Osculation for conic fibrations.

Smooth projective surfaces fibered in conics over a smooth curve are investigated with respect to their k-th osculatory behavior. Due to the bound for the dimension of their osculating spaces they do not differ at all from a general surface for k = 2, while their structure plays a significant role for k >= 3. The dimension of the osculating space at any point is studied taking into account the possible existence of curves of low degree transverse to the fibers, and several examples are discussed to illustrate concretely the various situations arising in this analysis. As an application, a complete description of the osculatory behavior of Castelnuovo surfaces is given. The case k = 3 for del Pezzo surfaces is also discussed, completing the analysis done for k = 2 in a previous paper by the authors (2001). Moreover, for conic fibrations X subset of P-N whose k-th inflectional locus has the expected codimension, a precise description of this locus is provided in terms of Chern classes. In particular, for N = 8, it turns out that either X is hypo-osculating for k = 3, or its third inflectional locus is 1-dimensional

Tear Secretion Induced by Selective Stimulation of Corneal and Conjunctival Sensory Nerve Fibers

Purpose. To measure the increase in tear secretion evoked by selective stimulation of the different populations of sensory receptors of the cornea and conjunctiva by using moderate and intense mechanical, chemical, and cold stimuli. Methods. Six healthy subjects participated in the study. Tear secretion was measured in both eyes by the Schirmer’s test conducted under control conditions and after stimulation of the center of the cornea and the temporal conjunctiva with a gas esthesiometer. Mechanical stimulation consisted in three pulses of 3 seconds’ duration of warmed air (at 34°C on the eye surface) applied at moderate (170 mL/min) and high (260 mL/min) flow rates. Cold thermal stimulation was made with cooled air that produced a corneal temperature drop of −1°C or −4.5°C. Chemical (acidic) stimulation was performed with a jet of gas containing a mixture of 80% CO2 in air. Results. The basal volume of tear secretion increased significantly (P < 0.05, paired t-test) after stimulation of the cornea with high-flow mechanical stimuli (260 mL/min), intense cooling pulses (−4.5°C), and chemical stimulation (80% CO2). The same stimuli were ineffective when applied to the conjunctiva. Moderate mechanical (170 mL/min) and cold (−1°C) stimulation of the cornea or the conjunctiva did not change significantly the volume of tear secretion. Conclusions. Reflex tear secretion caused by corneal stimulation seems to be chiefly due to activation of corneal polymodal nociceptors, whereas selective excitation of corneal mechanonociceptors or cold receptors appears to be less effective in evoking an augmented lacrimal secretion. Conjunctival receptors stimulated at equivalent levels do not evoke an increased tear secretion.