We show a Marcinkiewicz–Zygmund law of large numbers for jointly, dissociated exchangeable arrays, in L r ( ∈ 0 , 2 ) and almost surely. Then, we obtain iterated logarithm such arrays under weaker moment condition than the existing one.

We investigate, by “ à la Marcinkiewicz” techniques applied to the (asymptotic) density function, how dense systems of equal spheres of Rn, n ≥ 1, can be partitioned at infinity in order to allow the computation of their density as a true limit and not a limsup. The density of a packing of equal balls is the norm 1 of the characteristic function of the systems of balls in the sense of Marcinkie...

The authors nd necessary and su cient conditions for GDT weighted Marcinkiewicz inequalities based at Stieltjes zeros. c © 1998 Elsevier Science B.V. All rights reserved.

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

This paper presents the Physical Optics field calculation in terms of only line integrations by using the Modified Edge Representation technique (MER), the alternative way of the surface integration. Not only the diffracted fields as in the conventional method of equivalent edge currents (EEC) but also the scattering geometrical optics fields are expressed in terms of the MER line integrals. Th...

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We study the approximation properties of Runge-Kutta time discretizations of linear and semilinear parabolic equations, including incompressible Navier-Stokes equations. We derive asymptotically sharp error bounds and relate the temporal order of convergence, which is generally noninteger, to spatial regularity and the type of boundary conditions. The analysis relies on an interpretation of Run...

Part I. The Unrefined Trace Formula 7 1. The Selberg trace formula for compact quotient 7 2. Algebraic groups and adeles 11 3. Simple examples 15 4. Noncompact quotient and parabolic subgroups 20 5. Roots and weights 24 6. Statement and discussion of a theorem 29 7. Eisenstein series 31 8. On the proof of the theorem 37 9. Qualitative behaviour of J (f) 46 10. The coarse geometric expansion 53 ...