Showing papers on "Parametrization published in 1989"
596 citations
TL;DR: Examples presented here show that, in parametric curve interpolation, the choice of the interpolating nodes makes a great deal of difference in the resulting curve, and it is often suggested that a good choice of nodes is the cumulative chord length parametrization, but this is not so.
Abstract: In parametric curve interpolation, the choice of the interpolating nodes makes a great deal of difference in the resulting curve. Uniform parametrization is generally unsatisfactory. It is often suggested that a good choice of nodes is the cumulative chord length parametrization. Examples presented here, however, show that this is not so. Heuristic reasoning based on a physical analogy leads to a third parametrization, (the ‘centripetal model’), which almost invariably results in better shapes than either the chord length or the uniform parametrization. As with the previous two methods, this method is ‘global’ and is ‘invariant’ under similarity transformations. (It turns out that, in some sense, the method has been anticipated in a paper by Hosaka and Kimura.)
376 citations
TL;DR: The paper covers parametric representation and smoothness, parametric continuity, reparameterization and equivalent parameterization, beta-constraints, and arc-length parameterization.
Abstract: Some of the important basic results on geometric continuity of curves are presented in a self-contained manner. The paper covers parametric representation and smoothness, parametric continuity, reparameterization and equivalent parameterization, beta-constraints, and arc-length parameterization. >
180 citations
61 citations
TL;DR: A general (a,d) slope/offset straight-line parametrization is developed for which the Hough transform is compact and fast to compute, and which is as easy to interpret as the class (p, theta ) parametriation.
Abstract: The grid of discrete sampled data points in a digital image supports a limited set of lines at angles and displacements 'natural' to that grid. The effect of this implicit line quantization on the parametrization of the Hough transform is presented. The function describing the discrete Hough transforms line-detection sensitivity is derived. Expressions for the orientation, frequency, and popularity of lines in the natural set are given. The results obtained are of importance to data arrays of small size. The distribution of lines in the natural set is also important as it determines the precision and reliability with which straight lines can be measured on a discrete imaging array. From the natural line set concept, a general (a,d) slope/offset straight-line parametrization is developed for which the Hough transform is compact and fast to compute, and which is as easy to interpret as the class (p, theta ) parametrization. >
55 citations
29 citations
TL;DR: Methods for computing optimal controls are reviewed and compared in view of their applicability for solving real world problems andParametrization is presented as valuable and powerful tool to derive solutions being realizable in practical situations.
16 citations
ENEA1
TL;DR: In this article, a simple parametrization of the effects of gain degradation induced in high-current FELs by the inhomogeneous broadenings due to the energy spread and emittances of the electron beam is presented.
Abstract: In this paper we present a simple parametrization of the effects of gain degradation induced in high-current FELs by the inhomogeneous broadenings due to the energy spread and emittances of the electron beam. The parametrization is based on a fitting procedure of the numerical data. The accuracy of the fit is better than 1%.
16 citations
TL;DR: Approximation of parametric statistical models by exponential models is discussed, from the viewpoints of observed as well as of expected likelihood geometry, and the relation between the maximum likelihood estimators of the original model and the approximating models is studied.
Abstract: Approximation of parametric statistical models by exponential models is discussed, from the viewpoints of observed as well as of expected likelihood geometry. This extends a construction, in expected geometry, due to Amari. The approximations considered are parametrization invariant and local. Some of them relate to conditional models given exact or approximate ancillary statistics. Various examples are considered and the relation between the maximum likelihood estimators of the original model and the approximating models is studied.
15 citations
21 Jun 1989
TL;DR: A parametrization of all decentralized stabilizing controllers is provided in terms of a single parameter Q that is constrained to satisfy a finite number of quadratic equations and applies to linear time-invariant systems.
Abstract: A parametrization of all decentralized stabilizing controllers is provided in terms of a single parameter Q that is constrained to satisfy a finite number of quadratic equations. The results are presented in a general algebraic framework and apply to linear time-invariant systems. Implications of this parametrization for simultaneously stabilizing control are also discussed.
15 citations
21 Jun 1989
TL;DR: In this paper, a pseudogradient adaptive approach for slow adaptation is developed combining sensitivity results from the 1960's and recent developments in averaging and integral manifold methods, where the parametrization and number of parameters are not related to the plant order.
Abstract: A pseudogradient adaptive approach for slow adaptation is developed combining sensitivity results from the 1960's and recent developments in averaging and integral manifold methods. In this approach, the parametrization and number of parameters are not related to the plant order. Sufficient conditions for parameter convergence are developed using a-priori knowledge of a feedback system consisting of the plant and a nominal controller.
TL;DR: In this paper, a simple parametrization of all the suboptimal controllers of the standard sensitivity minimization problem is given, in particular, a simple parameterized controller for the H ∞ generalized interpolation problem.
TL;DR: A general parametrization of the semileptonic decays of the baryons obtained, as for the magnetic moments, performing a unitary transformation that connects the exact states to the model states is presented.
Abstract: We present a general parametrization of the semileptonic decays of the baryons obtained, as for the magnetic moments, performing a unitary transformation that connects the exact states to the model states. We show that again the nonrelativistic-quark-model (NRQM) description amounts to selecting certain terms among those of the general parametrization; in the no-flavor-breaking approximation the parametrization contains two parameters ($a$ and $b$) linearly related to the Cabibbo's $D$, $F$ and associated, in the NRQM language, to the one-quark and two-quark terms. The NRQM amounts to keeping the largest (one-quark) term with a coefficient $a(\ensuremath{\simeq}0.75)$; $b$ is 3-10% of $a$. Finally, we clarify the variety of possible terms that appear on going beyond the flavor symmetric approximation.
Journal Article•
TL;DR: In this paper, the problem of modeling an input-output data sequence is considered when applying equation error identification methods to matrix fraction description (MFD) models, and a notion of model equivalence is introduced that is related to the identification criterion.
Abstract: The problem of modeling an input-output data sequence is considered when applying equation error (least-squares) identification methods to matrix fraction description (MFD) models. In the case that a set of models has been parametrized using the notion of I/O (input/output) equivalence, it is shown that the identified model will be essentially dependent on the specific parameterization chosen. As an alternative, a notion of model equivalence is introduced that is related to the identification criterion. The pseudocanonical or overlapping parametrization of MFD models appears to constitute a set of canonical forms for this least-squares-based model equivalence. >
TL;DR: A minimal cover is given for the set of transfer functions corresponding to all ARMA systems in terms of this parametrization, the relation between the Kronecker indices and the prescribed column degrees is investigated, and the boundary of a certain parameter space is investigated.
TL;DR: A multichannel quantum-defect theory (MQDT) parametrization of two-photon ionization of atoms, suitable for use with ab initio calculations of perturbative 2PI amplitudes in the presence of intermediate- and/or final-state Rydberg resonances is developed.
Abstract: A multichannel quantum-defect theory (MQDT) parametrization of two-photon ionization (2PI) of atoms, suitable for use with ab initio calculations of perturbative 2PI amplitudes in the presence of intermediate- and/or final-state Rydberg resonances is developed. The rapid energy variation of such amplitudes is extracted in terms of elementary functions of energy and a set of MQDT parameters, which are ``smooth'' functions of energy. As an example, results of numerical computations of MQDT parameters for 2PI of atomic hydrogen (1s, 2s, and 3s) by circularly polarized light are presented. MQDT parameters for the many-channel case are derived, and an analysis of their energy dependence across Rydberg thresholds is given. The two-channel case is analyzed using phase-shifted Coulomb functions, and simple analytic formulas are given for the energy dependence of the amplitude as a function of a small set of physical parameters.
TL;DR: In this article, an efficient algorithm for the solution of the Euler equations of gas dynamics with a general convex equation of state was presented, based on solving linearized Riemann problems approximately, and in more than one dimension incorporating operator splitting.
Abstract: An efficient algorithm is presented for the solution of the Euler equations of gas dynamics with a general convex equation of state. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only one function evaluation in each computational cell is required by using a local parametrization of the equation of state. The scheme is applied to two standard test problems in gas dynamics for some specimen equations of state.
TL;DR: In this article, the stability of closed-loop MIMO systems with a low-order regulator has been investigated for a defined class of S1SO systems, and sufficient conditions for the closed loop dissipativeness and for the reduced-order compensator have been derived.
Abstract: The parameterization of MIMO systems in the open-loop balanced representation was introduced by Kabamba (1985) to show the advantages of using the balanced canonical form over other classical canonical forms as regards the guaranteed stability and minimality of the representation. The parameterization of MIMO systems in closed-loop balanced representation is introduced: the stability is guaranteed under particular conditions and the minimality is also assured. The importance that such a type of realization plays is fundamental in the synthesis of MIMO systems with assigned characteristic values; this allows us to investigate, for example, the stability of closed-loop systems with a low-order regulator. Indeed, for a defined class of MIMO systems, the introduced parameterization allows us to derive sufficient conditions for the closed-loop dissipativeness and for the stability of the reduced-order compensator, generalizing some results proved for S1SO systems.
TL;DR: In this paper, a parametrization of the groups SO(0,3) and SO↑(2,1) is presented that has simple, rational composition laws, albeit that it has a (quasigraded) structure.
Abstract: A useful parametrization of the groups SO(0,3) and SO↑(2,1) is presented that has simple, rational composition laws, albeit that it has a (quasigraded) structure. This ‘‘tangential’’ parametrization is also advantageous in providing a rather simple 1‐1 ‘‘picture’’ of the elements of the groups in question. As well, the parametrization allows an explicitly finite result for the composition law needed for the (abstract) Baker–Campbell–Hausdorff formula for exponentials of objects formed from the corresponding Lie algebras. This approach, in turn, allows a useful beginning to the problem of the determination of flows on the group manifold, i.e., the determination of analytic curves given the initial direction of the curve.
TL;DR: The radial dependencies of anr-space version of the meson-theoretical nucleon-nucleon potential of the Bonn group (OBEPR) are expressed through a set of Gaussians.
Abstract: The radial dependencies of anr-space version of the meson-theoretical nucleon-nucleon potential of the Bonn group (OBEPR) are expressed through a set of Gaussians. First results for the three-nucleon system are given.
TL;DR: In this article, a flexible parametrization of local density distributions in nuclei is suggested on the basis of local-scale point transformations performed on certain model many-particle wave functions.
Abstract: A flexible parametrization of local-density distributions in nuclei is suggested on the basis of local-scale point transformations performed on certain model many-particle wave functions. The new set of local densities can be helpful in many problems in nuclear physics. Two examples are considered: i) an analysis of experimental elastic electron scattering data and ii) variational calculations with effective interaction for reproducing the Hartree-Fock shell oscillations of the local-density distributions.
01 Jan 1989
TL;DR: In this article, an example of a Pick-Nevanlinna interpolation problem such that the coefficients of its Nevlanlinna's parametrization are not in HP, for p > 0, is presented.
Abstract: We construct an example of a Pick-Nevanlinna interpolation problem such that the coefficients of its Nevanlinna's parametrization are not in HP, for p > 0.
21 Jun 1989
TL;DR: In this paper, a general parametrization for a linear system is presented, which is the basis for the design of a direct model reference adaptive pole placement controller, and the exponentially weighted least-squares algorithm is employed to estimate the control parameters.
Abstract: A general parametrization for a linear system is presented. This parametrization is the basis for the design of a direct model reference adaptive pole placement controller. The exponentially weighted least-squares algorithm is employed to estimate the control parameters. In this case, the direct adaptive controller has the exponential weighting properties by the proposed method of selecting the sensitivity function filters.