Applied Mathematics Commons^™

Shear Driven Micro-Fluidic Pump For Cardiovascular Applications, Nihad E. Daidzic

Aviation Department Publications

A valveless shear-driven micro-fluidic pump design (SDMFP) for hemodynamic applications is presented in this work. One of the possible medical and biomedical applications is in-vivo hemodynamic (human blood circulation) support/assist. One or more SDMFPs can be inserted/implanted into vascular lumens in a form of a stent/duct in series and/or in parallel (bypass duct) to support blood circulation in-vivo. A comprehensive review of various micro-pump designs up to about mid 2000’s is given in [1,2]. Many of micropump designs considered are not suitable for in-vivo or even in-vitro medical/biomedical applications.

Operating principles, design, and SDMFP features are given in [3]. A …

Semantic Description Of Activities In Videos, Fillipe Dias Moreira De Souza

USF Tampa Graduate Theses and Dissertations

Description of human activities in videos results not only in detection of actions and objects but also in identification of their active semantic relationships in the scene. Towards this broader goal, we present a combinatorial approach that assumes availability of algorithms for detecting and labeling objects and actions, albeit with some errors. Given these uncertain labels and detected objects, we link them into interpretative structures using domain knowledge encoded with concepts of Grenander’s general pattern theory. Here a semantic video description is built using basic units, termed generators, that represent labels of objects or actions. These generators have multiple out-bonds, …

Six Septembers: Mathematics For The Humanist, Patrick Juola, Stephen Ramsay

Zea E-Books Collection

Scholars of all stripes are turning their attention to materials that represent enormous opportunities for the future of humanistic inquiry. The purpose of this book is to impart the concepts that underlie the mathematics they are likely to encounter and to unfold the notation in a way that removes that particular barrier completely. This book is a primer for developing the skills to enable humanist scholars to address complicated technical material with confidence. This book, to put it plainly, is concerned with the things that the author of a technical article knows, but isn’t saying. Like any field, mathematics operates …

Rainbow Perfect Matchings And Hamilton Cycles In The Random Geometric Graph, Deepak C. Bal, Patrick Bennett, Xavier Pérez‐Giménez, Paweł Prałat

Department of Mathematics Facuty Scholarship and Creative Works

Given a graph on n vertices and an assignment of colours to the edges, a rainbow Hamilton cycle is a cycle of length n visiting each vertex once and with pairwise different colours on the edges. Similarly (for even n) a rainbow perfect matching is a collection of independent edges with pairwise different colours. In this note we show that if we randomly colour the edges of a random geometric graph with sufficiently many colours, then a.a.s. the graph contains a rainbow perfect matching (rainbow Hamilton cycle) if and only if the minimum degree is at least 1 (respectively, …

Dynamics Of Multicultural Social Networks, Kristina B. Hilton

USF Tampa Graduate Theses and Dissertations

Historically human endeavors around the globe are in search of bilateral relationships. Knowledge and commerce has played a very significant role in increasing the ability for humans to connect for the betterment of the human species. As the means of communication improve, mutual benefits to the community as a whole also increase. Moreover, the benefits are filtered down to members of the overall community. Recent advancement in electronic communication technologies and in knowledge, in particular, physical, chemical, engineering and medical sciences and philosophies, have facilitated nearly instantaneous multi-cultural interactions. Local problems and solutions have become global. This has generated a …

The Statistical Dynamics Of Nonequilibrium Control, Grant Murray Rotskoff '09

Doctoral Dissertations

Living systems, even at the scale of single molecules, are constantly adapting to changing environmental conditions. The physical response of a nanoscale system to external gradients or changing thermodynamic conditions can be chaotic, nonlinear, and hence difficult to control or predict. Nevertheless, biology has evolved systems that reliably carry out the cell’s vital functions efficiently enough to ensure survival. Moreover, the development of new experimental techniques to monitor and manipulate single biological molecules has provided a natural testbed for theoretical investigations of nonequilibrium dynamics. This work focuses on developing paradigms for both understanding the principles of nonequilibrium dynamics and also …

Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, S.C. Mancas

Publications

A one-parameter family of Emden-Fowler equations defined by Lampariello’s parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

Daily Fantasy Sports: Chance Or Skill?, Danielle Bergner

Honors Projects in Mathematics

Online daily fantasy sports is a billion dollar industry that has caused controversy for the last few years with states debating its legal status. As of today, under the current United States federal laws and regulations, betting money on daily fantasy sports online is considered legal. However, several states have decided to ban these games within their borders believing they are based on chance and should be considered gambling which they have ruled to be illegal online. Each state has the right to make their own rules of what they consider gambling even if the federal government has allowed it. …

An Rbf Interpolation Blending Scheme For Effective Shock-Capturing, M. Harris, Eduardo Divo, Alain J. Kassab

Publications

In recent years significant focus has been given to the study of Radial basis functions (RBF), especially in their use on solving partial differential equations (PDE). RBF have an impressive capability of inter- polating scattered data, even when this data presents localized discontinuities. However, for infinitely smooth RBF such as the Multiquadrics, inverse Multiquadrics, and Gaussian, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary significantly depending on the field, particularly in locations of steep gradients, shocks, or discontinuities. Typically, the shape parameter is chosen …

A Framework For Predicting Impacts On Ecosystem Services From (Sub)Organismal Responses To Chemicals, Valery E. Forbes, Chris J. Salice, Bjorn Birnir, Randy J.F. Bruins, Peter Calow, Virginie Ducrot, Nika Galic, Kristina Garber, Bret C. Harvey, Henriette Jager, Andrew Kanarek, Robert Pastorok, Steve F. Railsback, Richard Rebarber, Pernille Thorbek

Department of Mathematics: Faculty Publications

Protection of ecosystem services is increasingly emphasized as a risk-assessment goal, but there are wide gaps between current ecological risk-assessment endpoints and potential effects on services provided by ecosystems. The authors present a framework that links common ecotoxicological endpoints to chemical impacts on populations and communities and the ecosystem services that they provide. This framework builds on considerable advances in mechanistic effects models designed to span multiple levels of biological organization and account for various types of biological interactions and feedbacks. For illustration, the authors introduce 2 case studies that employ well-developed and validated mechanistic effects models: the inSTREAM individual-based …

Discrete Fractional Hermite-Hadamard Inequality, Aykut Arslan

Masters Theses & Specialist Projects

This thesis is comprised of three main parts: The Hermite-Hadamard inequality on discrete time scales, the fractional Hermite-Hadamard inequality, and Karush-Kuhn- Tucker conditions on higher dimensional discrete domains. In the first part of the thesis, Chapters 2 & 3, we define a convex function on a special time scale T where all the time points are not uniformly distributed on a time line. With the use of the substitution rules of integration we prove the Hermite-Hadamard inequality for convex functions defined on T. In the fourth chapter, we introduce fractional order Hermite-Hadamard inequality and characterize convexity in terms of this …

Stability Of Linear Difference Systems In Discrete And Fractional Calculus, Aynur Er

Masters Theses & Specialist Projects

The main purpose of this thesis is to define the stability of a system of linear difference equations of the form,

∇y(t) = Ay(t),

and to analyze the stability theory for such a system using the eigenvalues of the corresponding matrix A in nabla discrete calculus and nabla fractional discrete calculus. Discrete exponential functions and the Putzer algorithms are studied to examine the stability theorem.

This thesis consists of five chapters and is organized as follows. In the first chapter, the Gamma function and its properties are studied. Additionally, basic definitions, properties and some main theorem of discrete calculus are …

Hemodynamic Differences Between Unstable And Stable Unruptured Aneurysms Independent Of Size And Location: A Pilot Study, Waleed Brinjikji, Bong Jae Chung, Carlos Jimenez, Christopher Putman, David F. Kallmes, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Background While clinical and angiographic risk factors for intracranial aneurysm instability are well established, it is reasonable to postulate that intra-aneurysmal hemodynamics also have a role in aneurysm instability. Objective To identify hemodynamic characteristics that differ between radiologically unstable and stable unruptured intracranial aneurysms. Materials and methods 12 pairs of unruptured intracranial aneurysms with a 3D rotational angiographic set of images and followed up longitudinally without treatment were studied. Each pair consisted of one stable aneurysm (no change on serial imaging) and one unstable aneurysm (demonstrated growth of at least 1 mm diameter or ruptured during follow-up) of matching size …

On The Classification Of The Second Minimal Orbits Of The Continuous Endomorphisms On The Real Line And Universality In Chaos, Naveed H. Iqbal

Theses and Dissertations

This dissertation presents full classification of second minimal odd periodic orbits of a continuous endomorphisms on the real line. A (2k + 1)-periodic orbit (k ≥ 3) is called second minimal for the map f , if 2k−1 is a minimal period of f in the Sharkovskii ordering. We prove that there are 4k−3 types of second minimal (2k+1)-orbits, each characterized with unique cyclic permutation and directed graph of transitions with accuracy up to inverses. The result is applied to the problem on the distribution of periodic windows within the chaotic regime of the bifurcation diagram of the one-parameter family …

Using Numerical Methods To Explore The Space Of Solutions Of A Nonlinear Partial Differential Equation, Subekshya Bidari

Senior Theses and Projects

No abstract provided.

A Coupled Localized Rbf Meshless/Drbem Formulation For Accurate Modeling Of Incompressible Fluid Flows, Leonardo Bueno, Eduardo Divo, Alain J. Kassab

Publications

Velocity-pressure coupling schemes for the solution of incompressible fluid flow problems in Computational Fluid Dynamics (CFD) rely on the formulation of Poisson-like equations through projection methods. The solution of these Poisson-like equations represent the pressure correction and the velocity correction to ensure proper satisfaction of the conservation of mass equation at each step of a time-marching scheme or at each level of an iteration process. Inaccurate solutions of these Poisson-like equations result in meaningless instantaneous or intermediate approximations that do not represent the proper time-accurate behavior of the flow. The fact that these equations must be solved to convergence at …

Haar Wavelet Solution Of Poisson’S Equation And Their Block Structures, The British University In Egypt, Ain Shams University

Basic Science Engineering

The structure of the algebraic system which results from the use of Haar wavelet when solving Poisson’s equation is studied. Haar wavelet technique is used to solve Poisson’s equation on a unit square domain. The form of collocation points are used at the mid points of the subintervals i.e at the odd multiple of the sub interval length labeling. It is proved that the coefficient matrix has symmetric block structure. Comparison with the tridagonal block structure obtained by the finite difference with the natural ordering is introduced. The numerical results have illustrated the superiority of the use of Haar wavelet …

The Air Force Fitness Test: Creating New Fitness Assessment Charts Using Waist To Height Ratios, John R. Griffith

Theses and Dissertations

The Air Force currently uses AFI 36-2905 for fitness standards and evaluation, but no study to our knowledge has evaluated these standards using large databases. Using a 5.38 million record database from the Air Force Fitness Management System, we evaluated how the abdominal circumference, body mass index (BMI), waist to height ratio (WtHR), and height to weight ratio correlated to fitness as assessed by the 1.5 mile aerobic run in the Air Force Fitness Test. Whether individually or adjusting for age group and gender, WtHR performed better that the rest with an average rank score of 1.1 with a relative …

Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh

Faculty Publications

The notions of rectifying subspaces and of rectifying submanifolds were introduced in [B.-Y. Chen, Int. Electron. J. Geom 9 (2016), no. 2, 1–8]. More precisely, a submanifold in a Euclidean m-space Em is called a rectifying submanifold if its position vector field always lies in its rectifying subspace. Several fundamental properties and classification of rectifying submanifolds in Euclidean space were obtained in [B.-Y. Chen, op. cit.]. In this present article, we extend the results in [B.-Y. Chen, op. cit.] to rectifying space- like submanifolds in a pseudo-Euclidean space with arbitrary codimension. In particular, we completely classify all rectifying space-like submanifolds …

P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

Western Research Forum

Global Exponential Stabilization on SO(3)