This article contains definitions and theorems concerning basic properties of following objects: - a field of subsets of given nonempty set; - a sequence of subsets of given nonempty set; - a oe-field of subsets of given nonempty set and events from this oe-field; - a probability i.e. oe

The problem of finding a point that satisfies the sufficient decrease and curvature condition is formulated in terms of finding a point in a set T (). We describe a search algorithms for this problem that produces a sequence of iterates that converge to a point in T () and that, except

Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : ` 2 (X) ! H : c 7! X x2X c(x)x: Whenever T is well-defined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding

parameter. We present the algorithms, their theoretical analysis and simulation results. 1 Introduction This article studies the problem of computing order statistics of large sequences of online or disk-resident data using as little main memory as possible. We focus on computing quantiles, which

this paper we consider the ARCH(p) model defined by the equations y t = oe t " t # oe

We determine the asymptotic limiting probability as m !1 that a random string of length m over some alphabet \Sigma can be determined uniquely by its substrings of length `. This is an abstraction of a problem faced when trying to sequence DNA clones by SBH. Research done while visiting Carnegie

1 Introduction Aggregate signatures. An aggregate signature (AS) scheme [7] is a digital signature scheme with theadditional property that a sequence oe1,..., oen of individual signatures--here oei is the signature, underthe underlying base signature scheme, of some message

Let M be a metric space on which we have k servers. A request is a point oe 2 M and is serviced either by moving a server to oe, with cost equal to the distance the server moved, or by conducting an excursion, with cost fi (smaller than this distance). Our aim is to service (on-line) any sequence

Abstract. We study the convergence of moments of square-integrable martingales, when the martingales converge to a (mixed) normal limit. 1. Introduction and basic facts 1.1. Let Mo, D) L, be a sequence of square-integrable local martingales defined on afiltered space (Q

This paper gives results on weak and strong convergence in L²(IR s ) r of the cascade sequence (OE k;n ) generated by the nonstationary matrix cascade algorithm OE k;n = jM j P j h k+1 (j)OE k+1;n\Gamma1 (M \Delta \Gammaj ); where for each k = 1; 2; : : : ; h k is a finite sequence of r