in surrogate pregnancies genetic parents have little opportunity for early bonding with their infants either prenatally (in utero) or during the immediate postnatal period. procedures commonly used to induce lactation include both pharmacologic and nonpharmacologic methods often in combination. studies reporting induced lactation are sparse due to the rarity of augmented lactation. here we repo...

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H(⊗1 C+) denotes the Hardy space of square integrable functions analytic in each variable separately. Let P be the natural projection of L(⊗1 C+) onto H(⊗1 C+). A Hankel operator with symbol b is the linear operator from H(⊗1 C+) to H(⊗1 C+) given by Hbφ = Pbφ. We show that ‖Hb‖ ≃ ‖Pb‖BMO(⊗n 1 C+), where the right hand norm is S.-Y. Chang and R. Fefferman product BMO. This fact has well known e...

Proof Let f : R → R be any smooth function that is identically 1 for t ≤ 0 and identically 0 for t ≥ 1. Since H k(R) is the completion of C∞(Rn), it is enough to show that every function φ ∈ C∞(Rn) ∩ H k(R) can be approximated in H k(R n) by functions in C∞ c (Rn). Consider the sequence φj(x) := φ(x)f(|x| − j). We have that φj ∈ C∞ c (Rn): in fact |x| is not differentiable at x = 0, but f(t) is...

We extend F.Pastjin's construction of uniform decomposable chains of finite rank to those of rank 'finite over a limit' and investigate infinite (length ω) products and unions of such chains. We derive an extension of Pastjin's characterisation to uniform decomposable chains of small transfinite rank (≤ ω + ω).

can be easily proved by either induction, Binet's formula, or ([1, p. 80]) by taking determinants in In this paper we give a bijective proof, based upon the following combinatorial interpretation of the Fibonacci numbers. Proof of (1). Let e = (2,..., 2); define the bijection ~r: A(n)×A(n)\(e, e)-~ A(n-1) ×A(n + 1)\(e,e) as follows. Let [bs)]eA(n) × A(n) and look for the first 1 in Case I. The ...