Let X, B and Y be three Dirichlet, Bernoulli and beta independent random variables such that X ∼ D(a0, . . . , ad), such that Pr(B = (0, . . . , 0, 1, 0, . . . , 0)) = ai/a with a = Pd i=0 ai and such that Y ∼ β(1, a). Then, as was proved by J. Sethuraman [11], X ∼ X(1 − Y ) + BY. This gives the stationary distribution of a simple Markov chain on a tetrahedron. If k is an integer, the present p...

We consider ecological difference equations of the form X i t+1 = X i t Ai(Xt) where X i t is a vector of densities corresponding to the subpopulations of species i (e.g. subpopulations of different ages or living in different patches), Xt = (X 1 t , X 2 t ,. .. , X m t) is state of the entire community, and Ai(Xt) are matrices determining the update rule for species i. These equations are perm...

We define the weighted Bergman space b p β (S T) consisting of temperature functions on the cylinder S T = S 1 × (0,T) and belonging to L p (Ω T ,t β dxdt), where Ω T = (0, 2) × (0,T). For β > −1 we construct a family of bounded projections of L p (Ω T ,t β dxdt) onto b p β (S T). We use this to get, for 1 < p < ∞ and 1/p +1/p = 1, a duality b p β (S T) * = b p β (S T), where β depends on p and β.

Proof of Proposition 1. Suppose an attribute value ai is not recorded in any of the data sources S1 through Sn for an entity instance. Then, from Assumptions 1 and 2 in the paper, we have P A= ai AS1 = ak AS2 = al ASn = atW i = k i = l i = t = P AS1 = ak A= ai P AS2 = al A= ai × · · ·×P ASn = at A= ai P AS1 = ak AS2 = al ASn = at P A= ai = 1−R A S1 / m− 1 1−RS2 / m− 1 × · · ·× 1−RSn / m− 1 P AS...

∞ i=1 aiεn−i, where the εi are i.i.d. with mean 0 and at least finite second moment, and the ai are assumed to satisfy |ai| = O(i) with β > 1/2. When 1/2 < β < 1, Xn is usually called a long-range dependent or long-memory process. For a certain class of Borel functions K(x1, . . . , xd+1), d≥ 0, from R to R, which includes indicator functions and polynomials, the stationary sequence K(Xn,Xn+1, ...

Given a set-comparison predicateP and given two lists of setsA = (A1, . . . , Am) and B = (B1, . . . , Bm), with all Ai, Bj ⊆ [n], the P-set join A ./P B is defined to be the set {(i, j) ∈ [n] × [n] | P(Ai, Bj)} ([n] denotes {1, 2, . . . , n}). When P(Ai, Bj) is the condition “Ai ∩ Bj 6= ∅” we call this the set-intersection-notempty join (a.k.a. the composition ofA and B); whenP(Ai, Bj) is “Ai∩...

PURPOSE The reduction in acquired infections (AI) due to methicillin-resistant Staphylococcus aureus (MRSA) with the mupirocin/chlorhexidine (M/C) decontamination regimen has not been well studied in intubated patients. We performed post hoc analysis of a prior trial to assess the impact of M/C on MRSA AI and colonization. METHODS We conducted a multicenter, placebo-controlled, randomized, do...

Using a fixed point theorem of strict-set-contraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x′(t) = x(t) h a(t)− n X i=1 ai(t) Z 0 −Ti x(t+θ) dμi(θ)− m X j=1 bj(t) Z 0 −T̂j x′(t+θ) dνj(θ) i , where the coefficients a, ai, bj are continuous and periodic functions, with the same period. The value...