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Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil 2019 University Politehnica of Bucharest

Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor TV on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and we ...


A Strength Test For The Borda Count, Jade Monroe Waring 2019 Bard College

A Strength Test For The Borda Count, Jade Monroe Waring

Senior Projects Spring 2019

When running an election with more than two candidates, there are many ways to choose the winner. A famous theorem of Arrow states that the only mathematically fair way to choose is to do so at random. Because this is not a desirable way to choose a winner of an election, many mathematicians have devised alternate ways of aggregating ballots. In my project I consider one of these ways -- the Borda Count, considered to be one of the most desirable from both the point of view of mathematics and economics -- and came up with a method to test the mathematical ...


From Constant To Stochastic Volatility: Black-Scholes Versus Heston Option Pricing Models, Hsin-Fang Wu 2019 Bard College

From Constant To Stochastic Volatility: Black-Scholes Versus Heston Option Pricing Models, Hsin-Fang Wu

Senior Projects Spring 2019

The Nobel Prize-winning the Black-Scholes Model for stock option pricing has a simple formula to calculate the option price, but its simplicity comes with crude assumptions. The two major assumptions of the model are that the volatility is constant and that the stock return is normally distributed. Since 1973, and especially in the 1987 Financial Crisis, these assumptions have been proven to limit the accuracy and applicability of the model, although it is still widely used. This is because, in reality, observing a stock return distribution graph would show that there is an asymmetry or a leptokurtic shown in the ...


Analyzing Mathematicians' Concept Images Of Differentials, Timothy Shawn McCarty 2019 West Virginia University

Analyzing Mathematicians' Concept Images Of Differentials, Timothy Shawn Mccarty

Graduate Theses, Dissertations, and Problem Reports

The differential is a symbol that is common in first- and second-year calculus. It is perhaps expected that a common mathematical symbol would be interpreted universally. However, recent literature that addresses student interpretations of differentials, usually in the context of definite integration, suggests that this is not the case, and that many interpretations are possible. Reviews of textbooks showed that there was not a lot of discussion about differentials, and what interpretations there were depended upon the context in which the differentials were presented. This dissertation explores some of these issues. Since students may not have the experience necessary to ...


The Frenet Frame And Space Curves, Catherine Elaina Eudora Ross 2019 Missouri State University

The Frenet Frame And Space Curves, Catherine Elaina Eudora Ross

MSU Graduate Theses

Essential to the study of space curves in Differential Geometry is the Frenet frame. In this thesis we generate the Frenet equations for the second, third, and fourth dimensions using the Gram-Schmidt process, which allows us to present the form of the Frenet equations for n-dimensions. We highlight several key properties that arise from the Frenet equations, expound on the class of curves with constant curvature ratios, as well as characterize spherical curves up to the fourth dimension. Methods for generalizing properties and characteristics of curves in varying dimensions should be handled with care, since the structure of curves often ...


Analysing Flow Free With One Pair Of Dots, Eliot Harris Roske 2019 Bard College

Analysing Flow Free With One Pair Of Dots, Eliot Harris Roske

Senior Projects Spring 2019

Flow Free is a smartphone puzzle game where the player is presented with an m by m grid containing multiple pairs of colored dots. In order to solve the puzzle, the player must draw a path connecting each pair of points so that the following conditions are met: each pair of dots is connected by a path, each square of the grid is crossed by a path, and no paths intersect. Based on these puzzles, this project looks at grids of size m by n with only one pair of dots to determine for which configurations of dots a solution ...


Rationality In Bargaining By Finite Automata, Jim Bell 2019 Wilfrid Laurier University

Rationality In Bargaining By Finite Automata, Jim Bell

Theses and Dissertations (Comprehensive)

Aspects of behavioral decision-making can be integrated into game-theoretic models of two-player bargaining using finite automata which can represent bargaining strategies in combination with various behavioral traits. The automata are used as bargaining agents who must jointly agree upon a fixed allocation of transferable utility in an infinite-horizon Rubinstein bargaining game. At each turn, the automata are given the opportunity to accept a proposed portion of the transferable utility, or to reject the proposal and make a counter-offer of their own. A round-robin tournament and ecological simulations were run to explore strategic dominance under different conditions. Principles of bargaining strategy ...


Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier 2019 Georgia Southern University

Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier

Electronic Theses and Dissertations

We explore a relatively new concept in edge-colored graphs called conflict-free connectivity. A conflict-free path is a (edge-) colored path that has an edge with a color that appears only once. Conflict-free connectivity is the maximal number of internally disjoint conflict-free paths between all pairs of vertices in a graph. We also define the c-conflict-free-connection of a graph G. This is the maximum conflict-free connectivity of G over all c-colorings of the edges of G. In this paper we will briefly survey the works related to conflict-free connectivity. In addition, we will use the probabilistic method to achieve a bound ...


Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta 2019 University of Connecticut, Storrs, CT USA

Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta

Communications on Stochastic Analysis

No abstract provided.


Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas 2019 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas

Communications on Stochastic Analysis

No abstract provided.


Exponential Inequalities For Exit Times For Stochastic Navier-Stokes Equations And A Class Of Evolutions, Po-Han Hsu, Padamanbhan Sundar 2019 Louisiana State University, Baton Rouge, LA USA

Exponential Inequalities For Exit Times For Stochastic Navier-Stokes Equations And A Class Of Evolutions, Po-Han Hsu, Padamanbhan Sundar

Communications on Stochastic Analysis

No abstract provided.


Composition Of Gaussian Noises From Successive Convex Integrations, Amites Dasgupta 2019 Indian Statistical Institute

Composition Of Gaussian Noises From Successive Convex Integrations, Amites Dasgupta

Communications on Stochastic Analysis

No abstract provided.


Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski 2019 Wrocław University of Science and Technology, Wrocław, Poland

Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski

Communications on Stochastic Analysis

No abstract provided.


Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, Manil T. Mohan 2019 Indian Statistical Institute

Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, Manil T. Mohan

Communications on Stochastic Analysis

No abstract provided.


Generalized Stochastic Burgers' Equation With Non-Lipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri 2019 Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

Generalized Stochastic Burgers' Equation With Non-Lipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri

Communications on Stochastic Analysis

No abstract provided.


Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski 2018 Wojciech Budzianowski Consulting Services

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


Stochastic Lagrangian Formulations For Damped Navier-Stokes Equations And Boussinesq System, With Applications, Kazuo Yamazaki 2018 Department of Mathematics, University of Rochester, Rochester, New York 14627, USA

Stochastic Lagrangian Formulations For Damped Navier-Stokes Equations And Boussinesq System, With Applications, Kazuo Yamazaki

Communications on Stochastic Analysis

No abstract provided.


New Filters For The Calibration Of Regime Switching Beta Dynamics, Robert J. Elliott, Carlton Osakwe 2018 University of Calgary

New Filters For The Calibration Of Regime Switching Beta Dynamics, Robert J. Elliott, Carlton Osakwe

Communications on Stochastic Analysis

No abstract provided.


Symmetric Presentations And Double Coset Enumeration, Charles Seager 2018 California State University, San Bernardino

Symmetric Presentations And Double Coset Enumeration, Charles Seager

Electronic Theses, Projects, and Dissertations

In this project, we demonstrate our discovery of original symmetric presentations and constructions of important groups, including nonabelian simple groups, and groups that have these as factor groups. The target nonabelian simple groups include alternating, linear, and sporadic groups. We give isomorphism types for each finite homomorphic image that has been found. We present original symmetric presentations of $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ as homomorphism images of the progenitors $2^{*20}$ $:$ $A_{5}$, $2^{*10}$ $:$ $PGL(2,9)$, $2^{*10}$ $:$ $Aut ...


Functional Central Limit Theorem For Additive Functionals Associated To The Generalized Nelson Hamiltonian, Soumaya Gheryani, Achref Majid, Habib Ouerdiane 2018 Faculty of Science, University of Tunis El Manar, Tunisia

Functional Central Limit Theorem For Additive Functionals Associated To The Generalized Nelson Hamiltonian, Soumaya Gheryani, Achref Majid, Habib Ouerdiane

Communications on Stochastic Analysis

No abstract provided.


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