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1.
The first aim in the present paper is to give an integral representation for Beppo Levi functions on R
n. Our integral representation is an extension of Sobolev's integral representation given for infinitely differentiable functions with compact support. As applications, continuity and differentiability properties of Beppo Levi functions are studied.Our second aim in this paper is to study the existence of limits at infinity for Beppo Levi functions. We also consider the existence of fine-type limits at infinity with respect to Bessel capacities, which yields the radial limit result at infinity. 相似文献
2.
Neil S. TrudingerXu-Jia Wang 《Journal of Functional Analysis》2002,193(1):1-23
In this paper, we continue previous investigations into the theory of Hessian measures. We extend our weak continuity result to the case of mixed k-Hessian measures associated with k-tuples of k-convex functions, on domains in Euclidean n-space, k=1,2,…,n. Applications are given to capacity, quasicontinuity, and the Dirichlet problem, with inhomogeneous terms, continuous with respect to capacity or combinations of Dirac measures. 相似文献
3.
We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W?1, p spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain Lp estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
4.
We investigate the links between Sobolev and Nash inequalities, capacity and hitting times estimates and ultracontractive semigroups, in a non-symmetric setting. 相似文献
5.
Unconventional antiferromagnetic correlations of the doped Haldane gapsystem Y 2 BaNi 1 - x Zn x O 5
V. Villar R. Mélin C. Paulsen J. Souletie E. Janod C. Payen 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(1):39-51
We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y2BaNi1-xZnxO5. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional
because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature.
We obtain a Curie-Weiss susceptibility χ(
T
) ∼
C
/(Θ +
T
) as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order.
We explain how to obtain the “impurity” susceptibility
(
T
) by subtracting the Haldane gap contribution to the total susceptibility. In the temperature range [1 K, 300 K] the experimental
data are well fitted by T
(
T
) =
C
imp
1 +
T
imp
/
T
. In the temperature range [100 mK, 1 K] the experimental data are well fitted by T
(
T
) =
A
ln(
T
/
T
c
), where T
c
increases with x. This fit suggests the existence of a finite Néel temperature which is however too small to be probed directly in our experiments.
We also obtain a maximum in the temperature dependence of the ac-susceptibility
(
T
) which suggests the existence of antiferromagnetic correlations at very low temperature.
Received 17 July 2001 相似文献
6.
Enthalpies of solution have been measured from 5 to 85°C for aqueous tetraethyl- and tetrapropylammonium bromides, and the integral heat method is employed to evaluate
for these electrolytes over a wide temperature range. Data taken from the literature have been used to evaluate
for aqueous Bu4NBr over a similar temperature range. These data, along with similar data for Me4NBr, previously reported, have been used to evaluate absolute ionic heat capacities. While the absolute values agree only qualitatively with two other methods of division, the temperature dependences of the three methods essentially agree up to 65°C. Heat capacities due to structural effects on the solvent, obtained by subtracting the inherent heat capacities of the ions, are extraordinarily positive for all four tetraalkylammonium ions and have negative temperature coefficients, indicating that all four ions, including the tetramethylammonium ion, are structure-making ions. 相似文献
7.
Gérald Perron François Quirion Daniel Lambert Jean Ledoux Lahouari Ghaicha R. Bennes Mireille Privat Jacques E. Desnoyers 《Journal of solution chemistry》1993,22(2):107-124
Phase diagrams, volumes and heat capacities of aqueous mixtures of 2,6-dimethylpyridine (2,6-L) and 2-isobutoxyethanol (iBE) and activities of 2,6-L in aqueous mixtures were measured in the monophasic region near the lower critical solution temperature (LCST). With 2,6-L some measurement were also made just above the LCST. From the temperature dependence of these data, partial molar relative enthalpies (2,6-L), expansibilities and the temperature derivative of heat capacities were calculated and show that iBE undergoes a microphase transition at low concentration which is not related to the phase separation. On the other hand, the properties of 2,6-L in the water-rich region at temperatures well below the LCST indicates that this solute has only a slight tendency to associate. The heat capacities of 2,6-L show an important increase near the LCST. Such changes are not observed for iBE and other alkoxyethanols and amines since these systems already exist in the form of microphases; the partial molar properties of iBE near the LCST are nearly equal to the molar values of the pure liquid, and the changes in thermodynamic properties corresponding to the macroscopic phase transition, are therefore too small to be measured by the present techniques. 相似文献
8.
Apparent molar heat capacities and volumes of amylamine (PentNH2) 0.02m, capronitrile (PentCN) 0.02m and nitropentane (PentNO2) 0.009m in decyltrimethylammonium bromide (DeTAB) micellar solutions, in water and in octane were measured at 25°C. By assuming that their concentration approaches the standard infinite dilution state, heat capacities and volumes were rationalized by means of previously reported equations following which the distribution constant between the aqueous and the micellar phase and heat capacity and volume of the additives in both phases are simultaneously derived. The present results are compared to those we have previously obtained for pentanol (PentOH). The thermodynamic properties of PentNH2 in water and in micellar phase are substantially identical to those of PentOH but different from those of PentCN and PentNO2 whereas the opposite behavior was observed in their pure liquid state and in octane. The nature of the solvent medium seems to affect the thermodynamic behavior of PentNH2. Also, the study of the apparent molar heat capacities of the amyl compounds investigated here in micellar solutions as a function of surfactant concentration shows evidence of a maximum at about 0.4m DeTAB, which can be attributed to a micellar structural transition. Accordingly, the solubilities of PentCN and PentNO2 as a function of the DeTAB concentration drop in the neighborhood of the concentration where heat capacities display the maximum. 相似文献
9.
10.
溶液的过剩热容是热力学的重要函数,对其测定与研究具有理论与实际意义.过剩热容不仅可检验溶液中分子间的相互作用,并可利用其计算混合物的热容.本文报告了用微量热仪对环乙烷一本等七个二元物系全浓度范围内在29815K、常压下过剩热容CEp进行的测定工作,上述体系是由具有 相似文献