Applied Mathematics Commons^™

(R1884) Motion Of Variable Mass Body In The Seventh-Degree Henon-Heiles System, Shiv K. Sahdev, Abdullah A. Ansari

Applications and Applied Mathematics: An International Journal (AAM)

The goal of this paper is to reveal numerically the generalized Henon-Heiles system, that is, in the seventh-degree potential function where the smallest body mass varies. Utilizing the seventh degree potential function, we determine the equations of motion for the variable mass generalized Henon-Heiles system. Then we perform the graphical works such as locations of parking points, allowed regions of motion, and attracting domain basins. Lastly, using the Meshcherskii space transformations, we investigate stability states for these parking points.

(R1888) On The Mackey-Glass Model With A Piecewise Constant Argument, Mehtap Lafci Büyükkahraman

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we deal with the Mackey-Glass model with piecewise constant argument. Because the corresponding difference equation is the difference solution of the equation, the difference equation can clearly predict the dynamic behavior of the equation. So, we look at how the difference equation behaves.We study the asymptotic stability of the equilibrium point of the difference equation and it is obtained that this point is a repeller under some conditions. Also, it is shown that every oscillatory solution of the difference equation has semi-cycles of length at least two, and every oscillatory solution of the difference equation is attracted …

(R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, Hameed Ullah Jan, Marjan Uddin, Arif Ullah, Naseeb Ullah

Applications and Applied Mathematics: An International Journal (AAM)

In engineering and mathematical physics, nonlinear evolutionary equations play an important role. Kawahara equation is one of the famous nonlinear evolution equation appeared in the theories of shallow water waves possessing surface tension, capillary-gravity waves and also magneto-acoustic waves in a plasma. Another specific subjective parts of arrangements for some of evolution equations evidenced by findings link belonging to their long-term actions named as eventual time periodicity discovered over solutions to IBVPs (initial-boundary-value problems). Here we investigate the solution’s eventual periodicity for generalized fifth order Kawahara equation (IBVP) on bounded domain in combination with periodic boundary conditions numerically exploiting mesh-free …

(R1995) Weighted Block-Wise Burst Error Correcting Codes, Amita Sethi, Arpana Sharma

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we construct new types of codes, called Weighted Block-wise Burst Error Correcting Codes (Weighted BBEC Codes), which are an improvement on the previously known block wise burst error correcting codes in the sense of their weight, i.e., (n = n₁ + n₂, k) linear codes that correct all the bursts of length b₁ (fixed) with the weight w₁ (w₁ ≤ b₁) or more (less) in the first sub-block of length n₁ and all the bursts of length b₂ (fixed) with the weight w₂ or more (less) …

(R1895) On Refinements And Generalizations Of Hadamard Inequalities For Riemann-Liouville (R-L) Integrals, Ghulam Farid, Sidra Bibi

Applications and Applied Mathematics: An International Journal (AAM)

The Hadamard inequality is a graphical interpretation of convex functions in the coordinate plane. We give its different variants for (R-L) fractional integrals of strongly exponentially (α, h − m)- convex functions. These inequalities are generalizations and refinements of Hadamard inequalities for Riemann-Liouville fractional integrals of exponentially; convex, m-convex, (α,m)-convex, (h − m)-convex, (s,m)-convex functions in combined forms. The error bounds of established inequalities are also obtained. Special cases of main results are mentioned, which have been already published by different authors.

(R1989) Mixed Convection Slippery Cross Fluid Flow Due To A Stratified Sheet Under The Effect Of Radiation Phenomenon, Nourhan I. Ghoneim, Ahmed M. Megahed

Applications and Applied Mathematics: An International Journal (AAM)

In view of the meaning of a two dimensional laminar Cross liquid in depicting an exhaustive assortment of experimental information, an assessment is done for a numerical and mathematical arrangement over a stratified extensible sheet. The non-dimensionality technique is brought into the controlling equations within the sight of the slip phenomenon and to make the solution more thorough. The data have been taken at a steady, viscous and laminar ow. Heat transfer across fluid is employed as a non-Newtonian fluid, where the fluid has a affected by radiation. Additionally, thermal radiation and heat generation are considered with the basic influence …

(R1976) A Novel Approach To Solve Fuzzy Rough Matrix Game With Two Players, Vinod Jangid, Ganesh Kumar, Gaurav Sharama, Vishnu Narayan Mishra

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes a new method for solving a two-person zero-sum fuzzy matrix game with goals, payoffs, and decision variables represented as triangular fuzzy rough numbers. We created a pair of fully fuzzy rough linear programming problems for players. Triangular fuzzy rough numbers can be used to formulate two fuzzy linear programming problems for the first player in the form of upper approximation intervals and lower approximation intervals. Two problems for the second player can be created in the same way. These problems have been split into five sub-crisp problems for the player first and five sub-crisp problems for the …

Region Detection & Segmentation Of Nissl-Stained Rat Brain Tissue, Alexandro Arnal

Open Access Theses & Dissertations

People who analyze images of biological tissue rely on the segmentation of structures as a preliminary step. In particular, laboratories studying the rat brain delineate brain regions to position scientific findings on a brain atlas to propose hypotheses about the rat brain and, ultimately, the human brain. Our work intersects with the preliminary step of delineating regions in images of brain tissue via computational methods.

We investigate pixel-wise classification or segmentation of brain regions using ten histological images of brain tissue sections stained for Nissl substance. We present a deep learning approach that uses the fully convolutional neural network, U-Net, …

Decision Making Under Uncertainty With A Special Emphasis On Geosciences And Education, Laxman Bokati

Open Access Theses & Dissertations

In many practical situations, we need to make a decision. In engineering, we need to decideon the best design of a system, and, for existing systems - on the best control strategy. In financial applications, we need to decide what is the best way to invest money. In geosciences, we need to decide whether we should explore a possible mineral deposit - or whether we should perform more experiments and measurements (and what exactly). In some cases, we can compute the exact consequences of each decision - e.g., if we are controlling a satellite. However, in many other cases, we …

Gmres Convergence Of Block Preconditioners For Nonsymmetric Matrices, Miguel A. Mascorro

Theses and Dissertations

GMRES is an iterative method for solving linear systems that minimizes the residual over the k-dimensional Krylov subspace at iteration k. Murphy, Golub and Wathen in [11] show that saddle point type matrices can be preconditioned so that GMRES converges in two or three steps. Ipsen in [10] extends this work to matrixes where the (2,2) block is nonzero. However, the three step convergence result no longer holds in this case. In this thesis we investigate how many more steps are needed for convergence as a function of the size of that (2,2) block.

Meshfree Methods For Pdes On Surfaces, Andrew Michael Jones

Boise State University Theses and Dissertations

This dissertation focuses on meshfree methods for solving surface partial differential equations (PDEs). These PDEs arise in many areas of science and engineering where they are used to model phenomena ranging from atmospheric dynamics on earth to chemical signaling on cell membranes. Meshfree methods have been shown to be effective for solving surface PDEs and are attractive alternatives to mesh-based methods such as finite differences/elements since they do not require a mesh and can be used for surfaces represented only by a point cloud. The dissertation is subdivided into two papers and software.

In the first paper, we examine the …

On Variants Of Sliding And Frank-Wolfe Type Methods And Their Applications In Video Co-Localization, Seyed Hamid Nazari

All Dissertations

In this dissertation, our main focus is to design and analyze first-order methods for computing approximate solutions to convex, smooth optimization problems over certain feasible sets. Specifically, our goal in this dissertation is to explore some variants of sliding and Frank-Wolfe (FW) type algorithms, analyze their convergence complexity, and examine their performance in numerical experiments. We achieve three accomplishments in our research results throughout this dissertation. First, we incorporate a linesearch technique to a well-known projection-free sliding algorithm, namely the conditional gradient sliding (CGS) method. Our proposed algorithm, called the conditional gradient sliding with linesearch (CGSls), does not require the …

On Clinical Use Of Infrared Cameras For Video-Based Estimation Of 3d Facial Kinematics, William Mackenzie Harrington

Theses and Dissertations

Neurological and neurodegenerative disorders such as Parkinson’s disease (PD), amyotrophic lateral sclerosis (ALS), and stroke can cause speech and orofacial motor impairments with devastating effects on quality of life. Analysis of orofacial movement provides vital information for early diagnosis and tracking disease progression, but current clinical practice relies on perceptual assessments performed by clinicians, which are unreliable and insensitive to early symptoms. New methods in machine learning have enabled automatic and objective assessment of orofacial kinematics from color and depth videos, hence we introduce MEADepthCamera, a mobile application for RGB-D video and audio recording and automatic estimation of 3D facial …

Kinetic Simulations Of Active Nematic Polymers In Channel Flow, Lacey Savoie Schenk

Mathematics & Statistics Theses & Dissertations

Suspensions of active nematic liquid crystalline polymers exhibit complex phenomena such as spontaneous flows, pattern formations, and defects. They have many applications in industry, commercial settings, and our daily lives. We employ the Kinetic Model for our research, an extensive model that couples the Smoluchowski Equation and the incompressible Navier-Stokes Equations to solve for the active nanorod number density function–a function dependent on the polymer’s physical orientation and space at a given time. Using this function, we can derive the polymer’s polarity and nematic orientations as well as other rheological properties. In this research, we conduct numerical simulations of active, …

Atlantic Surfclam (Spisula Solidissima) Population Demographics And Distribution Along The Middle Atlantic Bight, Mauricio González Díaz

OES Theses and Dissertations

The Atlantic surfclam (Spisula solidissima) is a long-lived benthic biomass dominant organism that occurs on the Middle Atlantic Bight (MAB) continental shelf between 10 m and 50 m. Trends in Atlantic surfclam population specific growth and mortality rates were analyzed using four decades of age and length observations obtained from NOAA stock surveys from the 1980s to 2010s in six regions distributed along the MAB. Atlantic surfclam specific growth rates and asymptotic lengths were estimated from the age and length observations using the von Bertalanffy growth model. The analysis showed that the Atlantic surfclam median asymptotic length in …

Statistical Methods For Meta-Analysis In Large-Scale Genomic Experiments, Wimarsha Thathsarani Jayanetti

Mathematics & Statistics Theses & Dissertations

Recent developments in high throughput genomic assays have opened up the possibility of testing hundreds and thousands of genes simultaneously. With the availability of vast amounts of public databases, researchers tend to combine genomic analysis results from multiple studies in the form of a meta-analysis. Meta-analysis methods can be broadly classified into two main categories. The first approach is to combine the statistical significance (pvalues) of the genes from each individual study, and the second approach is to combine the statistical estimates (effect sizes) from the individual studies. In this dissertation, we will discuss how adherence to the standard null …

Response Of Planetary Waves And Tides To The 2019 Southern Hemisphere Ssw And Q2dw Enhancement In Jan-Feb 2020 Observed By Condor Meteor Radar In Chile And Adelaide Meteor Radar In Australia, Alan Liu, Zishun Qiao, Iain Reid, Javier Fuentes, Chris Adami

Publications

A new multi-static meteor radar (CONDOR) has recently been installed in northern Chile. This CONDOR meteor radar (30.3°S, 70.7°W) and the Adelaide meteor radar (35°S, 138°E) have provided longitudinally spaced observations of the mean winds, tides and planetary waves of the PW-tides interaction cases we present here. We have observed a Quasi-6-Day Wave (Q6DW) enhancement in MLT winds at the middle latitudes (30.3°S, 35°S) during the unusual minor South Hemisphere SSW 2019 by the ground-based meteor radars. Tidal analysis also indicates modulation of the Q6DW w/ amplitude ~15 [m/s] and diurnal tides w/ amplitude ~60 [m/s]. Another case we present …

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 …

Training Rbf Neural Networks For The Solution Of Elliptic Boundary Value Problems, Andreas Karageorghis, C.S. Chen

Faculty Publications

We propose a radial basis function (RBF) neural network method for solving two- and three–dimensional second and fourth order elliptic boundary value problems (BVPs). The neural network in question is trained by minimizing a nonlinear least squares functional, thus determining the optimal values of the various RBF parameters involved. The functional minimization is carried out using standard MATLAB® software efficiently. Several numerical experiments are presented to demonstrate the efficacy of the proposed method.

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 …