Applied Mathematics Commons^™

Generalized Analytic Fourier-Feynman Transform Of Functionals In A Banach Algebra F_(A1,A2)^(A,B), Jae Gil Choi, David Skough, Seung Jun Chang

Department of Mathematics: Faculty Publications

We introduce the Fresnel type class F_(A1,A2)^(a,b).We also establish the existence of the generalized analytic Fourier-Feynman transform for functionals in the Banach algebra F_(A1,A2)^(a,b).

A Study Of Nonlinear Dynamics In Mathematical Biology, Joseph Ferrara

UNF Graduate Theses and Dissertations

We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically.

Cancer Quasispecies And Stem-Like Adaptive Aneuploidy, Domenico Napoletani, M. Signore, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we develop a theoretical frame to understand self-regulation of aneuploidy rate in cancer and stem cells. This is accomplished building upon quasispecies theory, by leaving its formal mathematical structure intact, but by drastically changing the meaning of its objects. In particular, we propose a novel definition of chromosomal master sequence, as a sequence of physically distinct whole or fragmented chromosomes, whose length is taken to be the sum of the copy numbers of each whole or fragmented chromosome. This fundamental change in the functional objects of quasispecies theory allows us to show that previously measured aneuploidy rates …

Subset Non Associative Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book for the first time we introduce the notion of subset non associative semirings. It is pertinent to keep on record that study of non associative semirings is meager and books on this specific topic is still rare. Authors have recently introduced the notion of subset algebraic structures. The maximum algebraic structure enjoyed by subsets with two binary operations is just a semifield and semiring, even if a ring or a field is used. In case semigroups or groups are used still the algebraic structure of the subset is only a semigroup. To construct a subset non associative …

Subset Interval Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of groupoids is meager and we have recently introduced the new notion of subset groupoids and have studied them. It is interesting to keep on record that interval groupoids have been studied by us in 2010. Further when the subsets of a loop are taken they also form only a subset groupoid and not a subset loop. Thus we do not have the concept of subset interval loop they only form a subset interval groupoid. Special elements like subset interval zero divisors, subset interval idempotents and subset interval units are studied. Concept of subset interval groupoid homomorphism is …

Algebraic Structures Using Subsets, Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of subsets and giving algebraic structure to these subsets of a set started in the mid 18th century by George Boole. The first systematic presentation of Boolean algebra emerged in 1860s in papers written by William Jevons and Charles Sanders Peirce. Thus we see if P(X) denotes the collection of all subsets of the set X, then P(X) under the op erations of union and intersection is a Boolean algebra. Next the subsets of a set was used in the construction of topological spaces. We in this book consider subsets of a semigroup or a group or a …

Fuzzy Analysis Of School Dropouts And Their Life After, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal, K. Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study and analyze the problem of school dropouts and their life after. The problems can by no means be analyzed by collecting the numerical data. For such data can only serve as information beyond that the data can be of no use, for the school dropouts suffer an environment change after becoming a school dropout. Thus the emotions of the school dropout; is technically involved. A school dropout can be a child labourer, a rag picker or a social miscreant or be in police custody or be in a rehabilitation home if he/she is a runaway. …

Fuzzy Neutrosophic Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, authors give the notion of different neutrosophic models like, neutrosophic cognitive maps (NCMs), neutrosophic relational maps (NEMs), neutrosophic relational equations (NREs), neutrosophic bidirectional associative memories (NBAMs) and neutrosophic associative memories (NAMs) for socio scientists. This book has six chapters. The first chapter introduces the basic concepts of neutrosophic numbers and notions about neutrosophic graphs which are essential to construct these neutrosophic models. In chapter two we describe the concept of neutrosophic matrices and the essential operations related with them which are used in the study and working of these neutrosophic models. However the reader must be familiar …

Variance On Topics Of Plane Geometry, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book contains 21 papers of plane geometry. It deals with various topics, such as: quasi-isogonal cevians, nedians, polar of a point with respect to a circle, anti-bisector, aalsonti-symmedian, anti-height and their isogonal. A nedian is a line segment that has its origin in a triangle’s vertex and divides the opposite side in Q equal segments. The papers also study distances between remarkable points in the 2D-geometry, the circumscribed octagon and the inscribable octagon, the circles adjointly ex-inscribed associated to a triangle, and several classical results such as: Carnot circles, Euler’s line, Desargues theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s theorem, …

Modeling The Human Gait Phases Using Granular Computing, Melaku Ayenew Bogale

Open Access Theses & Dissertations

Gait analysis is applied for the provision of diagnosis, evaluation, and for the design of therapeutic intervention for subjects suffering from neurological disorders. The benefits accruing from gait analysis are well established. People with neurological disorders like mild traumatic brain injury, Cerebral Palsy and Multiple Sclerosis, suffer associated functional gait problems. The symptoms and sign of these gait deficits are different from subject to subject and even for the same subject at different stage of the disease. Identifying these gait related abnormalities helps in the treatment planning and rehabilitation process.

The dynamic behavior of gait parameters is cyclic and the …

A Block Operator Splitting Method For Heterogeneous Multiscale Poroelasticity, Paul M. Delgado

Open Access Theses & Dissertations

Traditional models of poroelastic deformation in porous media assume relatively homogeneous material properties such that macroscopic constitutive relations lead to accurate results. Many realistic applications involve heterogeneous material properties whose oscillatory nature require multiscale methods to balance accuracy and efficiency in computation.

The current study develops a multiscale method for poroelastic deformation based on a fixed point iteration based operator splitting method and a heterogeneous multiscale method using finite volume and direct stiffness methods. To characterize the convergence

of the operator splitting method, we use a numerical root finding algorithm to determine a threshold surface in a non-dimensional parameter space …

Reduced-Order Modeling Using Orthogonal And Bi-Orthogonal Wavelet Transforms, Miguel Hernandez Iv

Open Access Theses & Dissertations

It is well known that model reduction methods borrow techniques typically found in data compression, and current state-of-the-art techniques for data compression are based on the wavelet transform. Given these facts, it is surprising that model reduction using wavelets has not received much attention and has not been adequately addressed in the literature. This research seeks to determine if wavelets can be used for model reduction and if wavelet model reduction is a viable alternative to existing model reduction methods.

In this work we propose a novel method for model reduction using wavelets. Specifically, we introduce techniques for deriving wavelet …

Multiple Subject Barycentric Discriminant Analysis (Musubada): How To Assign Scans To Categories Without Using Spatial Normalization, Hervé Abdi, Lynne J. Williams, Andrew C. Connolly, M. Ida Gobbini

Dartmouth Scholarship

We present a new discriminant analysis (DA) method called Multiple Subject Barycentric Discriminant Analysis (MUSUBADA) suited for analyzing fMRI data because it handles datasets with multiple participants that each provides different number of variables (i.e., voxels) that are themselves grouped into regions of interest (ROIs). Like DA, MUSUBADA (1) assigns observations to predefined categories, (2) gives factorial maps displaying observations and categories, and (3) optimally assigns observations to categories. MUSUBADA handles cases with more variables than observations and can project portions of the data table (e.g., subtables, which can represent participants or ROIs) on the factorial maps. Therefore MUSUBADA can …

On The Peakon And Soliton Solutions Of An Integrable Pde With Cubic Nonlinearities, Rossen Ivanov, Tony Lyons

Conference papers

The interest in the singular solutions (peakons) has been inspired by the Camassa-Holm (CH) equation and its peakons. An integrable peakon equation with cubic nonlinearities was first discovered by Qiao. Another integrable equation with cubic nonlinearities was introduced by V. Novikov . We investigate the peakon and soliton solutions of the Qiao equation.

Blow-Up Of Solutions To The Generalized Inviscid Proudman-Johnson Equation, Alejandro Sarria

LSU New Orleans Theses and Dissertations

The generalized inviscid Proudman-Johnson equation serves as a model for n-dimensional incompressible Euler flow, gas dynamics, high-frequency waves in shallow waters, and orientation of waves in a massive director field of a nematic liquid crystal. Furthermore, the equation also serves as a tool for studying the role that the natural fluid processes of convection and stretching play in the formation of spontaneous singularities, or of their absence.

In this work, we study blow-up, and blow-up properties, in solutions to the generalized, inviscid Proudman-Johnson equation endowed with periodic or Dirichlet boundary conditions. More particularly,regularity of solutions in an Lp setting will …

Title Ix Compliance: A Comparison Of Division I Equality, Jacqueline Leake

Honors Theses

The passage of Title IX of the Education Amendments of 1972 has had a significant impact on college athletics. However, there is still a large disparity between opportunities offered for men and women. This study determined the true gender equality within Division I athletics. Inequalities were assessed in the areas of athletic participation, athletically related student aid, recruiting expenses, and total expenses. Data from these areas were gathered from the Equity in Athletics Disclosure Analysis Cutting Tool. Ratios and the difference between the ideal and current values were calculated for each category. Institutions were ranked in each category, as well …

Decision Making Under Interval Uncertainty (And Beyond), Vladik Kreinovich

Departmental Technical Reports (CS)

To make a decision, we must find out the user's preference, and help the user select an alternative which is the best -- according to these preferences. Traditional utility-based decision theory is based on a simplifying assumption that for each two alternatives, a user can always meaningfully decide which of them is preferable. In reality, often, when the alternatives are close, the user is often unable to select one of these alternatives. In this chapter, we show how we can extend the utility-based decision theory to such realistic (interval) cases.

Nabla Fractional Calculus And Its Application In Analyzing Tumor Growth Of Cancer, Fang Wu

Masters Theses & Specialist Projects

This thesis consists of six chapters. In the first chapter, we review some basic definitions and concepts of fractional calculus. Then we introduce fractional difference equations involving the Riemann-Liouville operator of real number order between zero and one. In the second chapter, we apply the Brouwer fixed point and Contraction Mapping Theorems to prove that there exists a solution for up to the first order nabla fractional difference equation with an initial condition. In chapter three, we define a lower and an upper solution for up to the first order nabla fractional difference equation with an initial condition. Under certain …

Sensitivity Analysis In Magnetic Resonance Elastography And A Local Wavelength Reconstruction Based On Wave Direction, Christopher Gillam

All Dissertations

or the detection of early stage cancer. MRE utilizes interior data for its inverse problems, which greatly reduces the ill-posedness from which most traditional inverse problems suffer.
In this thesis, we first establish a sensitivity analysis for viscoelastic scalar medium with complex wave number and compare it with the purely elastic case. Also we estimate the smallest detectable inclusion for breast and liver, which is about twice larger than using the purely elastic model. We also found the existence of optimal frequency (50 Hz) that maximizes the detectability when the Voigt model is used.
Second, we propose a local wavelength …

Further Results On Fractional Calculus Of Saigo Operators, Praveen Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). The main object of the present paper is to study and develop the Saigo operators. First, we establish two results that give the image of the product of multivariable H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, multivariable H-function and …