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991.
We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L
p
-spaces over B, 1<p<∞. Under suitable ellipticity assumptions we can define a family of complex powers A
z
, zℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the
solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.
Received: 12 June 2001; in final form: 3 June 2002 /
Published online: 1 April 2003
Mathematics Subject Classification (2000): 35J70, 47A10, 35K57 相似文献
992.
E. N. Dancer 《Journal of Fixed Point Theory and Applications》2007,1(1):47-60
We discuss the calculation of homotopy indices on closed convex sets in a Banach space and then use these ideas to prove the
existence of multiple solutions of nonlinear elliptic equations. We obtain more information on the solutions than in earlier
work. A key idea is to calculate the homotopy index of the stable and mountain pass solutions and the connections joining
them.
Dedicated to the memory of Jean Leray 相似文献
993.
S. A. Klimin M. N. Popova E. P. Chukalina B. Z. Malkin A. R. Zakirov E. Antic-Fidancev Ph. Goldner P. Aschehoug G. Dhalenne 《Physics of the Solid State》2005,47(8):1425-1430
The absorption spectra of Yb2Ti2O7 single crystals and the luminescence and luminescence excitation spectra of Y2Ti2O7: Yb (1%) polycrystals were studied in the temperature range 4.2–300 K. The spectra were analyzed in terms of the crystal-field
theory and the exchange-charge model. Based on the set of crystal-field parameters found for Yb2Ti2O7, analogous sets of parameters were determined for other rare-earth titanates and proved to be in reasonable agreement with
all available experimental data.
__________
Translated from Fizika Tverdogo Tela, Vol. 47, No. 8, 2005, pp. 1376–1380.
Original Russian Text Copyright ? 2005 by Klimin, Popova, Chukalina, Malkin, Zakirov, Antic-Fidancev, Goldner, Aschehoug,
Dhalenne. 相似文献
994.
Christabel E. Fowler Catherine Buchber Joël Patarin Alain Walcarius 《Applied Surface Science》2007,253(12):5485-5493
Diatomaceous earth was functionalized by grafting organotrialkoxysilane precursors onto the surface of the porous silica cell walls of this biomineral. Vinyl- and mercapto-containing structures were prepared in aqueous media without disruption of the diatomic architecture. Successful grafting of the organic moieties was confirmed using solid state 29Si MAS NMR spectroscopy, and the presence of the intact diatom framework by scanning electron microscopy. The sorption properties of mercaptopropyl-functionalized diatoms towards heavy metals was studied by measuring the accessibility and diffusion rates of mercury(II) species to the binding sites (-SH) by the means of electrochemical methods. 相似文献
995.
Elżbieta Godlewska M. Mitoraj F. Devred B. E. Nieuwenhuys 《Journal of Thermal Analysis and Calorimetry》2007,88(1):225-230
A Ti–45.9Al–8Nb
(at%) alloy with a lamellar structure (γ+α2)
was oxidised in air at 700, 800, 850 and 900°C in isothermal and thermal
cycling conditions. The reaction progress was followed by thermogravimetric
measurements. In isothermal conditions the oxidation kinetics followed approximately
a parabolic rate law and the rate constants ranged from about 10–12
kg2 m–4 s–1
at 700°C to 10–10 kg2
m–4 s–1
at 900°C. The oxide scales were built of Al2O3
and TiO2, the former being the main component of the
outermost layer. The oxidation behaviour of Ti–45.9Al–8Nb was
referred to a commercial titanium alloy, WT4 (Ti–6Al–1Mn), and
selected oxidation-resistant alloys. 相似文献
996.
997.
The complex morphology of high-speed melt-spun nylon-6 fibres hydrated with D2O was investigated using 1H double-quantum-filtered spin-diffusion NMR experiments. The magnetisation exchange from selected crystalline domains along the fibrils and interfibrils was simulated with the help of a three-dimensional solution of a spin-diffusion equation approximated by a product of one-dimensional analytical NMR signals, which correspond to a lamellar morphology. This allows to measure the sizes of crystalline and less-mobile amorphous domains along the fibrils, as well as the diameter of the fibrils and interfibril distances. A series of nylon-6 fibres with extreme values of winding speed and draw ratio was investigated. The changes detected in the domain size along the fibrils and interfibrils show the same trend in the data obtained from wide-angle X-ray diffraction and small-angle X-ray scattering. 相似文献
998.
Martin E. V. Pedersen Lars S. Rishøj Henrik Steffensen Sanshui Xiao Niels Asger Mortensen 《Optical and Quantum Electronics》2007,39(10-11):903-911
Slow-light enhanced optical detection in liquid-infiltrated photonic crystals is theoretically studied. Using a scattering-matrix approach and the Wigner–Smith delay time concept, we show that optical absorbance benefits both from slow-light phenomena as well as a high filling factor of the energy residing in the liquid. Utilizing strongly dispersive photonic crystal structures, we numerically demonstrate how liquid-infiltrated photonic crystals facilitate enhanced light–matter interactions, by potentially up to an order of magnitude. The proposed concept provides strong opportunities for improving existing miniaturized absorbance cells for optical detection in lab-on-a-chip systems. 相似文献
999.
Tokeer Ahmad Kandalam V. Ramanujachary Samuel E. Lofland Ashok K. Ganguli 《Journal of Chemical Sciences》2006,118(6):513-518
Nanoparticles of complex manganites (viz. LaMnO3, La0.67Sr0.33MnO3 and La0.67Ca{0.33}MnO3) have been synthesized using the reverse micellar route. These manganites are prepared at 800‡C and the monophasic nature
of all the oxides has been established by powder X-ray diffraction studies. TEM studies show an average grain size of 68,
80 and 50 nm for LaMnO3, La0.67Sr0.33MnO3 and La0.67Ca{0.33}MnO3respectively. Ferromagnetic ordering is observed at around 250 K for LaMnO3, 350 K for La0.67Sr0.33MnO3 and 200 K for La0.67Ca{0.33}MnO3. These Curie temperatures correspond well with those reported for bulk materials with similar composition. 相似文献
1000.
Montecchi M. Nichelatti E. Montereali R.M. Piccinini M. Somma F. 《Optical and Quantum Electronics》2004,36(1-3):43-56
An analytical expression of the complex permittivity is derived for absorbing centres featuring inhomogeneous absorption-line broadening. Such an expression gives the dispersion law of the real part of the permittivity when the imaginary part has a Gaussian lineshape. Our mathematical approach starts from an overlap integral of Lorentzian-type dielectric susceptibilities weighted by a Gaussian probability distribution of the resonance absorption energies. The analytical solution found is consistent with the Kramers–Kronig relation. We demonstrate that, like in the case of homogeneous absorption-line broadening, the refractive index increases at photon energies lower than the resonance absorption energy also for inhomogeneous absorption-line broadening; if the absorbing centres emit Stokes-shifted radiation, such an increase can be exploited for passive and active waveguiding applications. An example is reported regarding active waveguides based on colour centres in a lithium fluoride crystal. 相似文献