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Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Dupin Submanifolds In Lie Sphere Geometry (Updated Version), Thomas E. Cecil, Shiing-Shen Chern
Dupin Submanifolds In Lie Sphere Geometry (Updated Version), Thomas E. Cecil, Shiing-Shen Chern
Mathematics Department Faculty Scholarship
A hypersurface Mn-1 in Euclidean space En is proper Dupin if the number of distinct principal curvatures is constant on Mn-1, and each principal curvature function is constant along each leaf of its principal foliation. This paper was originally published in 1989 (see Comments below), and it develops a method for the local study of proper Dupin hypersurfaces in the context of Lie sphere geometry using moving frames. This method has been effective in obtaining several classification theorems of proper Dupin hypersurfaces since that time. This updated version of the paper contains the original exposition together …
A Primer On Laplacian Dynamics In Directed Graphs, J. J. P. Veerman, R. Lyons
A Primer On Laplacian Dynamics In Directed Graphs, J. J. P. Veerman, R. Lyons
Mathematics and Statistics Faculty Publications and Presentations
We analyze the asymptotic behavior of general first order Laplacian processes on digraphs. The most important ones of these are diffusion and consensus with both continuous and discrete time. We treat diffusion and consensus as dual processes. This is the first complete exposition of this material in a single work.
A Normal Form For Words In The Temperley-Lieb Algebra And The Artin Braid Group On Three Strands, Jack Hartsell
A Normal Form For Words In The Temperley-Lieb Algebra And The Artin Braid Group On Three Strands, Jack Hartsell
Electronic Theses and Dissertations
The motivation for this thesis is the computer-assisted calculation of the Jones poly- nomial from braid words in the Artin braid group on three strands, denoted B3. The method used for calculation of the Jones polynomial is the original method that was created when the Jones polynomial was first discovered by Vaughan Jones in 1984. This method utilizes the Temperley-Lieb algebra, and in our case the Temperley-Lieb Algebra on three strands, denoted A3, thus generalizations about A3 that assist with the process of calculation are pursued.
Hyperplanes Equipartition With Cascading Makeev, Jialin Zhang
Hyperplanes Equipartition With Cascading Makeev, Jialin Zhang
Senior Projects Spring 2018
Given a finite number of masses in the Euclidean space, one could ask is it possible to equipartition these masses into equal parts. Fixing the collection of masses, and the amount of hyperplanes, the equipartition-ability depends on the dimension, and there exists a dimension of such equipartition is possible. In this paper, topology and combinatorics method are used for estimating the lower bound and upper bound of the dimension. In particular, we are looking equipartition problem together with Cascading Makeev Constrain.
Concerning The Construction Of Four-Bar Linkages And Their Topological Configuration-Spaces, Peter K. Servatius
Concerning The Construction Of Four-Bar Linkages And Their Topological Configuration-Spaces, Peter K. Servatius
Senior Projects Spring 2018
For a given linkage with one degree of freedom we can analyze the coupler curve created by any selected tracer point in relation to a driver link. The Watt Engine is a four-bar linkage constructed such that the tracer point draws an approximate straight line along a section of the coupler curve. We will explore the family of linkages that are created using Watt's parameters, along with linkages designed by other inventors; looking at methodologies of creating a linkage and the defining what we mean by approximate straight-line motion. Ultimately we will be creating our own linkage using what we …
A Single Shape From Multiple Cues: How Local And Global Information Organizes Shape Inference, Benjamin Kunsberg, Steven W. Zucker
A Single Shape From Multiple Cues: How Local And Global Information Organizes Shape Inference, Benjamin Kunsberg, Steven W. Zucker
MODVIS Workshop
No abstract provided.
Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek
Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek
Mathematics and Statistics Faculty Publications and Presentations
We consider an asymptotic stability of a circular system where the coupling Laplacians are different for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as confirmed by simulations in the paper, our results have an application also …
Preservation Of A Convergence Of A Sequence To A Set, Akira Iwasa, Masaru Kada, Shizuo Kamo
Preservation Of A Convergence Of A Sequence To A Set, Akira Iwasa, Masaru Kada, Shizuo Kamo
Faculty Publications
We say that a sequence of points converges to a set if every open set containing the set contains all but finitely many terms of the sequence. We investigate preservation of convergence of a sequence to a set in forcing extensions.
On The Geometry And Topology Of Moduli Spaces Of Multi-Polygonal Linkages, Michael Edward Holcomb
On The Geometry And Topology Of Moduli Spaces Of Multi-Polygonal Linkages, Michael Edward Holcomb
LSU Doctoral Dissertations
The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multi-polygonal linkages are studied. These spaces turn out to be compact …
Semicontinuity Of Dimension And Measure For Locally Scaling Fractals, L. B. Jonker, J. J. P. Veerman
Semicontinuity Of Dimension And Measure For Locally Scaling Fractals, L. B. Jonker, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
The basic question of this paper is: If you consider two iterated function systems close to one another in an appropriate topology, are the dimensions of their respective invariant sets close to one another? It is well-known that the Hausdorff dimension (and Lebesgue measure) of the invariant set do not depend continuously on the iterated function system. Our main result is that (with a restriction on the ‘non-conformality’ of the transformations) the Hausdorff dimension is a lower semi-continuous function in the C1- topology of the transformations of the iterated function system. The same question is raised of the …
On 2-Reptiles In The Plane, Sze-Man Ngai, Víctor F. Sirvent, J. J. P. Veerman, Yang Wang
On 2-Reptiles In The Plane, Sze-Man Ngai, Víctor F. Sirvent, J. J. P. Veerman, Yang Wang
Mathematics and Statistics Faculty Publications and Presentations
We classify all rational 2-reptiles in the plane. We also establish properties concerning rational reptiles in the plane in general.
The Cantor Set, Sam Alfred Pearsall
Intersecting Self-Similar Cantor Sets, J. J. P. Veerman
Intersecting Self-Similar Cantor Sets, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We define a self-similar set as the (unique) invariant set of an iterated function system of certain contracting affine functions. A topology on them is obtained (essentially) by inducing the C 1- topology of the function space. We prove that the measure function is upper semi-continuous and give examples of discontinuities. We also show that the dimension is not upper semicontinuous. We exhibit a class of examples of self-similar sets of positive measure containing an open set. If C 1 and C 2 are two self-similar sets C 1 and C 2 such that the sum of their dimensions …