Limit cases of reiteration theorems

We consider real interpolation methods defined by means of slowly varying functions and rearrangement invariant spaces, for which we present a collection of reiteration theorems for interpolation and extrapolation spaces. As an application we obtain interpolation formulas for Lorentz‐Karamata type spaces, for Zygmund spaces , and for the grand and small Lebesgue spaces.     

行为NA的随机变量阵列加权和的完全收敛性

In this paper we obtain theorems of complete convergence for weighted sums of arrays of rowwise negatively associated （NA） random variables. These results improve and extend the corresponding results obtained by Sung （2007）, Wang et al. （1998） and Li et al. （1995） in independent sequence case.     

Small ball probabilities for Gaussian random fields and tensor products of compact operators

We find the logarithmic -small ball asymptotics for a large class of zero mean Gaussian fields with covariances having the structure of ``tensor product'. The main condition imposed on marginal covariances is the regular behavior of their eigenvalues at infinity that is valid for a multitude of Gaussian random functions including the fractional Brownian sheet, Ornstein - Uhlenbeck sheet, etc. So we get the far-reaching generalizations of well-known results by Csáki (1982) and by Li (1992). Another class of Gaussian fields considered is the class of additive fields studied under the supremum-norm by Chen and Li (2003). Our theorems are based on new results on spectral asymptotics for the tensor products of compact self-adjoint operators in Hilbert space which are of independent interest.

     

Orthogonal polyanalytic polynomials and normal matrices

The Hermitian Lanczos method for Hermitian matrices has a well-known connection with a 3-term recurrence for polynomials orthogonal on a discrete subset of . This connection disappears for normal matrices with the Arnoldi method. In this paper we consider an iterative method that is more faithful to the normality than the Arnoldi iteration. The approach is based on enlarging the set of polynomials to the set of polyanalytic polynomials. Denoting by the number of elements computed so far, the arising scheme yields a recurrence of length bounded by for polyanalytic polynomials orthogonal on a discrete subset of . Like this slowly growing length of the recurrence, the method preserves, at least partially, the properties of the Hermitian Lanczos method. We employ the algorithm in least squares approximation and bivariate Lagrange interpolation.

     

The reaction front hypothesis in solid-state digestion: estimation of minimum size of viable seed body

An alternative mechanism for the anaerobic digestion of a bed of solids was recently proposed. A multizoned reaction front might form around a suitable body of seed material, then advance through the bed, within the solid phase. Such a solid-phase mechanism might coexist with liquid-phase digestion but one or the other of these two parallel mechanisms might generally be dominant. It is envisaged that solid-phase digestion would be favored by the presence of viable seed bodies: single particles of a suitable seed material above a minimum size or equivalent aggregates. A key determinant of the feasibility of this mechanism is expected to be the minimum viable size for a seed body (d _min). This would depend on the thickness of the reaction zones, some of which must initially be accommodated within the seed body. In this article, we present some theoretical estimates of d _min, which indicate a magnitude of 7–700 mm. Such values suggest that solid-phase digestion might be the norm in semi-dry waste digesters. Such digestion might be rare in unseeded landfills but it would appear likely that it could easily be initiated by suitable seeding.     

A Theory of the Self-Consistent and Space-Charge Effect in Hybrid-Magnicon Amplifier

A novel axially modulated, annular electron beam cusp-injected, slowly varied section opened cavity, hybrid-magnicon amplifier had been proposed I once. The hybrid-magnicon has wavelength up to millimeter wave bend. The while its non-self-consistent non-space-charge nonlinear numerical calculation method was discussed. But due to bunch effect is changing uniform distribution state of the annular electron beam in the driver cavity, and then dynamic force balances of the beam is changing. Therefore, besides the interaction force between electron beam and the rotating TM_n10 mode electromagnetic field also must consider the electromagnetic force of current density and the action force between the space-charges and the action force of the charge density grade, et al. effect. For some problems of theory, this report try discuss from Maxwell Equations.     

截断和大数律的收敛速度

本文研究了截断和大数律的收敛速度，证明了截断和（固定）完全收敛性定理以及大数律收敛速度的几个等价条件，从而推广了独立和的结果。     

On regular branching processes with infinite mean

A martingale, previously used to prove the classical almost sure convergence of the normed supercritical Galton-Watson branching process with finite mean without using probability generating functions, is here used to study similar behaviour for certain processes with infinite mean.     

Partial Sum Process for Records

Suppose the upper records from a sequence of i.i.d. random variables is in the domain of attraction of a normal distribution. Consider the D(0,1]-valued process {Z_n(·)} constructed by usual interpolation of the partial sums of the records. We prove that under some mild conditions, {Z_n} converges to a limiting Gaussian process in D(0,1]. As a consequence, the partial sums of records is asymptotically normal. AMS 2000 Subject Classification Primary—60F17 Secondary—60G70