Yadin David, EdD, PE, CCE, Matthew Baretich, PE PhD, William A. Hyman, PE, ScD, Wayne Morse, and James O. Wear, MSBME, CCE, FACCE From the Biomedical Engineering Consultants, LLC, Houston, Texas (Dr David); Baretich Engineering, Inc, Fort Collins, Colorado (Dr Baretich); Department of Biomedical Engineering, Texas A&M University, College Station (Dr Hyman); Morse Medical, Linc Facility Services...

In this paper, we reveal a remarkable connection between the Thue-Morse sequence and the Koch snowflake. Using turtle geometry and polygon maps, we realize the Thue-Morse sequence as the limit of polygonal curves in the plane. We then prove that a sequence of such curves converges to the Koch snowflake in the Hausdorff metric. In the final section we consider generalized Thue-Morse sequences an...

In an earlier work, we constructed the almost strict Morse n-category X which extends Cohen & Jones & Segal’s flow category. In this article, we define two other almost strict n-categories V and W where V is based on homomorphisms between real vector spaces and W consists of tuples of positive integers. The Morse index and the dimension of the Morse moduli spaces give rise to almost strict n-ca...

In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph theoretical operations. We use iterated Morse decomposition, which allows us to sidetrack many problems related to the standard discrete Morse theory. In particu...

The goal of this paper is to extend to infinite graphs the knownMorse inequalities for discrete Morse functions proved by R. Forman in the finite case. In order to get this result we shall use a special kind of infinite subgraphs on which a discrete Morse function is monotonous, namely, decreasing rays. In addition, we shall use this result to characterize infinite graphs by the number of criti...

We remark that the power diagrams from computer science are the spines of amoebas in algebraic geometry, or the hypersurfaces in tropical geometry. Our concept of a Morse poset generalizes to power diagrams. We show that there exists a discrete Morse function on the coherent triangulation, dual to the power diagram, such that its critical set equals the Morse poset of the power diagram. In the ...

Background: Despite progression of knowledge of nursing researcher about importance of psychometric principles of instruments of studies but it seems that this subject is not used correctly in nursing studies. This study is designed to critically assess the validity and reliability of instruments applied in studies published in Iranian nursing journals Methods: This study is a critical review o...

In the case of smooth manifolds, we use Forman’s discrete Morse theory to realize combinatorially any Thom-Smale complex coming from a smooth Morse function by a couple triangulation-discrete Morse function. As an application, we prove that any Euler structure on a smooth oriented closed 3-manifold has a particular realization by a complete matching on the Hasse diagram of a triangulation of th...

Bond-Order Conservation-Morse Potential (BOC-MP) method is used to carry out the calculationon the CO2+ H20 system. One of the best catalysts for methanol synthesis in catalytic reductionof CO2 with H2O is Cu/ZnO/A1203 whose surface is supported by with some amount of Pd orGa. Reduction of CO2 with H20 on Cu will result in methanol formation; while on Ni will lead tomethane formation. In the me...