An Optimal Control Problem Solution For Chemical Reactor, 2021 Prairie View A&M University
An Optimal Control Problem Solution For Chemical Reactor, Dias Nurmagambetov
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we describe one of the solutions of a nonlinear optimal control problem for a chemical reactor. A solution on finding a chemical reactor’s optimal temperature regime for having a maximum concentration of final product is presented. The optimal control has been found by immersion method for boundary value problem with a phase and control restrictions. This method is reducing the original boundary value problem to a special optimal control problem, using the general solution of the Fredholm integral equation of the first kind. With this method's solution had been created a software for the problem calculations. Analysis …
Orthogonality In Terms Of 2-Hh Norm And Bounded Linear Operators In Banach Spaces, 2021 Tribhuvan University
Orthogonality In Terms Of 2-Hh Norm And Bounded Linear Operators In Banach Spaces, Bhuwan P. Ojha, Prakash M. Bajracharya
Applications and Applied Mathematics: An International Journal (AAM)
In the present paper, the generalization of the Carlson orthogonality for functionals to operators in Banach spaces has been studied. We will also investigate various properties related to the Carlsson, Birkhoff-James, and Pythagorean orthogonality for operators. Kikianty and Dragomir (2010) mentioned in their paper by stating that Pythagorean and isosceles orthogonality through the medium of 2 − HH norm satisfies the non-degeneracy, symmetry and continuity properties without mentioning detailed proof. This paper provides the complete proof of these properties as well as the equivalency of additivity and homogeneity of the isosceles orthogonality with the help of 2 − HH norm. …
Anticipating Linear Stochastic Differential Equations With Adapted Coefficients, 2021 Louisiana State University, Baton Rouge, LA 70803, USA
Anticipating Linear Stochastic Differential Equations With Adapted Coefficients, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha
Journal of Stochastic Analysis
No abstract provided.
Applications Of Nonstandard Analysis In Probability And Measure Theory, 2021 Louisiana State University and Agricultural and Mechanical College
Applications Of Nonstandard Analysis In Probability And Measure Theory, Irfan Alam
LSU Doctoral Dissertations
This dissertation broadly deals with two areas of probability theory and investigates how methods from nonstandard analysis may provide new perspectives in these topics. In particular, we use nonstandard analysis to prove new results in the topics of limiting spherical integrals and of exchangeability.
In the former area, our methods allow us to represent finite dimensional Gaussian measures in terms of marginals of measures on hyperfinite-dimensional spheres in a certain strong sense, thus generalizing some previously known results on Gaussian Radon transforms as limits of spherical integrals. This first area has roots in the kinetic theory of gases, which is …
The Edwards Model For Fractional Brownian Loops And Starbursts, 2021 Technische Universität Kaiserslautern, Technomathematics Group, 67663 Kaiserslautern, Germany
The Edwards Model For Fractional Brownian Loops And Starbursts, Wolfgang Bock, Torben Fattler, Ludwig Streit
Journal of Stochastic Analysis
No abstract provided.
Alòs Type Decomposition Formula For Barndorff-Nielsen And Shephard Model, 2021 Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan
Alòs Type Decomposition Formula For Barndorff-Nielsen And Shephard Model, Takuji Arai
Journal of Stochastic Analysis
No abstract provided.
Mixed Generalized Fractional Brownian Motion, 2021 Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam, Saudi Arabia
Mixed Generalized Fractional Brownian Motion, Shaykhah Alajmi, Ezzedine Mliki
Journal of Stochastic Analysis
No abstract provided.
Krein Reproducing Kernel Modules In Clifford Analysis, 2021 Chapman University
Krein Reproducing Kernel Modules In Clifford Analysis, Daniel Alpay, Paula Cerejeiras, Uwe Kähler
Mathematics, Physics, and Computer Science Faculty Articles and Research
Classic hypercomplex analysis is intimately linked with elliptic operators, such as the Laplacian or the Dirac operator, and positive quadratic forms. But there are many applications like the crystallographic X-ray transform or the ultrahyperbolic Dirac operator which are closely connected with indefinite quadratic forms. Although appearing in many papers in such cases Hilbert modules are not the right choice as function spaces since they do not reflect the induced geometry. In this paper we are going to show that Clifford-Krein modules are naturally appearing in this context. Even taking into account the difficulties, e.g., the existence of different inner products …
Interfacial Dynamics And Ionic Transport Of Radiologic Contrast Media In Carbohydrate Matrix: Utility And Limits Of X-Ray Imaging, 2021 CUNY New York City College of Technology
Interfacial Dynamics And Ionic Transport Of Radiologic Contrast Media In Carbohydrate Matrix: Utility And Limits Of X-Ray Imaging, Lin Mousa, Hayley Sanchez, Subhendra Sarkar, Zoya Vinokur
Publications and Research
Hello, our names are Lin Mousa and Hayley Sanchez, this semester we participated in a research project dedicated to analyzing the interactions of contrast media with the molecular components of fruits to compare how they would react with the human brain. This project involved the injection of fruits with varying contrasts and the imaging of the diffusion and interactions of the contrast within the fruits with X-rays. With setup technical parameters on the x-ray equipment images were taken with identical setups at an hourly rate for several days. The final results of this experiment indicated that contrasts such as Gadolinium …
Exact Solutions To Optimal Control Problems For Wiener Processes With Exponential Jumps, 2021 Polytechnique Montréal, Montréal, Québec H3C 3A7, Canada
Exact Solutions To Optimal Control Problems For Wiener Processes With Exponential Jumps, Mario Lefebvre
Journal of Stochastic Analysis
No abstract provided.
The Generalized Riemann Hypothesis And Applications To Primality Testing, 2021 University of Connecticut
The Generalized Riemann Hypothesis And Applications To Primality Testing, Peter Hall
University Scholar Projects
The Riemann Hypothesis, posed in 1859 by Bernhard Riemann, is about zeros
of the Riemann zeta-function in the complex plane. The zeta-function can be repre-
sented as a sum over positive integers n of terms 1/ns when s is a complex number
with real part greater than 1. It may also be represented in this region as a prod-
uct over the primes called an Euler product. These definitions of the zeta-function
allow us to find other representations that are valid in more of the complex plane,
including a product representation over its zeros. The Riemann Hypothesis says that
all …
Evaluating The Historical Accuracy Of Blackwork Embroidery With Fractal Analysis, 2021 University of Lynchburg
Evaluating The Historical Accuracy Of Blackwork Embroidery With Fractal Analysis, Rhiannon Cire
Undergraduate Theses and Capstone Projects
The intricate monochromatic embroidery that graced the collars and cuffs of Renaissance nobility and domestic materials from that era has been little studied beyond the historical costuming and crafting communities. This style, known as blackwork, for it was traditionally done in black silk on white linen, exemplifies how complex and visually-appealing designs can arise from repetition of simple forms, often demonstrating the fractal property of self-similarity. Though most blackwork patterns are not true fractals, fractal analysis offers a means of objectively quantifying their complexity and new lens through which to examine this embroidery technique. The purpose of this study was …
Applying Emotional Analysis For Automated Content Moderation, 2021 University of Arkansas, Fayetteville
Applying Emotional Analysis For Automated Content Moderation, John Shelnutt
Computer Science and Computer Engineering Undergraduate Honors Theses
The purpose of this project is to explore the effectiveness of emotional analysis as a means to automatically moderate content or flag content for manual moderation in order to reduce the workload of human moderators in moderating toxic content online. In this context, toxic content is defined as content that features excessive negativity, rudeness, or malice. This often features offensive language or slurs. The work involved in this project included creating a simple website that imitates a social media or forum with a feed of user submitted text posts, implementing an emotional analysis algorithm from a word emotions dataset, designing …
Visual Analysis Of Historical Lessons Learned During Exercises For The United States Air Force Europe (Usafe), 2021 University of Nebraska at Omaha
Visual Analysis Of Historical Lessons Learned During Exercises For The United States Air Force Europe (Usafe), Samantha O'Rourke
Theses/Capstones/Creative Projects
Within the United States Air Force, there are repeated patterns of differences observed during exercises. After an exercise is completed, forms are filled out detailing observations, successes, and recommendations seen throughout the exercise. At the most, no two reports are identical and must be analyzed by personnel and then categorized based on common themes observed. Developing a computer application will greatly reduce the time and resources used to analyze each After Action Report. This application can visually represent these observations and optimize the effectiveness of these exercises. The visualization is done through graphs displaying the frequency of observations and recommendations. …
Determining Quantum Symmetry In Graphs Using Planar Algebras, 2021 William & Mary
Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody
Undergraduate Honors Theses
A graph has quantum symmetry if the algebra associated with its quantum automorphism group is non-commutative. We study what quantum symmetry means and outline one specific method for determining whether a graph has quantum symmetry, a method that involves studying planar algebras and manipulating planar tangles. Modifying a previously used method, we prove that the 5-cycle has no quantum symmetry by showing it has the generating property.
Zeta Function Regularization And Its Relationship To Number Theory, 2021 East Tennessee State University
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Electronic Theses and Dissertations
While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …
Constructions & Optimization In Classical Real Analysis Theorems, 2021 East Tennessee State University
Constructions & Optimization In Classical Real Analysis Theorems, Abderrahim Elallam
Electronic Theses and Dissertations
This thesis takes a closer look at three fundamental Classical Theorems in Real Analysis. First, for the Bolzano Weierstrass Theorem, we will be interested in constructing a convergent subsequence from a non-convergent bounded sequence. Such a subsequence is guaranteed to exist, but it is often not obvious what it is, e.g., if an = sin n. Next, the H¨older Inequality gives an upper bound, in terms of p ∈ [1,∞], for the the integral of the product of two functions. We will find the value of p that gives the best (smallest) upper-bound, focusing on the Beta and Gamma integrals. …
Sobolev Inequalities And Riemannian Manifolds, 2021 University of Connecticut
Sobolev Inequalities And Riemannian Manifolds, John Reever
Honors Scholar Theses
Sobolev inequalities, named after Sergei Lvovich Sobolev, relate norms in Sobolev spaces and give insight to how Sobolev spaces are embedded within each other. This thesis begins with an overview of Lebesgue and Sobolev spaces, leading into an introduction to Sobolev inequalities. Soon thereafter, we consider the behavior of Sobolev inequalities on Riemannian manifolds. We discuss how Sobolev inequalities are used to construct isoperimetric inequalities and bound volume growth, and how Sobolev inequalities imply families of other Sobolev inequalities. We then delve into the usefulness of Sobolev inequalities in determining the geometry of a manifold, such as how they can …
An Exploratory Analysis Of The Bgsu Learning Commons Student Usage Data, 2021 Bowling Green State University
An Exploratory Analysis Of The Bgsu Learning Commons Student Usage Data, Emily Eskuri
Honors Projects
The purpose of this study was to explore past student usage data in individualized tutoring sessions from the Learning Commons from two academic years. The Bowling Green State University (BGSU) Learning Commons is a learning assistance center that offers various services, such as individualized tutoring, math assistance, writing assistance, study hours, and academic coaching. There have been limited research studies into how big data and analytics can have an impact in higher education, especially research utilizing predictive analytics.
This project applied analytics to individualized tutoring data in the Learning Commons to create a better understanding of why those trends happen …
Construct Linear Quasi-Interpolants On Infinite Intervals, 2021 University of Missouri-St. Louis
Construct Linear Quasi-Interpolants On Infinite Intervals, Johara Farah Albaliwi
Dissertations
In solving the data interpolation problem, which is fundamental in data analysis, we typically deal with the data samples spread in a finite interval [a, b], which results in the operations involving finite-dimensional matrices. There are many interesting results developed under this framework. However, when the data samples are given from an infinite interval [a, ∞) (for certain special types of real-world applications), many existing results would not work anymore due to the special properties of the infinite data samples. A new framework should be established to support the infinite data samples.
In this dissertation, we develop a special tool …