For finitely generated modules N ( M over a Noetherian ring R, we study the following properties about primary decomposition: (1) The Compatibility property, which says that if Ass(M/N) = {P1, P2, . . . , Ps} and Qi is a Pi-primary component of N ( M for each i = 1, 2, . . . , s, then N = Q1 ∩Q2 ∩ · · · ∩Qs; (2) For a given subset X = {P1, P2, . . . , Pr} ⊆ Ass(M/N), X is an open subset of Ass(...

We consider a family of linear control systems ẋ = Ax+αBu where α belongs to a given class of persistently exciting signals. We seek maximal α-uniform stabilisation and destabilisation by means of linear feedbacks u = Kx. We extend previous results obtained for bidimensional singleinput linear control systems to the general case as follows: if the pair (A,B) verifies a certain Lie bracket gener...

— An upper bound of the expected order of magnitude is established for the number of Q-rational points of bounded height on Châtelet surfaces defined over Q.

In its most basic form, latent growth modeling (latent curve analysis) allows an assessment of individuals’change in a measured variable X over time. For simple linear models, as with other growth models, parameter estimates associated with the α construct (amount of X at a chosen temporal reference point) and β construct (growth in X per unit time) are not invariant with respect to choice of r...

Let d 2, and let fXv; v 2 Z d g be an i.i.d. family of non-negative random variables with common distribution F. Let N (n) be the maximum value of P v2 Xv over all connected subsets of Z d of size n which contain the origin. This model of \greedy lattice animals" was introduced by Cox et al. (1993) and Gandoll and Kesten (1994), who showed that if E X d 0 (log + X0) d+ < 1 for some > 0, then N ...

BACKGROUND Undernutrition in early life underlies 45% of child deaths globally. Stunting malnutrition (suboptimal linear growth) also has long-term negative effects on childhood development. Linear growth deficits accrue in the first 1000 d of life. Understanding the patterns and timing of linear growth faltering or recovery during this period is critical to inform interventions to improve infa...

Swanson was partially motivated by the analogous question for “Frobenius powers”, which has important applications to the theory of tight closure (the so-called “localization problem;” see [HH, Section 4]). Suppose now that R has prime characteristic p > 0 and q is a power of p. The Frobenius power I [q] of an ideal I is the ideal generated by all the qth powers of the elements (equivalently, t...

A linear bubble model of grain growth is introduced to study the conditions under which an isolated grain can grow to a size much larger than the surrounding matrix average (abnormal growth). We first consider the case of bubbles of two different types such that the permeability of links joining unlike bubbles is larger than that of like bubbles (a simple model of grain boundary anisotropy). St...