Tverberg Type Partitions: Sub-Regular And Elliptical Polygons,
2021
Bard College
Tverberg Type Partitions: Sub-Regular And Elliptical Polygons, Tobias Golz Timofeyev
Senior Projects Spring 2021
Tverberg's theorem states that given a set S of T(r,d)=(r-1)(d+1)+1 points in Rd, there exists a partition of S into r subsets whose convex hulls intersect. A feature of Tverberg's theorem is that T(r,d) is tight, so in this senior project we investigate Tverberg-type results when |S|. We found that in R2, given a set S of T(r,2)-2=3r-4 points, and assuming r=r1 r2, there exists a partition of S into r sets such that when grouped into r1 collections of r2 sets, the convex hulls of each collection overlap, and we …
Dimentia: Footnotes Of Time,
2021
Bard College
Dimentia: Footnotes Of Time, Zachary Hait
Senior Projects Spring 2021
Time from the physicist's perspective is not inclusive of our lived experience of time; time from the philosopher's perspective is not mathematically engaged, in fact Henri Bergson asserted explicitly that time could not be mathematically engaged whatsoever. What follows is a mathematical engagement of time that is inclusive of our lived experiences, requiring the tools of storytelling.
Analysis, Constructions And Diagrams In Classical Geometry,
2021
Chapman University
Analysis, Constructions And Diagrams In Classical Geometry, Marco Panza
MPP Published Research
Greek ancient and early modern geometry necessarily uses diagrams. Among other things, these enter geometrical analysis. The paper distinguishes two sorts of geometrical analysis and shows that in one of them, dubbed “intra-confgurational” analysis, some diagrams necessarily enter as outcomes of a purely material gesture, namely not as result of a codifed constructive procedure, but as result of a free-hand drawing.
Diagrams In Intra-Configurational Analysis,
2021
Chapman University
Diagrams In Intra-Configurational Analysis, Marco Panza, Gianluca Longa
MPP Published Research
In this paper we would like to attempt to shed some light on the way in which diagrams enter into the practice of ancient Greek geometrical analysis. To this end, we will first distinguish two main forms of this practice, i.e., trans-configurational and intra-configurational. We will then argue that, while in the former diagrams enter in the proof essentially in the same way (mutatis mutandis) they enter in canonical synthetic demonstrations, in the latter, they take part in the analytic argument in a specific way, which has no correlation in other aspects of classical geometry. In intra-configurational analysis, diagrams represent …
The Complex Propagation Of Light Explained Visually: How To Make A Hologram,
2021
Bard College
The Complex Propagation Of Light Explained Visually: How To Make A Hologram, Bruno Ray Becher
Senior Projects Spring 2021
The complexity of light’s wave nature is shown in the paths that light takes. In this project I will show several useful ways to imagine and predict how light will travel from one place to another. Once light is produced it does not immediately fill a room, instead it undulates through free space as if the space itself was a fluid. Once we understand the way light flows and interacts with its environment not only can we predict and control its shape with a hologram, but also discover clues which give secrets about where the light has been. Telescopes and …
Lagrangian Cobordisms Of Legendrian Pretzel Knots With Maximal Thurston-Bennequin Number,
2021
Bard College
Lagrangian Cobordisms Of Legendrian Pretzel Knots With Maximal Thurston-Bennequin Number, Raphael Barish Walker
Senior Projects Spring 2021
In the study of Legendrian knots, which are smoothly embedded circles constrained by a differential geometric condition, an actively-studied problem is to find conditions for the existence of Lagrangian cobordisms, which are Lagrangian surfaces whose slices specific Legendrian knots at either end. Any topological knot has infinitely many distinct Legendrian representatives, which are partially distinguished by the Thurston-Bennequin number tb, an integer invariant of Legendrian isotopy which is bounded above. We demonstrate a family of knots where each has a maximal-tb representative K admitting a Lagrangian cobordism from a stabilized Legendrian unknot, a property which guarantees the existence of a …
Cheeger Constants Of Two Related Hyperbolic Riemann Surfaces,
2021
Eastern Illinois University
Cheeger Constants Of Two Related Hyperbolic Riemann Surfaces, Ronald E. Hoagland
Masters Theses
This thesis concerns the study of the Cheeger constant of two related hyperbolic Riemann surfaces. The first surface R is formed by taking the quotient U2/Γ(4), where U2 is the upper half-plane model of the hyperbolic plane and Γ(4) is a congruence subgroup of PSL2(Z), an isometry group of U2 . This quotient is shown to form a Riemann surface which is constructed by gluing sides of a fundamental domain for Γ(4) together according to certain specified side pairings. To form the related Riemann surface R' , we follow a similar procedure, this time taking the …
Formal Power Series Approach To Nonlinear Systems With Static Output Feedback,
2021
Old Dominion University
Formal Power Series Approach To Nonlinear Systems With Static Output Feedback, G.S. Venkatesh, W. Steven Gray
Electrical & Computer Engineering Faculty Publications
The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and static output feedback is applied. The first step is to reconsider the so called Wiener-Fliess connection consisting of a Chen-Fliess series followed by a memoryless function. Of particular importance will be the contractive nature of this map, which is needed to show that the closed-loop system has a Chen-Fliess series representation. To explicitly compute the generating series, two Hopf algebras are needed, the existing output feedback Hopf algebra used to describe dynamic output …
Filaments, Fibers, And Foliations In Frustrated Soft Materials,
2020
University of Massachusetts Amherst
Filaments, Fibers, And Foliations In Frustrated Soft Materials, Daria Atkinson
Doctoral Dissertations
Assemblies of one-dimensional filaments appear in a wide range of physical systems: from biopolymer bundles, columnar liquid crystals, and superconductor vortex arrays; to familiar macroscopic materials, like ropes, cables, and textiles. Interactions between the constituent filaments in such systems are most sensitive to the distance of closest approach between the central curves which approximate their configuration, subjecting these distinct assemblies to common geometric constraints. Dual to strong dependence of inter-filament interactions on changes in the distance of closest approach is their relative insensitivity to reptations, translations along the filament backbone. In this dissertation, after briefly reviewing the mechanics and …
Modeling Residence Time Distribution Of Chromatographic Perfusion Resin For Large Biopharmaceutical Molecules: A Computational Fluid Dynamic Study,
2020
Claremont Colleges
Modeling Residence Time Distribution Of Chromatographic Perfusion Resin For Large Biopharmaceutical Molecules: A Computational Fluid Dynamic Study, Kevin Vehar
KGI Theses and Dissertations
The need for production processes of large biotherapeutic particles, such as virus-based particles and extracellular vesicles, has risen due to increased demand in the development of vaccinations, gene therapies, and cancer treatments. Liquid chromatography plays a significant role in the purification process and is routinely used with therapeutic protein production. However, performance with larger macromolecules is often inconsistent, and parameter estimation for process development can be extremely time- and resource-intensive. This thesis aimed to utilize advances in computational fluid dynamic (CFD) modeling to generate a first-principle model of the chromatographic process while minimizing model parameter estimation's physical resource demand. Specifically, …
Generalized Smarandache Curves Of Spacelike And Equiform Spacelike Curves Via Timelike Second Binormal In 𝕽𝟏 𝟒,
2020
Beni-Suef University
Generalized Smarandache Curves Of Spacelike And Equiform Spacelike Curves Via Timelike Second Binormal In 𝕽𝟏 𝟒, Emad Solouma
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we investigate spacelike Smarandache curves recording to the Frenet and the equiform Frenet frame of spacelike base curve with timelike second binormal vector in fourdimensional Minkowski space. Also, we compute the formulas of Frenet and equiform Frenet apparatus recording to the base curve. Furthermore, we give the geometric properties to these curves when is general helix.
Dynamic Neuromechanical Sets For Locomotion,
2020
University Of Tennessee Knoxville
Dynamic Neuromechanical Sets For Locomotion, Aravind Sundararajan
Doctoral Dissertations
Most biological systems employ multiple redundant actuators, which is a complicated problem of controls and analysis. Unless assumptions about how the brain and body work together, and assumptions about how the body prioritizes tasks are applied, it is not possible to find the actuator controls. The purpose of this research is to develop computational tools for the analysis of arbitrary musculoskeletal models that employ redundant actuators. Instead of relying primarily on optimization frameworks and numerical methods or task prioritization schemes used typically in biomechanics to find a singular solution for actuator controls, tools for feasible sets analysis are instead developed …
Classification Of Some First Order Functional Differential Equations With Constant Coefficients To Solvable Lie Algebras,
2020
St. Xavier’s College, Mapusa-Goa
Classification Of Some First Order Functional Differential Equations With Constant Coefficients To Solvable Lie Algebras, J. Z. Lobo, Y. S. Valaulikar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we shall apply symmetry analysis to some first order functional differential equations with constant coefficients. The approach used in this paper accounts for obtaining the inverse of the classification. We define the standard Lie bracket and make a complete classification of some first order linear functional differential equations with constant coefficients to solvable Lie algebras.We also classify some nonlinear functional differential equations with constant coefficients to solvable Lie algebras.
On Double Fuzzy M-Open Mappings And Double Fuzzy M-Closed Mappings,
2020
Government Arts College (Autonomous), J. J. College of Arts and Science (Autonomous)
On Double Fuzzy M-Open Mappings And Double Fuzzy M-Closed Mappings, J. Sathiyaraj, A. Vadivel, O. U. Maheshwari
Applications and Applied Mathematics: An International Journal (AAM)
We introduce and investigate some new class of mappings called double fuzzy M-open map and double fuzzy M-closed map in double fuzzy topological spaces. Also, some of their fundamental properties are studied. Moreover, we investigate the relationships between double fuzzy open, double fuzzy θ semiopen, double fuzzy δ preopen, double fuzzy M open and double fuzzy e open and their respective closed mappings.
Dual Pole Indicatrix Curve And Surface,
2020
University of Ordu
Dual Pole Indicatrix Curve And Surface, Süleyman Senyurt, Abdussamet Çalıskan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the vectorial moment vector of the unit Darboux vector, which consists of the motion of the Frenet vectors on any curve, is reexpressed in the form of Frenet vectors. According to the new version of this vector, the parametric equation of the ruled surface corresponding to the unit dual pole indicatrix curve is given. The integral invariants of this surface are rederived and illustrated by presenting with examples.
Nested Links, Linking Matrices, And Crushtaceans,
2020
Scripps College
Nested Links, Linking Matrices, And Crushtaceans, Madeline Brown
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Application Of Tda Mapper To Water Data And Bird Data,
2020
University of Wisconsin - La Crosse
Application Of Tda Mapper To Water Data And Bird Data, Wako Bungula
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Configuration Spaces For The Working Undergraduate,
2020
Reed College
Configuration Spaces For The Working Undergraduate, Lucas Williams
Rose-Hulman Undergraduate Mathematics Journal
Configuration spaces form a rich class of topological objects which are not usually presented to an undergraduate audience. Our aim is to present configuration spaces in a manner accessible to the advanced undergraduate. We begin with a slight introduction to the topic before giving necessary background on algebraic topology. We then discuss configuration spaces of the euclidean plane and the braid groups they give rise to. Lastly, we discuss configuration spaces of graphs and the various techniques which have been developed to pursue their study.
Perceiving Mathematics And Art,
2020
University of Arkansas, Fayetteville
Perceiving Mathematics And Art, Edmund Harriss
Mic Lectures
Mathematics and art provide powerful lenses to perceive and understand the world, part of an ancient tradition whether it starts in the South Pacific with tapa cloth and wave maps for navigation or in Iceland with knitting patterns and sunstones. Edmund Harriss, an artist and assistant clinical professor of mathematics in the Fulbright College of Arts and Sciences, explores these connections in his Honors College Mic lecture.
Dupin Submanifolds In Lie Sphere Geometry (Updated Version),
2020
College of the Holy Cross
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 …
