of immiscibility data in binary borate and germanate systems was performed in order to compare miscibility gap consolute temperatures with ionic potentials and radii of their associated cations. The trends obtained demonstrate that a selective solution mechanism similar to the one identified for the binary silicate systems is present in the borate and germanate binaries. More importantly, the borate and germanate immiscibility data permitted the identification of a new group of cations depicting an immiscibility behaviour different from the ones identified in binary silicate systems. The new group involves highly polarizable cations possessing a lone pair of electrons. This lone pair of electrons together with oxygen bonded by strong covalent bonds to modifier cations provides efficient shielding to the cations' nuclei which considerably reduces the coulombic repulsions and produces miscibility gaps with very low consolute temperatures. A new group of cations having an homogenizing effect on melts (i.e. a capacity to make immiscible melts single phase) is thus reported. Experimental and spectroscopic data suggest that miscibility gaps associated with cations having a lone pair of electrons exist in binary silicate systems such as TlO_1/2-SiO₂, PbO-SiO₂, SnO-SiO₂ and Bi₂O₃-SiO₂. The consolute temperature of their miscibility gaps is expected to be relatively low and metastable.