L'accès aux archives de la revue « Bulletin de la S. M. F. » (http: //smf.emath.fr/Publications/Bulletin/Presentation.html) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/ conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/
To investigate the behaviour of red cells in the microcirculation, we established a new capillary method using narrow fluorinated ethylenepropylene copolymer tubes with internal diameters of 12.5 and 25.0 microns. Red cell flow in the tubes under a given range of pressure was analysed through a video system connected to a microscope. The experimental condition was adjusted so that the velocity of the control normocytes would be compatible with that in corresponding vessels in vivo, 0.5-1.5 mm/s. In the 12.5 microns tube, normocytes obtained from 12 young normal volunteers ran in an axisymmetric edge-on orientation with a folded shape at higher pressures, but rolled along freely without deformation at lower pressures. Deformation during the passage of the microcytes obtained from four patients with polycythaemia vera complicated with iron-deficient microcytosis and 10 patients with iron deficiency anaemia was relatively mild, whereas that of the macrocytes obtained from eight patients with refractory anaemia was marked. Even after the screening effect at the tube entrance was taken into consideration, the velocities of both microcytes and macrocytes were found to be significantly lower than the control normocytes. Therefore this method may be a new way to investigate the flow properties of red cells in the microcirculation.
Abstract. It has been believed that the continued fraction expansion of (α, β) (1, α, β is a Q-basis of a real cubic field) obtained by the modified JacobiPerron algorithm is periodic. We conducted a numerical experiment (cf. Table B, Figure 1 and Figure 2) from which we conjecture the non-periodicity of the expansion of () ( x denoting the fractional part of x). We present a new algorithm which is something like the modified Jacobi-Perron algorithm, and give some experimental results with this new algorithm. From our experiments, we can expect that the expansion of (α, β) with our algorithm always becomes periodic for any real cubic field. We also consider real quartic fields.
IntroductionThe study of continued fractions has a long history dating back to J. Wallis (1616-1703) and Ch. Huygens (1629-1695) [8]. In particular, many kinds of higherdimensional continued fractions have been studied starting with K.G. Jacobi (1804-1851) [7]. A central problem has been to find a higher-dimensional generalization of Legendre's theorem concerning the periodic continued fractions. In fact, the following conjecture has been believed. 1, α 1 Figure 1 and Figure 2) from which we conjecture the non-periodicity of the expansion of (
Conjecture. Let) by the modified Jacobi-Perron algorithm.In this paper, we give some candidates of algorithms of continued fraction expansion of dimensions 2 and 3, which can be easily generalized to any dimension.By numerical experiments, we checked that, for instance, ( √ m / ∈ Q) obtained by our algorithm become periodic. We showed the periodicity
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.