Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- Algebraic geometry (1)
- Asymptotically equivalence (1)
- Betti curves (1)
- Characteristic class (1)
- Chern-Schwartz-MacPherson class (1)
-
- Chevalley basis (1)
- Clique topology (1)
- Computational intersection theory (1)
- Computer algebra (1)
- Curvature invariants (1)
- Differential Equations (1)
- Differential Forms (1)
- Double Lacunary Sequence (1)
- Double Statistical Convergence (1)
- Einstein equations (1)
- Equivalence problem (1)
- Euler characteristic (1)
- Exceptional Lie algebra (1)
- Exterior differential systems (1)
- F4 (1)
- Geometry (1)
- Group (1)
- Lie Derivative (1)
- Lie Groups (1)
- Mathematical problems (1)
- Neural coding (1)
- ODE (1)
- Ordinary (1)
- Ordinary Differential Equations (1)
- P-convergent (1)
- Publication
- Publication Type
- File Type
Articles 1 - 8 of 8
Full-Text Articles in Applied Mathematics
Asymptotically Double Lacunary Equivalent Sequences In Topological Groups, Ayhan Esi, M. K. Ozdemir
Asymptotically Double Lacunary Equivalent Sequences In Topological Groups, Ayhan Esi, M. K. Ozdemir
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we study the concept of asymptotically double lacunary statistical convergent sequences in topological groups and prove some inclusion theorems.
Algorithms To Compute Characteristic Classes, Martin Helmer
Algorithms To Compute Characteristic Classes, Martin Helmer
Electronic Thesis and Dissertation Repository
In this thesis we develop several new algorithms to compute characteristics classes in a variety of settings. In addition to algorithms for the computation of the Euler characteristic, a classical topological invariant, we also give algorithms to compute the Segre class and Chern-Schwartz-MacPherson (CSM) class. These invariants can in turn be used to compute other common invariants such as the Chern-Fulton class (or the Chern class in smooth cases).
We begin with subschemes of a projective space over an algebraically closed field of characteristic zero. In this setting we give effective algorithms to compute the CSM class, Segre class and …
Topological Data Analysis Of Biological Aggregation Models, Chad M. Topaz, Lori Ziegelmeier, Tom Halverson
Topological Data Analysis Of Biological Aggregation Models, Chad M. Topaz, Lori Ziegelmeier, Tom Halverson
Chad M. Topaz
Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate
Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate
Senior Honors Theses
Differential equations have bearing on practically every scientific field. Though they are prevalent in nature, they can be challenging to solve. Most of the work done in differential equations is dependent on the use of many methods to solve particular types of equations. Sophus Lie proposed a modern method of solving ordinary differential equations in the 19th century along with a coordinate free variation of finding the infinitesimal generator by combining the influential work of Élie Cartan among others in the field of differential geometry. The driving idea behind using symmetries to solve differential equations is that there exists a …
The Riemann Curvature Tensor, Its Invariants, And Their Use In The Classification Of Spacetimes, Jesse Hicks
The Riemann Curvature Tensor, Its Invariants, And Their Use In The Classification Of Spacetimes, Jesse Hicks
Presentations and Publications
The equivalence problem in general relativity is to determine whether two solutions of the Einstein field equations are isometric. Petrov has given a classification of metrics according to their isometry algebras. This talk discusses the use of the Petrov classification scheme, together with the use of scalar curvature invariants, to address the equivalence problem. These are the slides for a presentation at the Mathematics Association of America Spring 2015 conference at Brigham Young University.
A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson
A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson
Tutorials on... in 1 hour or less
Let I be a differential system on a manifold M. The infinitesimal symmetry algebra of I is the set of all vectors fields X on M such that preserve I. In this worksheet we present an example, due to E. Cartan of a rank 7 Pfaffian system on a 15-dimensional manifold whose infinitesimal symmetry algebra is the split real form of the exceptional Lie algebra f4 .
Clique Topology Reveals Intrinsic Geometric Structure In Neural Correlations, Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov
Clique Topology Reveals Intrinsic Geometric Structure In Neural Correlations, Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov
Department of Mathematics: Faculty Publications
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using …
Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache
Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.