Applied Mathematics Commons^™

How Effective Is Security Screening Of Airline Passengers?, Susan E. Martonosi, Arnold Barnett

All HMC Faculty Publications and Research

With a simple mathematical model, we explored the antiterrorist effectiveness of airport passenger prescreening systems. Supporters of these systems often emphasize the need to identify the most suspicious passengers, but they ignore the point that such identification does little good unless dangerous items can actually be detected. Critics often focus on terrorists' ability to probe the system and thereby thwart it, but ignore the possibility that the very act of probing can deter attempts at sabotage that would have succeeded. Using the model to make some preliminary assessments about security policy, we find that an improved baseline level of screening …

Abstract Semilinear Itó-Volterra Integro-Differential Stochastic Evolution Equations, David N. Keck, Mark A. Mckibben

Mathematics Faculty Publications

We consider a class of abstract semilinear stochastic Volterra integrodifferential equations in a real separable Hilbert space. The global existence and uniqueness of a mild solution, as well as a perturbation result, are established under the so-called Caratheodory growth conditions on the nonlinearities. An approximation result is then established, followed by an analogous result concerning a so-called McKean-Vlasov integrodi fferential equation, and then a brief commentary on the extension of the main results to the time-dependent case. The paper ends with a discussion of some concrete examples to illustrate the abstract theory.

On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth

Mathematics Faculty Publications

A proper short exact sequence in the category of locally compact abelian groups is said to be t-pure if φ(A) is a topologically pure subgroup of B, that is, if for all positive integers n. We establish conditions under which t-pure exact sequences split and determine those locally compact abelian groups K ⊕ D (where K is compactly generated and D is discrete) which are t-pure injective or t-pure projective. Calling the extension (*) almost pure if for all positive integers n, we obtain a complete description of the almost pure injectives and almost pure projectives in the category of …

Category 5 Hurricane Evacuation Analysis Of The Rio Grande Valley Of Texas: Maximum Flow Problem, Bart Webb

Theses and Dissertations - UTB/UTPA

The author evaluated the capability of evacuating the Rio Grande Valley of Texas (Hidalgo, Willacy, and Cameron Counties) in the event of a Category 5 hurricane.

This analysis determined the duration of an evacuation required for this region in the event of a Category 5 hurricane using the evacuation maps from the State of Texas, including areas where contraflow is proposed. The Ford and Fulkerson methodology was the basis of the Maximum Flow problem for the following Category 5 hurricane scenarios: 1) Evacuation constrained only by road capacity, 2) Evacuation constrained by a Department of Homeland Security checkpoint at Falfurrias, …

A Simplified Model For Growth Factor Induced Healing Of Wounds, F. J. Vermolen, E. Van Baaren, J. A. Adam

Mathematics & Statistics Faculty Publications

A mathematical model is developed for the rate of healing of a circular or elliptic wound. In this paper the regeneration, decay and transport of a generic 'growth factor', which induces the healing of the wound, is taken into account. Further, an equation of motion is derived for radial healing of a circular wound. The expressions for the equation of motion and the distribution of the growth factor are related in such a way that no healing occurs if the growth factor concentration at the wound edge is below a threshold value. In this paper we investigate the influence of …

Multiobjective Optimization Problems With Equilibrium Constraints, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to new applications of advanced tools of modern variational analysis and generalized differentiation to the study of broad classes of multiobjective optimization problems subject to equilibrium constraints in both finite-dimensional and infinite-dimensional settings. Performance criteria in multiobjectivejvector optimization are defined by general preference relationships satisfying natural requirements, while equilibrium constraints are described by parameterized generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and are handled in this paper via appropriate normal/coderivativejsubdifferential constructions that exhibit full calculi. Most of the results obtained are new even in finite dimensions, while the case of …

Allometric Extension For Multivariate Regression Models, Thaddeus Tarpey, Christopher T. Ivey

Mathematics and Statistics Faculty Publications

In multivariate regression, interest lies on how the response vector depends on a set of covariates. A multivariate regression model is proposed where the covariates explain variation in the response only in the direction of the first principal component axis. This model is not only parsimonious, but it provides an easy interpretation in allometric growth studies where the first principal component of the log-transformed data corresponds to constants of allometric growth. The proposed model naturally generalizes the two–group allometric extension model to the situation where groups differ according to a set of covariates. A bootstrap test for the model is …

Positive Solutions Of A Nonlinear N-Th Order Eigenvalue Problem, John R. Graef, Johnny Henderson, Bo Yang

Faculty Articles

For 1/2 < p < 1 fixed, values of lambda > 0 are determined for which there exist positive solutions of the n-th order differential equation u((n)) = lambda g(t)f(u), 0 < t < 1, satisfying the three-point boundary conditions, u((i-1)) (0) = u((n-2)) (P) = u((n-1)) (1) = 0, 1

The problem is converted to a third order differential-integro boundary value problem and then a recent result of Graef and Yang for third order boundary value problems is adapted. An example is included to illustrate the results.

Norming Algebras And Automatic Complete Boundedness Of Isomorphisms Of Operator Algebras, David R. Pitts

Department of Mathematics: Faculty Publications

We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C*-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomorphism of a C*-algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a C-algebra is similar to a -representation precisely when the image operator algebra -norms itself. We give …

A Stochastic Model For Psa Levels: Behavior Of Solutions And Population Statistics, Pavel Bělík, P W A Dayananda, John T. Kemper, Mikhail M. Shvartsman

Faculty Authored Articles

This paper investigates the partial differential equation for the evolving distribution of prostate-specific antigen (PSA) levels following radiotherapy. We also present results on the behavior of moments for the evolving distribution of PSA levels and estimate the probability of long-term treatment success and failure related to values of treatment and disease parameters. Results apply to a much wider range of parameter values than was considered in earlier studies, including parameter combinations that are patient specific.

Necessary Conditions In Multiobjective Optimization With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study multiobjective optimization problems with equilibrium constraints (MOECs) described by generalized equations in the form 0 is an element of the set G(x,y) + Q(x,y), where both mappings G and Q are set-valued. Such models particularly arise from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the general problems under consideration and for their important specifications using modern tools of variational analysis and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical example from bilevel programming with convex …

Existence Of Large Solutions To Semilinear Elliptic Equations With Multiple Terms, David N. Smith

Theses and Dissertations

We consider the semilinear elliptic equation Δu = p(x)u^α + q(x)u^β on a domain Ω ⊆ Rⁿ, n ≥ 3, where p and q are nonnegative continuous functions with the property that each of their zeroes is contained in a bounded domain Ω_p or Ω_q, respectively in Ω such that p is positive on the boundary of Ω_p and q is positive on the boundary of Ω_q. For Ω bounded, we show that there exists a nonnegative solution u such that u(x) → ∞ as x → ∂Ω if …

Optimizing The Replication Of Multi-Quality Web Applications Using Aco And Wolf, Judson C. Dressler

Theses and Dissertations

This thesis presents the adaptation of Ant Colony Optimization to a new NP-hard problem involving the replication of multi-quality database-driven web applications (DAs) by a large application service provider (ASP). The ASP must assign DA replicas to its network of heterogeneous servers so that user demand is satisfied and replica update loads are minimized. The algorithm proposed, AntDA, for solving this problem is novel in several respects: ants traverse a bipartite graph in both directions as they construct solutions, pheromone is used for traversing from one side of the bipartite graph to the other and back again, heuristic edge values …

A New Application Of The Channel Packet Method For Low Energy 1-D Elastic Scattering, Clint M. Zeringue

Theses and Dissertations

An algorithm is presented which uses the channel packet method (CPM) to simulate low-energy, wave-packet propagation and compute S-matrix elements. A four-by-four matrix containing the momentum, expansion coefficients of the reactants and products is introduced to account for initial and final states having both positive and negative momentum. The approach does not consider scattering from one side or the other, rather it considers both incoming and outgoing wave packets from the left and right simultaneously. Therefore, during one simulation all four S-matrix elements, and elements, S_+k,-K, S_{-k, +k}, S_{+k, +k} and S_-k,-k are computed. …

Bayesian Smoothing Of Irregularly-Spaced Data Using Fourier Basis Functions, Christopher J. Paciorek

Harvard University Biostatistics Working Paper Series

No abstract provided.

Phase Transitions And Change Of Type In Low-Temperature Heat, Ralph A. Saxton, Katarzyna Saxton

Mathematics Faculty Publications

Classical heat pulse experiments have shown heat to propagate in waves through crystalline materials at temperatures close to absolute zero. With increasing temperature, these waves slow down and finally disappear, to be replaced by diffusive heat propagation. Several features surrounding this phenomenon are examined in this work. The model used switches between an internal parameter (or extended thermodynamics) description and a classical (linear or nonlinear) Fourier law setting. This leads to a hyperbolic-parabolic change of type, which allows wavelike features to appear beneath the transition temperature and diffusion above. We examine the region around and immediately below the transition temperature, …

Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?, Haijun Wu, Zhimin Zhang

Mathematics Research Reports

We study adaptive finite element methods for elliptic problems with domain corner singularities. Our model problem is the two dimensional Poisson equation. Results of this paper are two folds. First, we prove that there exists an adaptive mesh (gauged by a discrete mesh density function) under which the recovered.gradient by the Polynomial Preserving Recovery (PPR) is superconvergent. Secondly, we demonstrate by numerical examples that an adaptive procedure with a posteriori error estimator based on PPR does produce adaptive meshes satisfy our mesh density assumption, and the recovered gradient by PPR is indeed supercoveregent in the adaptive process.

Thermal Imaging To Recover A Defect In Three Dimensional Objects, Breanne Baker

Mathematical Sciences Technical Reports (MSTR)

This paper focuses on the inverse problem of identifying an internal void in a bounded two- or three-dimensional region. Information, in form of a heat flux and temperature, is assumed to be obtainable only on the external boundary of the region. The reciprocity gap approach with a suitable test functions is used in both the two- and three-dimensional cases.

Non-Destructive Recovery Of Voids Within A Three Dimensional Domain Using Thermal Imaging, Victor B. Oyeyemi

Mathematical Sciences Technical Reports (MSTR)

We develop an algorithm capable of detecting the presence of spherical voids in a thermally conducting object. In addition, the process recovers both the radii and locations of each void. Our method involves the application of a known steady state heat flux to the object's boundary and measurement of the induced steady state temperature on the boundary.

Mean Field Effects For Counterpropagating Traveling Wave Solutions Of Reaction-Diffusion Systems, Andrew J. Bernoff, R. Kuske, B. J. Matkowsky, V. Volpert

All HMC Faculty Publications and Research

In many problems, e.g., in combustion or solidification, one observes traveling waves that propagate with constant velocity and shape in the x direction, say, are independent of y and z and describe transitions between two equilibrium states, e.g., the burned and the unburned reactants. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves having additional structure, such as traveling waves in the y and z directions, which can themselves be subject to instabilities as parameters are further varied. To investigate this scenario we consider a system of reaction-diffusion equations with a …

Charactarizations Of Linear Suboptimality For Mathematical Programs With Equilibrium Constraints, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant from the viewpoint of modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mainly focus on various classes of mathematical programs with equilibrium constraints (MPECs), whose principal role has been well recognized in optimization theory and its applications. Based on robust generalized differential calculus, we …

Study On Vortex Formation In The Pouring Basin By Direct Observation, J Runyoro

Tanzania Journal of Engineering and Technology (TJET)

Although the formation of vortex on the free surface of liquid draining from a container is often observed, relatively little is known about the phenomenon. When a liquid is drained from a container such as a bathtub through a bottom orifice, a dip on the surface known as vortex is formed. The vortex first appears as a small dimple in the free surface, which suddenly forms a cone-shaped hole. The vortex causes turbulences, which draws in air down into the orifice (drain). Generally, the issue of vortex formation is so common in our lives that possibly its occurrence seems to …

Comparison Of Two Different Transport Models To Predict Sediment Transport: Simiyu River, Tanzania, Case Study, F Mwanuzi1

Tanzania Journal of Engineering and Technology (TJET)

This paper presents the results of a study which focused at the spatial and temporal characteristics of sediment transport and deposition in the main river channels and floodplains. Two different numerical models were used to simulate stream flow and to analyze sediment transport and deposition in the river channels: (1) the SMS modules RMA2 and SED2D and (2) the SCALDIS model developed at the Free University of Brussels. Both numerical models contain a two-dimensional hydrodynamic module and a sediment transport module, allowing simulation of stream flow and sediment transport processes in river channels. However, they differ in the following aspects: …

Overview Of Hydraulics And Simiyu River Sediment Input Into Magu Bay, Lake Victoria, Tanzania, Alfonse Dubi

Tanzania Journal of Engineering and Technology (TJET)

Lake Victoria is experiencing multifaceted environmental and ecological problems. A  study of the problems needs a multidisciplinary approach. to establish the cause-effect relationships. The study focuses on the hydraulics of Lake Victoria's Magu Bay and Simiyu riverine input of suspended sediments and their distribution in the Bay. Sampling in the river mouth and the Bay was conducted aboard an 8m outboard engine wooden boat. Turbidity, currents speed and direction were measured using an "AANDERAA" multi-sensor self-recording current meter model 9 (RCM9). Water depth was measured using an echo-sounder type FISHIN' BUDDY II. Geographical positions of the sampling locations were obtained …

The Decomposition Kinetics Of Solids Thermodynamic Evidence For The Enthalpy Driven Cooling Of Reaction Environment Part 2, Akwilapo D

Tanzania Journal of Engineering and Technology (TJET)

The analysis of non-isothermal kinetic data for the decomposition of calcium carbonate, CaC03 (s) ~ CaO (s) + C02 (g) in flowing nitrogen, shows that the decomposition of solids is accompanied by self-cooling/heating of the reaction environment depending on the sample mass and heating rate. The correctness of the kinetic model is established by the calculation of the enthalpy change of the reaction. This is the thermodynamic evidence of endothermic enthalpy driven cooling of the reaction environment. The enthalpy change LJH = 179.33 kJmol-1 estimated from this work for the dissociation of CaC03 is in agreement with LJH = 179.17 …

Socio-Economic Impacts Of Computer Viruses In Tanzania, M Victor

Tanzania Journal of Engineering and Technology (TJET)

This paper reports on a research project conducted with an objective of identifying and assessing various approaches used by different computer users (Management, System Administrators and end users) in Tanzania to combat computer viruses (CVs), and to assess users' awareness level on CVs. Specifically, the study aimed at assessing the awareness level on CVs to the Tanzanian business community; analyze the socio -economic impact caused by CVs in Tanzania and; assess existing methods, capacity and limitations on controlling CVs in Tanzania. Data was collected using both questionnaires and interview from financial institutions such as NBC and BOT, and telecommunications sector …

Gasification Kinetics Of Ultrafine Coal Char Oxidation In Flame Reactions, G John

Tanzania Journal of Engineering and Technology (TJET)

Pulverized coal combustion is exceedingly complex with a  vast number of variables. In order to avoid the complications associated with the burning of coal char, a controlled study has been made of the oxidation of fine graphite in laminar methane-air flame as a contribution to the understanding of the more complex phenomena of the gasification kinetics of the char. The burning of methane is equivalent to the burning of volatiles and graphite oxidation is similar to that of coal char. Aspects of this have been simulated in experimental and computational studies of 4pm diameter graphite particle burning in methane -air …

Investigation Of The Stability Of Engine – Governor System Operated At Low Speeds, Cuthbert Mhilu

Tanzania Journal of Engineering and Technology (TJET)

During diesel engine operation, a tendency for the engine not to achieve a  steady idling speed has often been observed. During idling speed the engine tends to either race or stall as a result of poor and incorrect metering of the fuel, which is required for the combustion process and if severe, the engine will stop firing completely. 111 this research an investigation was made to establish knowledge on diesel engine stability operated at low speeds. The influence of a governor of an engine in the control of the engine speeds has also been investigated. In order to obtain information …

Methods Of Variational Analysis In Multiobjective Optimization, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns new applications of advanced methods of variational analysis and generalized differentiation to constrained problems of multiobjective/vector optimization. We pay the main attention to general notions of optimal solutions for multiobjective problems that are induced by geometric concepts. of extremality in variational analysis while covering various notions of Pareto and other type of optimality/efficiency conventional in multiobjective optimization. Based on the extremal principles in variational analysis and on appropriate tools of generalized differentiation with well-developed calculus rules, we derive necessary optimality conditions for broad classes of constrained multiobjective problems in the framework of infinite-dimensional spaces. Applications of variational …

Interacting With Data Using The Filehash Package For R, Roger Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

The filehash package for R implements a simple key-value style database where character string keys are associated with data values that are stored on the disk. A simple interface is provided for inserting, retrieving, and deleting data from the database. Utilities are provided that allow filehash databases to be treated much like environments and lists are already used in R. These utilities are provided to encourage interactive and exploratory analysis on large datasets. Three different file formats for representing the database are currently available and new formats can easily be incorporated by third parties for use in the filehash framework.