MARYLAND UNIV COLLEGE PARK Dept. of MATHEMATICS
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Works:  61 works in 64 publications in 1 language and 65 library holdings 

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MARYLAND UNIV COLLEGE PARK Dept. of MATHEMATICS
Lectures on the numerical solution of partial differential equations : proceedings of the Special Year in Numerical Analysis,
held at the University of Maryland, Department of Mathematics, College Park, MD, 1981(
Book
)
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
Contents: Adapting CourantFriedrichsLevy to the 1980's; Parametrization Methods for Approximation of Solutions of Elliptic Boundary Value Problems; Two Mixed Finite Element Methods for the Simply Supported Plat Problem; Approximation of Nonlinear Problems; Twodimensional Approximations of Threedimensional Models in Nonlinear Plate Theory; Changing Meshes in Timedependent Problems; Alternatingdirection Galerkin Methods for Parabolic Hyperbolic and Sobolev Partial Differential Equations; Galerkin Methods for Miscible Displacement Problems with Point Sources and SinksUnit Mobility Ratio Case; Overtaking of Shock Waves in Steady Twodimensional Supersonic Flows; Homogenization, Convex Analysis, and the Geometry Optimization of Engineering Structures; Stability and Error Bounds for a Fractional Step Scheme to Compute Weak Solutions of the Nonlinear Waterhammer Problem; Schauder Estimates for Finite Element Approximations of Second Order Elliptic Boundary Value Problems; Analysis of Some Contact Problems in Nonlinear Elasticity; Single Step Methods for Linear Differential Equations in Banach Spaces; The Quasioptimality in the Maximum Norm of the H1 Projection into Piecewise Linear Functions in the Plane: a Complete Proof (Second lecture); A Brief Survey of Parabolic Smoothing and How It Affects a Numerical Solution: Finite Differences and Finite Elements (Third lecture); Integral Equation Methods for Mixed Boundary Value Problems (Second lecture)
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
Contents: Adapting CourantFriedrichsLevy to the 1980's; Parametrization Methods for Approximation of Solutions of Elliptic Boundary Value Problems; Two Mixed Finite Element Methods for the Simply Supported Plat Problem; Approximation of Nonlinear Problems; Twodimensional Approximations of Threedimensional Models in Nonlinear Plate Theory; Changing Meshes in Timedependent Problems; Alternatingdirection Galerkin Methods for Parabolic Hyperbolic and Sobolev Partial Differential Equations; Galerkin Methods for Miscible Displacement Problems with Point Sources and SinksUnit Mobility Ratio Case; Overtaking of Shock Waves in Steady Twodimensional Supersonic Flows; Homogenization, Convex Analysis, and the Geometry Optimization of Engineering Structures; Stability and Error Bounds for a Fractional Step Scheme to Compute Weak Solutions of the Nonlinear Waterhammer Problem; Schauder Estimates for Finite Element Approximations of Second Order Elliptic Boundary Value Problems; Analysis of Some Contact Problems in Nonlinear Elasticity; Single Step Methods for Linear Differential Equations in Banach Spaces; The Quasioptimality in the Maximum Norm of the H1 Projection into Piecewise Linear Functions in the Plane: a Complete Proof (Second lecture); A Brief Survey of Parabolic Smoothing and How It Affects a Numerical Solution: Finite Differences and Finite Elements (Third lecture); Integral Equation Methods for Mixed Boundary Value Problems (Second lecture)
A Method for Online Testing by HOC (Higher Order Crossings)Processes(
Book
)
2 editions published between 1986 and 1987 in English and held by 2 WorldCat member libraries worldwide
The dynamics by which a stationary time series produces its zerocrossings and higher order zerocrossings sequentially in time is studied, illustrated, and applied in white noise testing. As the time series threads its sample path about this level the zerocrossing rate (the number of zerocrossings per unit time) converges in some sense as the series length increases. Similarly, the zerocrossing rate in the first difference of the series converges too, and the same can be said about the zerocrossing rates of higher order differences of the time series. This paper examines the dynamic process by which a time series and its higher order differences produce their respective zerocrossing counts sequentially in time for the purpose of white noise testing
2 editions published between 1986 and 1987 in English and held by 2 WorldCat member libraries worldwide
The dynamics by which a stationary time series produces its zerocrossings and higher order zerocrossings sequentially in time is studied, illustrated, and applied in white noise testing. As the time series threads its sample path about this level the zerocrossing rate (the number of zerocrossings per unit time) converges in some sense as the series length increases. Similarly, the zerocrossing rate in the first difference of the series converges too, and the same can be said about the zerocrossing rates of higher order differences of the time series. This paper examines the dynamic process by which a time series and its higher order differences produce their respective zerocrossing counts sequentially in time for the purpose of white noise testing
Some Generalizations of the Renewal Process(
Book
)
1 edition published in 1982 in English and held by 1 WorldCat member library worldwide
The greatest success, as well as the most severe limitations, of standard Reliability Theory have been due to its restriction to the study of independent failuretime random variables. Consider the case of Renewal Theory, which in the context of Reliability has led to the characterization of many classes of repair/replacement policies, and which appears to depend crucially on the assumption of independence for times between successive failures. In practical life, it is clear that successive replacements of failed components in a complicated assembly (say, an aircraft) may have some cumulative effect tending to shorten future times between replacements. Additionally, one can imagine that shocks to the system from failures of single components can affect the lifetimes of the remaining components, or even that the age of important components can be reflected in the operating characteristics and therefore in the hazard of failure of the system. (Author)
1 edition published in 1982 in English and held by 1 WorldCat member library worldwide
The greatest success, as well as the most severe limitations, of standard Reliability Theory have been due to its restriction to the study of independent failuretime random variables. Consider the case of Renewal Theory, which in the context of Reliability has led to the characterization of many classes of repair/replacement policies, and which appears to depend crucially on the assumption of independence for times between successive failures. In practical life, it is clear that successive replacements of failed components in a complicated assembly (say, an aircraft) may have some cumulative effect tending to shorten future times between replacements. Additionally, one can imagine that shocks to the system from failures of single components can affect the lifetimes of the remaining components, or even that the age of important components can be reflected in the operating characteristics and therefore in the hazard of failure of the system. (Author)
The hp Version of the Finite Element Method for Parabolic Equations. Part: 2. The hp Version in Time(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
The paper is the second in the series addressing the hp version of the finite element method for parabolic equations. The present paper addresses the case when in both variables, the spatial and time, the hp version is used. Error estimation is given and numerical computations are presented. In both cases we used the same p and q in all time intervals. The results show that the flexibility of the method, when properly employed, leads to the large increase of computational effectivity. Various adaptive approaches here will very effective tools for such an optimal choice. These aspects will be addressed in the forthcoming paper. (jhd)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
The paper is the second in the series addressing the hp version of the finite element method for parabolic equations. The present paper addresses the case when in both variables, the spatial and time, the hp version is used. Error estimation is given and numerical computations are presented. In both cases we used the same p and q in all time intervals. The results show that the flexibility of the method, when properly employed, leads to the large increase of computational effectivity. Various adaptive approaches here will very effective tools for such an optimal choice. These aspects will be addressed in the forthcoming paper. (jhd)
An Approach for Constructing Families of Homogenized Equations for Periodic Media: 2. Properties of the Kernel(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
The paper is the second in the series devoted to the study of constructions of families of homogenizations. In the first paper the properties of the kernel Phi (<dot>, h, t) were utilized. In this paper these properties are established. An integral representation of the solution to a differential equation we developed that models the equations that arise in the study of periodic media (e.g., composite materials). (jhd)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
The paper is the second in the series devoted to the study of constructions of families of homogenizations. In the first paper the properties of the kernel Phi (<dot>, h, t) were utilized. In this paper these properties are established. An integral representation of the solution to a differential equation we developed that models the equations that arise in the study of periodic media (e.g., composite materials). (jhd)
Final Report on the Special Year in Numerical Analysis, 198081(
Book
)
1 edition published in 1981 in English and held by 1 WorldCat member library worldwide
Contents: (1) List of Participants and Lectures in Numerical PDE Portion of Special Year; (2) Program, Abstracts of the 1Hour Invited Lectures, Abstracts of the 30Minute Selected Talks, and List of Registrants for the Conference on Applications of Numerical Analysis and Special Functions in Statistics; and (3) List of Participants and Lectures in Global Continuation Methods Portion of Special Year
1 edition published in 1981 in English and held by 1 WorldCat member library worldwide
Contents: (1) List of Participants and Lectures in Numerical PDE Portion of Special Year; (2) Program, Abstracts of the 1Hour Invited Lectures, Abstracts of the 30Minute Selected Talks, and List of Registrants for the Conference on Applications of Numerical Analysis and Special Functions in Statistics; and (3) List of Participants and Lectures in Global Continuation Methods Portion of Special Year
A Continuous Analogue of Sturm Sequences in the Context of SturmLiouville Equations. Revision(
Book
)
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
A shooting method is presented for finding the n sub th eigenvalue and eigenfunction of a SturmLiouville equation, in which the eigenvalue occurs nonlinearly. The method is verified in two ways: by applying the Sturm comparison and oscillation theorems to the continuous problem; and by applying Sturm sequences to a discretization. The method works for general (separated) boundary conditions, and provides an aposteriori error estimate for the approximate eigenvalue. Analogues of the Sturm comparison, oscillation and separation theorems are proved for the discrete problem. A related method, which involves critical lengths in the invariant imbedding method, is shown to be incorrect for general boundary conditions
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
A shooting method is presented for finding the n sub th eigenvalue and eigenfunction of a SturmLiouville equation, in which the eigenvalue occurs nonlinearly. The method is verified in two ways: by applying the Sturm comparison and oscillation theorems to the continuous problem; and by applying Sturm sequences to a discretization. The method works for general (separated) boundary conditions, and provides an aposteriori error estimate for the approximate eigenvalue. Analogues of the Sturm comparison, oscillation and separation theorems are proved for the discrete problem. A related method, which involves critical lengths in the invariant imbedding method, is shown to be incorrect for general boundary conditions
Higher Order Crossings from a Parametric Family of Linear Filters(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
When a time series is filtered, the effect of the filter can be described by counting the resulting number of zerocrossings. By extension, we can apply to a time series a family of filters and obtain the corresponding family of zerocrossing counts. The resulting family of counts is referred to as higher order crossings or HOC. Thus, HOC are zerocrossing counts observed in a time series and in its filtered versions. The main application of HOC is in the description of the oscillation observed in oscillatory time series. Moreover, in the special case of stationary Gaussian time series there are quite a few HOC families and also HOC sequences that determine the spectrum up to a constant. This paper is organized as follows. In section 2 we define and also give examples of HOC from parametric families of linear filters. We outline there our motivation for studying HOC in connection with oscillatory time series. In section 3 we construct an adaptive HOC sequence form (0.1) that converges to a frequency in the presence of noise. As a matter of fact, the main result there, Corollary 1, has prompted our interest in pursuing HOC in connection with parametric linear operations. In section 4 we obtain more results about the HOC family from (0.1). Our main result there is the connection between the zero crossing rate, as a function of the parameter, and the correlation generating function under the Gaussian assumption. In section 5 we analyze a vocal sound time series of a megaptera novaeangliae (humpback) whale
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
When a time series is filtered, the effect of the filter can be described by counting the resulting number of zerocrossings. By extension, we can apply to a time series a family of filters and obtain the corresponding family of zerocrossing counts. The resulting family of counts is referred to as higher order crossings or HOC. Thus, HOC are zerocrossing counts observed in a time series and in its filtered versions. The main application of HOC is in the description of the oscillation observed in oscillatory time series. Moreover, in the special case of stationary Gaussian time series there are quite a few HOC families and also HOC sequences that determine the spectrum up to a constant. This paper is organized as follows. In section 2 we define and also give examples of HOC from parametric families of linear filters. We outline there our motivation for studying HOC in connection with oscillatory time series. In section 3 we construct an adaptive HOC sequence form (0.1) that converges to a frequency in the presence of noise. As a matter of fact, the main result there, Corollary 1, has prompted our interest in pursuing HOC in connection with parametric linear operations. In section 4 we obtain more results about the HOC family from (0.1). Our main result there is the connection between the zero crossing rate, as a function of the parameter, and the correlation generating function under the Gaussian assumption. In section 5 we analyze a vocal sound time series of a megaptera novaeangliae (humpback) whale
Nonlinear Mechanics and Applied Analysis(
Book
)
3 editions published between 1991 and 1995 in English and held by 1 WorldCat member library worldwide
Many important Hamiltonian systems have periodic solutions that are associated with symmetries of the equations. While it is well known that stationary solutions of a Hamiltonian system can be characterized as extremals of the potential energy, it is less widely appreciated that symmetryrelated periodic solutions, or relative equilibria, can also be given a variational characterization, typically involving constraints. This variational characterization is important because if a periodic solution is associated with a constrained minimizer (in some sense), as opposed to merely being a stationary point, then a stability result is very often available. We are therefore left with the problem of characterizing those extremals of a constrained variational principle that are actually constrained local minima. It is shown how to apply the new results in the special context of Hamiltonian mechanics, and various stability and instability theorems are described. The machinery developed here can be viewed as an alternative to the energycasimir and energymomentum methods with the benefit that the necessary tests can be concretely and rigorously applied in several complex examples of physical importance
3 editions published between 1991 and 1995 in English and held by 1 WorldCat member library worldwide
Many important Hamiltonian systems have periodic solutions that are associated with symmetries of the equations. While it is well known that stationary solutions of a Hamiltonian system can be characterized as extremals of the potential energy, it is less widely appreciated that symmetryrelated periodic solutions, or relative equilibria, can also be given a variational characterization, typically involving constraints. This variational characterization is important because if a periodic solution is associated with a constrained minimizer (in some sense), as opposed to merely being a stationary point, then a stability result is very often available. We are therefore left with the problem of characterizing those extremals of a constrained variational principle that are actually constrained local minima. It is shown how to apply the new results in the special context of Hamiltonian mechanics, and various stability and instability theorems are described. The machinery developed here can be viewed as an alternative to the energycasimir and energymomentum methods with the benefit that the necessary tests can be concretely and rigorously applied in several complex examples of physical importance
Partial Likelihood Analysis of Time Series Models, with Application to RainfallRunoff Data(
Book
)
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
A general logisticautoregressive model for binary time series or longitudinal responses is presented, generalizing the discretetime Cox (1972) model with timedependent covariates as well as the recent regression models of Kaufmann (1987) for categorical timeseries. Since this model is formulated in terms of the timeseries covariates which are not themselves explicitly modelled, the largesample theory of parameterestimation must be justified by means of Partial Likelihood in the sense of Cox (1975), using theoretical results like those of Wong (1986). The largesample theory also justifies goodness of fit tests analogous to the chisquared tests of Schoenfeld (1980) and to the tests based on sums of (normalized) squared residuals used in logistic regression. These ideas are illustrated by analysis of a rainfallrunoff hydrological dataset previously analyzed by Yakowitz (1987)
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
A general logisticautoregressive model for binary time series or longitudinal responses is presented, generalizing the discretetime Cox (1972) model with timedependent covariates as well as the recent regression models of Kaufmann (1987) for categorical timeseries. Since this model is formulated in terms of the timeseries covariates which are not themselves explicitly modelled, the largesample theory of parameterestimation must be justified by means of Partial Likelihood in the sense of Cox (1975), using theoretical results like those of Wong (1986). The largesample theory also justifies goodness of fit tests analogous to the chisquared tests of Schoenfeld (1980) and to the tests based on sums of (normalized) squared residuals used in logistic regression. These ideas are illustrated by analysis of a rainfallrunoff hydrological dataset previously analyzed by Yakowitz (1987)
Lecture Notes in Mathematics. A Collection of Informal Reports and Seminars. 155. Several Complex Variables I Maryland 1970(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Contents: Automorphic forms with integral Fourier coefficients; Spaces of Kleinien groups; The pluricanonical map of a complex surface; Algebraic methods in the theory of modular forms; Verschwindungssatze fur analytische kohomologiegruppen auf komplexen raumen; Residues on complex spaces; A remark on boundary values of functions of several complex variables; Some remarks on Selberg's zeta functions; On automorphisms and equivalences of Siegel domains; Cohomology with bounds on complex spaces; Reduction of the fields of modular functions and the rings of functions on padic manifolds; Value distribution of holomorphic maps; Extension of coherent analytic subsheaves; and Periodic entire functions and reducible Banach algebras
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Contents: Automorphic forms with integral Fourier coefficients; Spaces of Kleinien groups; The pluricanonical map of a complex surface; Algebraic methods in the theory of modular forms; Verschwindungssatze fur analytische kohomologiegruppen auf komplexen raumen; Residues on complex spaces; A remark on boundary values of functions of several complex variables; Some remarks on Selberg's zeta functions; On automorphisms and equivalences of Siegel domains; Cohomology with bounds on complex spaces; Reduction of the fields of modular functions and the rings of functions on padic manifolds; Value distribution of holomorphic maps; Extension of coherent analytic subsheaves; and Periodic entire functions and reducible Banach algebras
ZeroCrossings Analysis(
Book
)
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
A coherent development of zero crossing based methods and theory appropriate for fast signal analysis are advanced. Quite a few ideas pertaining to zero crossing counts found in the literature can be expressed and interpreted with the help of this more general setup. A central issue addressed in some detail, is the fruitful connection which exists between zero crossing counts and linear filtering. This connection is explored and interpreted with the help of a certain zero crossing spectral representation, is then applied in spectral analysis, detection and discrimination. Zero crossing counts in filtered time series are called higher order crossings. The theme of the work is that higher order crossings analysis provides a useful descriptive as well as analytical tool that can in many respects match spectral analysis. To a great extent these two types of analysis are in fact equivalent, but each emphasizes a different point of view. Advantages offered by higher order crossings are great simplicity and a drastic data reduction
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
A coherent development of zero crossing based methods and theory appropriate for fast signal analysis are advanced. Quite a few ideas pertaining to zero crossing counts found in the literature can be expressed and interpreted with the help of this more general setup. A central issue addressed in some detail, is the fruitful connection which exists between zero crossing counts and linear filtering. This connection is explored and interpreted with the help of a certain zero crossing spectral representation, is then applied in spectral analysis, detection and discrimination. Zero crossing counts in filtered time series are called higher order crossings. The theme of the work is that higher order crossings analysis provides a useful descriptive as well as analytical tool that can in many respects match spectral analysis. To a great extent these two types of analysis are in fact equivalent, but each emphasizes a different point of view. Advantages offered by higher order crossings are great simplicity and a drastic data reduction
Lecture Notes in Mathematics. A Collection of Informal Reports and Seminars. 185. Several Complex Variables II Maryland 1970(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Contents: Some transcendental methods in the study of algebraic cycles; Analytic structures on the space of flat vector bundles over a compact Riemann surface; Analytic continuation on Banach spaces; On certain representations of semisimple algebraic groups; Some numbertheoretical results on real analytic automorphic forms; Recent results on analytic mappings and plurisubharmonic functions in topological linear spaces; Remarks on the Kobayashi metric; Cohomology spaces associated with a certain group extension; Class fields over real quadratic fields in the theory of modular functions; An Osgood type extension theorem for coherent analytic sheaves; Complex manifolds and unitary representations
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Contents: Some transcendental methods in the study of algebraic cycles; Analytic structures on the space of flat vector bundles over a compact Riemann surface; Analytic continuation on Banach spaces; On certain representations of semisimple algebraic groups; Some numbertheoretical results on real analytic automorphic forms; Recent results on analytic mappings and plurisubharmonic functions in topological linear spaces; Remarks on the Kobayashi metric; Cohomology spaces associated with a certain group extension; Class fields over real quadratic fields in the theory of modular functions; An Osgood type extension theorem for coherent analytic sheaves; Complex manifolds and unitary representations
On Nearest Neighbor Degeneracies of Indistinguishable Particles(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
Arrangement degeneracies suggested by sufficient statistics associated with binary stationary m'th order Markov chains are discussed, and are shown to correspond and generalize some degeneracies arising when indistinguishable particles are placed on a onedimensional lattice with n compartments. From these statistics it is possible to define an mth order unit. The arrangement degeneracy obtained from s 1's and ns O's so that lower order units are placed in higher order units is solved. However, the most general arrangement degeneracy associated with all the sufficient statistics of a given order is difficult. For this case only the 3rd order arrangement degeneracy is obtained, the 1st and 2nd orders being relatively simple. These results are applied in determining the asymptotic distributions of rare events. (Author)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
Arrangement degeneracies suggested by sufficient statistics associated with binary stationary m'th order Markov chains are discussed, and are shown to correspond and generalize some degeneracies arising when indistinguishable particles are placed on a onedimensional lattice with n compartments. From these statistics it is possible to define an mth order unit. The arrangement degeneracy obtained from s 1's and ns O's so that lower order units are placed in higher order units is solved. However, the most general arrangement degeneracy associated with all the sufficient statistics of a given order is difficult. For this case only the 3rd order arrangement degeneracy is obtained, the 1st and 2nd orders being relatively simple. These results are applied in determining the asymptotic distributions of rare events. (Author)
Efficiencies of PartialLikelihoodBased Inferences Concerning Survival Regression Models(
Book
)
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
This paper addresses four important issues in largesimple survival analysis: 1) the inadequacy of a fullliklihood approach to the problem of testing, with rightcensored survival data and within a regression model for hazards of failure, the hypothesis that the mechanism of failure does not depend on a designated subset of timedependent covariates; 2) the definition of an appropriate 'fulllikelihood', for survival problems with timedependent covariate processes Z sub i (t), by means of Cox's (1975) notion of Partial Likelihood; 3) general justification of the assertion by Peto and Peto (1972) of 'asymptotic efficiency' in a semiparametric sense for partiallikelihoodscore teststatistics; and 4) formulation of semiparametric efficiency questions in the Survival setting (whether at the nullhypothesis or not), which have been described previously (Begun et al. 1983) as Hilbertspace projection problems, concretely in terms of calculusofvariations problems. (Author)
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
This paper addresses four important issues in largesimple survival analysis: 1) the inadequacy of a fullliklihood approach to the problem of testing, with rightcensored survival data and within a regression model for hazards of failure, the hypothesis that the mechanism of failure does not depend on a designated subset of timedependent covariates; 2) the definition of an appropriate 'fulllikelihood', for survival problems with timedependent covariate processes Z sub i (t), by means of Cox's (1975) notion of Partial Likelihood; 3) general justification of the assertion by Peto and Peto (1972) of 'asymptotic efficiency' in a semiparametric sense for partiallikelihoodscore teststatistics; and 4) formulation of semiparametric efficiency questions in the Survival setting (whether at the nullhypothesis or not), which have been described previously (Begun et al. 1983) as Hilbertspace projection problems, concretely in terms of calculusofvariations problems. (Author)
Estimation of the Parameters in Stationary Autoregressive Processes After Hard Limiting(
Book
)
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
The parameters of a stationary AR(p) process are estimated after clipping. This estimation is based in part on the number of certain runs in the binary series. Very little precision is lost due to this quantization but the expected number of arithmetical operations which are saved is at least (p+2)n where counting a run is considered as an operation and n is the series size. (Author)
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
The parameters of a stationary AR(p) process are estimated after clipping. This estimation is based in part on the number of certain runs in the binary series. Very little precision is lost due to this quantization but the expected number of arithmetical operations which are saved is at least (p+2)n where counting a run is considered as an operation and n is the series size. (Author)
New Techniques in Signal and Image Processing(
)
1 edition published in 1999 in English and held by 0 WorldCat member libraries worldwide
A multidimensional periodicity detection algorithm is established, and implementation has been made on ECoG data and with broadband and I/f noise. The algorithm requires the characterization of periodic continuous wavelet transforms, and the solution of an optimization problem coupled with an averaging method for mixednorm spaces. A transition of this technology has been made to TechnoSciences, Inc. in their NASA supported work for Health Maintenance of jet engines using eddy current sensors. A multidimensional irregular sampling technique is also established, and the corresponding algorithm solves signal reconstruction problems in MRI for sampled spectral data on interleaving spirals related to fast imaging techniques. The tools required are our results from the theory of frames, as well as the BeurlingLandau analysis of balayage
1 edition published in 1999 in English and held by 0 WorldCat member libraries worldwide
A multidimensional periodicity detection algorithm is established, and implementation has been made on ECoG data and with broadband and I/f noise. The algorithm requires the characterization of periodic continuous wavelet transforms, and the solution of an optimization problem coupled with an averaging method for mixednorm spaces. A transition of this technology has been made to TechnoSciences, Inc. in their NASA supported work for Health Maintenance of jet engines using eddy current sensors. A multidimensional irregular sampling technique is also established, and the corresponding algorithm solves signal reconstruction problems in MRI for sampled spectral data on interleaving spirals related to fast imaging techniques. The tools required are our results from the theory of frames, as well as the BeurlingLandau analysis of balayage
The Role of Frame Force in Quantum Detection(
)
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
A general method is given to solve tight frame optimization problems, borrowing notions from classical mechanics. In this paper, we focus on a quantum detection problem, where the goal is to construct a tight frame that minimizes an error term, which in quantum physics has the interpretation of the probability of a detection error. The method converts the frame problem into a set of ordinary differential equations using concepts from classical mechanics and orthogonal group techniques. The minimum energy solutions of the differential equations are proven to correspond to the tight frames that minimize the error term. Because of this perspective, several numerical methods become available to compute the tight frames. Beyond the applications of quantum detection in quantum mechanics, solutions to this frame optimization problem can be viewed as a generalization of classical matched filtering solutions. As such, the methods we develop are a generalization of fundamental detection techniques in radar
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
A general method is given to solve tight frame optimization problems, borrowing notions from classical mechanics. In this paper, we focus on a quantum detection problem, where the goal is to construct a tight frame that minimizes an error term, which in quantum physics has the interpretation of the probability of a detection error. The method converts the frame problem into a set of ordinary differential equations using concepts from classical mechanics and orthogonal group techniques. The minimum energy solutions of the differential equations are proven to correspond to the tight frames that minimize the error term. Because of this perspective, several numerical methods become available to compute the tight frames. Beyond the applications of quantum detection in quantum mechanics, solutions to this frame optimization problem can be viewed as a generalization of classical matched filtering solutions. As such, the methods we develop are a generalization of fundamental detection techniques in radar
Numerical Methods for Nonclassical Gas Dynamics Involving MultiPhase, Reactive Flows(
)
1 edition published in 1996 in English and held by 0 WorldCat member libraries worldwide
This report documents recent progress in the field of numerical analysis of problems in fluid mechanics. The modeling equations include gas dynamics, incompressible flow, their viscous extensions, reactive flow and multiphase flow. Applications of these advanced methods in the areas of modeling blast wave environments and shock loading of nonclassical materials are discussed. New algorithms for problems involving coupled wave speed and source term stiffness, along with improved versions of multimaterial extensions of the underlying compressible algorithm are discussed. (AN)
1 edition published in 1996 in English and held by 0 WorldCat member libraries worldwide
This report documents recent progress in the field of numerical analysis of problems in fluid mechanics. The modeling equations include gas dynamics, incompressible flow, their viscous extensions, reactive flow and multiphase flow. Applications of these advanced methods in the areas of modeling blast wave environments and shock loading of nonclassical materials are discussed. New algorithms for problems involving coupled wave speed and source term stiffness, along with improved versions of multimaterial extensions of the underlying compressible algorithm are discussed. (AN)
Nonlinear Waves in Mechanics and Gas Dynamics(
)
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
The proposer has studied nonlinear hyperbolicparabolic partial differential equations related to gas dynamics and mechanics. Hyperbolic conservation laws with relaxation are studied with applications to kinetic theory, elasticity with memory and gas flow with thermononequilibrium in mind. Nonlinear waves for the compressible NavierStokes equations are studied for their stability and timeasymptotic behavior. The singular behavior of the magenetohydrodynamics shock waves in the small dissipation limits is clarified, in particular, it is shown that intermediate shocks are stable uniformly with regards to the strength of dissipations only for 2dimensional model, and not for 3dimensional model
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
The proposer has studied nonlinear hyperbolicparabolic partial differential equations related to gas dynamics and mechanics. Hyperbolic conservation laws with relaxation are studied with applications to kinetic theory, elasticity with memory and gas flow with thermononequilibrium in mind. Nonlinear waves for the compressible NavierStokes equations are studied for their stability and timeasymptotic behavior. The singular behavior of the magenetohydrodynamics shock waves in the small dissipation limits is clarified, in particular, it is shown that intermediate shocks are stable uniformly with regards to the strength of dissipations only for 2dimensional model, and not for 3dimensional model
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