"Lagrangian Disks" In M-Theory,
2020
CUNY City College
"Lagrangian Disks" In M-Theory, Sebastián Franco, Sergei Gukov, Sangmin Lee, Rak-Kyeong Seong, James Sparks
Publications and Research
While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G2 holonomy spaces and to Spin(7) metrics on 8-manifolds with T2 fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M4] on …
Explicit Pseudo-Kähler Metrics On Flag Manifolds,
2020
Georgia Southern University
Explicit Pseudo-Kähler Metrics On Flag Manifolds, Thomas A. Mason Iii
College of Graduate Studies: Theses & Dissertations
The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) Kähler structure, famously used to realize the group's irreducible representations in holomorphic sections of certain line bundles (Borel-Weil theorem). Less well-known are the (indefinite) invariant pseudo-Kähler structures they also admit, which can be used to realize the same representations in higher cohomology of the sections (Bott), and whose analogues in a non-compact setting lead to new representations (Kostant-Langlands). The purpose of this thesis is to give an explicit description of these metrics in the case of the unitary group G=Un.
Effects Of Aperiodicity And Frustration On The Magnetic Properties Of Artificial Quasicrystals,
2020
University of Kentucky
Effects Of Aperiodicity And Frustration On The Magnetic Properties Of Artificial Quasicrystals, Barry Farmer
Theses and Dissertations--Physics and Astronomy
Quasicrystals have been shown to exhibit physical properties that are dramatically different from their periodic counterparts. A limited number of magnetic quasicrystals have been fabricated and measured, and they do not exhibit long-range magnetic order, which is in direct conflict with simulations that indicate such a state should be accessible. This dissertation adopts a metamaterials approach in which artificial quasicrystals are fabricated and studied with the specific goal of identifying how aperiodicity affects magnetic long-range order. Electron beam lithography techniques were used to pattern magnetic thin films into two types of aperiodic tilings, the Penrose P2, and Ammann-Beenker tilings. SQUID …
Invariance And Invertibility In Deep Neural Networks,
2020
Virginia Commonwealth University
Invariance And Invertibility In Deep Neural Networks, Han Zhang
Theses and Dissertations
Machine learning is concerned with computer systems that learn from data instead of being explicitly programmed to solve a particular task. One of the main approaches behind recent advances in machine learning involves neural networks with a large number of layers, often referred to as deep learning. In this dissertation, we study how to equip deep neural networks with two useful properties: invariance and invertibility. The first part of our work is focused on constructing neural networks that are invariant to certain transformations in the input, that is, some outputs of the network stay the same even if the input …
What's Your Sphericity Index? Rationalizing Surface Area And Volume,
2020
Old Dominion University
What's Your Sphericity Index? Rationalizing Surface Area And Volume, John A. Adam
Mathematics & Statistics Faculty Publications
Virginia Standards of Learning include mathematical content related to the surface area and the volume of various geometric objects. In the seventh grade, “Students... solve problems involving volume and surface area” In the eighth grade, “Proportional reasoning is expounded upon as students solve a variety of problems. Students find the volume and surface area of more complex three dimensional figures”. In high school geometry, “The student... use[s] surface area and volume of three-dimensional objects to solve practical problems” (Virginia Department of Education, 2016). The challenge is to find scenarios that are engaging to students and keep them interested in the …
Neutrosophic Local Function And Generated Neutrosophic Topology,
2020
University of New Mexico
Neutrosophic Local Function And Generated Neutrosophic Topology, A. A. Salama, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper we introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to find new neutrosophic topology. The basic structure, especially a basis for such generated neutrosophic topologies and several relations between different topological neutrosophic ideals and neutrosophic topologies are also studied here. Possible application to GIS topology rules are touched upon.
The Geometry Of The Orthological Triangles,
2020
University of New Mexico
The Geometry Of The Orthological Triangles, Florentin Smarandache, Ion Patrascu
Branch Mathematics and Statistics Faculty and Staff Publications
Plants and trees grow perpendicular to the plane tangent to the soil surface, at the point of penetration into the soil; in vacuum, the bodies fall perpendicular to the surface of the Earth - in both cases, if the surface is horizontal. Starting from the property of two triangles to be orthological, the two authors have designed this work that seeks to provide an integrative image of elementary geometry by the prism of this "filter". Basically, the property of orthology is the skeleton of the present work, which establishes many connections of some theorems and geometric properties with it. The …
Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations,
2020
University of North Florida
Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations, Murphy Griffin
UNF Graduate Theses and Dissertations
We study a problem at the intersection of harmonic morphisms and real analytic Milnor fibrations. Baird and Ou establish that a harmonic morphism from G: \mathbb{R}^m \setminus V_G \rightarrow \mathbb{R}^n\setminus \{0\} defined by homogeneous polynomials of order p retracts to a harmonic morphism \psi|: S^{m-1} \setminus K_\epsilon \rightarrow S^{n-1} that induces a Milnor fibration over the sphere. In seeking to relax the homogeneity assumption on the map G, we determine that the only harmonic morphism $\varphi: \mathbb{R}^m \setminus V_G \rightarrow S^{m-1}\K_\epsilon$ that preserves \arg G is radial projection. Due to this limitation, we confirm Baird and Ou's result, yet establish …
Jones Polynomial For Graphs Of Twist Knots,
2019
Ağrı İbrahim Çeçen University
Jones Polynomial For Graphs Of Twist Knots, Abdulgani Şahin, Bünyamin Şahin
Applications and Applied Mathematics: An International Journal (AAM)
We frequently encounter knots in the flow of our daily life. Either we knot a tie or we tie a knot on our shoes. We can even see a fisherman knotting the rope of his boat. Of course, the knot as a mathematical model is not that simple. These are the reflections of knots embedded in threedimensional space in our daily lives. In fact, the studies on knots are meant to create a complete classification of them. This has been achieved for a large number of knots today. But we cannot say that it has been terminated yet. There are …
Regular Semiopen Sets On Intuitionistic Fuzzy Topological Spaces In Sostak’S Sense,
2019
Annamalai University
Regular Semiopen Sets On Intuitionistic Fuzzy Topological Spaces In Sostak’S Sense, G. Saravanakumar, S. Tamilselvan, A. Vadivel
Applications and Applied Mathematics: An International Journal (AAM)
We introduce the concepts of fuzzy (r; s)-regular semi (resp. (r; s)-α, (r; s)-pre, (r; s)-β open sets, their respective interior and closure operators on intuitionistic fuzzy topological spaces in ˆ Sostak’s sense and then we investigate some of their characteristic properties.
On Nearly Kähler Finsler Spaces,
2019
Shahed University
On Nearly Kähler Finsler Spaces, Z. Didehkhani, B. Najafi, N. Heidari
Applications and Applied Mathematics: An International Journal (AAM)
Ichijy¯o introduced (a; b; J)-manifolds as a special class of generalized Randers manifolds. We introduce generalized (a; b; J)-manifolds. A partial negative answer to Ichijy¯o’s open problem on nearly Kähler Finsler manifolds is given. The condition under which generalized (a; b; J)- manifolds are Berwaldian is obtained. Finally, we prove that under a mild assumption a nearly Kähler Finsler manifold is Landsbergian.
Fuzzy Semi-S-Irresolute Continuous Mappings In Šostak’S Fuzzy Topological Spaces,
2019
Government Arts College, Chidambaram
Fuzzy Semi-S-Irresolute Continuous Mappings In Šostak’S Fuzzy Topological Spaces, B. Vijayalakshmi, J. Praba, M. Saraswathi, A. Vadivel
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the concepts of fuzzy semi-S-irresolute open map, fuzzy semi-S-irresolute closed map and fuzzy semi-S-irresolute homeomorphism to the fuzzy topological spaces in Šostak’s sense are introduced and studied. Some of their characteristic properties are considered. Also a comparison between these new types of functions are established by giving examples.
New Notions From (R; S)-Generalized Fuzzy E-Open Sets,
2019
Government Arts College (Autonomous), Karur
New Notions From (R; S)-Generalized Fuzzy E-Open Sets, A. Vadivel, P. Periyasamy, V. Chandrasekar, G. Saravanakumar
Applications and Applied Mathematics: An International Journal (AAM)
The present article discuss (r; s)-generalized fuzzy e-border, (r; s)-generalized fuzzy e-exterior and (r; s)-generalized fuzzy e-frontier in double fuzzy topologies. Furthermore, some characterizations of generalized double fuzzy e-continuous, generalized double fuzzy e-open, generalized double fuzzy e-closed and generalized double fuzzy e-closure-irresolute functions are studied and investigated. Moreover, the interrelations among the new concepts are discussed with some necessary examples.
Graded Quivers, Generalized Dimer Models And Toric Geometry,
2019
CUNY Graduate Center
Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan
Publications and Research
The open string sector of the topological B-model on CY (m+2)-folds is described by m-graded quivers with superpotentials. This correspondence extends to general m the well known connection between CY (m+2)-folds and gauge theories on the world-volume of D(5-2m)-branes for m = 0, ..., 3. We introduce m-dimers, which fully encode the m-graded quivers and their superpotentials, in the case in which the CY (m+2)-folds are toric. Generalizing the well known m = 1,2 cases, m-dimers significantly simplify the connection between geometry and m-graded quivers. A key …
Loop Homology Of Bi-Secondary Structures,
2019
Illinois State University
Loop Homology Of Bi-Secondary Structures, Andrei Bura
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
The Energy-Spectrum Of Bicompatible Sequences,
2019
Illinois State University
The Energy-Spectrum Of Bicompatible Sequences, Wenda Huang
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Diffusion And Consensus On Weakly Connected Directed Graphs,
2019
Portland State University
Diffusion And Consensus On Weakly Connected Directed Graphs, J. J. P. Veerman, Ewan Kummel
Mathematics and Statistics Faculty Publications and Presentations
Let G be a weakly connected directed graph with asymmetric graph Laplacian L. Consensus and diffusion are dual dynamical processes defined on G by x˙=−Lx for consensus and p˙=−pL for diffusion. We consider both these processes as well their discrete time analogues. We define a basis of row vectors {γ¯i}ki=1 of the left null-space of L and a basis of column vectors {γi}ki=1 of the right null-space of L in terms of the partition of G into strongly connected components. This allows for complete characterization of the asymptotic behavior of both diffusion and consensus --- discrete and continuous --- in …
The T3,T4-Conjecture For Links,
2019
University of Nebraska-Lincoln
The T3,T4-Conjecture For Links, Katie Tucker
Department of Mathematics: Dissertations, Theses, and Student Research
An oriented n-component link is a smooth embedding of n oriented copies of S1 into S3. A diagram of an oriented link is a projection of a link onto R2 such that there are no triple intersections, with notation at double intersections to indicate under and over strands and arrows on strands to indicate orientation. A local move on an oriented link is a regional change of a diagram where one tangle is replaced with another in a way that preserves orientation. We investigate the local moves t3 and t4, which are …
On Integrability Of Semi-Invariant Submanifolds Of Trans-Sasakian Finsler Manifolds,
2019
Usak University
On Integrability Of Semi-Invariant Submanifolds Of Trans-Sasakian Finsler Manifolds, Nesrin Caliskan, Ayse F. Saglamer, Nurten Kilic
Applications and Applied Mathematics: An International Journal (AAM)
We introduce the notion of trans-Sasakian Finsler manifold, then study semi-invariant submanifold F^m = (Y, Y', F) of a trans-Sasakian Finsler manifold F^{2n+1} + (bar-Y, bar-Y', bar-F) and we discuss the integrability conditions of the distrubitions of the semi-invariant submanifolds of the trans-Sasakian Finsler manifold.
A Comparison Of Original And Inverse Motion In Minkowski Plane,
2019
Fatsa Science High School
A Comparison Of Original And Inverse Motion In Minkowski Plane, Kemal Eren, Soley Ersoy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we investigate the inflection circle, circling-point curve, and center-point curve for the original and inverse motion of Minkowski planes, and we also deal with their degenerate cases individually. For this purpose, we consider the trajectory of origin with respect to the instantaneous invariants of Bottema in Minkowski plane by using hyperbolic numbers. Finally, we give the geometric interpretation of the circling-point and center-point curves by comparing the original and inverse motion in Minkowski planes.
