For applications in spatial statistics, an important property of a random set X in R k is its rst contact distribution. This is the distribution of the distance from a xed point 0 to the nearest point of X, where distance is measured using scalar dilations of a xed test set B. We show that, if B is convex and contains a neighbourhood of 0, the rst contact distribution function F B is absolutely...

Let Y be a convex set in IR k deened by polynomial inequalities and equations of degree at most d 2 with integer coeecients of binary length l. We show that if Y \ ZZ k 6 = ;, then Y contains an integral point of binary length ld O(k 4). For xed k, our bound implies a polynomial-time algorithm for computing an integral point y 2 Y. In particular, we extend Lenstra's theorem on the polynomial-ti...

We study a renormalization operator for families of one dimensional maps close to x 7! p + r(1 x ) 2 , 2 ( 1 2 ; 1). Such functions occur in the study of cascades of homoclinic doubling bifurcations in three dimensional di erential equations. For values of close to 1 2 , we prove the existence of a xed point of the renormalization operator, whose linearization at the xed point has two unstable ...

in the present paper, we introduces the notion of integral type contractive mapping with respect to ordered s-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered s-metric space. moreover, we give an example to support our main result.

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...

Dit proefschrift is goedgekeurd door de promotor: 'Alles komt voort uit de chaos', wordt er in de Griekse Anthologie gezegd. En in-derdaad, alles komt voort uit de chaos. Buiten de wiskunde, die enkel met dode getallen en loze formules te maken heeft en derhalve volmaakt logisch kan zijn, is de wetenschap niet meer dan een kinderspel in de schemering, het willen vangen van vogelschaduwen en het...

with a xed point of multiplier = e 2 i at the origin. Take to be real and irrational. For generic choice of (in the sense of Baire category), Cremer showed that there is no local linearizing coordinate near the origin. We will say brie y that the origin is a Cremer point, or that P is a Cremer polynomial . According to Sullivan and Douady, the existence of such a Cremer point implies that the J...

Determining xed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences. An algorithm for nding common xed points of nonexpansive mappings in Hilbert space, essentially due to Halpern, is analyzed. The main theorem extends Wittmann's recent work and partially generalizes a result by Lions. Algorithms of this kind have been applied to the convex feasibility pro...

A new method for kinematic calibration of a robot is presented, based on triaxial measurement of acceleration by a sensor xed to the robot end-point. The kinematic parameters are evaluated by means of a series of simple tests (two for each joint). In these tests each joint, except the one under consideration, is kept xed. Acceleration and encoder output are then acquired. Simulations and experi...