Effects of Cobalt Chloride in Junctional Epithelium and Reduced Enamel Epithelium of the Rat Maxillary First Molar

Cobalt is one of the main components of cast metal alloys broadly used in dentistry. It is the constituent of 45 to 70% of numerous prosthetic works. There are evidences that metal elements cause systemic and local toxicity. The purpose of the present study was to evaluate the effects of cobalt on the junctional epithelium and reduced enamel epithelium of the first superior molar in rats, during lactation. To do this, 1-day old rats were used, whose mothers received 300mg of cobalt chloride per liter of distilled water in the drinker, during lactation. After 21 days, the rat pups were killed with an anesthetic overdose. The heads were separated, fixed in ""alfac"", decalcified and embedded in paraffin. Frontal sections stained with hematoxylin and eosin were employed. Karyometric methods allowed to estimate the following parameters: biggest, smallest and mean diameters, D/d ratio, perimeter, area, volume, volume/area ratio, eccentricity, form coefficient and contour index. Stereologic methods allow to evaluate: cytoplasm/nucleus ratio, cell and cytoplasm volume, cell number density, external surface/basal membrane ratio, thickness of the epithelial layers and surface density. All the collected data were subjected to statistic analysis by the non-parametric Wilcoxon-Mann-Whitney test. The nuclei of the studied tissues showed smaller values after karyometry for: diameters; perimeter, area, volume and volume/area ratio. Stereologically, it was observed, in the junctional epithelium and in the reduced enamel epithelium, smaller cells with scarce cytoplasm, reflected in the greater number of cells per mm3 of tissue. In this study, cobalt caused epithelial atrophy, indicating a direct action on the junctional and enamel epithelium.

Effects of Cadmium on the Rat Salivary Glands, During Lactation

Cadmium (Cd) in air, drinking water and food has the potential to affect the health of people, mainly those who live in highly industrialized regions. Cd affects placental function, can cross the placental barrier and directly modify fetal development. Once the organism is particularly susceptible to the exposition to the Cd during the perinatal period, and that this metal can be excreted in the milk, the aim of the present work was to study the effects of the constant exposition to drinkable water containing low levels of Cd during the lactation, on the salivary glands of the rat. Female rats received ad libitum drinking water containing 300mg/l of CdCl2 throughout the whole lactation. Control animals received a similar volume of water without Cd. Lactant rats (21 day old) were killed by lethal dose of anesthetic. The salivary glands were separated, fixed in ""alfac"" solution for 24 h, and serially sectioned. The 6 mu m thick sections were stained with hematoxylin and eosin. Nuclear glandular parameters were estimated, as well as cytoplasm and cell volume, nucleus/cytoplasm ratio, number and surface density, diameters and cell thickness. Mean body weight was 34.86 g for the control group and 18.56 g for the Cd-treated group. Histologically, the glandular acini were significantly smaller, the gland ducts were similar in both groups studied. The connective tissue was more abundant. In conclusion, the salivary glands (submandibular, parotid and sublingual) showed retarded growth after Cd intoxication.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

In this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

Spectral flow and iteration of closed semi-Riemannian geodesics

We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration, determining its asymptotic behavior.

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Maslov index in semi-Riemannian submersions

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the projected geodesic pi omicron gamma : I -> B in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.