Applied Mathematics Commons^™

The Uav Continuous Coverage Problem, Taegyun Ha

Theses and Dissertations

The purpose of this research is to develop a method to find an optimal UAV cyclic schedule to provide maximum coverage over a target area to support an ISR mission. The goal is to reach continuous coverage. UAV continuous coverage of a target area is crucial for the success of an ISR mission. Even the smallest coverage gap may jeopardize the success of the mission. Ideally it is desirable to obtain continuous coverage of a target area but the stochastic nature of the problem makes continuous coverage without gaps unlikely. However, it is still possible to obtain a high coverage …

Maximizing Strike Planning Efficiency For A Given Class Of Targets, Necip Dirik

Theses and Dissertations

Strike planning is one of the fundamental tasks of the Turkish Air Force and involves assignment of strike aircraft to targets with a maximum level of efficiency. Therefore, planning an optimal strike plan based on the preferences of the decision maker is crucial. The efficiency of the strike plan in this research implies attacking the maximum number of targets while considering target priority and the desired level of damage on each target. Another objective is to minimize the cost of the plan. This research develops an exact model that maximizes the efficiency of the strike plan using LINGO with Excel …

First-Order And Second-Order Optimality Conditions For Nonsmooth Constrained Problems Via Convolution Smoothing, Andrew C. Eberhard, Boris S. Mordukhovich

Mathematics Research Reports

This paper mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials, and secondorder subdifferentials defined via coderivatives of first-order constructions.

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

Phenotypic Variance Predicts Symbiont Population Densities In Corals: A Modeling Approach, Robert Van Woesik, Kazuyo Shiroma, Semen Koksal

Ocean Engineering and Marine Sciences Faculty Publications

We test whether the phenotypic variance of symbionts (Symbiodinium) in corals is closely related with the capacity of corals to acclimatize to increasing seawater temperatures. Moreover, we assess whether more specialist symbionts will increase within coral hosts under ocean warming. The present study is only applicable to those corals that naturally have the capacity to support more than one type of Symbiodinium within the lifetime of a colony; for example, Montastraea annularis and Montastraea faveolata. Methodology/Principal Findings: The population dynamics of competing Symbiodinium symbiont populations were projected through time in coral hosts using a novel, discrete time optimal-resource model. Models …

An Analytical And Numerical Treatment Of The Carter Constant For Inclined Elliptical Orbits About A Massive Kerr Black Hole, Peter Komorowski, Sree Ram Valluri, Martin Houde

WORLDiscoveries Research Showcase

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits. The value of Q for bound orbits is non-negative; and an increase in Q corresponds to an increase in i. For a Schwarzschild black hole, the polar orbit represents the boundary between the prograde and retrograde orbits at which Q is at its maximum value. The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or Abutment, to …

Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz

Mathematical Sciences Technical Reports (MSTR)

We address the problem of aligning the 3D structures of two proteins. Our pairwise comparisons are based on a new optimization model that is succinctly expressed in terms of linear transformations and highlights the problem’s intrinsic geometry. The optimization problem is approximately solved with a new polynomial time algorithm. The worst case analysis of the algorithm shows that the solution is bounded by a constant depending only on the data of the problem.

Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich

Mathematics Research Reports

This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order necessary optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in our preceding work [1] establishing qualitative and quantitative relationships between conventional metric regularity jsubregularity and Lipschitzian/calmness properties in the framework of parametric generalized equations in arbitrary Banach spaces. This paper provides, on one hand, significant extensions of the major results in [1] to new partial metric regularity and hemiregularity properties. …

Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, Christa Gaskill, Jennifer Forbes-Stovall, Bruce Kessler, Mike Young, Claire A. Rinehart, Sigrid Jacobshagen

Mathematics Faculty Publications

Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computercontrolled measuring machine that limits the test beam to wavelengths reported …

Integer Functions On The Cycle Space And Edges Of A Graph, Dan Slilaty

Mathematics and Statistics Faculty Publications

A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any Z-module homomorphism of a graph’s cycle space to Z that satisfies these two properties for all cycles must be such a map induced from an edge direction …

Higher Homotopy Operations And Cohomology, David Blanc, Mark W. Johnson, James M. Turner

University Faculty Publications and Creative Works

We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams. © 2010 ISOPP.

A Majorization Algorithm For Constrained Correlation Matrix Approximation, Daniel J. Simon, Jeff Abell

Electrical and Computer Engineering Faculty Publications

We desire to find a correlation matrix of a given rank that is as close as possible to an input matrix R, subject to the constraint that specified elements in must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization algorithm to solve the problem. Although many correlation matrix approximation approaches have been proposed, this specific problem, with the rank specification and the constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples.

The Camassa-Holm Hierarchy And Soliton Perturbations, Georgi Grahovski, Rossen Ivanov

Conference papers

The theory of soliton perturbations is considered. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of “squared solutions” of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be viewed as a GFT where the expansions of the solutions have generalised Fourier coefficients given by the scattering data. The GFT provides a natural setting for the analysis of small perturbations to an integrable equation: starting from a purely soliton solution one can ’modify’ …

Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, Todd Kapitula, Kody J. H. Law, Panayotis G. Kevrekidis

University Faculty Publications and Creative Works

In this paper we consider the existence and spectral stability of excited states in two-species Bose-Einstein condensates in the case of a pancake magnetic trap. Each new excited state found in this paper is to leading order a linear combination of two one-species dipoles, each of which is a spectrally stable excited state for one-species condensates. The analysis is done via a Lyapunov-Schmidt reduction and is valid in the limit of weak nonlinear interactions. Some conclusions, however, can be made at this limit which remain true even when the interactions are large.

Singular Points Of Real Sextic Curves I, David A. Weinberg, Nicholas J. Willis

Faculty Publications - Department of Mathematics

A complete classification of the individual types of singular points is given for irreducible real sextic curves. This classification is derived by using the computer algebra system Maple. There are 191 types of singular points for real irreducible sextic curves. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. A significant portion of the proof consists of a sequence of large symbolic computations that can be done nicely using Maple.

Parallelization Of The Wolff Single-Cluster Algorithm, Jevgenijs Kaupužs, Jānis Rimšāns, Roderick V.N. Melnik

Mathematics Faculty Publications

A parallel [open multiprocessing (OpenMP)] implementation of the Wolff single-cluster algorithm has been developed and tested for the three-dimensional (3D) Ising model. The developed procedure is generalizable to other lattice spin models and its effectiveness depends on the specific application at hand. The applicability of the developed methodology is discussed in the context of the applications, where a sophisticated shuffling scheme is used to generate pseudorandom numbers of high quality, and an iterative method is applied to find the critical temperature of the 3D Ising model with a great accuracy. For the lattice with linear size L=1024, we have …

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 …