Applied Mathematics Commons^™

Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in the Dirichlet boundary conditions. The underlying parabolic control system is functioning under hard/pointwise constraints on control and state variables. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We develop a constructive approach to the minimax control design of constrained parabolic systems that is based on certain characteristic features of the parabolic dynamics …

Two Soliton Interactions Of Bd.I Multicomponent Nls Equations And Their Gauge Equivalent, Vladimir Gerdjikov, Georgi Grahovski

Conference papers

Using the dressing Zakharov-Shabat method we re-derive the effects of the two-soliton interactions for the MNLS equations related to the BD.I-type symmetric spaces. Next we generalize this analysis for the Heisenberg ferromagnet type equations, gauge equivalent to MNLS.

Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth

Mathematics Faculty Publications

We study the existence of continuous periodic solutions of a neutral delay integral equation of advanced type. In the analysis we employ three fixed point theorems: Banach, Krasnosel'skii, and Krasnosel'skii-Schaefer. Krasnosel'skii-Schaefer fixed point theorem requires an a priori bound on all solutions. We employ a Liapunov type method to obtain such bound.

Basic Social Math: A Linguistic Upgrade For Decision Analysis And Social Dynamics Research., Jared Hanson

MA TESOL Collection

There are foundational errors in the mathematical frameworks currently used in Economic and Decision Theories. Recent systemic failures in the interdependent business and educational sectors also show that many practices based on these theories are unsustainable in the changing dynamics of the global economy. A new approach is needed in social science research and systems engineering. This paper examines how the new understandings of complex systems, the role of emotion in cognition, and the core dynamics of decision making can help us correct these errors and to create a general framework for systemic innovation. It argues for the development of …

Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=O Bi, where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.

Strong Orbit Equivalence And Residuality, Brett M. Werner

Electronic Theses and Dissertations

In this dissertation, we consider notions of equivalence between minimal Cantor systems, in particular strong orbit equivalence. By constructing the systems, we show that there exist two nonisomorphic substitution systems that are both Kakutani equivalent and strongly orbit equivalent. We go on to define a metric on a strong orbit equivalence class of minimal Cantor systems and prove several properties about the metric space. If the strong orbit equivalence class contains a finite rank system, we show that the set of finite rank systems is residual in the metric space. The last result shown is that set of systems with …

On The Accuracy Of Explicit Finite-Volume Schemes For Fluctuating Hydrodynamics, Aleksandar Donev, Eric Vanden-Eijnden, Alejandro Garcia, John B. Bell

Faculty Publications

This paper describes the development and analysis of finite-volume methods for the Landau–Lifshitz Navier–Stokes (LLNS) equations and related stochastic partial differential equations in fluid dynamics. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by the addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation relation. Originally derived for equilibrium fluctuations, the LLNS equations have also been shown to be accurate for nonequilibrium systems. Previous studies of numerical methods for the LLNS equations focused primarily on measuring variances and correlations computed at equilibrium and for selected nonequilibrium flows. In this paper, we introduce a more systematic approach …

Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=O Bi, where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.

A Vision For Acms, James Bradley

ACMS Journal 2010-2011

This paper presents a vision for the mission of the ACMS. It considers some plausible connections between mathematics and theology as well as some big questions that Christian mathematicians might fruitfully explore. It examines the current cultural norms of the mathematics guild, why these are problematic for Christians, and some possible ways the ACMS might respond.

Spectral Methods For The Hamiltonian Systems, Nairat Kanyamee

Wayne State University Dissertations

We conduct a systematic comparison of spectral methods with some

symplectic methods in solving Hamiltonian dynamical systems. Our

main emphasis is on the non-linear problems. Numerical evidence has

demonstrated that the proposed spectral collocation method preserves

both energy and symplectic structure up to the machine error in each

time (large) step, and therefore has a better long time behavior.

Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.

Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

For a new class of neuron models we demonstrate here that typical membrane action potentials and spike-bursts are only transient states but appear to be asymptotically stable; and yet such metastable states are plastic — being able to dynamically change from one action potential to another with different pulse frequencies and from one spike-burst to another with different spike-per-burst numbers. The pulse and spike-burst frequencies change with individual ions’ pump currents while their corresponding metastable-plastic states maintain the same transmembrane voltage and current profiles in range. It is also demonstrated that the plasticity requires two one-way ion pumps operating in …

Bass’ Nk Groups And Cd H-Fibrant Hochschild Homology, G. Cortiñas, C. Haesemeyer, Mark E. Walker, C. Weibel

Department of Mathematics: Faculty Publications

The K-theory of a polynomial ring R[t ] contains the K-theory of R as a summand. For R commutative and containing Q, we describe K∗(R[t ])/K∗(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology.

We use this to address Bass’ question, whether K_n(R) = K_n(R[t ]) implies K_n(R) = K_n(R[t₁, t₂]). The answer to this question is affirmative when R is essentially of …

Methods Of Variational Analysis In Pessimistic Bilevel Programming, Samarathunga M. Dassanayaka

Wayne State University Dissertations

Bilevel programming problems are of growing interest both from theoretical and practical points of view. These models are used in various applications, such as economic planning, network design, and so on. The purpose of this dissertation is to study the pessimistic (or strong) version of bilevel programming problems in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data) and can be treated by using appropriate tools of modern variational analysis and generalized differentiation developed by B. Mordukhovich.

This dissertation begins with analyzing pessimistic bilevel programs, formulation of the problems, literature review, practical application, existence of …

A Generalized Nonlinear Model For The Evolution Of Low Frequency Freak Waves, Jonathan Blackledge

Articles

This paper presents a generalized model for simulating wavefields associated with the sea surface. This includes the case when `freak waves' may occur through an effect compounded in the nonlinear (cubic) Schrodinger equation. After providing brief introductions to linear sea wave models, `freak waves' and the linear and nonlinear Schrodinger equations, we present a unified model that provides for a piecewise continuous transition from a linear to a nonlinear state. This is based on introducing a fractional time derivative to develop a fractional nonlinear partial differential equation with a stochastic source function. In order to explore the characteristics of this …

Mesoscopic Methods In Engineering And Science, Alfons Hoekstra, Li-Shi Luo, Manfred Krafczyk

Mathematics & Statistics Faculty Publications

(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the …

High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang

University of Kentucky Doctoral Dissertations

Scientific computing and computer simulation play an increasingly important role in scientific investigation and engineering designs, supplementing traditional experiments, such as in automotive crash studies, global climate change, ocean modeling, medical imaging, and nuclear weapons. The numerical simulation is much cheaper than experimentation for these application areas and it can be used as the third way of science discovery beyond the experimental and theoretical analysis. However, the increasing demand of high resolution solutions of the Partial Differential Equations (PDEs) with less computational time has increased the importance for researchers and engineers to come up with efficient and scalable computational techniques …

Voting In Agreeable Societies, Deborah E. Berg '06, Serguei Norine, Francis E. Su, Robin Thomas, Paul Wollan

All HMC Faculty Publications and Research

No abstract provided in this article.

An Amazing Mathematical Card Trick, Arthur T. Benjamin

All HMC Faculty Publications and Research

A magician gives a member of the audience 20 cards to shuffle. After the cards are thoroughly mixed, the magician goes through the deck two cards at a time, sometimes putting the two cards face to face, sometimes back to back, and sometimes in the same direction. Before dealing each pair of cards into a pile, he asks random members of the audience if the pair should be flipped over or not. He goes through the pile again four cards at a time and before each group of four is dealt to a pile, the audience gets to decide whether …

Sex, Mixability, And Modularity, Adi Livnat, Christos Papadimitriou, Nicholas Pippenger, Marcus W. Feldman

All HMC Faculty Publications and Research

The assumption that different genetic elements can make separate contributions to the same quantitative trait was originally made in order to reconcile biometry and Mendelism and ever since has been used in population genetics, specifically for the trait of fitness. Here we show that sex is responsible for the existence of separate genetic effects on fitness and, more generally, for the existence of a hierarchy of genetic evolutionary modules. Using the tools developed in the process, we also demonstrate that in terms of their fitness effects, separation and fusion of genes are associated with the increase and decrease of the …

Statistical Analysis Of Wastewater Remediation And Bio-Fuels Production Of Algae, Jay D. Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The Logan city wastewater treatment system consists of a series of seven large aerated ponds (460 acres) that biologically treats 15 million gallons per day of wastewater from Logan city and six other communities. Tighter regulations of allowed phosphorus levels in the effluent have recently been implemented due to environmental concerns of a downstream reservoir. The Biological Engineering program at Utah State University, the Bio-fuels Center, the Utah Water Research Laboratory (UWRL) and the city of Logan are working together to remediate the wastewater treatment system using microalgae. Algal growth requires the uptake of phosphorus. Thus, phosphorus in the effluent …

Grading Practice Influence On The Value Of An Assigned Grade, Carrie Bala

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This article presents results of a study of grading practice influence on the value of an assigned grade. The value of an assigned grade, as an indication of student achievement of learning goals, was measured using the Utah Criterion-Referenced Test (CRT) in the subjects of Geometry and Algebra 2. The grading policies of six mathematics teachers at the same high school were categorized according to grading practice and their combined 587 students' scores on the Utah CRT were collected and analyzed. The findings suggest that certain grading practices , such as the use of a 1-4 scale and a criterion-referenced …

A Time Series Analysis Of The New Jersey Meadowlands Weather And Air Quality Data, Steven Spero

Theses, Dissertations and Culminating Projects

This research applies time series methods to determine relationships among a set of weather variables which are continually monitored in the Hackensack Meadowlands region of northern New Jersey. Weather data includes chemical and atmospheric factors. Chemical factors are Nitrogen Oxide, atmospheric Ozone, Carbon Monoxide, and Carbon Dioxide. Weather factors are wind speed, barometric pressure, air temperature, humidity, and solar radiation. Additionally, traffic density and time of week are brought in as categorical factors. This research attempts to (a) introduce the reader to various time series methodologies, (b) find a significant and efficient model for forecasting Nitrogen Oxide levels, and (c) …

From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng

Department of Mathematics: Faculty Publications

The purpose of this paper is to incorporate well-established ecological principles into a foodweb model consisting of four trophic levels --- abiotic resources, plants, herbivores, and carnivores. The underlining principles include Kimura's neutral theory of genetic evolution, Liebig's Law of the Minimum for plant growth, Holling's functionals for herbivore foraging and carnivore predation, the One-Life Rule for all organisms, and Lotka-Volterra's model for intraand interspecific competitions. Numerical simulations of the model led to the following statistical findings: (a) particular foodwebs can give contradicting observations on biodiversity and productivity, in particular, all known functional forms -- - positive, negative, sigmoidal, and …

Neutrosophic Bilinear Algebras And Their Generalizations, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras, n>2. This book has five chapters. The reader should be well-versed with the notions of linear algebras as well as the concepts of bilinear algebras and n- linear algebras. Further the reader is expected to know about neutrosophic algebraic structures as we have not given any detailed literature about it. The first chapter is introductory in nature and gives a few essential definitions and references for the reader to make use of the literature in case the reader is not thorough with the basics. …

Advances And Applications Of Dsmt For Information Fusion (In Chinese), Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Proposed Problems Of Mathematics (Vol. Ii), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The first book of “Problèmes avec et sans … problèmes!” was published in Morocco in 1983. I collected these problems that I published in various Romanian or foreign magazines (amongst which: “Gazeta Matematică”, magazine which formed me as problem solver, “American Mathematical Monthly”, “Crux Mathematicorum” (Canada), “Elemente der Mathematik” (Switzerland), “Gaceta Matematica” (Spain), “Nieuw voor Archief” (Holland), etc. while others are new proposed problems in this second volume.

These have been created in various periods: when I was working as mathematics professor in Romania (1984-1988), or co-operant professor in Morocco (1982-1984), or emigrant in the USA (1990-1997). I thank to …

Fusion Of Sources Of Evidence With Different Importances And Reliabilities, Florentin Smarandache, Jean Dezert, J.M. Tacnet

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a new approach for combining sources of evidences with different importances and reliabilities. Usually, the combination of sources of evidences with different reliabilities is done by the classical Shafer’s discounting approach. Therefore, to consider unequal importances of sources, if any, a similar reliability discounting process is generally used, making no difference between the notion of importance and reliability. In fact, in multicriteria decision context, these notions should be clearly distinguished. This paper shows how this can be done and we provide simple examples to show the differences between both solutions for managing importances and reliabilities of sources. …

Probability Models For Blackjack Poker, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

For simplicity in calculation, previous analyses of blackjack poker have employed models which employ sampling with replacement. in order to assess what degree of error this may induce, the purpose here is to calculate results for a typical hand where sampling without replacement is employed. It is seen that significant error can result when long runs are required to complete the hand. The hand examined is itself of particular interest, as regards both its outstanding expectations of high yield and certain implications for pair splitting of two nines against the dealer's seven. Theoretical and experimental methods are used in order …

Properties Of The Generalized Laplace Transform And Transport Partial Dynamic Equation On Time Scales, Chris R. Ahrendt

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation, we first focus on the generalized Laplace transform on time scales. We prove several properties of the generalized exponential function which will allow us to explore some of the fundamental properties of the Laplace transform. We then give a description of the region in the complex plane for which the improper integral in the definition of the Laplace transform converges, and how this region is affected by the time scale in question. Conditions under which the Laplace transform of a power series can be computed term-by-term are given. We develop a formula for the Laplace transform for …