http://www.bibsonomy.org/burst/user/dmartins/aBibSonomy BuRST Feed for /user/dmartins/a2008-08-21T05:13:02+02:00robotica-bibhttp://www.bibsonomy.org/bibtex/2c594c22429cc663507654c6665223822/dmartinsdmartins2008-03-02T02:12:02+01:00function; data structure optimization; ray rigidity; of molecule; penalty a distances; X interatomic intermolecular <span style="color:#555555;">Bruce <a href="http://www.bibsonomy.org/author/Hendrickson">Hendrickson</a> </span><em>SIAM J. Optim.</em><em>5(4):835-857</em>(<em>1995</em>)Sun Mar 02 02:12:02 CET 2008SIAM J. Optim.4835-857The molecule problem: Exploiting structure in global optimization.51995function; data structure optimization; ray rigidity; of molecule; penalty a distances; X interatomic intermolecular Discusses the problem of determining the structure of a molecule when some (but not all) of the interatomic distances are known, this can be, for example, from nuclear magnetic resonance data. The concept of rigidity is introduced which is closely related to the complexity of the corresponding graph; and a penalty function that penalizes inconsistencies in the data which are found to occur and produces a most probable result. An algorithm, the ABBIE ``divide and conquer'' algorithm, uses various tricks to reduce the size of the graph corresponding to the intermolecular distances that are known. Various details of the optimization process are related to recent results in graph theory.\par The reviewer notes: The problem is similar to the old one of determining a structure from X ray data. Obviously, systematic graph theoretical studies will help in both problems. robotica-bibhttp://www.bibsonomy.org/bibtex/2b573401440f057fa42baa50802c5e30c/dmartinsdmartins2008-03-02T02:12:02+01:00of a the groups linear space homotopy convex simplexwise 2-disk homeomorphisms <span style="color:#555555;">Ethan D. <a href="http://www.bibsonomy.org/author/Bloch">Bloch</a> and Robert <a href="http://www.bibsonomy.org/author/Connelly">Connelly</a> and David W. <a href="http://www.bibsonomy.org/author/Henderson">Henderson</a> </span>(<em>1984</em>)Sun Mar 02 02:12:02 CET 2008161-175The space of simplexwise linear homeomorphisms of a convex 2-disk.231984of a the groups linear space homotopy convex simplexwise 2-disk homeomorphisms Let $K\sp n$ be a finite simplicial complex whose underlying space $\vert K\sp n\vert$ is a combinatorial n-dimensional disk in ${\bbfR}\sp n$. Let $L(K\sp n)$ be the space, with the compact open topology, of all the homeomorphisms of $\vert K\sp n\vert$ that are affinely linear on each simplex of $K\sp n$ and the identity on B$d(\vert K\sp n\vert)$. Interest in the homotopy properties of the space $L(K\sp n)$ was first initiated with the smoothing theory. Conditions on the existence and uniqueness of differentiable structures on a combinatorial manifold can be formulated in terms of the homotopy groups of this and some related spaces [see {\it S. S. Cairns}, Ann. Math., II. Ser. 45, 207-217 (1944); {\it R. Thom}, Proc. Int. Congr. Math. 1958, 248-255 (1960; Zbl 137, 426) and {\it N. H. Kuiper}, Diff. and Comb. Topology, 3-22 (1965; Zbl 171, 444)]. Recently, there has been a revival of interest in these spaces due to their connection to the Smale conjecture that the space of all the orientation preserving diffeomorphisms of $S\sp 3$ is of the same homotopy type as the special orthogonal group SO(4) [see {\it A. E. Hatcher}, Proc. Int. Congr. Math., Helsinki 1978, Vol. 2, 463-468 (1980; Zbl 455.57014)]. \par In the present paper, the authors prove that when $n=2$, the space $L(K\sp n)$ is homeomorphic to the Euclidean space ${\bbfR}\sp{2k}$, where k is the number of interior vertices (i.e., vertices not lying on B$d(\vert K\sp n\vert))$ of $K\sp n$. This is about the best possible result one could obtain for the two-dimensional case and is a great improvement of the previous results of Cairns that $\pi\sb 0(L(K\sp 2))=0$ and of the reviewer that $\pi\sb 1(L(K\sp 2))=0$. As a consequence of the present result, the following theorem of Smale can be derived as a corollary: the space of diffeomorphisms of a smooth 2-disk, fixed on the boundary, is contractible. The proof of the present result involves some difficult and ingenious geometric arguments.robotica-bibhttp://www.bibsonomy.org/bibtex/24cfb3db1b445c824723b35c0a7c49ec6/dmartinsdmartins2008-03-02T02:12:02+01:00a {flexible derivation of algebra} octahedron; polyhedra; polynomial; computer volume; <span style="color:#555555;">A.V. <a href="http://www.bibsonomy.org/author/Astrelin">Astrelin</a> and I.Kh. <a href="http://www.bibsonomy.org/author/Sabitov">Sabitov</a> </span><em>Russ. Math. Surv.</em><em>50(5):1085-1087</em>(<em>1995</em>)Sun Mar 02 02:12:02 CET 2008Russ. Math. Surv.51085-1087{A minimal-degree polynomial for determining the volume of an octahedron from its metric.} 501995a {flexible derivation of algebra} octahedron; polyhedra; polynomial; computer volume; {This note discusses the derivation of a polynomial for the volume of a octahedron, when the edge lengths of it are given. It is known that the volume of a flexible polyhedron with those edge lengths doesn't depend on the realization. For octahedra there are 8 realizations, and therefore the polynomial that describes the volume must have degree 8. The derivation of this polynomial is done by using a computer algebra system.}