We show that the Hardy-Littlewood maximal operator and a class of Calderón-Zygmund singular integrals satisfy the strong type
modular inequality in variable Lp spaces if and only if the variable exponent p(x) ∼ const.
Received: 15 September 2004 相似文献
Basic principles of the generalized lattice model of multicomponent condensed systems are formulated. Short-range parts of interatomic interactions are taken into account by means of the geometric constraints method. Long-range parts of the interactions are taken into account in mean field approximation. The expression for Helmholtz free energy is obtained. A system of integral equations for the equilibrium distributions of components is derived. The asymptotic properties of its solutions are investigated. Moment expansion of interatomic interactions and localization of integral terms in free energy is obtained. A Ginzburg–Landau-like functional of free energy is derived. 相似文献
The effect of ethylene glycol (EG) on the formation of whiskers and fibers of complex oxides with the general formula MCo2O4 upon the thermolysis of M1/3Co2/3C2O4 (M = Zn, Mn) oxalates has been studied. New compounds (solvates) are formed when powdered oxalates are heated with EG. In the solvates, EG molecules substitute for water molecules according to the reaction M1/3Co2/3C2O4 · 2H2O + HOCH2CH2OH = M1/3Co2/3C2O4(HOCH2CH2OH) + 2H2O. The solvates have been characterized using X-ray powder diffraction, microscopy, IR spectroscopy, thermogravimetry, and chemical analysis. The shape, structure, and particle size of the thermolysis products of EG-modified oxalates have been determined using scanning electron microscopy. 相似文献
The restricted Hartree-Fock method was used to determine the cycle size effects on the geometric parameters of several inorganic templates, cyclophosphazenes PnNnX2n (X = H, F, Cl; n = 2, 3, 4). A topological analysis of local electronic properties at the electron density critical points of bonds allowed us to quantitatively characterize the chemical bond in cyclophosphazenes and its dependence on the cycle size and substituents at phosphorus. The calculated distributions of the electron density Laplacian and electron pair localization functions revealed the special features of the electronic structure of the nitrogen and phosphorus atoms. These results explain the nature of noncovalent interactions between the P atoms of one cyclophosphazene molecule and the N atoms of the other. 相似文献
A method for calculating the parameters of formation of vacancies in crystals formed by spherically symmetrical atoms was developed. Both quantum effects at low temperatures and the possibility of the delocalization of atoms at high temperatures were studied. The parameters of formation of vacancies in carbon subgroup element crystals C-diam, Si, Ge, α-Sn, and Pb were calculated. The inclusion of the delocalization of atoms was shown to increase the enthalpy, entropy, and volume of vacancy formation. At low temperatures, the parameters of vacancy formation were found to depend strongly on the temperature, and the entropy of vacancy formation became negative. At high temperatures, close agreement with experimental data and theoretical estimates reported by other authors was obtained. The temperature dependence of vacancy parameters was studied for diamond heated isobarically from 100 to 4500 K. The applicability scope of the Arrhenius equation with a temperature-independent activation energy is discussed. The validity of the “compensation rule” (correlation between the entropy and enthalpy of vacancy formation) was demonstrated. It was also shown that the volume and entropy of vacancy formation were correlated over the whole temperature range studied.
In this paper we obtain a number of Maharam-type slice integral representations, with respect to scalar measures, for positive
projections in Dedekind complete vector lattices and f-algebras.
AMS Classification: 47B65, 46A40, 06F25 相似文献