Abstract Let K be a simplicial complex on vertex set V . is called d - Leray if the homology groups of any induced subcomplex are trivial in dimensions and higher. collapsible it can reduced to void by sequentially removing simplex size at most that contained unique maximal face. Motivated results Eckhoff Montejano Oliveros “tolerant” versions Helly’s theorem, we define t tolerance , $${\mathca...

This paper present the investigation of possible causes incessant road failure associated with subgrade soils Niger delta using mineralogical and geotechnical properties assessment. Geotechnical revealed clayey sand form bulk composed generally fine to medium grains low intermediate plasticity. Based on AASHTO soil classifies as A-2 A-6 granular being dominant. The average values obtained for C...

We show a novel design method of one-DOF deployable mechanism based on a space curve, through creating a curved folding and discretizing the folding into rigid origami. By interpreting constant angle curved folding as a flat-foldable quadrilateral mesh origami, we design novel irregular tessellated, cylindrical, and cellular flatly collapsible structures, whose behavior is easily controlled by ...

We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere. The proof uses the properties of tree models of chordal graphs.

A self-retaining retractor has been designed to enable one surgeon to perform cholecystectomy and exploration of the bile duct with a minimum of assistance. The instrument consists of a horseshoe shaped collapsible frame and four specially designed blades. It is ideally suited for a right subcostal or a transverse incision. Adjustment and removal for performing on-table cholangiography and reap...

This chapter gives an overview of the main physiological applications of collapsible tube flows and reviews the major theoretical and computational developments of the past twenty-five years, ranging from lumped-parameter models to three-dimensional Navier–Stokes simulations. We also discuss some of the significant questions that, despite substantial progress, still remain open. 16 M. HEIL AND ...

We present extremal constructions connected with the property of simplicial collapsibility. (1) For each d ≥ 2, there are collapsible (and shellable) simplicial d-complexes with only one free face. Also, there are non-evasive d-complexes with only two free faces. (Both results are optimal in all dimensions.) (2) Optimal discrete Morse vectors need not be unique. We explicitly construct a contra...