Browsing Mathematics by Title
Now showing items 106-125 of 188
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On an inverse problem for fractional connection Laplacians
Classical inverse problems seek to determine the unknown coefficients of a PDE from boundary or local measurements of solutions. In the past few years, there has been a sharp increase in attention paid to inverse problems ... -
On Computing the Tate Shafarevich group order and type of some rational elliptic curves of conductor less than a million.
In this dissertation, I will present the tabulation of the Tate Shafarevich group order and type of around 4.5 million rational elliptic curves of conductor less than a million. These curves were obtained from the database ... -
On Cross Sections to the Horocycle and Geodesic Flows on Quotients by Hecke Triangle Groups
The study of continuous dynamical systems via surfaces of section is one of the standard techniques in nonlinear mathematics. This is done by considering the intersections of trajectories in a phase space with a subspace ... -
On f-vectors of polytopes and matroids
The f-vector of a simplicial complex is a fundamental invariant that counts the number of faces in each dimension. A natural question in the theory of simplicial complexes is to understand the relationship between the ... -
On Inverse Problems and Machine Learning
This document is related to Ill-Posed and Inverse problems particularly focused on economicmeasurements. In 2015, I proposed to myself to work both analytically and numerically on a very fresh and surprising idea: to predict ... -
On numerics and inverse problems
In this thesis, two projects in inverse problems are described. The first concerns a simple mathematical model of synthetic aperture radar with undirected beam, modeled as a 2D circular Radon transform with centers restricted ... -
On Particle Interaction Models
(2014-02-24)This dissertation deals with three problems in Stochastic Analysis which broadly involve interactions, either between particles (Chapters 1 and 2), or between particles and the boundary of a C2 domain (Chapter 3). In Chapter ... -
On Selmer groups and factoring p-adic L-functions
Samit Dasgupta has proved a formula factoring a certain restriction of a 3-variable Rankin-Selberg p-adic L-function as a product of a 2-variable p-adic L-function related to the adjoint representation of a Hida family and ... -
On singularities of generic projection hypersurfaces
(2006)The present work studies singularities of hypersurfaces arising from generic projections of smooth projective varieties, in the context of Du Bois and semi log canonical singularities. It is demonstrated that Du Bois ... -
On special Lagrangian equations
(2014-02-24)In this paper we study the special Lagrangian equation and related equations. Special Lagrangian equation originates in the special Lagrangian geometry by Harvey-Lawson [HL1]. In subcritical phases, we construct singular ... -
On T-Semisimplicity of Iwasawa Modules and Some Computations with Z3-Extensions
For certain Zp-extensions of abelian number fields, we study the Iwasawa module associated to the ideal class groups. We show that generic Zp-extensions of abelian number fields are T-semisimple. We also construct the ... -
On the Duflot filtration for equivariant cohomology rings
We study the Fp-cohomology rings of the classifying space of a compact Lie group G using methods from equivariant cohomology. Building on ideas of Duflot and Symonds we study a “rank filtration” on the p-toral equivariant ... -
On the g2-number of various classes of spheres and manifolds
For a $(d-1)$-dimensional simplicial complex $\Delta$, we let $f_i=f_i(\Delta)$ be the number of $i$-dimensional faces of $\Delta$ for $-1\leq i\leq d-1$. One classic problem in geometric combinatorics is the following: ... -
On the gamma_2-positivity of Smooth Toric Threefolds
In this thesis we consider the classification of smooth toric varieties with positive second chern character. We give a complete proof, without using the classification of smooth toric Fano threefolds, that the only such ... -
On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities
A central question in geometric measure theory is whether geometric properties of a set translate into analytical ones. In 1960, E. R. Reifenberg proved that if an $n$-dimensional subset $M$ of $\mathbb{R}^{n+d}$ is well ... -
On the integral Chow rings of various moduli stacks of curves
The contents of this thesis are focused on the intersection theory of the stack of marked(stable or smooth) elliptic curves. We first recount some results on equivariant intersection theory, then give an exposition of some ... -
On the mod 2 general linear group homology of totally real number rings
(1997)We study the mod 2 homology of the general linear group of rings of integers in totally real number fields. In particular, for certain such rings R, we construct a space JKR and show that the mod 2 homology of JKR is a ... -
On weak quantum symmetry and Frobenius-Perron theory
Chapter 1 describes the history and notion of a fusion category, as well as some natural settings where fusion categories appear. We discuss the fact that every fusion category is equivalent to the representation category ... -
Optimization Enabled Kalman Smoothing
Kalman smoothing has tremendous importance in a wide range of time series analysis applications. Classic algorithms use Gaussian assumptions to simplify estimation but optimization tools can be used to unlock more modeling ... -
The Ornstein-Uhlenbeck Process In Neural Decision-Making: Mathematical Foundations And Simulations Suggesting The Adaptiveness Of Robustly Integrating Stochastic Neural Evidence
(2013-02-25)This master's thesis reviews the concepts behind a stochastic process known as the Ornstein-Uhlenbeck Process, and then uses that process as a way to investigate neural decision making. In particular, MATLAB simulations ...