Applied Mathematics

This paper describes the control of an electric wheel chair with voice commands. This chair has been developed and built at the U.A.H. Electronic Department and financed by the ONCE Fotmdation (Spain). The first prototype consists of voice recosnition, motor control, user interface and central processor modules. The electronic system allows the chair user a safe, easy ride, and guarantees the concordance between user commands and actual trajectories. Furthermore, the system has been designed to allow the addition of future features, like obstacle and stair detection and the tele.-commanding of electrical household appliances from the chair.

High speed liquid jet forms when a bubble collapses near a solid boundary. The formation of the jet has both advantages and disadvantages as it causes erosion and damage in the nearby turbomachinery and can be beneficially applied in surface cleaning, fluid pumping, etc. In this paper, three-dimensional bubble oscillation between two curved rigid plates is modeled using boundary integral method (BIM). The bubble is incepted at different locations between the plates to investigate the eccentricity effects on the bubble shape, jet formation, etc. The modified Laplacian smoothing technique is implemented on the bubble surface during the jet development to reduce element distortion. The new model is validated with the Rayleigh-Plesset equation as well as with the available experimental data. It was found that the jet velocity increases, and the number of jets is reduced from two to one as the bubble is horizontally shifted away from the centroid. When the bubble is incepted on the horizontal axisymmetric line the jet is horizontal. However, the jet direction changes as the bubble is incepted closer to one of the plates. Finally, the pressure and velocity fields of the fluid surrounding the bubble are provided for better interpretation of the results.

In this paper, we study the linear fractional programming (LFP) problems under intuitionistic fuzzy setting. The problem is considered as a fully fuzzy linear fractional programming problem where the variables and parameters both are characterized by trapezoidal intuitionistic fuzzy number. Ranking of intuitionistic fuzzy numbers has been used to solve the problem by simplex method. An algorithm has been developed to present our approach. One numerical example has been solved to demonstrate our methodology.

We present the first tableau-based decision procedure for PDL with nominals. The procedure is based on a prefix-free clausal tableau system designed as a basis for gracefully degrading reasoners. The clausal system factorizes reasoning into regular, propositional, and modal reasoning. This yields a modular decision procedure and pays off in transparent correctness proofs.

Designing efficient and stable algorithm for finding the eigenvalues and eigenvectors is very important from the static as well as the dynamic aspect in coupled problems. Modal analysis requires first few significant eigenvectors and eigenvalues while direct integration requires the highest value to ascertain the length of the time step that satisfies the stability condition. The paper first presents the modification of the well known WYD method for a solution of single field problems: an efficient and numerically stable algorithm for computing eigenvalues and the corresponding eigenvectors. The modification is based on the special choice of the starting vector. The starting vector is the static solution of displacements for the applied load, defined as the product of the mass matrix and the unit displacement vector. The starting vector is very close to the theoretical solution, which is important in cases of small subspaces. Additionally, the paper briefly presents the adopted formulation for solving the fluid-structure coupled systems problems which is based on a separate solution for each field. Individual fields (fluid and structure) are solved independently, taking in consideration the interaction information transfer between them at every stage of the iterative solution process. The assessment of eigenvalues and eigenvectors for multiple fields is also presented. This eigen problem is more complicated than the one for the ordinary structural analysis, as the formulation produces non-symmetrical matrices. Finally, a numerical example for the eigen solution coupled fluidstructure problem is presented to show the efficiency and the accuracy of the developed algorithm.

Long term Atlantic tropical storm activity is described by the time series of the yearly Accumulated Cyclone Energy (ACE) Index for the time interval 1851-2007. ACE is a measure of total wind energy for North Atlantic basin and land falling tropical cyclone activity. Since the ACE index reflects a combination of storm intensity and duration it is a better measure of overall activity and likely damage than the number of either basin or land falling tropical storms or hurricanes. The yearly ACE time series is non-stationary, and one step toward detecting possible long-term quasi-periods is to detrend the original data. In this paper, we use a procedure for data transformation by which ACE index is fitted in least square sense with polynomials of increasing order, followed by detrend. It is shown that, with some approximation, the obtained time series is cyclostationary, and a multi-decadal oscillation is detectable, as indicated by the power spectrum analysis.

The adjustment of grid steps which guarantees that particles methods yield no numerical diffusion inevitably induces overshooting errors in the solution of the parabolic partial differential equations with space variable coefficients. In this paper we give an evaluation of the overshooting errors of the "global random walk" algorithm (GRW), a computational efficient method used in simulations for transport in environmental problems. The evaluation is performed by comparisons between the GRW solutions and those of the "biased global random walk" algorithm (BGRW), a cellular automaton, which is computationally more expensive but is also free of overshooting errors. The reference problem was the diffusive transport in a random velocity field, a model for the transport of the contaminant solutes in groundwater. The evaluation reveals that, for an optimum choice of the parameters, GRW results for time intervals of practical interest lie in ranges of acceptable precisi...

We discuss a prototypical reaction-diffusion-flow problem in saturated/unsaturated porous media. The special features of our problem are: the reaction produces water and therefore the flow and transport are coupled in both directions and moreover, the reaction may alter the microstructure. This means we have a variable porosity in our model. For the spatial discretization we propose a mass conservative scheme based on the mixed finite element method (MFEM). The scheme is semiimplicit in time. Error estimates are obtained for some particular cases. We apply our finite element methodology for the case of concrete carbonation -one of the most important physico-chemical processes affecting the durability of concrete.

The Global Random Walk algorithm (GRW) performs a simultaneous tracking on a fixed grid of huge numbers of particles at costs comparable to those of a single-trajectory simulation by the traditional Particle Tracking (PT) approach. Statistical ensembles of GRW simulations of a typical advection-dispersion process in groundwater systems with randomly distributed spatial parameters are used to obtain reliable estimations of the input parameters for the upscaled transport model and of their correlations, input-output correlations, as well as full probability distributions of the input and output parameters.

Transport processes in heterogeneous media such as ionized plasmas, natural porous media, and turbulent atmosphere are often modeled as diffusion processes in random velocity fields. Using the Itô formalism, we decompose the second spatial moments of the concentration and the equivalent effective dispersion coefficients in terms corresponding to various physical factors which influence the transport. We explicitly define "ergodic" dispersion coefficients, independent of the initial conditions and completely determined by local dispersion coefficients and velocity correlations. Ergodic coefficients govern an upscaled process which describes the transport at large tine-space scales. The non-ergodic behavior at finite times shown by numerical experiments for large initial plumes is explained by "memory terms" accounting for correlations between initial positions and velocity fluctuations on the trajectories of the solute molecules.

We identify sufficient conditions under which evolution equations for probability density functions (PDF) of random concentrations are equivalent to Fokker-Planck equations. The novelty of our approach is that it allows consistent PDF approximations by densities of computational particles governed by Itô processes in concentration-position spaces. Accurate numerical solutions are obtained with a global random walk (GRW) algorithm, stable, free of numerical diffusion, and insensitive to the increase of the total number of computational particles. The system of Itô equations is specified by drift and diffusion coefficients describing the PDF transport in the physical space, provided by up-scaling procedures, as well as by drift and mixing coefficients describing the PDF transport in concentration spaces. Mixing models can be obtained similarly to classical PDF approaches or, alternatively, from measured or simulated concentration time series. We compare their performance for a GRW-PDF numerical solution to a problem of contaminant transport in heterogeneous groundwater systems.

An alternate formulation of the classical vehicle routing problem (VRP) is considered for distributing fresh potatoes from warehouse to the food outlet or shop. We propose a new-heuristic (metaheuristic) method to solve the problem, based on the Cross-Entropy method. In order to better estimate the objective function at each point in the domain, we incorporate Monte Carlo sampling. This creates many practical issues, especially the decision as to when to draw new samples and how many samples to use. We also develop a framework for obtaining exact solutions and tight lower bounds for the problem under various conditions by grouping the destination. This is used to assess the performance of the algorithm. Numerical results are presented for various problem instances to illustrate the ideas. Finally, solution obtained by Cross-Entropy compared with Branch and Bound Algorithm. It is proved that two methods have similar solution, with number of iteration was similar relatively.

An alternate formulation of the classical vehicle routing problem (VRP) is considered for distributing fresh potatoes from warehouse to the food outlet or shop. We propose a new-heuristic (metaheuristic) method to solve the problem, based on the Cross-Entropy method. In order to better estimate the objective function at each point in the domain, we incorporate Monte Carlo sampling. This creates many practical issues, especially the decision as to when to draw new samples and how many samples to use. We also develop a framework for obtaining exact solutions and tight lower bounds for the problem under various conditions by grouping the destination. This is used to assess the performance of the algorithm. Numerical results are presented for various problem instances to illustrate the ideas. Finally, solution obtained by Cross-Entropy compared with Branch and Bound Algorithm. It is proved that two methods have similar solution, with number of iteration was similar relatively.

Creating effective and efficient production planning becomes one of the most intriguing efforts for most of the Indonesian enterprises. This study introduces an optimization model of product mix to solve the production planning problems, by considering certain multi-constraint: limited existing resources, objectives to be achieved, and fuzzy characteristics of demand and production costs. By applying Fuzzy Mixed Integer Linear Goal Programming, this study tries to determine the optimal solutions of product mix. The study consists of several steps: capacity constraint resource analysis, formulation of the optimization models, determines the products mix and the multi-criteria objective value. The proposed product mix model is then validated by conducting a preliminary study to one enterprise. The preliminary study showed that the proposed model is able to provide an increase of multi-criteria objective value by 4.81% compared to the existing conditions.

We consider a spatially distributed population dynamics model with excitable predator-prey kinetics, where species propagate in space due to their taxis with respect to each other’s gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wave tips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatiotemporal activity, unknown in reaction-diffusion population models.

Ventricular tachycardia and fibrillation are potentially lethal cardiac arrhythmias generated by high frequency, irregular spatio-temporal electrical activity. Re-entrant propagation has been demonstrated as a mechanism generating these arrhythmias in computational and in vitro animal models of these arrhythmias. Re-entry can be idealised in homogenous isotropic virtual cardiac tissues as spiral and scroll wave solutions of reaction-diffusion equations. A spiral wave in a bounded medium can be terminated if its core reaches a boundary. Ventricular tachyarrhythmias in patients are sometimes observed to spontaneously self-terminate. One possible mechanism for self-termination of a spiral wave is meander of its core to an inexcitable boundary. We have previously proposed the hypothesis that the spatial extent of meander of a re-entrant wave in the heart can be directly related to its probability of self-termination, and so inversely related to its lethality. Meander in two-dimensional ...

In this paper we consider some new classes of integral equations that arise from Lie symmetry analysis. Specifically, we consider the task of obtaining solutions of a Cauchy problem for some classes of second order hyperbolic partial differential equations. Our analysis leads to new integral equations of nonconvolution type, which can be solved by classical methods. We derive solutions of these integral equations, which in turn lead to solutions of the associated Cauchy problems.

In this paper we establish different representations of the so-called Yor integral, which is one of the key ingredient in mathematical finance, in particular, to compute normalized prices of Asian options. We show, that the Yor integral is related with the Kontorovich-Lebedev transform. Also we discuss its relationship with a system of polynomials recently introduced by the author. We derive new important properties of these polynomials, including upper bounds, an exact asymptotic behavior for large values of their degree and explicit formula of coefficients.

The Salem problem to verify whether Fourier-Stieltjes coefficients of the Minkowski question mark function vanish at infinity is solved recently affirmatively. In this paper by using methods of classical analysis and special functions we solve a Salem-type problem about the behavior at infinity of a linear combination of the Fourier-Stieltjes transforms. Moreover, as a consequence of the Salem problem, some asymptotic relations at infinity for the Fourier-Stieltjes coefficients of a power m ∈ N of the Minkowski question mark function are derived.

An essential generalization of the Lebedev index transform with the square of the Macdonald function is investigated. Namely, we consider a family of integral operators with the positive kernel K (iτ+α)/2 (x) 2 , α ≥ 0, x > 0, τ ∈ R, where K µ (z) is the Macdonald function and i is the imaginary unit. Mapping properties such as the boundedness, compactness, invertibility are investigated for these operators and their adjoints in the Lebesgue weighted spaces. Inversion theorems are proved. Important particular cases are exhibited. As an interesting application, a solution of the initial value problem for the second order differential difference equation, involving the Laplacian, is obtained.

Discrete analogs of the classical Kontorovich-Lebedev transforms are introduced and investigated. It involves series with the modified Bessel function or Macdonald function K in (x), x > 0, n ∈ N, i is the imaginary unit, and incomplete Bessel functions. Several expansions of suitable functions and sequences in terms of these series and integrals are established. As an application, a Dirichlet boundary value problem in the upper half-plane for inhomogeneous Helmholtz equation is solved.

In this work, we present a fractional model of Cahn-Allen equation associated with newly introduced Atangana-Baleanu (AB) derivative of fractional order which uses Mittag-Leffler function as the nonsingular and non-local kernel. The existence and uniqueness of this modified fractional model are discussed by employing the fixed-point postulate. An efficient scheme homotopy perturbation transform technique (HPTT) which is an amalgamation of homotopy perturbation technique with Laplace transform is used to examine this time-fractional phase-field model numerically. Also, convergence and error analysis of the proposed technique is presented. The numerical simulations are analyzed graphically as well as in tabulated form.

We develop space-time adaptive and high-order methods for valuing American options using a partial differential equation (PDE) approach. The linear complementarity problem arising due to the free boundary is handled by a penalty method. Both finite difference and finite element methods are considered for the space discretization of the PDE, while classical finite differences, such as Crank-Nicolson, are used for the time discretization. The high-order discretization in space is based on an optimal finite element collocation method, the main computational requirements of which are the solution of one tridiagonal linear system at each time step, while the resulting errors at the gridpoints and midpoints of the space partition are fourth-order. To control the space error, we use adaptive gridpoint distribution based on an error equidistribution principle. A time stepsize selector is used to further increase the efficiency of the methods. Numerical examples show that our methods converge fast and provide highly accurate options prices, Greeks, and early exercise boundaries.

We study a parallel implementation on a Graphics Processing Unit (GPU) of Alternating Direction Implicit (ADI) time-discretization methods for solving time-dependent parabolic Partial Differential Equations (PDEs) in three spatial dimensions with mixed spatial derivatives in a variety of applications in computational finance. Finite differences on uniform grids are used for the spatial discretization of the PDEs. As examples, we apply the GPU-based parallel methods to price European rainbow and European basket options, each written on three assets. Numerical results showing the efficiency of the parallel methods are provided.

Quadratic Spline Collocation (QSC) methods of optimal order of convergence have been recently developed for the solution of elliptic Partial Differential Equations (PDEs). In this paper, linear solvers based on Fast Fourier Transforms (FFT)are developed for the solution of the QSC equations. The complexity of the FFT solvers is O(N2 log N), where N is the gridsize in one dimension. These direct solvers can handle PDEs with coefficients in one variable or constant, and Dirichlet, Neumann, alternating Dirichlet-Neumann or periodic boundary conditions, along at least one direction of a rectangular domain. General variable coefficient PDEs are handled by preconditioned iterative solvers. The preconditioner is the QSC matrix arising from a constant coefficient PDE. The convergence analysis of the preconditioner is presented. It is shown that, under certain conditions, the convergence rate is independent of the gridsize. The preconditioner is solved by FFT techniques, and integrated with ...

Currently in most global meteorological applications, low-order finite difference or finite element methods, or the spectral transform method are used. The spectral transform method, which yields high-order approximations, requires Legendre transforms. The Legendre transforms have a computational complexity of O(N 3 ), where N is the number of subintervals in one dimension, and thus render the spectral transform method unscalable. In this study, we present an alternative numerical method for solving the shallow water equations (SWEs) on a sphere in spherical coordinates. In this implementation, the SWEs are discretized in time using the two-level semi-Lagrangian semi-implicit method, and in space on staggered grids using the quadratic spline Galerkin method. We show that, when applied to a simplified version of the SWEs, the method yields a neutrally stable solution for the meteorologically significant Rossby waves. Moreover, we demonstrate that the Helmholtz equation arising from the discretization and solution of the SWEs should be derived algebraically rather than analytically, in order for the method to be stable with respect to the Rossby waves. These results are verified numerically using Boyd's equatorial wave equations [J.P. Boyd, Equatorial solitary waves. Part I. Rossby solitons, J. Phys. Oceanogr. 10 (1980) [1699][1700][1701][1702][1703][1704][1705][1706][1707][1708][1709][1710][1711][1712][1713][1714][1715][1716][1717] with initial conditions chosen to generate a soliton.

A thesis submitted in conformity wit h the requirements for the degree of Master of Science Graduate Department of Computer Science University of Toronto Copyright @ 2000 by Kit Sun Ng The author has gcanted a nonexclusive licence dîowing the National L i i of Canada to copies of diis thesis in microform, paper or electronic formats. The author retains ownership of the copyright in this thesis. Neither the may be printed or othawise reproduced without the author's L'auteur a accord6 me licence non exclusive parnettant A la Bibliothdque nationale du Canada de reproduire, pr&r, distribuer ou vendre des copies de cette Wse sous la forme de microfiche/iiim, de reproduction sur papier ou siu fonnat électronique. L'auteur conserve la propriété du droit d'auteur qui protège cette bitse. Ni la these ni des extraits substantiels de celle-ci ne doivent &ûe imprimes ou autrement reproduits sans son autorisation.

A new collocation method based on quadratic splines is presented for second order two‐point boundary value problems. First, O(h4) approximations to the first and second derivative of a function are derived using a quadratic‐spline interpolant of u. Then these approximations are used to define an O(h4) perturbation of the given boundary value problem. Second, the perturbed problem is used to define a collocation approximation at interval midpoints for which an optimal O(h3‐J) global estimate for the jth derivative of the error is derived. Further, O(h4‐J) error bounds for the jth derivative are obtained for certain superconvergence points. It should be observed that standard collocation at midpoints gives O(h2‐J) bounds. Results from numerical experiments are reported that verify the theoretical behaviour of the method.

We develop optimal quadratic and cubic spline collocation methods for solving linear secondorder two-point boundary value problems on non-uniform partitions. To develop optimal non-uniform partition methods, we use a mapping function from uniform to non-uniform partitions and develop expansions of the error at the non-uniform collocation points of some appropriately defined spline interpolants. The existence and uniqueness of the spline collocation approximations are shown, under some conditions. Optimal global and local orders of convergence of the spline collocation approximations and derivatives are derived, similar to those of the respective methods for uniform partitions. Numerical results on a variety of problems, including a boundary layer problem, and a non-linear problem, verify the optimal convergence of the methods, even under more relaxed conditions than those assumed by theory.

We consider Quadratic Spline Collocation (QSC) methods for linear second order elliptic Partial Differential Equations (PDEs). The standard Cannulation of these methods leads to non-optimal approximations. In order (0 derive optimal QSC approximations, high order perturbations of the PDE problem arc generated. These perturbations can be applied either to die POE problem operators or to the right sides, thus leading 10 two different fonnulations of optimal QSC methods. The convergence properties of the QSC methods arc studied. Optimal 0 (h J-j) global error estimates for the j.th partial derivative are obtained for a certain class of problems. Moreover, O(h4-j ) error bounds for the j-th partial derivative are obtained at certain sets of points. Results from numerical experiments verify the theoretical behaviour of Lhe QSC methods. Performance results also show that the QSC methods arc very effective from the computational point of view. The QSC methods have been implemented efficiently on parallel machines.

Since the beginnings of computational science, iterative methods were essential tools in the solution of nonlinear problems, such as nonlinear systems of equations and eigenvalue computations. It was also soon recognized that some of the most efficient linear solvers were based on iterative methods. Moreover, iterative methods are in the core of optimization algorithms. Throughout the last half a century, iterative methods have been the subject of intense research and development, and have been attracting increasing interest by scientists and engineers. The need of solving larger and larger problems, that were deemed to be infeasible in the past, gave a spark to the development of highperformance and parallel solution techniques. Iterative methods are in general much more suited for massively parallel computation than direct methods. New areas, such as domain decomposition, have developed alongside parallel iterative techniques. Preconditioning techniques incorporated into iterative methods allow the solution of very large sparse linear systems arising from multidimensional and other large-scale problems. New emerging application areas, such as computational biology, computational engineering, financial engineering create new opportunities and offer new challenges for iterative methods. About ninety participants from all over the world gathered in Toronto for the seventh IMACS international symposium on iterative methods in scientific computing, May 5-8, 2005. The symposium provided a forum to present and discuss the use of iterative methods in scientific computing problems, with emphasis in recent developments, future research directions, and new application areas. The symposium featured eight invited talks, seven minisymposia with 3-4 talks each, about 30 contributed talks, as well as 15 student papers, taking part in the student paper competition. Topics spanned from core iterative methods and eigenvalues to preconditioning, multigrid and parallel computation, as well as optimization, nonlinear equations and differential equations. Applications such as data and web mining, image processing, computational finance and computational fluid dynamics received special attention. The symposium received funding from the Fields Institute, the Faculty of Mathematics at the University of Waterloo and MITACS, so that 13 requests for funding by students and postdoctoral fellows were at least partially satisfied, and five awards were given to student paper competition winners. The Bahen Centre for Information Technology (BCIT) at the University of Toronto served as hosting venue. The high-ceiling hallways of BCIT were the ideal place for informal discussions and breaks, while the projectors in the rooms booked for the conference were working full-time during scientific sessions. Many participants indicated their appreciation of the high quality of the talks and interaction. On the social front, participants enjoyed the hospitality of downtown Chinatown and of the Greek village by the Danforth, as well as the ethnic diversity and colour of Baldwin street. Photos from the conference are found in and cc/imacs05/Photos1/ courtesy of David Kincaid and Omar Halabieh. This special issue of the Applied Numerical Mathematics journal is sponsored by IMACS and contains eleven selected papers presented at the conference. Among the eighteen papers submitted, these were the papers accepted for publication after the refereeing process. The range of topics covered by these papers is wide, spanning from core

We introduce the classes of color blind and typhlotic cellular automata, that is, cellular automata that commute with all symbol permutations and all symbol mappings, respectively. We show that color blind cellular automata form a relatively large subclass of all cellular automata which contains an intrinsically universal automaton. On the other hand, we give simple characterizations for the color blind CA which are also group homomorphisms, and for general typhlotic CA, showing that both must be trivial in most cases.

It is a question of Hochman whether any two one-dimensional mixing SFTs with the same entropy are topologically conjugate when their periodic points are removed. We give a negative answer, in fact we prove the stronger result that there is a canonical correspondence between topological conjugacies of transitive SFT and topological conjugacies between the systems obtained by removing the periodic points. This stronger result does not extend to topological conjugacies between mixing sofic shifts, or mixing SFTs with the eventually periodic points removed (for any reasonable definition of the term). In the one-sided case this extends to general shift-commuting continuous maps between mixing SFTs, while in the two-sided case it does not.

We study internal Lie algebras in the category of subshifts on a fixed group -or Lie algebraic subshifts for short. We show that if the acting group is virtually polycyclic and the underlying vector space has dense homoclinic points, such subshifts can be recoded to have a cellwise Lie bracket. On the other hand there exist Lie algebraic subshifts (on any finitely-generated non-torsion group) with cellwise vector space operations whose bracket cannot be recoded to be cellwise. We also show that one-dimensional full vector shifts with cellwise vector space operations can support infinitely many compatible Lie brackets even up to automorphisms of the underlying vector shift, and we state the classification problem of such brackets. From attempts to generalize these results to other acting groups, the following questions arise: Does every f.g. group admit a linear cellular automaton of infinite order? Which groups admit abelian group shifts whose homoclinic group is not generated by finitely many orbits? For the first question, we show that the Grigorchuk group admits such a CA, and for the second we show that the lamplighter group admits such group shifts.

We introduce the classes of color blind and typhlotic cellular automata, that is, cellular automata that commute with all symbol permutations and all symbol mappings, respectively. We show that color blind cellular automata form a relatively large subclass of all cellular automata which contains an intrinsically universal automaton. On the other hand, we give simple characterizations for the color blind CA which are also group homomorphisms, and for general typhlotic CA, showing that both must be trivial in most cases.

The description of the precursor fields in a single-resonance Lorentz model dielectric is considered in the singular and weak dispersion limits. The singular dispersion limit is obtained as the damping approaches zero and the material dispersion becomes increasingly concentrated about the resonance frequency. The algebraic peak amplitude decay of the Brillouin precursor with propagation distance z Ͼ 0 then changes from a z -1/2 to a z -1/3 behavior. The weak dispersion limit is obtained as the material density decreases to zero. The material dispersion then becomes vanishingly small everywhere and the precursors become increasingly compressed in the space-time domain immediately following the speed-of-light point ͑z , t͒ = ͑z , z / c͒. In order to circumvent the numerical difficulties introduced in this case, an approximate equivalence relation is derived that allows the propagated field evolution due to an ultrawideband signal to be calculated in an equivalent dispersive medium that is highly absorptive.

We discuss the transient effects associated with short-pulse propagation in a linearly dispersive medium by comparing optical precursors with 0 pulses. The classical and quantum effects were, in the past, treated independently due to the different time scales. Using results from recent studies [Phys. Rev. Lett. 96, 143901 (2006)] as well as the discussions by Varoquaux et al. [Phys. Rev. B. 34, 7617 (1989)] and Bürck [Hyperfine Interact. 123, 483 (1999)], we show analytically that precursors and 0 pulses describe the same physical phenomenon. We also show that most published results of transient pulse propagation can be expressed using one overarching equation. Finally, we give a physical interpretation of the analogy between precursors and 0 pulses as a medium-impulse response using a Green's function.

The dynamical motion of laser-micromachined copper springs used for a meso-scale vibration-based power generator was successfully modeled using ANSYS to reveal 3 modes of multi-directional vibratory motion due to a pure vertical input vibration. A MATLAB simulation was also used to predict the voltage output of the micro power generator system with coupled electrical and mechanical damping effects. The simulated output matched experimental results closely. These capabilities are essential for the successful design and development of a miniature, low-frequency, and robust micro energy generator that could be potentially used to convert human mechanical energy into usefully electrical power to operate devices such as mobile phones and heart-pacers. Thus far, 1cm 1 meso-scale generators are demonstrated capable of producing up to 4V AC with instantaneous peak power of 80mW, at input frequencies ranging from 60 to 120Hz with ~200μηι input vibration amplitude. A generator capable of producing 2V DC output with 40μ\ν power after voltage rectification, and able to drive a commercial infrared wireless signal transmitter to send 140ms pulse trains with ~60sec power generation time was also demonstrated. The ANSYS model and MATLAB simulation results are presented and compared with the experimental results in this paper.

We develop a new approach for the estimation of a multivariate function based on the economic axioms of monotonicity and quasiconvexity. We prove the existence of the nonparametric least squares estimator (LSE) for a monotone and quasiconvex function and provide two characterizations for it. One of these characterizations is useful from the theoretical point of view, while the other helps in the computation of the estimator. We show that the LSE is almost surely unique and is the solution to a mixed-integer quadratic optimization problem. We prove consistency and find finite sample risk bounds for the LSE under both fixed lattice and random design settings for the covariates. We illustrate the superior performance of the LSE against existing estimators via simulation. Finally, we use the LSE to estimate the production function for the Japanese plywood industry and the cost function for hospitals across the US.

A graph Γ is said to be locally primitive if, for each vertex α, the stabilizer in Aut Γ of α induces a primitive permutation group on the set of vertices adjacent to α. In 1978, Richard Weiss conjectured that for a finite vertex-transitive locally primitive graph Γ, the number of automorphisms fixing a given vertex is bounded above by some function of the valency of Γ. In this paper we prove that the conjecture is true for finite non-bipartite graphsprovided that it is true in the case in which Aut Γ contains a locally primitive subgroup that is almost simple.

We prove the existence of chaotic motions in a planar restricted four body problem, establishing that the system is not integrable. The idea of the proof is to verify the hypotheses of a topological forcing theorem. The forcing theorem applies to two freedom Hamiltonian systems where the stable and unstable manifolds of a saddle-focus equilibrium intersect transversally in the energy level set of the equilibrium. We develop a mathematically rigorous computer assisted argument which verifies the hypotheses of the forcing theorem, and we implement our approach for the restricted four body problem. The method is constructive and works far from any perturbative regime and for non-equal masses. Being constructive, our argument results in useful byproducts like information about the locations of transverse connecting orbits, quantitative information about the invariant manifolds, and upper/lower bounds on transport times.

For sequentially monitoring and controlling average and variability of an online manufacturing process, x¯ and s control charts are widely utilized tools, whose constructions require the data to be real (precise) numbers. However, many quality characteristics in practice, such as surface roughness of optical lenses, have been long recorded as fuzzy data, in which the traditional x¯ and s charts have manifested some inaccessibility. Therefore, for well accommodating this fuzzy-data domain, this paper integrates fuzzy set theories to establish the fuzzy charts under a general variable-sample-size condition. First, the resolution-identity principle is exerted to erect the sample-statistics’ and control-limits’ fuzzy numbers (SSFNs and CLFNs), where the sample fuzzy data are unified and aggregated through statistical and nonlinear-programming manipulations. Then, the fuzzy-number ranking approach based on left and right integral index is brought to differentiate magnitude of fuzzy numbe...

A binary linear code is called LCD if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on the size of an LCD code of given length and minimum distance. In addition, we show that this polynomial is, in general, an invariant of a matrix group of dimension 4 and order 12. Also, we sketch a Gleason formula for this weight enumerator.