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Articles 1 - 30 of 249
Full-Text Articles in Mathematics
Probabilistic Modeling Of Social Media Networks, Distinguishing Phylogenetic Networks From Trees, And Fairness In Service Queues, Md Rashidul Hasan
Probabilistic Modeling Of Social Media Networks, Distinguishing Phylogenetic Networks From Trees, And Fairness In Service Queues, Md Rashidul Hasan
Mathematics & Statistics ETDs
In this dissertation, three primary issues are explored. The first subject exposes who-saw-from-whom pathways in post-specific dissemination networks in social media platforms. We describe a network-based approach for temporal, textual, and post-diffusion network inference. The conditional point process method discovers the most probable diffusion network. The tool is capable of meaningful analysis of hundreds of post shares. Inferred diffusion networks demonstrate disparities in information distribution between user groups (confirmed versus unverified, conservative versus liberal) and local communities (political, entrepreneurial, etc.). A promising approach for quantifying post-impact, we observe discrepancies in inferred networks that indicate the disproportionate amount of automated bots. …
Modified Geometries, Clifford Algebras And Graphs: Their Impact On Discreteness, Locality And Symmetr, Roma Sverdlov
Modified Geometries, Clifford Algebras And Graphs: Their Impact On Discreteness, Locality And Symmetr, Roma Sverdlov
Mathematics & Statistics ETDs
In this dissertation I will explore the question whether various entities commonly used in quantum field theory can be “constructed". In particular, can spacetime be “constructed" out of building blocks, and can Berezin integral be “constructed" in terms of Riemann integrals.
As far as “constructing" spacetime out of building blocks, it has been attempted by multiple scientific communities and various models were proposed. But the common downfall is they break the principles of relativity. I will explore the ways of doing so in such a way that principles of relativity are respected. One of my approaches is to replace points …
Multilevel Optimization With Dropout For Neural Networks, Gary Joseph Saavedra
Multilevel Optimization With Dropout For Neural Networks, Gary Joseph Saavedra
Mathematics & Statistics ETDs
Large neural networks have become ubiquitous in machine learning. Despite their widespread use, the optimization process for training a neural network remains com-putationally expensive and does not necessarily create networks that generalize well to unseen data. In addition, the difficulty of training increases as the size of the neural network grows. In this thesis, we introduce the novel MGDrop and SMGDrop algorithms which use a multigrid optimization scheme with a dropout coarsening operator to train neural networks. In contrast to other standard neural network training schemes, MGDrop explicitly utilizes information from smaller sub-networks which act as approximations of the full …
Using Physics-Informed Neural Networks For Multigrid In Time Coarse Grid Equations, Jonathan P. Gutierrez
Using Physics-Informed Neural Networks For Multigrid In Time Coarse Grid Equations, Jonathan P. Gutierrez
Mathematics & Statistics ETDs
For parallel-in-time integration methods, the multigrid-reduction-in-time (MGRIT) method has shown promising results in both improved convergence and increased computational speeds when solving evolution problems. However, one problem the MGRIT algorithm currently faces is it struggles solving hyperbolic problems efficiently. In particular, hyperbolic problems are generally solved using explicit methods and this causes issues on the coarser multigrid levels, where larger (coarser) time step sizes can violate the stability condition. In this thesis, physics-informed neural networks (PINNs) are used to evaluate the coarse grid equations in the MGRIT algorithm with the goal to improve convergence for problems with hyperbolic behavior, as …
Neutrosophic Treatment Of The Modified Simplex Algorithm To Find The Optimal Solution For Linear Models, Florentin Smarandache, Maissam Ahmad Jdid
Neutrosophic Treatment Of The Modified Simplex Algorithm To Find The Optimal Solution For Linear Models, Florentin Smarandache, Maissam Ahmad Jdid
Branch Mathematics and Statistics Faculty and Staff Publications
Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and …
Optimal Agricultural Land Use: An Efficient Neutrosophic Linear Programming Method, Maisam Jdid, Florentin Smarandache
Optimal Agricultural Land Use: An Efficient Neutrosophic Linear Programming Method, Maisam Jdid, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
The increase in the size of the problems facing humans, their overlap, the division of labor, the multiplicity of departments, as well as the diversity of products and commodities, led to the complexity of business and the emergence of many administrative and production problems. It was necessary to search for appropriate methods to confront these problems. The science of operations research, with its diverse methods, provided the optimal solutions. It addresses many problems and helps in making scientific and thoughtful decisions to carry out the work in the best way within the available capabilities. Operations research is one of the …
Medical Diagnosis Via Refined Neutrosophic Fuzzy Logic: Detection Of Illness Using Neutrosophic Sets, K. Hemabala, B. Srinivasa Kumar, Florentin Smarandache
Medical Diagnosis Via Refined Neutrosophic Fuzzy Logic: Detection Of Illness Using Neutrosophic Sets, K. Hemabala, B. Srinivasa Kumar, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in refined neutrosophic fuzzy sets.
On Refined Neutrosophic Finite P-Group, Sunday Adesina Adebisi, Florentin Smarandache
On Refined Neutrosophic Finite P-Group, Sunday Adesina Adebisi, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
The neutrosophic automorphisms of a neutrosophic groups G (I) , denoted by Aut(G (I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G (I) which is also a neutrosophic homomorphism. Moreover, suppose that X1 = X(G (I)) is the neutrosophic group of inner neutrosophic auto-morphisms of a neutrosophic group G (I) and Xn the neutrosophic group of inner neutrosophic automorphisms of Xn-1. In this paper, we show that if any neutrosophic group of the sequence G (I), X1, X2, … is the identity, then G (I) is nilpotent.
Mitigation Impact Of Statewide Non-Pharmaceutical Policies On Covid-19: An Application Of Infectious Disease Transmission Model And Partially Observed Markov Process To New Mexico, Xingya Ma
Mathematics & Statistics ETDs
This thesis is an application of epidemiological models for infectious disease transmission and the use of partially observed Markov process (POMP) for model fitting. It focuses on COVID-19 pandemic in the state of New Mexico. The analysis covered March 2020 to June 2021. Daily data of COVID19 cases and deaths and a daily index of eleven statewide government non-pharmaceutical intervention (NPI) policies were collected from six public sources and were validated. These data were integrated through the Susceptible-Exposed-Infected-Removed (SEIR) model. Estimated daily transmission rates between the model compartments quantify the impact of the mitigation policies, and show that transmission rates …
Convexity Of Regularized Optimal Transport Dissimilarity Measures For Signed Signals, Christian P. Fowler
Convexity Of Regularized Optimal Transport Dissimilarity Measures For Signed Signals, Christian P. Fowler
Mathematics & Statistics ETDs
Debiased Sinkhorn divergence (DS divergence) is a distance function of
regularized optimal transport that measures the dissimilarity between two
probability measures of optimal transport. This thesis analyzes the advantages of
using DS divergence when compared to the more computationally expensive
Wasserstein distance as well as the classical Euclidean norm. Specifically, theory
and numerical experiments are used to show that Debiased Sinkhorn divergence
has geometrically desirable properties such as maintained convexity after data
normalization. Data normalization is often needed to calculate Sinkhorn
divergence as well as Wasserstein distance, as these formulas only accept
probability distributions as inputs and do not directly …
Statistical Methods For Differential Gene Expression Analysis Under The Case-Cohort Design, Lidong Wang
Statistical Methods For Differential Gene Expression Analysis Under The Case-Cohort Design, Lidong Wang
Mathematics & Statistics ETDs
Differential gene expression analysis has the potential to discover candidate biomarkers, therapeutic targets, and gene signatures. How to save money when using an unaffordable sample is a practical question. The case-cohort (CCH) study design can blend the economy of case-control studies with the advantages of cohort studies. But it has not been seen in the medical research literature where high-throughput genomic data were involved.
A score test does not need to fit the Cox PH model iteratively; hence, it can save computing time and avoid potential convergence issues. We developed a score test under the CCH design to identify DEGs …
Functional Data Analysis Of Covid-19, Nichole L. Fluke
Functional Data Analysis Of Covid-19, Nichole L. Fluke
Mathematics & Statistics ETDs
This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1st, 2020 and goes through March 31st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …
Music Genre Classification By Convolutional Neural Networks, Usame Suud
Music Genre Classification By Convolutional Neural Networks, Usame Suud
Mathematics & Statistics ETDs
In today’s world, deep learning models are widely used in a variety of fields. Audio
applications include speech recognition, audio classification, and music information
retrieval. In this paper, we will focus on the classification of music genres using an
artificial neural network. The development of audio machine learning techniques has
created an independence from traditional, more time-consuming signal processing
techniques. Starting with raw audio data, we will gain an understanding of what
audio is and its digital representation. Then, the focus will be on obtaining frequency
information from audio signals through the use of spectrograms. Transforming the
spectrograms into the …
Machine Learning Model Comparison And Arma Simulation Of Exhaled Breath Signals Classifying Covid-19 Patients, Aaron Christopher Segura
Machine Learning Model Comparison And Arma Simulation Of Exhaled Breath Signals Classifying Covid-19 Patients, Aaron Christopher Segura
Mathematics & Statistics ETDs
This study compared the performance of machine learning models in classifying COVID-19 patients using exhaled breath signals and simulated datasets. Ground truth classification was determined by the gold standard Polymerase Chain Reaction (PCR) test results. A residual bootstrapped method generated the simulated datasets by fitting signal data to Autoregressive Moving Average (ARMA) models. Classification models included neural networks, k-nearest neighbors, naïve Bayes, random forest, and support vector machines. A Recursive Feature Elimination (RFE) study was performed to determine if reducing signal features would improve the classification models performance using Gini Importance scoring for the two classes. The top 25% of …
Robust Uncertainty Quantification With Analysis Of Error In Standard And Non-Standard Quantities Of Interest, Zachary Stevens
Robust Uncertainty Quantification With Analysis Of Error In Standard And Non-Standard Quantities Of Interest, Zachary Stevens
Mathematics & Statistics ETDs
This thesis derives two Uncertainty Quantification (UQ) methods for differential equations that depend on random parameters: (\textbf{i}) error bounds for a computed cumulative distribution function (\textbf{ii}) a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria. Both UQ approaches utilize adjoint-based \textit{a posteriori} error analysis in order to accurately estimate the error in samples of numerically approximated quantities of interest. The adaptive MLMC algorithm developed in this thesis relies on the adjoint-based error analysis to adaptively create meshes and accurately monitor a stopping criteria. This is in contrast to classical MLMC algorithms which employ either a …
Applications Of Machine Learning Algorithms In Materials Science And Bioinformatics, Mohammed Quazi
Applications Of Machine Learning Algorithms In Materials Science And Bioinformatics, Mohammed Quazi
Mathematics & Statistics ETDs
The piezoelectric response has been a measure of interest in density functional theory (DFT) for micro-electromechanical systems (MEMS) since the inception of MEMS technology. Piezoelectric-based MEMS devices find wide applications in automobiles, mobile phones, healthcare devices, and silicon chips for computers, to name a few. Piezoelectric properties of doped aluminum nitride (AlN) have been under investigation in materials science for piezoelectric thin films because of its wide range of device applicability. In this research using rigorous DFT calculations, high throughput ab-initio simulations for 23 AlN alloys are generated.
This research is the first to report strong enhancements of piezoelectric properties …
Sparse Spectral-Tau Method For The Two-Dimensional Helmholtz Problem Posed On A Rectangular Domain, Gabriella M. Dalton
Sparse Spectral-Tau Method For The Two-Dimensional Helmholtz Problem Posed On A Rectangular Domain, Gabriella M. Dalton
Mathematics & Statistics ETDs
Within recent decades, spectral methods have become an important technique in numerical computing for solving partial differential equations. This is due to their superior accuracy when compared to finite difference and finite element methods. For such spectral approximations, the convergence rate is solely dependent on the smoothness of the solution yielding the potential to achieve spectral accuracy. We present an iterative approach for solving the two-dimensional Helmholtz problem posed on a rectangular domain subject to Dirichlet boundary conditions that is well-conditioned, low in memory, and of sub-quadratic complexity. The proposed approach spectrally approximates the partial differential equation by means of …
Eigenfunction Restriction Estimates For Curves With Nonvanishing Geodesic Curvatures In Compact Riemannian Surfaces With Nonpositive Sectional Curvatures, Chamsol Park
Mathematics & Statistics ETDs
For 2 ≤ p < 4, we study the Lp norms of restrictions of eigenfunctions of the Laplace-Beltrami operator on smooth compact 2-dimensional Riemannian manifolds. Burq, G\´erard, and Tzvetkov [12], and Hu [21] found eigenfunction restriction estimates for a curve with nonvanishing geodesic curvatures. We will explain how the proof of the known estimates helps us to consider the case where the given smooth compact Riemannian manifold has nonpositive sectional curvatures. For p = 4, we will also obtain a logarithmic analogous estimate, by using arguments in Xi and Zhang [37], Sogge [33], and Bourgain [10]. At the end of this dissertation, we will talk about a future work, which is a follow up study for higher dimensional analogues of the above curve cases.
Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano
Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano
Electrical and Computer Engineering ETDs
Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect produced …
New Development Of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, And Neutrosophic Plithogenic Optimizations, Florentin Smarandache, Yanhui Guo
New Development Of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, And Neutrosophic Plithogenic Optimizations, Florentin Smarandache, Yanhui Guo
Branch Mathematics and Statistics Faculty and Staff Publications
This collective book presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic symmetry, as well as their applications in the real world.
Sparse Domination Of The Martingale Transform, Michael Scott Kutzler
Sparse Domination Of The Martingale Transform, Michael Scott Kutzler
Mathematics & Statistics ETDs
Linear operators are of huge importance in modern harmonic analysis. Many operators can be dominated by finitely many sparse operators. The main result in this thesis is showing a toy operator, namely the Martingale Transform is dominated by a single sparse operator. Sparse operators are based on a sparse family which is simply a subset of a dyadic grid. We also show the A2 conjecture for the Martingale Transform which follows from the sparse domination of the Martingale Transform and the A2 conjecture for sparse operators.
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Multiple Baseline Interrupted Time Series: Describing Changes In New Mexico Medicaid Behavioral Health Home Patients’ Care, Jessica Reno
Multiple Baseline Interrupted Time Series: Describing Changes In New Mexico Medicaid Behavioral Health Home Patients’ Care, Jessica Reno
Mathematics & Statistics ETDs
In 2016, the CareLink New Mexico behavioral health homes program began enrolling Medicaid recipients with the goal of increasing care coordination, improving access to services, and decreasing long-term costs of care for adults with serious mental illness (SMI) and children with severe emotional disturbance (SED). To evaluate these aims, a retrospective interrupted time series study using Medicaid claims data was designed. First, a comparable subset of non-enrolled individuals was selected from the pool of Medicaid recipients with SMI or SED using propensity score matching. Then, segmented regression was applied to three outcomes: total Medicaid charges, number of outpatient behavioral health …
Optimal Transport Driven Bayesian Inversion With Application To Signal Processing, Elijah F. Perez
Optimal Transport Driven Bayesian Inversion With Application To Signal Processing, Elijah F. Perez
Mathematics & Statistics ETDs
This paper will outline a Debiased Sinkhorn Divergence driven Bayesian inversion framework. Conventionally, a Gaussian Driven Bayesian framework is used when performing Bayesian inversion. A major issue with this Gaussian framework is that the Gaussian likelihood, driven by the L2 norm, is not affected by phase shift in a given signal. This issue has been addressed in [1] using a Wasserstein framework. However, the Wasserstein framework still has an issue because it assumes statistical independence when multidimensional signals are analyzed. This assumption of statistical independence cannot always be made when analyzing signals where multiple detectors are recording one event, say …
Applications Of Evidence Theory To High-Consequence Systems Safety, Christina Marie Deffenbaugh
Applications Of Evidence Theory To High-Consequence Systems Safety, Christina Marie Deffenbaugh
Mathematics & Statistics ETDs
Issues linked to abnormal environments (like high-consequence systems safety, e.g., nuclear weapon components, bridges, apartment buildings, etc.) may have insufficient information to use either classical statistical methods or Bayesian approaches for calculating associated probabilistic risks, so there is often a requirement for another method that can deal with a low-information situation to obtain a risk assessment. Belief/plausibility measures of uncertainty from A. P. Dempster and G. Shafer’s Evidence Theory is one such method. This thesis has two goals. First, a brief discussion on belief/plausibility measures as an application of Evidence Theory will familiarize the audience with its history and how …
The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021), Florentin Smarandache, Maykel Leyva-Vazquez
The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021), Florentin Smarandache, Maykel Leyva-Vazquez
Branch Mathematics and Statistics Faculty and Staff Publications
Este es el cuarto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se su impacto en Latinoamérica junto con enlaces a los principales artículos y libros. Los conjuntos neutrosóficos, la lógica neutrosófica, la probabilidad neutrosófica, la estadística neutrosófica, el precálculo neutrosófico, el cálculo neutrosófico, la psicología neutrosófica, la sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, …
Theory And Application Of Hypersoft Set, Florentin Smarandache, Muhammad Saeed, Muhammad Saqlain, Mohamed Abdel-Baset
Theory And Application Of Hypersoft Set, Florentin Smarandache, Muhammad Saeed, Muhammad Saqlain, Mohamed Abdel-Baset
Branch Mathematics and Statistics Faculty and Staff Publications
Aims and Scope Florentin Smarandache generalize the soft set to the hypersoft set by transforming the function �� into a multi-argument function. This extension reveals that the hypersoft set with neutrosophic, intuitionistic, and fuzzy set theory will be very helpful to construct a connection between alternatives and attributes. Also, the hypersoft set will reduce the complexity of the case study. The Book “Theory and Application of Hypersoft Set” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic, intuitionistic, and fuzzy information. Our goal is to develop a strong relationship with the MCDM solving techniques and to …
Solving Neutrosophic Linear Equations Systems Using Symbolic Computation (Resolucion De Sistemas De Ecuaciones Lineales Neutrosóficas Mediante Computación Simbólica), Maykel Leyva-Vazquez, Florentin Smarandache
Solving Neutrosophic Linear Equations Systems Using Symbolic Computation (Resolucion De Sistemas De Ecuaciones Lineales Neutrosóficas Mediante Computación Simbólica), Maykel Leyva-Vazquez, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we apply the concept of neutrosophic numbers to solve a systems of neutrophic linear equations using symbolic computation. Also, we utilize Jupyter, which is supported in Google Colaboratory for performing symbolic computation. The sympy library of Python is used to perform the process of neutrosophic computation. Systems of neutrosophic linear equations are solved through symbolic computation in Python. A case study was developed for the determination of vehicular traffic with indeterminacy. This king of computation opens new ways to deal with indeterminacy in real-world problems.
Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache
Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true. The NeutroTheorem and AntiTheorem are generalizations and alternatives of …
Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova
Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova
Mathematics & Statistics ETDs
The present work offers an investigation of dynamics and stability of nonlinear waves in Hamiltonian systems. The first part of the manuscript discusses the classical problem of water waves on the surface of an ideal fluid in 2D. We demonstrate how to construct the Stokes waves, and how to apply a continuation method to find waves in close vicinity to the limiting Stokes wave. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for the fluid. We provide numerical evidence that pairs of unstable eigenvalues of …
From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov
From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov
Mathematics & Statistics ETDs
In this work we concentrate on two separate topics which pose certain numerical challenges. The first topic is the spin dynamics of electrons in high-energy circular accelerators. We introduce a stochastic differential equation framework to study spin depolarization and spin equilibrium. This framework allows the mathematical study of known equations and new equations modelling the spin distribution of an electron bunch. A spin distribution is governed by a so-called Bloch equation, which is a linear Fokker-Planck type PDE, in general posed in six dimensions. We propose three approaches to approximate solutions, using analytical and modern numerical techniques. We also present …