A Mean-Value Laplacian For Finsler Spaces

Part I of this thesis defines a Laplacian A for a Finsler space; we obtain A by requiring that ( A f) ( x) for a function f measures the infinitesimal average of f around x. This A is a linear, elliptic, 2nd-order differential operator. Furthermore, Af can be written in a divergence form, like the Riemannian Laplacian, but with respect to a canonical osculating Riemannian metric and Busemann's intrinsic volume form. We interpret divergence form as the result of minimizing a certain energy functional on Finsler space, and further use this approach to define harmonic forms, and harmonic mappings between Finsler manifolds. As a byprod-uct of the Laplacian, in Part I1 we derive a simple volume-form inequality which characterizes Riemannian manifolds, and define a scalar invariant V ( x) for Finsler spaces. We show that, on a Berwald space, the met-ric's first derivatives vanish in normal co-ordinates, and use that result t

In vitro effect of low intensity laser on the cytotoxicity produced by substances released by bleaching gel

This in vitro study aimed to analyze the effect of different parameters of phototherapy with low intensity laser on the viability of human dental pulp fibroblasts under the effect of substances released by bleaching gel. Cells were seeded into 96 wells plates (1 x 10³ cells/well) and placed in contact with culture medium conditioned by a 35 % hydrogen peroxide bleaching gel for 40 minutes, simulating the clinical condition of the in-office bleaching treatment. Cells cultured in ideal growth conditions served as positive control group (PC), and the cells grown in conditioned medium and non-irradiated served as negative control group (NC). Cells grown in conditioned medium were submitted to a single irradiation with a diode laser (40 mW, 0.04 cm²) emitting at visible red (660 nm; RL) or near infrared (780 nm; NIR) using punctual technique, in contact mode and energy densities of 4, 6 or 10 J/cm². The cell viability was analyzed through the MTT reduction assay immediately and 24 hours after the irradiation. The data was compared by ANOVA followed by the Tukey's test (p < 0.05). The cell viability increased significantly in 24 hours within each group. The PC presented cell viability significantly higher than NC in both experimental times. Only the NIR/10 J/cm² group presented cell viability similar to that of PC in 24 hours. The phototherapy with low intensity laser in defined parameters is able to compensate the cytotoxic effects of substances released by 35 % hydrogen peroxide bleaching gel

On the radar method in general-relativistic spacetimes.

If a clock, mathematically modeled by a parametrized timelike curve in a general-relativistic spacetime, is given, the radar method assigns a time and a distance to every event which is sufficiently close to the clock. Several geometric aspects of this method are reviewed and their physical interpretation is discussed.Comment: Written version of talk given at 359th WE Heraeus Seminar ``Lasers, Clocks, and Drag-Free. New Technologies for Testing Relativistic Gravity in Space.'' Bremen, 2005; to appear in H. Dittus, C. L{\"a}mmerzahl, S. G. Turyshev (eds.): ``Lasers, Clocks, and Drag-Free Control. Exploration of Relativistic Gravity in Space.'' Springer, 200

Ecology, Evolution, Ethics: In Search of a Meta-paradigm – An Introduction

Evolutionary, ecological and ethical studies are, at the same time, specific scientific disciplines and, from an historical point of view, structurally linked domains of research. In a context of environmental crisis, the need is increasingly emerging for a connecting epistemological framework able to express a common or convergent tendency of thought and practice aimed at building, among other things, an environmental policy management respectful of the planet’s biodiversity and its evolutionary potential