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Applied Mathematics

2006

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Articles 1 - 30 of 164

Full-Text Articles in Physical Sciences and Mathematics

Interacting With Local And Remote Data Respositories Using The Stashr Package, Sandrah P. Eckel, Roger Peng Dec 2006

Interacting With Local And Remote Data Respositories Using The Stashr Package, Sandrah P. Eckel, Roger Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

The stashR package (a Set of Tools for Administering SHared Repositories) for R implements a simple key-value style database where character string keys are associated with data values. The key-value databases can be either stored locally on the user's computer or accessed remotely via the Internet. Methods specific to the stashR package allow users to share data repositories or access previously created remote data repositories. In particular, methods are available for the S4 classes localDB and remoteDB to insert, retrieve, or delete data from the database as well as to synchronize local copies of the data to the remote version …

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Change-Point Tests For Precipitation Data, Michael Robbins Dec 2006

Change-Point Tests For Precipitation Data, Michael Robbins

All Theses

A new method is required for change-point testing of precipitation data that is capable of applying valid precipitation models. First, stochastic precipation models are researched and classified. Typically, the occurrence of rain is modeled using a two-state, first-order Markov chain, and the intensity of rain is modeled using a two-parameter gamma distribution. Using the likelihood ratio test statistic, methods are devoloped for testing for fixed and unknown change-points. These methods are developed for various models, including the MC/gamma model and simplified versions. The distribution of the LRT is unknown, however its asymptotic distribution is known for both the fixed and …

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Numerical And Asymptotical Study Of Three-Dimensional Wave Packets In A Compressible Boundary Layer, Eric Forgoston, Michael Viergutz, Anatoli Tumin Dec 2006

Numerical And Asymptotical Study Of Three-Dimensional Wave Packets In A Compressible Boundary Layer, Eric Forgoston, Michael Viergutz, Anatoli Tumin

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initialvalue problem. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as Mode S and Mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectra are analyzed numerically for a hypersonic flow. A comprehensive study of the spectrum is performed, including Reynolds number, Mach number and temperature …

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Asymmetric Games For Convolution Systems With Applications To Feedback Control Of Constrained Parabolic Equations, Boris S. Mordukhovich Dec 2006

Asymmetric Games For Convolution Systems With Applications To Feedback Control Of Constrained Parabolic Equations, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to the study of some classes of feedback control problems for linear parabolic equations subject to hard/pointwise constraints on both Dirichlet boundary controls and state dynamic/output functions in the presence of uncertain perturbations within given regions. The underlying problem under consideration, originally motivated by automatic control of the groundwater regime in irrigation networks, is formalized as a minimax problemof optimal control, where the control strategy is sought as a feedback law. Problems of this type are among the most important in control theory and applications - while most challenging and difficult. Based on the Maximum Principle …

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Suboptimal Feedback Control Design Of Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich Dec 2006

Suboptimal Feedback Control Design Of Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns minimax control problems forlinear 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 an efficient approach to the minimax control design of constrained parabolic systems that is based on certain characteristic features of the parabolic dynamics including …

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Generalized Differentiation Of Parameter-Dependent Sets And Mappings, Boris S. Mordukhovich, Bingwu Wang Dec 2006

Generalized Differentiation Of Parameter-Dependent Sets And Mappings, Boris S. Mordukhovich, Bingwu Wang

Mathematics Research Reports

The paper concerns new aspects of generalized differentiation theory that plays a crucial role in many areas of modern variational analysis, optimization, and their applications. In contrast to the majority of previous developments, we focus here on generalized differentiation of parameter-dependent objects (sets, set-valued mappings, and nonsmooth functions), which naturally appear, e.g., in parametric optimization and related topics. The basic generalized differential constructions needed in this case are different for those known in parameter-independent settings, while they still enjoy comprehensive calculus rules developed in this paper.

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Optimal Control Of Nonconvex Differential Inclusions, Boris S. Mordukhovich Dec 2006

Optimal Control Of Nonconvex Differential Inclusions, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns new aspects of generalized differentiation theory that plays a crucial role in many areas of modern variational analysis, optimization, and their applications. In contrast to the majority of previous developments, we focus here on generalized differentiation of parameter-dependent objects (sets, set-valued mappings, and nonsmooth functions), which naturally appear, e.g., in parametric optimization and related topics. The basic generalized differential constructions needed in this case are different for those known in parameter-independent settings, while they still enjoy comprehensive calculus rules developed in this paper.

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Epi-Convergent Discretization Of The Generalizaed Bolza Problem In Dynamic Optimization, Boris S. Mordukhovich, Teemu Pennanen Dec 2006

Epi-Convergent Discretization Of The Generalizaed Bolza Problem In Dynamic Optimization, Boris S. Mordukhovich, Teemu Pennanen

Mathematics Research Reports

The paper is devoted to well-posed discrete approximations of the so-called generalized Bolza problem of minimizing variational functionals defined via extended-real-valued functions. This problem covers more conventional Bolza-type problems in the calculus of variations and optimal control of differential inclusions as well of parameterized differential equations. Our main goal is find efficient conditions ensuring an appropriate epi-convergence of discrete approximations, which plays a significant role in both the qualitative theory and numerical algorithms of optimization and optimal control. The paper seems to be the first attempt to study epi-convergent discretizations of the generalized Bolza problem; it establishes several rather general …

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A Partially Discretized Age-Dependent Population Model With An Additional Stucture, Jean Tchuenche Dec 2006

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.

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Explicit Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek Dec 2006

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, …

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Oscillations Of Hyperbolic Systems With Functional Arguments, Yutaka Shoukaku, Norio Yoshida Dec 2006

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.

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Stability Analysis For An Seir Age-Structured Epidemic Model Under Vaccination, M. El-Doma Dec 2006

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.

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Oscillation Criteria For First-Order Forced Nonlinear Difference Equations, Ravi P. Agarwal, Said R. Grace, Tim Smith Dec 2006

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.

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Global Stability Results And Well Posedness Of An Si Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma Dec 2006

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.

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A Bayesian Approach For Bandwidth Selection In Kernel Density Estimation With Censored Data, Chinthaka Kuruwita Dec 2006

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 …

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Topology Of Attractors From Two-Piece Expanding Maps, Youngna Choi Dec 2006

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.

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Guiding Of Laser Beams In Plasmas By Radiation Cascade Compression, Serguei Y. Kalmykov, Gennady Shvets Nov 2006

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 …

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Spatio-Temporal Analysis Of Areal Data And Discovery Of Neighborhood Relationships In Conditionally Autoregressive Models, Subharup Guha, Louise Ryan Nov 2006

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.

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Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements On [0,1], Bruce Kessler Nov 2006

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 …

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Strings, Chains, And Ropes, Darryl H. Yong Nov 2006

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.

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Bayesian Wavelet-Based Methods For The Detection Of Multiple Changes Of The Long Memory Parameter, Kyungduk Ko Nov 2006

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 …

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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 Nov 2006

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.

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Energy In Vectorial Relativity: E ≈ M.C2, Jorge A. Franco Nov 2006

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 …

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Gravitation In Vectorial Relativity, Jorge A. Franco Nov 2006

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 …

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Posterminaries: After Nabarro, Alexander H. King Nov 2006

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.

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Abstract Semilinear Itó-Volterra Integro-Differential Stochastic Evolution Equations, David N. Keck, Mark A. Mckibben Nov 2006

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.

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On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth Nov 2006

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 …

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How Effective Is Security Screening Of Airline Passengers?, Susan E. Martonosi, Arnold Barnett Nov 2006

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 …

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A Simplified Model For Growth Factor Induced Healing Of Wounds, F. J. Vermolen, E. Van Baaren, J. A. Adam Nov 2006

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 …

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Injection, Trapping, And Acceleration Of Electrons In A Three-Dimensional Nonlinear Laser Wakefield, Serguei Y. Kalmykov, Leonid M. Gorbunov, Patrick Mora, Gennady Shvets Oct 2006

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 …

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