Vocal cord dysfunction, a syndrome of paradoxical inspiratory closure of the vocal cords, is becoming more frequently recognized and diagnosed recently since its initial modern description 30 years ago. Initially described as single case reports, the first case series in 1983 helped to clarify the typical patient and findings of vocal cord dysfunction. Recent investigations have elucidated specific etiologies such as gastroesophageal reflux, exercise, and irritants as causative factors in addition to the numerous associated psychologic factors. Speech therapy and psychotherapy have been used extensively with vocal cord dysfunction patients, but the optimal treatment has yet to be prospectively studied. This manuscript provides a comprehensive review of the reported causative factors and treatments for vocal cord dysfunction.
Knowledge of the normal liver size is essential for making the scintigraphic estimate of hepatomegaly. A nomogram for sonographic liver size versus height of the patient was developed for the normal pediatric patient. Liver size was measured as the longitudinal liver length in the plane midway between the xiphoid and the right lateral liver margin. Scintigraphic and sonographic measurements showed a good correlation. The scintigraphic nomogram was developed using the experimentally determined relationship between the two modalities.
Let X denote an irreducible affine algebraic curve over the complex numbers. Let &{X) be the ring of regular functions on X. Denote by 3{X) the ring of differential operators on X. We wish to characterize (f(X) as a ring theoretic invariant of 3{X). It is proved that @{X) equals the set of all locally ad-nilpotent elements oi3f(X) if and only if X is not simply connected. However, for most simply connected curves, we show there exists a maximal commutative subalgebra oi3f{X)t consisting of locally ad-nilpotent elements, which is not isomorphic to (f(X).
Introduction.Let X be a curve, that is, an irreducible affine algebraic curve over C. Write &{X) for the ring of regular functions on X and 3{X) for the ring of differential operators on X. See [8] for the basic definitions and facts about rings of differential operators on curves. This paper is motivated by the following question. If X and Y are curves with 3{X) = 3(Y) 9 is X = YΊ Write X for the normalization of X. Stafford [9] considers this question for X with X = A 1 , the affine line. He shows that 3{X) = 2{X) if and only if X = X. He also shows that if X is the cubic cusp y 2 = x 3 and Ϋ = A 1 , then X = Y if and only if 3{X) = 3(Y). Higher dimensional non-isomorphic varieties can have isomorphic rings of differential operators, see Levasseur, Smith and Stafford [2].If u e 3{X\ define ad(w) e End c (^(X)) by ad(κ)(u) = [u,v] = uυ -vu. We say u is locally ad-nilpotent if for every v e 2f{X) there exists neN with ad(u) n (v) = 0. Write jr(X) = {ue 3J{X)\u is locally ad-nilpotent}.Note that if ϋ: 3{Y) -> 3{X) is an isomorphism then ϋ(yT(Y)) = Jf(X). It follows from the definition oΐ3{X) that &{X) is a maximal commutative subalgebra oϊ3J(X) and that @(X) is contained in yV{X). If genus {X) > 0 then shows that &{X) = jr\x). Hence if3(X) = 3(Y) with genus(X) > 0 then X = Y.This paper expands on Makar-Limanov's result to prove the following theorem. Let π: X -> X denote the canonical surjection.
Let X and Y be nonisomorphic irreducible affine algebraic curves over the complex numbers C. Let D{X) and D{Y) be their rings of differential operators (see
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