Nuclear magnetic resonance spectroscopy of rat ventricles following chronic hypoxia: A model of right ventricular hypertrophy

Nuclear magnetic resonance spectroscopy was used to study the effect of chronic hypoxia on both right (RV) and left ventricular and septal (LV + S) muscle. Rats in the hypoxic group, kept in a hypobaric chamber at $\text{1}\text{2}$ atm pressure for 2 weeks, developed right, but not left, ventricular hypertrophy (p < 0.001). Tissues were studied within 2.5 h of return to air. T₁ and T₂ relaxation times of RV, LV + S and thigh muscle (Th) from hypoxic and control rats were compared. The T₂ value distinguished hypoxic from control RV (p < 0.002), but not hypoxic from control LV + S or Th, indicating that the change in relaxation time reflects cellular hypertrophy, and not hypoxemia. For hypoxic rats only the T₂ value distinguished each muscle type: RV from LV + S (p < 0.009), RV from Th (p < 0.001) and LV + S from Th (p < 0001). The T₁ value did not identify either the hypoxic or control group or the type of muscle. Percent water content was similar for all tissues. For hypoxic RV, T₂ correlated with the percent water content (r = 0.89; p < 0.01). The sensitivity of T₂ to the cellular changes associated with hypoxic RV hypertrophy could provide a means of detecting right ventricular hypertrophy.     

Galois stratification over Frobenius fields

New first-order conformally covariant differential operators P_k on spinor-k-forms, i.e., tensor products of contravariant spinors with k-forms, in an arbitrary n-dimensional pseudo-Riemannian spin manifold, are introduced. This provides a series of generalizations of the Dirac operator $\text{?}\text{?}$, in analogy with the series of generalizations (introduced by the author in [1]) of the Maxwell operator and the conformally covariant Laplacian $\text{□}$ on functions. In particular, new intertwining operators for representations of SU(2, 2) and SO(p + 1, q + 1) are found. Related nonlinear covariant operators are also introduced, and mixed nonlinear covariant systems are obtained by coupling to the Yang-Mills-Higgs-Dirac system in dimension 4. The spinor-form bundle is isomorphic with E⁽³⁾ = E ? E ? E, where E is the spin bundle, and the P_k give a covariant operator on sections of E⁽³⁾. This is generalized to a covariant operator on E^{(2l + 1)}. The relation of powers of these operators to higher-order covariant operators on lower spin bundles (analogous to the relation between $\text{?}\text{?}$ and $\text{□}$) is discussed.     

Meromorphic zeta functions for analytic flows

We extend to hyperbolic flows in all dimensions Rugh's results on the meromorphic continuation of dynamical zeta functions. In particular we show that the Ruelle zeta function of a negatively curved real analytic manifold extends to a meromorphic function on the complex plane.Dedicated to Steve SmaleThis work was supported in part by I.H.E.S. and the National Science Foundation.     

Symbolic dynamics for triangle groups

We generalize E. Artin’s continued fraction coding of the geodesics on the modular surface to any finite index subgroup Θ of a nonuniform hyperbolic triangle group Γ. D. Mayer’s study of the Selberg zeta function of PSl (2, Z ) is extended to Θ and its group representations. We give representatives for Γ-primitive conjugacy classes and derive a Markov system of interval maps for Γ and a Markov partition for the billiard flow on Γ\ SH ² . This leads to identities for values of the dilogarithm function at algebraic numbers. We also find the Γ-analogues of Gauss measure on [0,1]. Oblatum 16-VIII-1993 & 15-VIII-1994 & 2-I-1996     

Torsion and closed geodesics on complex hyperbolic manifolds

Summary LetX be a compact complex manifold covered by complex hyperbolicn-space with the induced metric. Each stable horocycle has a cocomplex structure preserved by the geodesic flow. To a closed geodesic one can thus associate a piece of the Poincaré map with a holomorphic fixed point. The resulting Atiyah-Bott fixed point indices, together with the length and multiplicity of as a periodic orbit, determine the contribution of to certain zeta functionsR _p(z), 0pn. From the leading coefficient ofR _p atZ=0 and the Hodge numbersh ^ij (X) we calculate the Ray-Singer -torsionT _p (X). This indicates that the known connections between torsion and the dynamical features of closed orbits continue to hold in the holomorphic category.Corresponding results hold for the -torsion of a flat unitary bundle, extending certain formulas of Ray and Singer to the casen>1.Partially supported by the Sloan Foundation and the National Science Foundation