The use of ureteric double-J stents and the Lich-Gregoir (extravesical) technique of ureteroneocystotomy have both been shown to decrease the rate of urologic complications in adult kidney transplantation (Tx). There are, however, few studies of the systematic use of stents in pediatric renal Tx. Between 1991 and 1997, 32 consecutive pediatric renal transplant recipients routinely received a 6F-12 cm indwelling double-J stent and were studied prospectively. These patients were compared with 32 consecutive pediatric recipients in whom a stent was not used. The latter were transplanted between 1987 and 1991 and formed the control group. All patients had a Lich-Gregoir ureteroneocystotomy. Stents were removed under general-anesthetic cystoscopy 2 3 weeks after Tx. Immunosuppression for stented patients was polyclonal antibody induction, delayed (7-10 days) cyclosporin A, azathioprine, and prednisone. The control group received the same triple drug regimen but with no induction in 29 of the 32 patients. All patients were followed-up with at least one ultrasound evaluation in the first month, and a renal scan and repeat ultrasound were performed if there was any rise in serum creatinine. In the stented group there were two patients with urinary leak and no obstructions. In the non-stented group there were no leaks and one obstruction. There was no graft loss owing to urologic complications in either group. There were three cases of stent expulsion (all in girls) and one case of stent migration in the posterior urethra (a boy). The 1-yr graft survival rate was 90.6% in the stented group and 65.6% in the non-stented group. The prophylactic use of an indwelling ureteral stent in pediatric renal Tx did not reduce the risk of urinary leakage or obstruction. Stent migration is a common phenomenon and, while not a serious complication, is traumatic to children. Furthermore, removal of an internalized double-J stent requires a general anesthetic. We recommend using a stent for selected patients only.
We construct a wide subcategory of the category of finite association schemes with a collection of desirable properties. Our subcategory has a first isomorphism theorem analogous to that of groups. Also, standard constructions taking schemes to groups (thin radicals and thin quotients) or algebras (adjacency algebras) become functorial when restricted to our category. We use our category to give a more conceptual account for a result of Hanaki concerning products of characters of association schemes; i.e. we show that the virtual representations of an association scheme form a module over the representation ring of the thin quotient of the association scheme.Definition 2.1. Given a finite set X, an association scheme, or scheme, on X, is a set S consisting of nonempty subsets s ∈ P(X × X) and satisfying the following axioms.1. S is a partition of X × X;{y ∈ X : (x, y) ∈ p and (y, z) ∈ q} = a r pq .We call the integers a r pq the structure constants of the scheme S.for each g ∈ G. Then it is easy to show that S(G) is a scheme. Moreover,Definition 2.3. Suppose S is a scheme on a finite set X, and P, Q ⊆ S. Then the complex product of P and Q, denoted PQ is {r ∈ S : a r pq > 0 for some p ∈ P, q ∈ Q}.Complex product determines an associative product on P(S). If p, q ∈ S, we write pq, pQ and Pq for {p}{q}, {p}Q and P{q} respectively. Definition 2.4. If S is a scheme on a finite set X, then a nonempty subset T ⊆ S is a closed subset of S if TT = T.If T ⊆ S is closed, then the finiteness of X implies that t * ∈ T whenever t ∈ T.Example 2.5. If G is a group, then a subset T of the scheme S(G) on G is closed if and only if there is a subgroup K ≤ G such that T = {k˜: k ∈ K}. Definition 2.6. A morphism from a scheme S on X to a scheme T on Y is a function φ : X ∪ S → Y ∪ T such that φ(X) ⊆ Y, φ(S) ⊆ T, and whenever s ∈ S and (x 1 , x 2 ) ∈ s, we have (φ(x 1 ), φ(x 2 )) ∈ φ(s).A morphism is an isomorphism if it has an inverse, or, equivalently, if it is a bijection. We will typically denote the restriction of φ to X or S by φ, rather than φ| X or φ| S . When context permits, we will often just write φ : S → T, rather than φ : X ∪ S → Y ∪ T, to indicate a morphism from a scheme S to a scheme T.
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