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51.
A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.
52.
51.Introducti0nandMainResultlnthepaperL1J,Caffarelli,NirenbergandSpruckdiscussedtheDirichletproblemforthenonlinearellipticequationforunknownu=u(x):{':<;;>:,<";>:are,vxeD,(1-1)where0lsab0undedstrictlyconvexdomaininR"withsmoothboundaryare,K(u)=(K,(u),Kz(u),..',K"(u))denotestheprincipalcurvaturesofthegraph(x,u(x))andfisofaspecialnatureasinL2J'L3j.Typicalcasesoftheequationin(1.l),whichweretreatedaswellbyIvochkina[4J,isf=Sl/*(K),whereS*(K)arethee1ementarysymmetricfunctions,Recently,Ivochki… 相似文献
53.
A.G. Kartsatos 《Journal of Mathematical Analysis and Applications》2004,290(1):76-85
The main purpose of this work is to obtain blow-up results for solutions of the inequality
54.
A (u1,
u2, . . . )-parking function of length
n is a sequence (x1,
x2, . . . ,
xn)
whose order
statistics (the sequence (x(1),
x(2), . . . ,
x(n)) obtained by rearranging the original sequence in
non-decreasing order) satisfy
x(i)
u(i).
The Gonarov polynomials g
n
(x; a0, a
1, . . . , a
n-1) are
polynomials biorthogonal to the linear functionals (a
i)
Di,
where (a) is evaluation at
a and D
is differentiation. In this paper, we give explicit formulas for the first and second moments of
sums of u-parking functions using Gonarov polynomials by
solving a linear recursion based on a decomposition of the set of sequences of positive integers.
We also give a combinatorial proof of one of the formulas for the expected sum. We specialize
these formulas to the classical case when u
i=a+
(i-1)b and obtain, by
transformations with Abel identities, different but equivalent
formulas for expected sums. These formulas are used to verify the classical case of the
conjecture that the expected sums are increasing functions of the gaps
ui+1
- ui.
Finally, we give analogues of our results for real-valued parking functions.AMS Subject Classification: 05A15, 05A19, 05A20, 05E35. 相似文献
55.
HARNACK ESTIMATES FOR WEAK SOLUTIONS OF EQUATIONS OF NON-NEWTONIAN POLYTROPIC FILTRATION 总被引:2,自引:1,他引:1
YANG Shixin 《数学年刊B辑(英文版)》2001,22(1):63-74
51. IntroductionIn this paper we investigate the local behavior of nonnegative weak solutions for theequations of non-Newtonian polytropic filtrationac -- div(IDumlp--'Dam) = 0,m(p -- 1) < 1,m > 0,p > l, in D'(flT),u E CI..(0, T; L?o.(n)), urn E Lro.(0, T; WI:)l(fl)), (1.1)where n is an open set of R", N 2 1, 0 < T < ool fiT ~ fix (0, T), and D ~ (k,', e).Equation (1.1) appears in a number of applications to describe the evolution of diffusion.The evolution HLaplacian equationut ~ … 相似文献
56.
L. P. Falaleev 《Mathematical Notes》2000,67(4):505-511
We obtain a sharp value for the constant in the leading term of the deviation of a function belonging to the class Lip1 α from the generalized Abel-Poisson operators specified by the summation factors
of the conjugate Fourier series in the case 0 < α <l ≤ 1.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 595–602, April, 2000. 相似文献
57.
We have studied the structural behavior of lead monoxide (PbO) as a function of pressure via angular dispersive X-ray diffraction employing two different pressure transmitting media that were quasi-hydrostatic (N2) and non-hydrostatic (MgO), respectively. Besides litharge (-PbO) and massicot (β-PbO), which are both stable at ambient pressure, there is an orthorhombic γ-PbO phase which appears upon application of pressure to -PbO. We have found that the orthorhombic γ-PbO phase is favored by shear stress under non-hydrostatic conditions. -PbO shows strong anisotropy in compressibility. The a-axis is rather incompressible with a linear stiffness coefficient of Ka0=540(30) GPa whereas the c-axis stiffness is Kc0=25(1) GPa. The bulk modulus of -PbO is K0=23.1(3) GPa and its derivative . 相似文献
58.
59.
We derive a representation formula for the solutions of the navier-Stokes flow in three dimensions in absence of boundary in terms of stochastic current lines. This pictures generalizes an analogous one given in two dimensions and on the other hand the classical Lafrangian picture for the Euler flow. We prove a Vanishing viscosity limit for the whole structure 相似文献
60.
Alain ValtzChien-Bin Soo Christophe Coquelet Dominique RichonDaniel Amoros Hubert Gayet 《Fluid Phase Equilibria》2011,309(1):15-19
To simulate cyclohexane to cyclohexanol oxidation reactors, the acquisition and modeling of vapor-liquid equilibria of the key components, under the process conditions, are essential. n-Hexanoic acid is a co-product of the reaction. Vapor-liquid equilibrium data are reported for the cyclohexane + n-hexanoic acid binary system at four temperatures: 413, 423, 464 and 484 K. All measurements have been carried out using an apparatus based on the “static-analytic” method, with two ROLSI™ pneumatic capillary samplers. The generated data are successfully correlated using two equations of state, the Peng-Robinson (PR) and the Perturbed Chain Statistical Association Fluid Theory (PC-SAFT). Both models are capable of representing the experimental data, but the PC-SAFT EoS uses less binary interaction parameters. 相似文献