Analysis Commons^™

Chebyshev Type Inequalities Involving The Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function In The Kernel, S. D. Purohit, N. Jolly, M. K. Bansal, Jagdev Singh, Devendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Recently, several authors have investigated Chebyshev type inequalities for numerous fractional integral operators. Being motivated by the work done by earlier researchers and their numerous applications in probability, transform theory, numerical quadrature, statistical problems and its significance in fractional boundary value problems. We aim to evaluate Chebyshev type inequalities involving fractional integral operator containing multi-index Mittag-Leffler function in the kernel. Admissible connections of the results mentioned in this article to those associated with previously established familiar fractional integral operators have been pointed out.

Ruscheweyh-Goyal Derivative Of Fractional Order, Its Properties Pertaining To Pre-Starlike Type Functions And Applications, Ritu Agarwal, G. S. Paliwal

Applications and Applied Mathematics: An International Journal (AAM)

The study of the operators possessing convolution form and their properties is considered advantageous in geometric function theory. In 1975 Ruscheweyh defined operator for analytic functions using the technique of convolution. In 2005, Goyal and Goyal generalized the Ruscheweyh operator to fractional order (which we call here Ruscheweyh-Goyal differential operator) using Srivastava-Saigo fractional differential operator involving hypergeometric function. Inspired by these earlier efforts, we discuss the properties of the Ruscheweyh-Goyal derivative of arbitrary order. We define a class of pre-starlike type functions involving the Ruscheweyh-Goyal fractional derivative and obtain the inclusion relation. Further, we prove that Ruscheweyh-Goyal derivative operator preserve …

Class Of Integrals Involving Generalized Hypergeometric Function, D. L. Suthar, Teklay Hailay, Hafte Amsalu, Jagdev Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we establish some definite integrals involving generalized hypergeometric function, product of algebraic functions, Jacobi function, Legendre function and general class of polynomials. Certain special cases of the main results are also pointed out.

Preparing For The Future: The Effects Of Financial Literacy On Financial Planning For Young Professionals, Tanay Singh

Senior Theses

Purpose – Many people between the age of 20 and 34 have not considered planning financially for the future in any significant capacity and in doing so, they limit their potential savings. The purpose of this study is to examine what financial expectations are for people in the early stages of their career and determine if improving financial literacy and revealing financial realities helps to produce more accurate or realistic expectations. Ultimately, the goal is to better prepare participants in the study for the working world and increased responsibilities outside of the college/university environment by getting them to start thinking …

Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown

Murray State Theses and Dissertations

Data and algorithmic modeling are two different approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classification and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to find the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in different cases depending on the data set. In our case, the data …

Tropical Cyclone Hazards In Relation To Propagation Speed, Jiehao Huang

Dissertations and Theses

As the population and infrastructure along the US East Coast increase, it becomes increasingly important to study the characteristics of tropical cyclones that can impact the coast. A recent study shows that the propagation speed of tropical cyclones has slowed over the past 60 years, which can lead to greater accumulation of precipitation and greater storm surge impacts. The study presented herein is meant to examine and analyze the relationships that exist between the propagation speed of tropical cyclones, their surface wind strength, displacement angles, and cyclone averaged winds. This analysis is focused on tropical cyclones spanning from 1950-2015 in …

Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins

College of Graduate Studies: Theses & Dissertations

In biology, minimizing a free energy functional gives an equilibrium shape that is the most stable in nature. The formulation of these functionals can vary in many ways, in particular they can have either a smooth or sharp interface. Minimizing a functional can be done through variational calculus or can be proved to exist using various analysis techniques. The functionals investigated here have a smooth and sharp interface and are analyzed using analysis and variational calculus respectively. From the former we find the condition for extremum and its second variation. The second variation is commonly used to analyze stability of …

On A Hybrid Technique To Handle Analytical And Approximate Solutions Of Linear And Nonlinear Fractional Order Partial Differential Equations, Kamal Shah, Hammad Khalil, Ahmet Yildirim

Applications and Applied Mathematics: An International Journal (AAM)

This manuscript is devoted to consider Natural transform (NT) coupled with homotopy perturbation method (HPM) for obtaining series solutions to some linear and nonlinear fractional partial differential equations (FPDEs). By means of NT, we obtain the transformed problem which is then solved by using HPM. By means of Stehfest’s numerical algorithm and using the dual relationship of NT and Laplace transform, we calculate inverse NT for approximate solutions. The series solutions we obtain using the proposed method are in close agreement with the exact solutions. We apply the proposed method to some interesting problems to illustrate our main results.

Solutions Of The Generalized Abel’S Integral Equation Using Laguerre Orthogonal Approximation, N. Singha, C. Nahak

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical approximation is drafted for solving the generalized Abel’s integral equation by practicing Laguerre orthogonal polynomials. The proposed approximation is framed for the first and second kinds of the generalized Abel’s integral equation. We have utilized the properties of fractional order operators to interpret Abel’s integral equation as a fractional integral equation. It offers a new approach by employing Laguerre polynomials to approximate the integrand of a fractional integral equation. Given examples demonstrate the simplicity and suitability of the method. The graphical representation of exact and approximate solutions helps in visualizing a solution at discrete points, …

Application Of Reduced Differential Transform Method For Solving Two-Dimensional Volterra Integral Equations Of The Second Kind, Seyyedeh R. Moosavi Noori, Nasir Taghizadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose new theorems of the reduced differential transform method (RDTM) for solving a class of two-dimensional linear and nonlinear Volterra integral equations (VIEs) of the second kind. The advantage of this method is its simplicity in using. It solves the equations straightforward and directly without using perturbation, Adomian’s polynomial, linearization or any other transformation and gives the solution as convergent power series with simply determinable components. Also, six examples and numerical results are provided so as to validate the reliability and efficiency of the method.

On The Weighted Pseudo Almost Periodic Solutions Of Nicholson’S Blowflies Equation, Ramazan Yazgan, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

This study is concerned with the existence, uniqueness and global exponential stability of weighted pseudo almost periodic solutions of a generalized Nicholson’s blowflies equation with mixed delays. Using some differential inequalities and a fixed point theorem, sufficient conditions were obtained for the existence, uniqueness of at the least a weighted pseudo almost periodic solutions and global exponential stability of this solution. The results of this study are new and complementary to the previous ones can be found in the literature. At the end of the study an example is given to show the accuracy of our results.

General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr

LSU New Orleans Theses and Dissertations

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation …

Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, Abbie Hendley

Master's Theses

For this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their accuracy and scalability can be improved. We will solve the heat equation in one-dimension with two cases to observe the behaviors of the errors using KSS methods. The first case will implement KSS methods with trigonometric initial conditions, then another case where the initial conditions are polynomial functions. We will also look at both the time-independent and time-dependent …

Design Of Metamaterials For Optics, Abiti Adili

LSU Doctoral Dissertations

First part of this dissertation studies the problem of designing metamaterial crystals with double negative effective properties for applications in optics by investigating the conditions necessary for generating novel dispersion properties in a metamaterial crystal with subwavelength microstructure. This provides novel optical properties created through local resonances tied to the geometry of the media in subwavelength regime.

In the second part, this dissertation studies the representation formula used to describe band structures in photonic crystals with plasmonic inclusions. By using layer potential techniques, a magnetic dipole operator describing the tangential component of the electrical field generated by magnetic distribution is …

Generalized Bagley-Torvik Equation And Fractional Oscillators, Mark Naber, Lucas Lymburner

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the driving force. The properties of the effective decay rate and the oscillation frequency with respect to the order of the fractional damping are also studied. It is found that the effective decay rate and oscillation frequency have a complex dependency on the order of the derivative of the damping term and exhibit properties one might expect of a thermodynamic Equation of …

Generalized Differential Transform Method For Solving Some Fractional Integro-Differential Equations, S. Shahmorad, A. A. Khajehnasiri

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we use a generalized form of two-dimensional Differential Transform (2D-DT) to solve a new class of fractional integro-differential equations. We express some useful properties of the new transform as a proposition and prove a convergence theorem. Then we illustrate the method with numerical examples.

Transient Thermal Stresses Due To Axisymmetric Heat Supply In A Semi-Infinite Thick Circular Plate, S. D. Warbhe, K. C. Deshmukh

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with the determination of thermal stresses in a semi-infinite thick circular plate of a finite length and infinite extent subjected to an axisymmetric heat supply. A thick circular plate is considered having constant initial temperature and arbitrary heat flux is applied on the upper and lower face. The governing heat conduction equation has been solved by using integral transform technique. The results are obtained in terms of Bessel’s function. The thermoelastic behavior has been computed numerically and illustrated graphically for a steel plate.

Generalized Growth And Faber Polynomial Approximation Of Entire Functions Of Several Complex Variables In Some Banach Spaces, Devendra Kumar, Manisha Vijayran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the relationship between the generalized order of growth of entire functions of many complex variables m(m ≥ 2) over Jordan domains and the sequence of Faber polynomial approximations in some Banach spaces has been investigated. Our results improve the various results shown in the literature.

Unified Ball Convergence Of Inexact Methods For Finding Zeros With Multiplicity, Ioannis K. Argyros, Santhosh George

Applications and Applied Mathematics: An International Journal (AAM)

We present an extended ball convergence of inexact methods for approximating a zero of a nonlinear equation with multiplicity m; where m is a natural number. Many popular methods are special cases of the inexact method.

Functional Dimension Of Solution Space Of Differential Operators Of Constant Strength, Morteza Shafii-Mousavi

Applications and Applied Mathematics: An International Journal (AAM)

A differential operator with constant coefficients is hypoelliptic if and only if its solution space is of finite functional dimension. We extend this property to operators with variable coefficient. We prove that an equally strong differential operator with variable coefficients has the same property. In addition, we extend the Zielezny’s result to operators with variable coefficients; prove that an operator with analytic coefficients on ℝⁿ is elliptic if and only if locally the functional dimension of its solution space is the same as the Euclidean dimension n.

Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium, Dilip K. Jaiswal, Gulrana _

Applications and Applied Mathematics: An International Journal (AAM)

One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs.

Dynamic Attribute-Level Best Worst Discrete Choice Experiments, Amanda Working, Mohammed Alqawba, Norou Diawara

Mathematics & Statistics Faculty Publications

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are …

Approximations In Reconstructing Discontinuous Conductivities In The Calderón Problem, George H. Lytle

Theses and Dissertations--Mathematics

In 2014, Astala, Päivärinta, Reyes, and Siltanen conducted numerical experiments reconstructing a piecewise continuous conductivity. The algorithm of the shortcut method is based on the reconstruction algorithm due to Nachman, which assumes a priori that the conductivity is Hölder continuous. In this dissertation, we prove that, in the presence of infinite-precision data, this shortcut procedure accurately recovers the scattering transform of an essentially bounded conductivity, provided it is constant in a neighborhood of the boundary. In this setting, Nachman’s integral equations have a meaning and are still uniquely solvable.

To regularize the reconstruction, Astala et al. employ a high frequency …

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.

The Encyclopedia Of Neutrosophic Researchers - Vol. 3, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

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.

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 …

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 …

Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

SMU Data Science Review

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as recommended or non-recommended affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that reviews …