as 23i-i lz*l +|«'t|—»0, for fixed /. Systems of the form (1.1) are of considerable interest in dynamics, and play an important role in many branches of applied mathematics. Usually the right-hand side does not involve any derivatives. In dynamics, where t represents the time, a natural problem is the determination of the behavior of the solutions for large values of the time, and this is the c...

We prove the termination of 4-fold canonical flips. This paper is a supplement of [KMM, Theorem 5-1-15] and [M, Main Theorem 2.1]. We prove that a sequence of 4-fold log flips for canonical pairs terminates after finitely many steps. Let us recall the definition of canonical flips, which is slightly different from the usual one (cf. [S, (2.11) Adjoint Diagram]). Definition 1 (Canonical flip). L...

This paper studies the problem of how much space is saved, on average, when a TRIE is pruned back to a minimal discriminating preex. Exact gures (on average, half the space is saved) are given for binary trees. All trees with n nodes and m leaves are assumed equally likely. The calculations are based on an unusual form of recurrence relation.

In this note we consider the fluid queue driven by an M / M /1 queue as analysed by Virtamo and Norros [5]. We show that the stationary buffer content in this model can be easily analysed by looking at embedded time points. This approach gives the stationary buffer content distribution in terms of the modified Bessel function of the first kind of order one. By using a suitable integral represen...

1 Introduction Caicedo [1] and others [3] have observed that monadic quantifiers cannot count the number of classes of an equivalence relation. This implies the existence of a binary quantifier which is not definable by monadic quantifiers. The purpose of this paper is to show that binary quantifiers cannot count the dimension of a vector space. Thus we have an example of a ternary quantifier w...