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101.
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.
相似文献
102.
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 qm=4.4 nm−1. At 60 °C the xerogels exhibit an apparent surface fractal structure with a fractal dimension DS∼2.5 in a length scale ranging from 1/q1∼1 to 1/qm∼0.22 nm. This structure becomes extremely rough at 120 °C (DS∼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. 相似文献
103.
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 . 相似文献
104.
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 TlO1/2-SiO2, PbO-SiO2, SnO-SiO2 and Bi2O3-SiO2. The consolute temperature of their miscibility gaps is expected to be relatively low and metastable. 相似文献
105.
106.
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 相似文献
107.
A.A. George Michael 《Topology and its Applications》2006,153(14):2591-2612
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)). 相似文献
108.
L. Sauguet B. Ameduri B. Boutevin 《Journal of polymer science. Part A, Polymer chemistry》2006,44(15):4566-4578
The radical terpolymerization of 8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene with vinylidene fluoride (VDF) and perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride is presented. Changing the feed compositions of these three fluorinated comonomers enabled us to obtain different random‐type poly[vinylidene fluoride‐ter‐perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride‐ter‐8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene] terpolymers containing various sulfonyl fluoride and brominated side groups. Yields higher than 70% were reached in all cases. The hydrolysis of the sulfonyl fluoride group into the ? SO3Li function in the presence of lithium carbonate was quantitatively achieved without the content of VDF being affected, and so dehydrofluorination of the VDF base unit was avoided. These original terpolymers were then crosslinked via dangling bromine atoms in the presence of a peroxide/triallyl isocyanurate system, which produced films insoluble in organic solvents such as acetone and dimethylformamide (which totally dissolved uncured terpolymers). The acidification of ? SO3Li into the ? SO3H function enabled protonic membranes to be obtained. The thermal stabilities of the crosslinked materials were higher than those of the uncured terpolymers, and their electrochemical performances were investigated. According to the contents of the sulfonic acid side functions, the ion‐exchange capacities ranged from 0.6 to 1.5 mequiv of H+/g, whereas the water uptake and conductivities ranged from 5–26% (±11%) and from 0.5 to 6.0 mS/cm, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4566–4578, 2006 相似文献
109.
In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b, ±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and Ramani–Grammaticos–Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic‐pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painlevé VI functions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
110.
Marc Visseaux Mickael Terrier Andr Mortreux Pascal Roussel 《Comptes Rendus Chimie》2007,10(12):1195-1199
The reaction of one equivalent of Nd(BH4)3(THF)3 with an half equivalent of dialkylmagnesium in the presence of a stoichiometric amount of pentamethylcyclopentadiene cleanly affords a new kind of half-sandwich of neodymium that is stable toward comproportionation. This strategy can be advantageously applied to generate in situ catalysts allowing the controlled polymerisation of isoprene. 相似文献