Applied Mathematics Commons^™

Invariants Of Legendrian Products, Peter Lambert-Cole

LSU Doctoral Dissertations

This thesis investigates a construction in contact topology of Legendrian submanifolds called the Legendrian product. We investigate and compute invariants for these Legendrian submanifolds, including the Thurston-Bennequin invariant and Maslov class; Legendrian contact homology for the product of two Legendrian knots; and generating family homology.

Conical Representations For Direct Limits Of Riemannian Symmetric Spaces., Matthew Glenn Dawson

LSU Doctoral Dissertations

We extend the definition of conical representations for Riemannian symmetric space to a certain class of infinite-dimensional Riemannian symmetric spaces. Using an infinite-dimensional version of Weyl's Unitary Trick, there is a correspondence between smooth representations of infinite-dimensional noncompact-type Riemannian symmetric spaces and smooth representations of infinite-dimensional compact-type symmetric spaces. We classify all smooth conical representations which are unitary on the compact-type side. Finally, a new class of non-smooth unitary conical representations appears on the compact-type side which has no analogue in the finite-dimensional case. We classify these representations and show how to decompose them into direct integrals of irreducible conical …

Extremal Problems In Matroid Connectivity, John Tyler Moss

LSU Doctoral Dissertations

Matroid k-connectivity is typically defined in terms of a connectivity function. We can also say that a matroid is 2-connected if and only if for each pair of elements, there is a circuit containing both elements. Equivalently, a matroid is 2-connected if and only if each pair of elements is in a certain 2-element minor that is 2-connected. Similar results for higher connectivity had not been known. We determine a characterization of 3-connectivity that is based on the containment of small subsets in 3-connected minors from a given list of 3-connected matroids. Bixby’s Lemma is a well-known inductive tool in …

Selected Problems On Matroid Minors, Jesse Taylor

LSU Doctoral Dissertations

This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and Cunningham and Edmonds's tree decomposition for connected matroids. One of the most well-known excluded-minor results in matroid theory is Tutte's characterization of binary matroids. The class of binary matroids is one of the most widely studied classes of matroids, and its members have many attractive qualities. This motivates the study of matroid classes that are close to being …

Is Big Data Enough? A Reflection On The Changing Role Of Mathematics In Applications, Domenico Napoletani, Marco Panza, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

The advent of computers, and especially high-performance computers, has had a dramatic impact on the way in which mathematics is done and even more on how mathematics is applied, as demonstrated by the growth of computational mathematics as well as what goes under the name of “experimental mathematics”, to which a journal is now devoted. More importantly, computers are now used to perform highly complex computations in order to apply mathematical models to a variety of empirical problems that could never be attacked otherwise.

Modelling And Analysis On Noisy Financial Time Series, Jinsong Leng

Research outputs 2014 to 2021

Building the prediction model(s) from the historical time series has attracted many researchers in last few decades. For example, the traders of hedge funds and experts in agriculture are demanding the precise models to make the prediction of the possible trends and cycles. Even though many statistical or machine learning (ML) models have been proposed, however, there are no universal solutions available to resolve such particular prob-lem. In this paper, the powerful forward-backward non-linear filter and wavelet-based denoising method are introduced to remove the high level of noise embedded in financial time series. With the filtered time series, the statistical …

Analysis Of Power Efficiency Of A Direct-Driven Locally Fabricated Permanent Magnet Ac Generator For Small-Scale Wind Power Applications In Tanzania, Mussa Iddi Mgwatu Dr.

Tanzania Journal of Engineering and Technology (TJET)

The use of direct-driven permanent magnet alternating current (AC) generators offers the opportunity to reduced costs and increased system efficiency. This type of generator could be the best alternative for rural population whom are not connected to the national grid. To improve the design and efficiency of locally fabricated generators, it is imperative to characterize both their mechanical and electrical parameters. This paper presents the analysis of power efficiency of the synchronous permanent AC generator locally fabricated in Tanzania. In this case, load resistance and rotational speed are characterized using designed experiment. The output current and voltage of the generator …

Thermolysis And Kinetics Of Scrap Tyre And Bagasse For Energy Utilization, Petro Ndalila

Tanzania Journal of Engineering and Technology (TJET)

The increase of energy demand has brought concern to find alternative fuel that will at least sustain the requirement. Bagasse and scrap tyre are waste generated in our industrial activities, which can be used in energy production to subsidize the demand. This paper, aim to study the decomposition behaviour and kinetics of biomass (bagasse) and scrap tyre as preliminary stage of fuel sample analysis to be considered for energy production in gasification/combustion or pyrolysis facilities. The behaviour demonstrated with thermogravimetric analyzer (TGA), shows that all samples have high volatile amount release, 84.21% for bagasse and 85.08% for scrap tyre, which …

Optimising The Performance Of Roundabouts In Dar Es Salaam City, David Mfinanga

Tanzania Journal of Engineering and Technology (TJET)

Intersections are one of the major bottlenecks that aggravate congestion in road networks; effective control of which is an important strategy in improving traffic flow. While developing countries have found it hard to adopt sophisticated means of intersection control, they have also not optimised the performance of roundabouts. This paper reviews the performance of roundabouts, which have become increasingly popular in recent years, as simple and low cost forms of intersection control. The performance of three major roundabouts in Dar es Salaam has been analysed and results show that roundabouts can accommodate high traffic volumes without causing excessive delays. The …

A Study On The Integration Of A Novel Absorption Chiller Into A Microscale Combined Cooling, Heating, And Power (Micro-Cchp) System, Scott J. Richard

LSU New Orleans Theses and Dissertations

This study explores the application of micro-CCHP systems that utilize a 30 kW gas microturbine and an absorption chiller. Engineering Equation Solver (EES) is used to model a novel single-effect and double-effect water-lithium bromide absorption chiller that integrates the heat recovery unit and cooling tower of a conventional CCHP system into the chiller’s design, reducing the cost and footprint of the system. The results of the EES model are used to perform heat and material balances for the micro-CCHP systems employing the novel integrated chillers, and energy budgets for these systems are developed. While the thermal performance of existing CCHP …

Using Delay-Differential Equations For Modeling Calcium Cycling In Cardiac Myocytes, Ryan Thompson

Theses

The cycling of calcium at the intracellular level of cardiac cells plays a key role in the excitation-contraction process. The interplay between ionic currents, buffering agents, and calcium release from the sarcoplasmic reticulum (SR) is a complex system that has been shown experimentally to exhibit complex dynamics including period-2 states (alternans) and higher-order rhythms. Many of the calcium cycling activities involve the sensing, binding, or diffusion of calcium between intracellular compartments; these are physical processes that take time and typically are modeled by “relaxation” equations where the steady-state value and time course of a particular variable are specified through an …

Stability And Entanglement In An Optomechanical System, Matthew Schumacher

Theses

Optomechanical systems are currently of great interest as they lie at the boundary between quantum and classical mechanics, promising fundamental insights as well as new technologies. The practical operation of an optomechanical system requires that it satisfy the criteria of mechanical stability. Further, for quantum applications, it is important to characterize the degree of nonclassical correlation present between the mechanical and optical subsystems. In this study, we analyze the stability and entanglement in an optomechanical system where couplings linear as well as quadratic in the mechanical displacement are present simultaneously. Such systems can be realized experimentally. Our analysis of the …

Instability Indices For Matrix Polynomials, Todd Kapitula, Elizabeth Hibma, Hwa Pyeong Kim, Jonathan Timkovich

University Faculty Publications and Creative Works

There is a well-established instability index theory for linear and quadratic matrix polynomials for which the coefficient matrices are Hermitian and skew-Hermitian. This theory relates the number of negative directions for the matrix coefficients which are Hermitian to the total number of unstable eigenvalues for the polynomial. Herein we extend the theory to *-even matrix polynomials of any finite degree. In particular, unlike previously known cases we show that the instability index depends upon the size of the matrices when the degree of the polynomial is greater than two. We also consider Hermitian matrix polynomials, and derive an index which …

Elementary Differential Equations With Boundary Value Problems, William F. Trench

Textbooks Collection

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa- ration in linear algebra.

In writing this book I have been guided by the these principles:

An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. …

Modelling The Role Of Cloud Density On The Removal Of Gaseous Pollutants And Particulate Matters From The Atmosphere, Shyam Sundar, Rajan K. Sharma, Ram Naresh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a six dimensional nonlinear mathematical model is proposed to study the effect of the density of cloud droplets (formed due to the presence of vapors in the atmosphere) on the removal of pollutants, both gaseous and particulate, from the atmosphere. We assume that there exist six nonlinearly interacting phases in the atmosphere i.e. the vapor phase, the phase of cloud droplets, the phase of raindrops, the phase of gaseous pollutants, the phase of particulate matters and the phase of gaseous pollutants absorbed in raindrops. It is further assumed that the dynamics of the system undergo ecological type …

Dispersion Of A Solute In Hartmann Two-Fluid Flow Between Two Parallel Plates, J. P. Kumar, J. C. Umavathi

Applications and Applied Mathematics: An International Journal (AAM)

The paper presents an analytical solution for the dispersion of a solute in a conducting immiscible fluid flowing between two parallel plates in the presence of a transverse magnetic field. The fluids in both the regions are incompressible, electrically conducting and the transport properties are assumed to be constant. The channel walls are assumed to be electrically insulating. Separate solutions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The results are tabulated for various values of viscosity ratio, pressure gradient and Hartman number on the effective Taylor dispersion coefficient and volumetric …

Asymptotic Properties Of Solutions Of Two Dimensional Neutral Difference Systems, Thiagarajan Revathi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we obtain sufficient conditions for the asymptotic properties of solutions of two dimensional neutral difference systems. Our result extends some existing results in the literature. An example is given to illustrate the result.

Some New Sequence Spaces, Kuldip Raj, Sunil K. Sharma

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper we introduce some new sequence spaces defined by a Musielak-Orlicz function on semi normed spaces. We make an effort to study some topological properties and inclusion relations between these spaces. The study of sequence spaces over n -normed spaces has also been initiated in this paper.

Generalized Fractional Integral Of The Product Of Two Aleph-Functions, R. K. Saxena, J. Ram, D. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This paper is devoted to the study and develops the generalized fractional integral operators for a new special function, which is called Aleph-function. The considered generalized fractional integration operators contain the Appell hypergeometric function F₃ as a kernel. We establish two results of the product of two Aleph-functions involving Saigo-Maeda operators. On account of the general nature of the Saigo-Maeda operators and the Aleph-function, some results involving Saigo, Riemann-Liouville and Erdélyi-Kober integral operators are obtained as special cases of the main result.

Using Fuzzy Linear Regression To Estimate Relationship Between Forest Fires And Meteorological Conditions, Hande G. Akdemir, Fatma Tiryaki

Applications and Applied Mathematics: An International Journal (AAM)

Each year, millions of hectares of forest land are destroyed by fires causing great financial loss and ecological damage. In this paper, our aim is to study the effect of the variation of meteorological conditions on the total burned area in hectares, by using fuzzy linear regression analysis based on Tanaka’s approaches. The total burned area is considered a dependent variable. Air temperature (in ºC), relative humidity (in %), wind speed (in km/h) and rainfall (in mm/m² ) are considered to be independent variables. The relationship between input and output data is estimated using data provided in data mining …