Physical Sciences and Mathematics Commons^™

A Partially Discretized Age-Dependent Population Model With An Additional Stucture, Jean Tchuenche

Applications and Applied Mathematics: An International Journal (AAM)

A semi-discretization method for solving an age-dependent population dynamics model with an additional structure is proposed. This method, unlike previous ones, considers the partial discretization which reduces the model equation into a first order ordinary differential equation. The latter is then solved explicitly and conditions under which second order accuracy arises are given. While the approach adopted is basically analytical, the main result shows that the sum of errors is bounded. An extension to the non-trivial case where growth depends on the additional parameter leads to a Riccati equation, and the existence and
convergence of solutions are proved.

Explicit Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek

Miscellaneous (presentations, translations, interviews, etc)

We show that any symmetry of a smooth strict feedforward system is conjugated to a scaling translation and any 1-parameter family of symmetries to a family of scaling translations along the first variable. We compute explicitly those symmetries by finding the conjugating diffeomorphism. We deduce, in accordance with our previous work, that a smooth system is feedback equivalent to a strict feedforward form if and only if it gives rise to a sequence of systems, such that each element of the sequence, firstly, possesses an infinitesimal symmetry whose flow is conjugated to a 1- parameter families of scaling translations and, …

Oscillations Of Hyperbolic Systems With Functional Arguments, Yutaka Shoukaku, Norio Yoshida

Applications and Applied Mathematics: An International Journal (AAM)

Hyperbolic systems with functional arguments are studied, and sufficient conditions are obtained for every solution of boundary value problems to be weakly oscillatory (that is, at least one of its components is oscillatory) in a cylindrical domain. Robin-type boundary condition is considered. The approach used is to reduce the multi-dimensional oscillation problems to one-dimensional oscillation problems by using some integral means of solutions.

Stability Analysis For An Seir Age-Structured Epidemic Model Under Vaccination, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SEIR age-structured epidemic model is investigated when susceptible and immune individuals are vaccinated indiscriminately and the force of infection of proportionate mixing type. We determine the steady states and obtain an explicitly computable threshold condition, and then study the stability of the steady states.

Global Stability Results And Well Posedness Of An Si Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SI age-structured epidemic model for a vertically as well as horizontally transmitted disease is investigated when the fertility and mortality rates depend on age and the force of infection of proportionate mixing assumption type. We prove the well posedness of the model as well as the global stability for endemic equilibriums.

Topology Of Attractors From Two-Piece Expanding Maps, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this paper we study the topology of the invariant sets derived from two-piece expanding maps. We classify the conditions under which the invariant sets are topological attractors, and show that the set of attractors is open and dense in the set of invariant sets derived by two-piece expanding maps.

Oscillation Criteria For First-Order Forced Nonlinear Difference Equations, Ravi P. Agarwal, Said R. Grace, Tim Smith

Publications

Some new criteria for the oscillation of first-order forced nonlinear difference equations are established.

A Bayesian Approach For Bandwidth Selection In Kernel Density Estimation With Censored Data, Chinthaka Kuruwita

All Theses

Estimating an unknown probability density function is a common problem arising frequently in many scientific disciplines. Among many density estimation methods, the kernel density estimators are widely used. However, the classical kernel density estimators suffer from an intrinsic problem as they assign positive values outside the support of the target density. This problem is commonly known as the `Spill over` effect. A modification to the regular kernel estimator is proposed to circumvent this problem. The proposed method uses a lognormal kernel and can be used even in the presence of censoring to estimate any density with a positive support without …

Guiding Of Laser Beams In Plasmas By Radiation Cascade Compression, Serguei Y. Kalmykov, Gennady Shvets

Serge Youri Kalmykov

The near-resonant beatwave excitation of an electron plasma wave (EPW) can be employed for generating trains of few-fs electromagnetic pulses in rarefied plasmas. The EPW produces a co-moving index grating that induces a laser phase modulation at the beat frequency. Consequently, the cascade of sidebands red- and blue-shifted from the fundamental by integer multiples of the beat frequency is generated in the laser spectrum. When the beat frequency is lower than the electron plasma frequency, the phase chirp enables laser beatnote compression by the group velocity dispersion [S. Kalmykov and G. Shvets, Phys. Rev. E 73, 46403 (2006)]. In the …

Spatio-Temporal Analysis Of Areal Data And Discovery Of Neighborhood Relationships In Conditionally Autoregressive Models, Subharup Guha, Louise Ryan

Harvard University Biostatistics Working Paper Series

No abstract provided.

Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements On [0,1], Bruce Kessler

Mathematics Faculty Publications

Geronimo, Hardin, et al have previously constructed orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on $[0,1]$. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on $[0,1]$ is insufficient for extending spline scaling vectors to scaling vectors that are both orthogonal and balanced. We are able, however, to use this technique to extend spline scaling vectors to balanced, biorthogonal scaling vectors, and we provide two large classes of this type of scaling vector, with approximation order two and three, respectively, with …

Strings, Chains, And Ropes, Darryl H. Yong

All HMC Faculty Publications and Research

Following Antman [Amer. Math. Mon., 87 (1980), pp. 359–370], we advocate a more physically realistic and systematic derivation of the wave equation suitable for a typical undergraduate course in partial differential equations. To demonstrate the utility of this derivation, three applications that follow naturally are described: strings, hanging chains, and jump ropes.

Bayesian Wavelet-Based Methods For The Detection Of Multiple Changes Of The Long Memory Parameter, Kyungduk Ko

Mathematics Faculty Publications and Presentations

Long memory processes are widely used in many scientific fields, such as economics, physics, and engineering. Change point detection problems have received considerable attention in the literature because of their wide range of possible applications. Here we describe a wavelet-based Bayesian procedure for the estimation and location of multiple change points in the long memory parameter of Gaussian autoregressive fractionally integrated moving average models (ARFIMA(p, d, q)), with unknown autoregressive and moving average parameters. Our methodology allows the number of change points to be unknown. The reversible jump Markov chain Monte Carlo algorithm is used for posterior inference. The method …

Prepms: Tof Ms Data Graphical Preprocessing Tool, Yuliya V. Karpievitch, Elizabeth G. Hill, Adam J. Smolka, Jeffrey S. Morris, Kevin R. Coombes, Keith A. Baggerly, Jonas S. Almeida

Jeffrey S. Morris

We introduce a simple-to-use graphical tool that enables researchers to easily prepare time-of-flight mass spectrometry data for analysis. For ease of use, the graphical executable provides default parameter settings experimentally determined to work well in most situations. These values can be changed by the user if desired. PrepMS is a stand-alone application made freely available (open source), and is under the General Public License (GPL). Its graphical user interface, default parameter settings, and display plots allow PrepMS to be used effectively for data preprocessing, peak detection, and visual data quality assessment.

Energy In Vectorial Relativity: E ≈ M.C2, Jorge A. Franco

Jorge A Franco

In previous work it was shown that assumptions, y = y' and z = z’, within Lorentz Transformations were needless, and therefore groundless. Because of such assumptions, Lorentz Transformations (LT) depend on the body’s spatial orientation, i.e. the well-known transverse and longitudinal transformations of magnitudes, characterized by different scaling factors. On the contrary, the development of LT without assumptions, brought about new transformations that do not depend on spatial orientation and a unique mass definition, m = °m /[1 –(v/c)^2]^(3/2). As it is known, Einstein arrived at two definitions: transverse mass mT = °m /[1 –(v/c)^2]^ (1/2) and longitudinal mass …

Gravitation In Vectorial Relativity, Jorge A. Franco

Jorge A Franco

It is known that Kepler’s Laws can be derived from the Newton’s Law of Universal Gravitation. For doing this, mass is considered as an invariable parameter. Although this consideration works wonderfully to solve most of problems in astronomy calculations, as in all physics, when body’s speeds are so high and very precise measurements are required, the referred Kepler Laws do not cope enough what is expected. That’s why the General Theory of Relativity materialized. As it was indirectly pointed out by Einstein in 1905, Newton and Kepler Laws do not consider the relativistic variation of mass with its velocity. In …

Posterminaries: After Nabarro, Alexander H. King

Alexander H. King

With the passing of Frank Nabarro in July of this year, we have lost one of the founding fathers of materials science. His name appears in many of the textbooks from which we train our students today, and also on the spines of several volumes on dislocation theory, including his classic monograph on the subject. He rightly stands among the gods of our field. Ninety years old at his death, he was a sprightly dancer at the frontiers of knowledge, right up to the end.

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.

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 …

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 …

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 …

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, …

Injection, Trapping, And Acceleration Of Electrons In A Three-Dimensional Nonlinear Laser Wakefield, Serguei Y. Kalmykov, Leonid M. Gorbunov, Patrick Mora, Gennady Shvets

Serge Youri Kalmykov

It is demonstrated that the accelerating and focusing phases of the nonlinear three-dimensional axisymmetric laser wake can almost entirely overlap starting from a certain distance behind the laser pulse in homogeneous plasma. Such field structure results from the curvature of phase fronts due to the radially inhomogeneous relativistic shift of plasma frequency. Consequently, the number of trapped low-energy electrons can be much greater than that predicted by the linear wake theory. This effect is favorable for quasi-monoenergetic acceleration of a considerable charge (several hundreds of pC) to about 1 GeV per electron in the plasma wakefield driven by an ultrashort …

Snapshots Of Laser Wakefields, Nicholas H. Matlis, Steven A. Reed, Stepan S. Bulanov, Vladimir Chvykov, Galina Kalintchenko, Takeshi Matsuoka, Pascal Rousseau, Victor Yanovsky, Anatoly Maksimchuk, Serguei Y. Kalmykov, Gennady Shvets, Michael C. Downer

Serge Youri Kalmykov

Tabletop plasma accelerators can now produce GeV-range electron beams and femtosecond X-ray pulses, providing compact radiation sources for medicine, nuclear engineering, materials science and high-energy physics. In these accelerators, electrons surf on electric fields exceeding 100 GeV m^{−1}, which is more than 1,000 times stronger than achievable in conventional accelerators. These fields are generated within plasma structures (such as Langmuir waves or electron density ‘bubbles’) propagating near light speed behind laser or charged-particle driving pulses. Here, we demonstrate single-shot visualization of laser-wakefield accelerator structures for the first time. Our ‘snapshots’ capture the evolution of multiple wake periods, detect structure variations …

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 …

An Elliptic Equation With No Monotonicity Condition On The Nonlinearity, Gregory S. Spradlin

Greg S. Spradlin Ph.D.

An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree theory argument must be used.

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.

A Mathematical Regression Of The U.S. Gross Private Domestic Investment 1959-2001, Byron E. Bell

Byron E. Bell

SUMMARY OF PROJECT What did I do? A study of the role the U.S. stock markets and money markets have possibly played in the Gross Private Domestic Investment (GPDI) of the United States from the year 1959 to the year 2001 and I created a Multiple Linear Regression Model (MLRM).

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 …