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## Sequence Spaces l p,q in Probabilistic Characterizations of Weak Type Operators

### Journal of Mathematical Sciences (2004-04-01) 120: 1733-1751 , April 01, 2004

We study operators
$$T:X \mapsto L_ \circ ([0,1],{\mathcal{M}},m)$$
(not necessarily linear) defined on a quasi-Bahach space *X* and taking values in the space of real-valued Lebesgue-measurable functions. Factorization theorems for linear and superlinear operators with values in the space
$$L_ \circ $$
are proved with the help of the Lorentz sequence spaces
$$l_{p,q} $$
. Sequences of functions belonging to fixed bounded sets in the spaces
$$L_{p,\infty } $$
are characterized for
$$0 < p < \infty $$
and
$$0 < q \leqslant p$$
. The possibility of distinguishing weak type operators (bounded in the space
$$L_{p,\infty } $$
) from operators factorizable through
$$L_{p,\infty } $$
is obtained in terms of sequences of independent random variables. A criterion under which an operator is symmetrically bounded in order in
$$L_{p,r} ,{\text{ }}0 < r \leqslant \infty $$
, is established. Some refinements of the above-mentioned results are obtained for translation shift-invariant sets and operators. Bibliography: 30 titles.

## Linear Analysis with Delay: The single link case

### The Mathematics of Internet Congestion Control (2004-01-01): 67-81 , January 01, 2004

In the previous chapters, we have studied the relationship between congestion control and resource allocation, and studied the stability of congestion control algorithms in the absence of feedback delay. We will now study the stability of congestion control algorithms in the presence of delay. In this chapter, we restrict our attention to the case of a single link accessed by one or many sources to get acquainted with the tools and techniques used to study stability. In the next chapter, we will extend these results to the case of general topology networks, accessed by a set of heterogeneous sources.

## Hechler’s theorem for the null ideal

### Archive for Mathematical Logic (2004-07-01) 43: 703-722 , July 01, 2004

### Abstract.

We prove the following theorem: For a partially ordered set *Q* such that every countable subset of *Q* has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, there is a basis of the null ideal of the real line which is order-isomorphic to *Q* with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing. The corresponding theorem for the meager ideal was established by Bartoszyński and Kada.

## Stochastic Integration for Compensated Poisson Measures and the Lévy-Itô Formula

### Proceedings of the International Conference on Stochastic Analysis and Applications (2004-01-01): 145-167 , January 01, 2004

This is a review paper which presents in a unified way part of the results obtained in [38] and [2], where stochastic integrals of Banach valued random (resp. deterministic) functions w.r.t. compensated Poisson random measures are studied. As a consequence, the Lévy-Itô decomposition theorem for additive processes on Banach spaces is presented here in its stronger formulation (than [17], [8]), proposed in [2], for the special case where the additive processes are Lévy processes.

## Completeness of Spaces of Harmonic Functions under Restricted Supremum Norms

### Computational Methods and Function Theory (2004-08-01) 4: 43-45 , August 01, 2004

Let *E* be a subset of a domain Ω in Euclidean space. This note verifies a conjecture of Arcozzi and Björn concerning the completeness of the space of harmonic functions *u* on Ω that are bounded on *E*, where the supremum norm is taken with respect to the restriction of *u* to *E*.

## Itération de pliages de quadrilatères

### Inventiones mathematicae (2004-07-01) 157: 147-194 , July 01, 2004

*Iteration of quadrilateral foldings.* Starting with a quadrilateral *q*_{0}=(*A*_{1},*A*_{2},*A*_{3},*A*_{4}) of ℝ^{2}, one constructs a sequence of quadrilaterals *q*_{n}=(*A*_{4n+1},...,*A*_{4n+4}) by iteration of foldings: *q*_{n}=ϕ_{4}°ϕ_{3}°ϕ_{2}°ϕ_{1}(*q*_{n-1}) where the folding ϕ_{j} replaces the vertex number *j* by its symmetric with respect to the opposite diagonal (see Fig. 1).

We study the dynamical behavior of this sequence. In particular, we prove that:

– The drift ${v:= \lim_{n\rightarrow\infty}}\frac{1}{n} q_n$ exists.

– When none of the *q*_{n} is isometric to *q*_{0}, then the drift *v* is zero if and only if one has max*a*_{j}+min*a*_{j}≤1/2∑*a*_{j} where *a*_{1},...,*a*_{4} are the sidelengths of *q*_{0}.

– For Lebesgue almost all *q*_{0} the sequence (*q*_{n}-*nv*)_{n≥1} is dense on a bounded analytic curve with a center or an axis of symmetry. However, for Baire generic *q*_{0}, the sequence (*q*_{n}-*nv*)_{n≥1} is unbounded (see Figs. 2 to 7).

## Small Size Designs in Nonlinear Models Computed by Stochastic Optimization

### mODa 7 — Advances in Model-Oriented Design and Analysis (2004-01-01): 71-79 , January 01, 2004

### Summary

Optimality criteria, that are functions of the mean square error matrix, are expressed as integrals of the density of the parameter estimator. The optimum design is obtained by an accelerated stochastic optimization method. The estimator is modified to reflect prior knowledge about the parameters, and to take into account the boundary of the parameter space. Results of (1992) are extended and improved by that. Computer results are presented on examples.

## Stetige Verteilungen

### Einführung in die Wahrscheinlichkeits-theorie und Statistik (2004-01-01): 155-176 , January 01, 2004

## Volume Contents

### Statistical Inference for Stochastic Processes (2004-10-01) 7: 353-354 , October 01, 2004

## High-Order Compact Schemes with Filters on Multi-block Domains

### Journal of Scientific Computing (2004-12-01) 21: 321-339 , December 01, 2004

This paper presents the results of using high-order compact schemes with a high-order filter on multi-block domains. The Linearized Euler Equations (LEE) are solved on a uniform mesh for benchmark problems in one and two dimensions. Also a two dimensional mixing layer is solved by using Large-Eddy Simulation (LES). Three different boundary schemes are compared. The results compare well with the exact solutions and single-block domain results. The effect of the number of points of overlap among the subdomains is investigated. Having four points of overlap is chosen as a compromise between accuracy and efficiency.