Recently, we introduced a new class of symmetry algebras, called satellite algebras, which connect with one another wavefunctions belonging to different potentials of a given family, and corresponding to different energy eigenvalues. Here the role of the factorization method in the construction of such algebras is investigated. A general procedure for determining an so(2,2) or so(2,1) satellite...

In this paper we use the nudged elastic band technique from computational chemistry to investigate sampled highdimensional data from a natural image database. We randomly sample 8×8 and 9×9 high-contrast patches of natural images and create a density estimator believed as a Morse function. By the Morse function we build one-dimensional cell complexes from the sampled data. Using one-dimensional...

Sir—Several risk factors associated with falls in hospitalised patients have been identified [1, 2]. Although a substantial number of assessment instruments for identifying hospitalised patients at risk of falling exists [3], their generalisability is limited [4] because only a few [2, 5] have been tested in settings other than those in which they were originally developed. The Morse Fall Scale...

Samples of leaf litter were collected from 22 woodland sites throughout Prince Edward Island, Canada. Eighty-two specimens belonging to 15 species litter-dwelling land snails recovered 20 the samples. One-third species— Carychium exile H.C. Lea, 1842, Helicodiscus shimeki Hubricht, 1982, Strobilops labyrinthicus (Say, 1817), Perpolita binneyana (Morse, 1864), and Striatura ferrea Morse, 1864—we...

Segmentation of 3D data (some time 4D data) is a very challenging problem in applications exploiting Marine GIS data. To tackle this problem, this paper proposes a topological approach based on the Digital Morse theory which is a kind of Discrete Morse theory to high dimension Grid points. The essence of the approach concerns detecting critical points in the High dimension Data, which represent...

Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifold. From this construction we define a sequence of symplectic invariants classifying the isotopy classes of Lagrangian spheres in a symplectic 4-manifold.

In this report, we discuss two papers that deal with computing Morse function on triangulated manifolds. Axen [1] gives an algorithm for computing Morse function on a triangulated manifold of arbitrary dimension but it not practical because of its space requirement. Hence, he describes an algorithm for computing critical points and their Morse indices for a 2-manifold. Edelsbrunner et al. [2] d...

We define and study Vassiliev invariants for (long) Morse knots. It is shown that there are Vassiliev invariants which can distinguish some topologically equivalent Morse knots. In particular, there is an invariant of order 3 for Morse knots with one maximum that distinguishes two different representations of the figure eight knot. We also present the results of computer calculations for some i...

We consider the problem of prescribing conformally scalar curvature on compact manifolds positive Yamabe class in dimension . prove new existence results using Morse theory and some analysis blowing-up solutions under suitable pinching conditions function. also provide nonexistence showing sharpness our assumptions, both terms structure prescribed © 2021 Wiley Periodicals LLC.

The essential structural information of discrete Morse functions is captured by so-called Morse matchings. We show that computing optimal Morse matchings is NP-hard and give an integer programming formulation for the problem. Then we present first polyhedral results for the corresponding polytope and report on some preliminary computational results.