BACKGROUND AND OBJECTIVES To assess the accuracy of the ultrasound (US) to predict the depth to reach lumbar intrathecal and epidural spaces in order to decrease the number of puncture attempts. METHODS Thirty-one patients (25 males and 6 females), ASA I or II participated in this study. The transversal ultrasound image of the lumbar spine was obtained at the level of the L3-L4 space. An anes...

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversa...

A center-transversal line for two finite point sets in R is a line with the property that any closed halfspace that contains it also contains at least one third of each point set. It is known that a center-transversal line always exists,but the best known algorithm for finding such a line takes roughly n time. We propose an algorithm that finds a center-transversal line in O(nκ(n)) worst-case t...

The dynamics of an interface connecting a stationary stripe pattern with a homogeneous state is studied. The conventional approach which describes this interface, Newell–Whitehead–Segel amplitude equation, does not account for the rich dynamics exhibited by these interfaces. By amending this amplitude equation with a nonresonate term, we can describe this interface and its dynamics in a unified...

In 2012, the first three authors established a relationship between the transversal number and the domination number of uniform hypergraphs. In this paper, we establish a relationship between the total transversal number and the total domination number of uniform hypergraphs. We prove tight asymptotic upper bounds on the total transversal number in terms of the number of vertices, the number of...

Many classes of symmetric transversal designs have been constructed from generalized Hadamard matrices and they are necessarily class regular. In [2] we constructed symmetric transversal designs using spreads of Z 2n p with p a prime. In this article we show that most of them admit no class regular automorphism groups. This implies that they are never obtained from generalized Hadamard matrices...

Let S be used to denote a nite set of planar geometric objects. Deene a polygon transversal of S as a closed simple polygon that simultaneously intersects every object in S, and a minimum polygon transversal of S as a polygon transversal of S with minimum perimeter. If S is a set of points then the minimum polygon transversal of S is the convex hull of S. However, when the objects in S have som...

Ingleton [8, p. 123] raised the question of characterizing the class of transversal matroids that are representable over some particular field F. He noted that when F = GF(2), this problem had already been solved by de Sousa and Welsh [6] who showed that the class of binary transversal matroids coincides with the class of graphic transversal matroids. The latter class had earlier been character...