Let a finite number of line segments be located in the plane. Let be a circle that surrounds the segments. Define the region enclosed by these segments to be those points that cannot be connected to by a continuous curve, unless the curve intersects some segment. We show that the area of the enclosed region is maximal precisely when the arrangement of segments defines a simple polygon that sati...

BACKGROUND Use of short-acting β(2)-agonists in chronic obstructive pulmonary disease (COPD) during treatment with long-acting β(2)-agonists is recommended as needed, but its effectiveness is unclear. The purpose of this study was to assess the additional bronchodilating effect of increasing doses of salbutamol during acute and chronic treatment with formoterol in patients with COPD. METHODS ...

The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$,  we mean an ideal $I$ of $R$ such that $Ineq R$.  We say that a proper ideal $I$ of a ring $R$ is a  maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ Isubseteq A$ and $Ineq A$ is a prime ideal. That is, among all the proper ideals of $R$,...

Later on in [2], Grekos refined the previous results, in some cases, by introducing the infimum of the radii of curvature r(Γ ) of the curve. He succeeded in showing an upper bound of the shape N(Γ ) l(Γ )r(Γ )−1/3 and conversely constructed a family of curves Γ0 with N(Γ0) l(Γ0)r(Γ0)−1/3. Naturally, Grekos’ results suppose that the curve has at least C2-regularity. In fact, this is the maximal...

From results about digital convexity, we define a reversible polygon that faithfully represents the maximal convex and concave parts of a digital curve. Such a polygon always exists and is unique in the general case. It is computed from a given digital curve in linear-time using well-known routines: adding a point at the front of a digital straight segment and removing a point from the back of ...

Shioda described in his article [6] a method to compute the Lefschetz number of a Delsarte surface. In one of his examples he uses this method to compute the rank of an elliptic curve over kptq. In this article we find all elliptic curves over kptq for which his method is applicable. For these curves we also compute the maximal Mordell-Weil rank.

We prove that the number of maximal points in a random sample taken uniformly and independently from a convex polygon is asymptotically normal in the sense of convergence in distribution. Many new results for other planar regions are also derived. In particular, precise Poisson approximation results are given for the number of maxima in regions bounded above by a nondecreasing curve.

Let t --> gamma(t), 0 </= t </= 1, be a smooth curve in IR(n). Define the maximal function [unk](f) by [unk](f)(x) = sup(0<h</=1) (1/h) (0) (h) f(x - gamma(t)) dt. We state conditions under which parallel[unk](f) parallel(p) </= A(p) parallelf parallel(p), for 1 < p </= infinity.

Given a smooth non-hyperelliptic curve C of genus 3 and a maximal isotropic subgroup (w.r.t. the Weil pairing) L ⊂ Jac(C)[2], there exists a smooth curve C′ s.t. Jac(C′) = Jac(C)/L. This construction is symmetric. i.e. if we start with C′ and the dual flag on it, we get C. A previous less explicit approach was taken by Donagi and Livné (see [DL]). The advantage of our construction is that it is...

We studied the relationship between the force and velocity of microtubule sliding in demembranated sperm flagella of the sea urchin, Hemicentrotus pulcherrimus, under auxotonic conditions following a quick release of the tension between sliding microtubules. The shape of the force-velocity curve was independent of the concentration of Mg-ATP over the range of 3.7 to 350 microM and appeared eith...