Applied Mathematics | Open Access Articles | Digital Commons Network™

Tripleta De Estructura Neutrosófica Y Tripleta De Estructura Neutrosófica Extendida, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

En el presente estudio se realiza una revisión de las tripletas de estructura neutrosófica y tripleta de estructura neutrosófica extendida, con el fin de introducir nuevos conceptos a emplear en trabajos futuros.

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Grado De Dependencia E Independencia De Los (Sub) Componentes De Conjuntos Borrosos Y Neutrosóficos, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

La introducción del grado de dependencia (y en consecuencia el grado de independencia) entre los componentes del conjunto difuso, y también entre los componentes del conjunto neutrosófico, se introduce por primera vez en la quinta edición del libro de Neutrosofía en el año 2006, basado en los elementos descritos en dicha edición del libro, se comienza a conocer conceptos de conjuntos neutrosóficos de los componentes borrosos así como los grados de dependencia e independencia, Por tal motivo el objetivo del presente trabajo es extender el conjunto neutrosófico refinado, teniendo en cuenta la grado de dependencia o independencia de los subcomponentes …

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Forecasting Crashes, Credit Card Default, And Imputation Analysis On Missing Values By The Use Of Neural Networks, Jazmin Quezada

Open Access Theses & Dissertations

A neural network is a system of hardware and/or software patterned after the operation of neurons in the human brain. Neural networks,- also called Artificial Neural Networks - are a variety of deep learning technology, which also falls under the umbrella of artificial intelligence, or AI. Recent studies shows that Artificial Neural Network has the highest coefficient of determination (i.e. measure to assess how well a model explains and predicts future outcomes.) in comparison to the K-nearest neighbor classifiers, logistic regression, discriminant analysis, naive Bayesian classifier, and classification trees. In this work, the theoretical description of the neural network methodology …

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Associated Primes And Syzygies Of Linked Modules, Olgur Celikbas, Mohammad T. Dibaei, Mohsen Gheibi, Arash Sadeghi, Ryo Takahaski

Department of Mathematics: Faculty Publications

Motivated by the notion of geometrically linked ideals, we show that over a Gorenstein local ring R, if a Cohen-Macaulay R-module M of grade g is linked to an R-module N by a Gorenstein ideal c, such that AssR(M)\AssR(N) = ;, then M R N is isomorphic to direct sum of copies of R=a, where a is a Gorenstein ideal of R of grade g + 1. We give a criterion for the depth of a local ring (R;m; k) in terms of the homological dimensions of the modules linked to the syzygies of the residue eld k. As a …

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Persistence Metrics For A River Population In A Two-Dimensional Benthic-Drift Model, Yu Jin, Qihua Huang, Julia Blackburn, Mark A. Lewis

Department of Mathematics: Faculty Publications

The study of population persistence in river ecosystems is key for understanding population dynamics, invasions, and instream flow needs. In this paper, we extend theories of persistence measures for population models in one-dimensional rivers to a benthic-drift model in two-dimensional depth- averaged rivers. We define the fundamental niche and the source and sink metric, and establish the net reproductive rate R₀ to determine global persistence of a population in a spatially heterogeneous two-dimensional river. We then couple the benthic-drift model into the two-dimensional computational river model, River2D, to study the growth and persistence of a population and its source …

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A Statistical Investigation Of Stock Market Activity And Instances Of Financial Crime, Elizabeth G. Biggs

Theses and Dissertations

This project aims to identify a possible statistical relationship between the stock market and incidences of financial crime in Illinois, Texas, and Utah through big data analysis techniques using data from the FBI’s Federal Bureau of Investigation’s National Incident-Based Reporting System (NIBRS) database. By analyzing the occurrences of financial crime by location, year, and type in relation to the S&P 500’s percent change in close price on the first day of the calendar year, it will be possible to determine if a statistical relationship exists between the two. In addition, regression analysis was performed in order to predict financial crime …

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Eigenvalues And Approximation Numbers, Ryan Chakmak

CMC Senior Theses

While the spectral theory of compact operators is known to many, knowledge regarding the relationship between eigenvalues and approximation numbers might be less known. By examining these numbers in tandem, one may develop a link between eigenvalues and l^p spaces. In this paper, we develop the background of this connection with in-depth examples.

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New Reproducing Kernel Hilbert Spaces On Plane Regions, Their Properties, And Applications To Partial Differential Equations, Jabar S. Hassan

Doctoral Dissertations

"We introduce new reproducing kernel Hilbert spaces W₂^(m,n) (D) on unbounded plane regions D. We study linear non-homogeneous hyperbolic partial differential equation problems on D with solutions in various reproducing kernel Hilbert spaces. We establish existence and uniqueness results for such solutions under appropriate hypotheses on the driver. Stability of solutions with respect to the driver is analyzed and local uniform approximation results are obtained which depend on the density of nodes. The local uniform approximation results required a careful determination of the reproducing kernel Hilbert spaces on which the elementary …

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Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we give necessary conditions for stability of flocks in R. We focus on linear arrays with decentralized agents, where each agent interacts with only a few its neighbors. We obtain explicit expressions for necessary conditions for asymptotic stability in the case that the systems consists of a periodic arrangement of two or three different types of agents, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single agent (...1-1-1) held that the first moment of certain coefficients governing the interactions between agents has to be …

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Kings In The Direct Product Of Digraphs, Morgan Norge

Theses and Dissertations

A k-king in a digraph D is a vertex that can reach every other vertex in D by a directed path of length at most k. A king is a vertex that is a k-king for some k. We will look at kings in the direct product of digraphs and characterize a relationship between kings in the product and kings in the factors. This is a continuation of a project in which a similar characterization is found for the cartesian product of digraphs, the strong product of digraphs, and the lexicographic product of digraphs.

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Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

Articles

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …

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Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov

Articles

Abstract. The present paper is dedicated to integrable models with Mikhailov reduction groups G_R ≃ D_h. Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the G_R-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with D_h symmetries are presented.

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Lozenge Tilings Of A Halved Hexagon With An Array Of Triangles Removed From The Boundary, Part Ii, Tri Lai

Department of Mathematics: Faculty Publications

Proctor's work on staircase plane partitions yields an exact enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi later ex- tended this tiling enumeration to a halved hexagon with a triangle cut o from the boundary. In his previous paper, the author proved a common generalization of Proctor's and Rohatgi's results by enumerating lozenge tilings of a halved hexagon in the case an array of an arbitrary number of triangles has been removed from a non-staircase side. In this paper we consider the other case when the array of tri- angles has been removed from the …

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Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright

Mathematics & Statistics ETDs

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to …

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Fibonacci And Lucas Differential Equations, Esra Erkus-Duman, Hakan Ciftci

Applications and Applied Mathematics: An International Journal (AAM)

The second-order linear hypergeometric differential equation and the hypergeometric function play a central role in many areas of mathematics and physics. The purpose of this paper is to obtain differential equations and the hypergeometric forms of the Fibonacci and the Lucas polynomials. We also write again these polynomials by means of Olver’s hypergeometric functions. In addition, we present some relations between these polynomials and the other well-known functions.

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Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan

Applications and Applied Mathematics: An International Journal (AAM)

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.

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Simplifying Coefficients In A Family Of Ordinary Differential Equations Related To The Generating Function Of The Laguerre Polynomials, Feng Qi

Applications and Applied Mathematics: An International Journal (AAM)

In the paper, by virtue of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Laguerre polynomials.

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Conformable Derivative Operator In Modelling Neuronal Dynamics, Mehmet Yavuz, Burcu Yaşkıran

Applications and Applied Mathematics: An International Journal (AAM)

This study presents two new numerical techniques for solving time-fractional one-dimensional cable differential equation (FCE) modeling neuronal dynamics. We have introduced new formulations for the approximate-analytical solution of the FCE by using modified homotopy perturbation method defined with conformable operator (MHPMC) and reduced differential transform method defined with conformable operator (RDTMC), which are derived the solutions for linear-nonlinear fractional PDEs. In order to show the efficiencies of these methods, we have compared the numerical and exact solutions of fractional neuronal dynamics problem. Moreover, we have declared that the proposed models are very accurate and illustrative techniques in determining to approximate-analytical …

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Induced Hesitant 2-Tuple Linguistic Aggregation Operators With Application In Group Decision Making, Tabasam Rashid, Ismat Beg, Raja N. Jamil

Applications and Applied Mathematics: An International Journal (AAM)

In this article, hesitant 2-tuple linguistic arguments are used to evaluate the group decision making problems which have inter dependent or inter active attributes. Operational laws are developed for hesitant 2-tuple linguistic elements and based on these operational laws hesitant 2- tuple weighted averaging operator and generalized hesitant 2- tuple averaging operator are proposed. Combining Choquet integral with hesitant 2-tuple linguistic information, some new aggregation operators are defined, including the hesitant 2-tuple correlated averaging operator, the hesitant 2-tuple correlated geometric operator and the generalized hesitant 2-tuple correlated averaging operator. These proposed operators successfully manage the correlations among the elements. After …

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Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms …

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Markov Chains And Generalized Wavelet Multiresolutions, Myung-Sin Song, Palle Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We develop some new results for a general class of transfer operators, as they are used in a construction of multi-resolutions. We then proceed to give explicit and concrete applications. We further discuss the need for such a constructive harmonic analysis/dynamical systems approach to fractals.

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The Compensation For Few Clusters In Clustered Randomized Trials With Binary Outcomes, Lily Stalter

Mathematics & Statistics ETDs

Cluster randomized trials are increasingly popular in epidemiological and medical research. When analyzing the data from such studies it is imperative that the hierarchical structure of the data be taken into account. Multilevel logistic regression is used to analyze clustered data with binary outcomes. Previous literature shows that a greater number of clusters is more important than a large number of subjects per cluster. This paper investigates if it is possible to compensate for the increased bias found for parameter estimates when the number of clusters is decreased. A simulation study was conducted where the absolute percent relative bias for …

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Translation Theorems For The Fourier-Feynman Transform On The Product Function Space C2 A,B, [0,T], Seung Jun Chang, Jae Gil Choi, David Skoug

Department of Mathematics: Faculty Publications

In this article, we establish the Cameron{Martin translation theo- rems for the analytic Fourier{Feynman transform of functionals on the product function space C2 a;b[0; T]. The function space Ca;b[0; T] is induced by the gener- alized Brownian motion process associated with continuous functions a(t) and b(t) on the time interval [0; T]. The process used here is nonstationary in time and is subject to a drift a(t). To study our translation theorem, we introduce a Fresnel-type class Fa;b A1;A2 of functionals on C2 a;b[0; T], which is a generaliza- tion of the Kallianpur and Bromley{Fresnel class FA1;A2 . We then …

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Modeling Association In Microbial Communities With Clique Loginear Models, Adrian Dobra, Camilo Valdes, Dragana Ajdic, Bertrand S. Clarke, Jennifer Clarke

Department of Mathematics: Faculty Publications

There is a growing awareness of the important roles that microbial communities play in complex biological processes. Modern investigation of these often uses next generation sequencing of metagenomic samples to determine community composition. We propose a statistical technique based on clique loglinear models and Bayes model averaging to identify microbial components in a metagenomic sample at various taxonomic levels that have significant associations. We describe the model class, a stochastic search technique for model selection, and the calculation of estimates of posterior probabilities of interest. We demonstrate our approach using data from the Human Microbiome Project and from a study …

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Quantitative Validation Of Simulated Sea Ice Displacements, Bryan R. Mccormick

Mathematics & Statistics ETDs

Accurate simulations of Arctic sea ice are important for forecasting as well as for understanding the global climate. However, quantitative measures for simulation displacements are underutilized. We present five such measures proposed as being useful in the validation of simulated sea ice displacements. Using drifting buoy and satellite measurements of sea ice motion as observation, we apply the metrics in a comparison of observed displacements and predicted displacements from the Arctic sea ice simulation MPM\_ice. We find the metric scores are useful for comparing simulations and observations. The metrics also brought to light problems in the simulation MPM_ice, demonstrating their …

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Cartan Triples, Allan P. Donsig, Adam H. Fuller, David R. Pitts

Department of Mathematics: Faculty Publications

We introduce the class of Cartan triples as a generalization of the notion of a Car- tan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi’s theorem to this setting. This context contains that of Fulman’s generalization of Cartan MASAs and we discuss his generalization in an appendix.

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Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Full-Text Articles in Applied Mathematics

Tripleta De Estructura Neutrosófica Y Tripleta De Estructura Neutrosófica Extendida, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Grado De Dependencia E Independencia De Los (Sub) Componentes De Conjuntos Borrosos Y Neutrosóficos, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Forecasting Crashes, Credit Card Default, And Imputation Analysis On Missing Values By The Use Of Neural Networks, Jazmin Quezada

Open Access Theses & Dissertations

Associated Primes And Syzygies Of Linked Modules, Olgur Celikbas, Mohammad T. Dibaei, Mohsen Gheibi, Arash Sadeghi, Ryo Takahaski

Department of Mathematics: Faculty Publications

Persistence Metrics For A River Population In A Two-Dimensional Benthic-Drift Model, Yu Jin, Qihua Huang, Julia Blackburn, Mark A. Lewis

Department of Mathematics: Faculty Publications

A Statistical Investigation Of Stock Market Activity And Instances Of Financial Crime, Elizabeth G. Biggs

Theses and Dissertations

Eigenvalues And Approximation Numbers, Ryan Chakmak

CMC Senior Theses

New Reproducing Kernel Hilbert Spaces On Plane Regions, Their Properties, And Applications To Partial Differential Equations, Jabar S. Hassan

Doctoral Dissertations

Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

Kings In The Direct Product Of Digraphs, Morgan Norge

Theses and Dissertations

Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

Articles

Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov

Articles

Lozenge Tilings Of A Halved Hexagon With An Array Of Triangles Removed From The Boundary, Part Ii, Tri Lai

Department of Mathematics: Faculty Publications

Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright

Mathematics & Statistics ETDs

Fibonacci And Lucas Differential Equations, Esra Erkus-Duman, Hakan Ciftci

Applications and Applied Mathematics: An International Journal (AAM)

Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan

Applications and Applied Mathematics: An International Journal (AAM)

Simplifying Coefficients In A Family Of Ordinary Differential Equations Related To The Generating Function Of The Laguerre Polynomials, Feng Qi

Applications and Applied Mathematics: An International Journal (AAM)

Conformable Derivative Operator In Modelling Neuronal Dynamics, Mehmet Yavuz, Burcu Yaşkıran

Applications and Applied Mathematics: An International Journal (AAM)

Induced Hesitant 2-Tuple Linguistic Aggregation Operators With Application In Group Decision Making, Tabasam Rashid, Ismat Beg, Raja N. Jamil

Applications and Applied Mathematics: An International Journal (AAM)

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Markov Chains And Generalized Wavelet Multiresolutions, Myung-Sin Song, Palle Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

The Compensation For Few Clusters In Clustered Randomized Trials With Binary Outcomes, Lily Stalter

Mathematics & Statistics ETDs

Translation Theorems For The Fourier-Feynman Transform On The Product Function Space C2 A,B, [0,T], Seung Jun Chang, Jae Gil Choi, David Skoug

Department of Mathematics: Faculty Publications

Modeling Association In Microbial Communities With Clique Loginear Models, Adrian Dobra, Camilo Valdes, Dragana Ajdic, Bertrand S. Clarke, Jennifer Clarke

Department of Mathematics: Faculty Publications

Quantitative Validation Of Simulated Sea Ice Displacements, Bryan R. Mccormick

Mathematics & Statistics ETDs

Cartan Triples, Allan P. Donsig, Adam H. Fuller, David R. Pitts

Department of Mathematics: Faculty Publications

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

Annual Symposium on Biomathematics and Ecology Education and Research

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

Annual Symposium on Biomathematics and Ecology Education and Research