26 research outputs found
A numerical computation on the structure of the roots of q-extension of Genocchi polynomials
AbstractIn this work we observe the behavior of real roots of the q-extension of Genocchi polynomials, cn,q(x), using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the cn,q(x) for −1<q<0. Finally, we give a table for the solutions of the q-extension of Genocchi polynomials
On the composition of convex envelopes for quadrilinear terms
International audienceWithin the framework of the spatial Branch-and-Bound algorithm for solving Mixed-Integer Nonlinear Programs, different convex relaxations can be obtained for multilinear terms by applying associativity in different ways. The two groupings ((x1x2)x3)x4 and (x1x2x3)x4 of a quadrilinear term, for example, give rise to two different convex relaxations. In [6] we prove that having fewer groupings of longer terms yields tighter convex relaxations. In this paper we give an alternative proof of the same fact and perform a computational study to assess the impact of the tightened convex relaxation in a spatial Branch-and-Bound setting
A numerical computation on the structure of the roots of <mml:math altimg="si16.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>q</mml:mi></mml:math>-extension of Genocchi polynomials
Bilateral teleoperation for linear force sensorless 3D robots
It is well known that for bilateral teleoperation, force feedback information is needed. In this paper, we propose a control approach for bilateral teleoperation with uncertainties in the model of the slave robot and which does not use force sensors for haptic feedback. The controller design is based on a cyclic switching algorithm. In the first phase of the cyclic algorithm, we estimate the environmental force acting on the slave robot and in the second phase a tracking controller ensures that the position of the slave robot is tracking the position of the master robot. A stability analysis of the overall closed-loop system is presented and the approach is illustrated by means of an example
microRNAs expression correlates with levels of APP, DYRK1A, hyperphosphorylated Tau and BDNF in the hippocampus of a mouse model for Down syndrome during ageing
On convex relaxations of quadrilinear terms
Quadrilinear, Trilinear, Bilinear, Convex relaxation, Reformulation, Global optimization, Spatial branch and bound, MINLP,