<div dir="ltr"><span style="font-size:12.8000001907349px">Degerli Liste uyeleri</span><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px">04 Agustos 2015 saat 16.00 da <b>Bursa Tekni Universitesi'nden Ayse BORAT</b></div><div style="font-size:12.8000001907349px"><span style="font-size:12.8000001907349px"><b><br></b></span></div><div style="font-size:12.8000001907349px"><span style="font-size:12.8000001907349px"><b>"Higher dimensional motion planners for F(R^n,k)"</b> adlı bir konuşma verecektir </span>Sizleri konusmalara bekliyoruz.</div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px">Ekte konusmanin ozeti sunulmustur.</div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px">Selamlar ve saygilar</div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px">cenap ozel</div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px">HIGHER DIMENSIONAL MOTION PLANNERS FOR F(R
n, k) </div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px">AYS¸E BORAT </div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px">Abstract
Two of the main problems in Topological Robotics are to compute the topological
complexity and to give a motion planner of a given space. </div><div style="font-size:12.8000001907349px">The importance of motion
planners follow not only from the fact that they give explicit motion planning
algorithms but also from the fact that such algorithms can be used to compute
topological complexity. </div><div style="font-size:12.8000001907349px">In this talk, we will introduce m-dimensional motion planners for the spaces
F(R
n, k) = {(x1, x2, · · · , xk) ∈ R
n|xi ̸= xj}. </div><div style="font-size:12.8000001907349px">This construction of the m-dimensional
motion planners tells that that TCm(F(R
n, k)) ≤ m(k −1)+ 1. </div><div style="font-size:12.8000001907349px">On the other hand,
regarding Theorem 1.3 in [1], this result is optimal when n is odd, but it is 1 unit
away from being optimal when n is even. </div><div style="font-size:12.8000001907349px"><br></div><div style="font-size:12.8000001907349px">References </div><div style="font-size:12.8000001907349px">[1] J. Gonzalez, M. Grant, Sequential motion planning of non-colliding particles in Euclidean
spaces (accepted for publication in the Proceedings of the American Mathematical Society). </div><div style="font-size:12.8000001907349px">[2] H. Mas-Ku, E. Torres-Giese, Motion planning algorithm for configuration spaces, Bol. Soc.
Mat. Mex., DOI: DOI 10.1007/s40590-014-0046-2. <br></div></div>