On The Geometry Of Virtual Knots,
2012
Boise State University
On The Geometry Of Virtual Knots, Rachel Elizabeth Byrd
Boise State University Theses and Dissertations
The Dehn complex of prime, alternating virtual links has been shown to be non-positively curved in the paper "Generalized knot complements and some aspherical ribbon disc complements" by J. Harlander and S. Rosebrock (2003) [7]. This thesis investigates the geometry of an arbitrary alternating virtual link. A method is constructed for which the Dehn complex of any alternating virtual link may be decomposed into Dehn complexes with non-positive curvature. We further study the relationship between the Dehn space and Wirtinger space, and we relate their fundamental groups using generating curves on surfaces. We conclude with interesting examples of Dehn complexes …
Session D-3: Discrete Mathematics: A Great Curriculum Connector,
2012
Illinois Mathematics and Science Academy
Session D-3: Discrete Mathematics: A Great Curriculum Connector, Donald Porzio
Professional Learning Day
Many topics that fall under the umbrella of Discrete Mathematics cut across the traditional high school curriculum areas of algebra, geometry, and pre-calculus. Come try some classroom-ready hands-on Discrete Mathematics activities that illustrate the true interconnectedness of mathematics.
Logarithmic Spirals And Projective Geometry In M.C. Escher's "Path Of Life Iii",
2012
Bridgewater State University
Logarithmic Spirals And Projective Geometry In M.C. Escher's "Path Of Life Iii", Heidi Burgiel, Matthew Salomone
Journal of Humanistic Mathematics
M.C. Escher's use of dilation symmetry in Path of Life III gives rise to a pattern of logarithmic spirals and an oddly ambiguous sense of depth.
The Seaborgium Chemical Table,
2012
Butler University
The Seaborgium Chemical Table, Jeremiah Farrell
Scholarship and Professional Work - LAS
The diagram is an example of a connected, cubic graph with its ten nodes labelled with the letters of SEABORGIUM, chemical element 106. Connected means it is in one piece and cubic means that each node has exactly three edges on it.
Integral Conditions For The Vanishing Of The Cohomology Of Open Sets In Cn,
2012
Politecnico di Milano
Integral Conditions For The Vanishing Of The Cohomology Of Open Sets In Cn, Fabrizio Colombo, M. E. Luna-Elizarrarás, Irene Sabadini, M. Shapiro, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we develop and extend some techniques introduced in [1] to find integral conditions for the vanishing of the cohomology of open bounded sets in Cn with values in the sheaf of holomorphic functions.
Connected Inverse Limits With A Set-Valued Function,
2012
University of Richmond
Connected Inverse Limits With A Set-Valued Function, Van C. Nall
Department of Math & Statistics Faculty Publications
In this paper we provide techniques to build set-valued functions whose resulting inverse limits will be connected.
Π/2-Angle Yao Graphs Are Spanners,
2012
Carleton University
Π/2-Angle Yao Graphs Are Spanners, Prosenjit Bose, Mirela Damian, Karim Douïeb, Joseph O'Rourke, Ben Seamone, Michiel Smid, Stefanie Wuhrer
Computer Science: Faculty Publications
We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor 8(29+23√ 2). Enroute to this, we also show that the Yao graph Y∞4 in the L∞ metric is a planar spanner with stretch factor 8.
Upper Bounds In The Ohtsuki-Riley-Sakuma Partial Order On 2-Bridge Knots,
2012
University of California, Los Angeles
Upper Bounds In The Ohtsuki-Riley-Sakuma Partial Order On 2-Bridge Knots, Scott M. Garrabrant, Jim Hoste, Patrick D. Shanahan
Mathematics, Statistics and Data Science Faculty Works
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} has an upper bound. As an application we answer a question of Suzuki, showing that there is no upper bound for the set consisting of the trefoil and figure-eight knots.
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization,
2012
University of Houston
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization, Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg
Mathematics, Statistics and Data Science Faculty Works
The purpose of the present article is to demonstrate that by adopting a unifying differential geometric perspective on certain themes in physics one reaps remarkable new dividends in both microscopic and macroscopic domains. By replacing algebraic objects by tensor-transforming objects and introducing methods from the theory of differentiable manifolds at a very fundamental level we obtain a Kottler-Cartan metric-independent general invariance of the Maxwell field, which in turn makes for a global quantum superstructure for Gauss-Amp`ere and Aharonov-Bohm “quantum integrals.” Beyond this, our approach shows that postulating a Riemannian metric at the quantum level is an unnecessary concept and our …
Spatial Graphs With Local Knots,
2012
Loyola Marymount University
Spatial Graphs With Local Knots, Erica Flapan, Blake Mellor, Ramin Naimi
Mathematics, Statistics and Data Science Faculty Works
It is shown that for any locally knotted edge of a 3-connected graph in S3, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in S3.
Odd Or Even: Uncovering Parity Of Rank In A Family Of Rational Elliptic Curves,
2012
Colby College
Odd Or Even: Uncovering Parity Of Rank In A Family Of Rational Elliptic Curves, Anika Lindemann
Honors Theses
Puzzled by equations in multiple variables for centuries, mathematicians have made relatively few strides in solving these seemingly friendly, but unruly beasts. Currently, there is no systematic method for finding all rational values, that satisfy any equation with degree higher than a quadratic. This is bizarre. Solving these has preoccupied great minds since before the formal notion of an equation existed. Before any sort of mathematical formality, these questions were nested in plucky riddles and folded into folk tales. Because they are so simple to state, these equations are accessible to a very general audience. Yet an astounding amount of …
The Geometry Of Homological Triangles,
2012
University of New Mexico
The Geometry Of Homological Triangles, Florentin Smarandache, Ion Patrascu
Branch Mathematics and Statistics Faculty and Staff Publications
This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a “filter” through which remarkable notions and theorems from the geometry of the triangle are unitarily passed. Our research is structured in seven chapters, the first four are dedicated to the homology of the triangles while the last ones to their applications. In the first chapter one proves the theorem of homological triangles (Desargues, 1636), one survey the remarkable pairs of homological …
Quasi Set Topological Vector Subspaces,
2012
University of New Mexico
Quasi Set Topological Vector Subspaces, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors introduce four types of topological vector subspaces. All topological vector subspaces are defined depending on a set. We define a quasi set topological vector subspace of a vector space depending on the subset S contained in the field F over which the vector space V is defined. These quasi set topological vector subspaces defined over a subset can be of finite or infinite dimension. An interesting feature about these spaces is that there can be several quasi set topological vector subspaces of a given vector space. This property helps one to construct several spaces with …
Cardinal Functions And Integral Functions,
2012
University of New Mexico
Cardinal Functions And Integral Functions, Florentin Smarandache, Mircea Selariu, Marian Nitu
Branch Mathematics and Statistics Faculty and Staff Publications
This paper presents the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics. Centric functions will also be presented in the introductory section, because they are, although widely used in undulatory physics, little known. In centric mathematics, cardinal sine and cosine are dened as well as the integrals. Both circular and hyperbolic ones. In eccentric mathematics, all these central functions multiplies from one to innity, due to the innity of possible choices where to place a point. This point is called eccenter S(s;") which lies in the plane of unit circle UC(O;R = …
Centric Cardinal Sine Function,
2012
University of New Mexico
Centric Cardinal Sine Function, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
According to any standard dictionary, the word "cardinal" is synonymous with "principal", "essential", "fundamental". In centric mathematics (CM), or ordinary mathematics, cardinal is, on the one hand, a number equal to a number of finite aggregate, called the power of the aggregate, and on the other hand, known as the sine cardinal sinc(x) or cosine cardinal cosc(x), is a special function defined by the centric circular function (CCF). sin(x) and cos(x) are commonly used in undulatory physics (see Figure 1) and whose graph, the graph of cardinal sine, which is called as "Mexican hat" (sombrero) because of its shape.
A New Algorithm For Solving Shortest Path Problem On A Network With Imprecise Edge Weight,
2011
Thapar University
A New Algorithm For Solving Shortest Path Problem On A Network With Imprecise Edge Weight, Amit Kumar, Manjot Kumar
Applications and Applied Mathematics: An International Journal (AAM)
Nayeem and Pal (Shortest path problem on a network with imprecise edge weight, Fuzzy Optimization and Decision Making 4, 293-312, 2005) proposed a new algorithm for solving shortest path problem on a network with imprecise edge weight. In this paper the shortcomings of the existing algorithm, (Nayeem and Pal, 2005) are pointed out and to overcome these shortcomings a new algorithm is proposed. To show the advantages of the proposed algorithm over existing algorithm the numerical examples presented in (Nayeem and Pal, 2005) are solved using the proposed algorithm and obtained results are discussed.
Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself,
2011
Institute for Applied Mathematics, University of Hanover, D-30167 Hanover, Germany
Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, Joachim Escher, Rossen Ivanov, Boris Kolev
Articles
The geodesic equations of a class of right invariant metrics on the semi-direct product of two Diff(S) groups are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra are found.
Common Edge-Unzippings For Tetrahedra,
2011
Smith College
Common Edge-Unzippings For Tetrahedra, Joseph O'Rourke
Computer Science: Faculty Publications
It is shown that there are examples of distinct polyhedra, each with a Hamiltonian path of edges, which when cut, unfolds the surfaces to a common net. In particular, it is established for infinite classes of triples of tetrahedra.
Similarity Solution For Flow Of A Micro-Polar Fluid Through A Porous Medium,
2011
Al-Azhar University
Similarity Solution For Flow Of A Micro-Polar Fluid Through A Porous Medium, Kh. S. Mekheimer, R. E. Abo-Elkhair, S. Z. -A. Husseny, A. T. Ali
Applications and Applied Mathematics: An International Journal (AAM)
The equations of two dimensional incompressible steady micro-polar fluid flows through a porous medium are studied. Lie group analysis is employed and the solutions corresponding to the translational symmetry are developed. A boundary value problem is investigated and the results are sketched graphically. The effect on the flow of the porosity coefficient of the porous medium and the micro-polar parameters are observed.
Extending List Colorings Of Planar Graphs,
2011
Harvey Mudd College
Extending List Colorings Of Planar Graphs, Sarah Loeb
HMC Senior Theses
In the study of list colorings of graphs, we assume each vertex of a graph has a specified list of colors from which it may be colored. For planar graphs, it is known that there is a coloring for any list assignment where each list contains five colors. If we have some vertices that are precolored, can we extend this to a coloring of the entire graph? We explore distance constraints when we allow the lists to contain an extra color. For lists of length five, we fix $W$ as a subset of $V(G)$ such that all vertices in $W$ …
