Some Topics In Leavitt Path Algebras And Their Generalizations.,
2021
Indian Statistical Institute
Some Topics In Leavitt Path Algebras And Their Generalizations., Mohan R. Dr.
Doctoral Theses
The purpose of this section is to motivate the historical development of Leavitt algebras, Leavitt path algebras and their various generalizations and thus provide a context for this thesis. There are two historical threads which resulted in the definition of Leavitt path algebras. The first one is about the realization problem for von Neumann regular rings and the second one is about studying algebraic analogs of graph C ∗ -algebras. In what follows we briefly survey these threads and also introduce important concepts and terminology which will recur throughout.
Comparing Leibniz With Newton,
2021
St. John's College, Annapolis
Comparing Leibniz With Newton, Peter C. Kaemingk
Agora
This essay attempts to analyze the differences between the calculus systems of Newton and Leibniz, mainly regarding the foundations and justifications of their art of calculus.
Scaling Limits Of Some Random Interface Models.,
2021
Indian Statistical Institute
Scaling Limits Of Some Random Interface Models., Biltu Dan Dr.
Doctoral Theses
In this thesis, we study some probabilistic models of random interfaces. Interfaces between different phases have been topic of considerable interest in statistical physics. These interfaces are described by a family of random variables, indexed by the ddimensional integer lattice, which are considered as a height configuration, namely they indicate the height of the interface above a reference hyperplane. The models are defined in terms of an energy function (Hamiltonian), which defines a Gibbs measure on the set of height configurations. More formally, letÏ• = {Ï•x}x∈Z dbe a collection of real numbers indexed by the d-dimensional integer lattice Z d. …
On The Inertia Conjecture And Its Generalizations.,
2021
Indian Statistical Institute
On The Inertia Conjecture And Its Generalizations., Soumyadip Das Dr.
Doctoral Theses
This thesis concerns problems related to the ramification behaviour of the branched Galois covers of smooth projective connected curves defined over an algebraically closed field of positive characteristic. Our first main problem is the Inertia Conjecture proposed by Abhyankar in 2001. We will show several new evidence for this conjecture. We also formulate a certain generalization of it which is our second problem, and we provide evidence for it. We give a brief overview of these problems in this introduction and reserve the details for Chapter 4.Let k be an algebraically closed field, and U be a smooth connected affine …
Perron Theorem For Delay Differential Equations,
2021
University of Arkansas Little Rock
Perron Theorem For Delay Differential Equations, William Barker
Theses and Dissertations
This note discusses results furthering the study of bounded solutions of non-homogeneous second-order differential equations with delay. The equation of interest has already been shown to possess unique bounded solutions in accordance to Perron's Theorem. We will determine the negativity of the solutions given a positive forcing term by establishing a uniform bound regarding small time delay.
Generalized Grassmann Algebras And Applications To Stochastic Processes,
2021
Chapman University
Generalized Grassmann Algebras And Applications To Stochastic Processes, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we present the groundwork for an Itô/Malliavin stochastic calculus and Hida's white noise analysis in the context of a supersymmetry with Z3-graded algebras. To this end, we establish a ternary Fock space and the corresponding strong algebra of stochastic distributions and present its application in the study of stochastic processes in this context.
Novel Theorems And Algorithms Relating To The Collatz Conjecture,
2021
The University of Texas at Austin
Novel Theorems And Algorithms Relating To The Collatz Conjecture, Michael R. Schwob, Peter Shiue, Rama Venkat
Mathematical Sciences Faculty Research
Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.
The Structure Of Finite Commutative Idempotent Involutive Residuated Lattices,
2021
Chapman University
The Structure Of Finite Commutative Idempotent Involutive Residuated Lattices, Peter Jipsen, Olim Tuyt, Diego Valota
Mathematics, Physics, and Computer Science Faculty Articles and Research
We characterize commutative idempotent involutive residuated lattices as disjoint unions of Boolean algebras arranged over a distributive lattice. We use this description to introduce a new construction, called gluing, that allows us to build new members of this variety from other ones. In particular, all finite members can be constructed in this way from Boolean algebras. Finally, we apply our construction to prove that the fusion reduct of any finite member is a distributive semilattice, and to show that this variety is not locally finite.
Controlled Branching Processes With Continuous Time,
2021
University of Extremadura, Spain
Controlled Branching Processes With Continuous Time, Miguel Gonzalez, Manuel Molina, Ines Del Puerto, Nikolay Yanev, George Yanev
School of Mathematical & Statistical Sciences Faculty Publications
A class of controlled branching processes with continuous time is introduced and some limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.
Generalized Girsanov Transform Of Processes And Zakai Equation With Jumps,
2021
Ritsumeikan Univ., Kusatsu, 525-8577, Japan
Generalized Girsanov Transform Of Processes And Zakai Equation With Jumps, Masatoshi Fujisaki, Takashi Komatsu
Journal of Stochastic Analysis
No abstract provided.
On The Solutions Of Three-Variable Frobenius-Related Problems Using Order Reduction Approach,
2021
Illinois Wesleyan University
On The Solutions Of Three-Variable Frobenius-Related Problems Using Order Reduction Approach, Tian-Xiao He, Peter J.-S. Shiue, Rama Venkat
Mathematical Sciences Faculty Research
This paper presents a new approach to determine the number of solutions of three-variable Frobenius-related problems and to find their solutions by using order reducing methods. Here, the order of a Frobenius-related problem means the number of variables appearing in the problem. We present two types of order reduction methods that can be applied to the problem of finding all nonnegative solutions of three-variable Frobenius-related problems. The first method is used to reduce the equation of order three from a three-variable Frobenius-related problem to be a system of equations with two fixed variables. The second method reduces the equation of …
Expansion Of The Department Of Mathematics At Princeton University And The Founding Of The School Of Mathematics At The Institute For Advanced Study: 1900-1950,
2021
University of Nebraska at Kearney
Expansion Of The Department Of Mathematics At Princeton University And The Founding Of The School Of Mathematics At The Institute For Advanced Study: 1900-1950, Andrew Beman-Cavallaro
Great Plains Graduate Review
From 1900 to 1950 Princeton, New Jersey, hosted two of the most prestigious institutions and provided a location for the expansive mathematical investigations taking place just before, during, and immediately after the Second World War. Princeton University and the Institute for Advanced Study housed, fed, and provided workspaces for an array of Mathematicians uncovering new research methodologies (resulting in the defeat of both the Nazi Party and the Empire of Nippon), the foundation for modern experimental Mathematics, and expansions of Theoretical and Applied Physics.
Conservative Unconditionally Stable Decoupled Numerical Schemes For The Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq System,
2021
Missouri University of Science and Technology
Conservative Unconditionally Stable Decoupled Numerical Schemes For The Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq System, Wenbin Chen, Daozhi Han, Xiaoming Wang, Yichao Zhang
Mathematics and Statistics Faculty Research & Creative Works
We propose two mass and heat energy conservative, unconditionally stable, decoupled numerical algorithms for solving the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq system that models thermal convection of two-phase flows in superposed free flow and porous media. The schemes totally decouple the computation of the Cahn-Hilliard equation, the Darcy equations, the heat equation, the Navier-Stokes equations at each time step, and thus significantly reducing the computational cost. We rigorously show that the schemes are conservative and energy-law preserving. Numerical results are presented to demonstrate the accuracy and stability of the algorithms.
Cohomological Blow Ups Of Graded Artinian Gorenstein
Algebras Along Surjective Maps,
2021
Northeastern University
Cohomological Blow Ups Of Graded Artinian Gorenstein Algebras Along Surjective Maps, Anthony Iarrobino, Pedro Macias Marques, Chris Mcdaniel, Alexandra Seceleanu, Junzo Watanabe
Department of Mathematics: Faculty Publications
We introduce the cohomological blow up of a graded Artinian Gorenstein (AG) algebra along a surjective map, which we term BUG (Blow Up Gorenstein) for short. This is intended to translate to an algebraic context the cohomology ring of a blow up of a projective manifold along a projective submanifold. We show, among other things, that a BUG is a connected sum, that it is the general fiber in a flat family of algebras, and that it preserves the strong Lefschetz property. We also show that standard graded compressed algebras are rarely BUGs, and we classify those BUGs that are …
On The Uniqueness Of Solutions To Martingale Problems For Diffusion Operators With Progressively Measurable Random Coefficients,
2021
Kanazawa university, Kanazawa, 920-1192, Japan
On The Uniqueness Of Solutions To Martingale Problems For Diffusion Operators With Progressively Measurable Random Coefficients, Masaaki Tsuchiya
Journal of Stochastic Analysis
No abstract provided.
Particle Representation For The Solution Of The Filtering Problem. Application To The Error Expansion Of Filtering Discretizations,
2021
Imperial College London, Huxley's Building,180 Queen's Gate, London SW7 2AZ, United Kingdom
Particle Representation For The Solution Of The Filtering Problem. Application To The Error Expansion Of Filtering Discretizations, Dan Crisan, Thomas G. Kurtz, Salvador Ortiz-Latorre
Journal of Stochastic Analysis
No abstract provided.
An Anti-Symmetric Version Of Malliavin Calculus,
2021
Ritsumeikan University, 1-1-1 Nojihagashi, Kusatsu 525-8577, Japan
An Anti-Symmetric Version Of Malliavin Calculus, Jirô Akahori, Tomo Matsusita, Yasufumi Nitta
Journal of Stochastic Analysis
No abstract provided.
Localized Learning: A Possible Alternative To Current Deep Learning Techniques,
2021
University of Cincinnati
Localized Learning: A Possible Alternative To Current Deep Learning Techniques, Javier Viana, Kelly Cohen, Anca Ralescu, Stephan Ralescu, Vladik Kreinovich
Departmental Technical Reports (CS)
At present, the most efficient deep learning technique is the use of deep neural networks. However, recent empirical results show that in some situations, it is even more efficient to use "localized" learning -- i.e., to divide the domain of inputs into sub-domains, learn the desired dependence separately on each sub-domain, and then "smooth" the resulting dependencies into a single algorithm. In this paper, we provide theoretical explanation for these empirical successes.
Freedom Of Will, Physics, And Human Intelligence: An Idea,
2021
Czech Technical University in Prague
Freedom Of Will, Physics, And Human Intelligence: An Idea, Miroslav Svitek, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
Among the main fundamental challenges related to physics and human intelligence are: How can we reconcile the free will with the deterministic character of physical equations? What is the physical meaning of extra spatial dimensions needed to make quantum physics consistent? and Why are we often smarter than brain-simulating neural networks? In this paper, we show that while each of these challenges is difficult to resolve on its own, it may be possible to resolve all three of them if we consider them together. The proposed possible solution is that human reasoning uses the extra spatial dimensions. This may sound …
What Is A Reasonable Way To Make Predictions?,
2021
The University of Texas at El Paso
What Is A Reasonable Way To Make Predictions?, Leonardo Orea Amador, Vladik Kreinovich
Departmental Technical Reports (CS)
Predictions are usually based on what is called laws of nature: many times, we observe the same relation between the states at different moments of time, and we conclude that the same relation will occur in the future. The more times the relation repeats, the more confident we are that the same phenomenon will be re-peated again. This is how Newton's laws and other laws came into being. This is what is called inductive reasoning. However, there are other reasonable approaches. For example, assume that a person speeds and is not caught. This may be repeated two times, three times …
