Approximative Approach Research Articles

Korrigierte Schätzgleichungen für allgemeine Regressionsmodelle mit Fehlern in den Variablen / Corrected Estimating Equations for General Regression Models with Errors in the Variables

Zusammenfassung Nach einer kurzen Einführung in die Theorie der erwartungstreuen Schätzgleichungen für allgemeine Regressionsmodelle und der korrigierten Schätzgleichungen für Regressionsmodelle mit fehlerbehafteten Kovariablen wird die Approximationsgüte eines auf Reihenentwicklung basierenden Ansatzes von Stefanski diskutiert.

The use of service limits for efficient operation of multistation single-medium communication systems

Time limits are the major mechanisms used for controlling a large variety of multistation single-medium computer-communication systems like the FDDI network and the IEEE 802.4 Token Bus. The proper use of these mechanisms is still not understood and rules for efficient system operation are not available. The authors' objective is the derivation of such rules. They use a cyclic polling model with different service limits (k-limited service) at the different queues, thus emulating time limits. They are interested in determining these k-limit values so as to minimize the mean waiting cost of messages in the system. A simple approximative approach is proposed for two major problems: one in which a limit is set on the token rotation time and one in which no limits are imposed. The approach is tested for a variety of cases and is shown to be very effective. >

Functional integral equation for the complete effective action in quantum field theory

Based on a methodological analysis of the effective action approach certain conceptual foundations of quantum field theory are reconsidered to establish a quest for an equation for the effective action. Relying on the functional integral formulation of Lagrangian quantum field theory a functional integral equation for the complete effective action is proposed which can be understood as a certain fixed point condition. This is motivated by a critical attitude towards the distinction artificial from an experimental point of view between classical and effective action. While for free field theories nothing new is accomplished, for interacting theories the concept differs from the established paradigm. The analysis of this new concept is concentrated on gauge field theories treating QED as the prototype model. An approximative approach to the functional integral equation for the complete effective action of QED is exploited to obtain certain nonperturbative information about the quadratic kernels of the action. As particular application the approximative calculation of the QED coupling constant $\alpha$ is explicitly studied. It is understood as one of the characteristics of a fixed point given as a solution of the functional integral equation proposed. Finally, within the present approach the vacuum energy problem is considered and possible implications on the induced gravity concept are contemplated.

Anharmonic Self-Consistent Theory of Crystals. I. A 1 d Quartic Crystal Model

Abstract We apply the Unsymmetrized Self-Consistent-Field-Method (USCFM) to a linear infinite chain of identical atoms with a quartic pair interaction potential. We show that an exact solution of the USCFM can be found in terms of a single auxiliary function ℒ1 which is studied here in details. We use it to calculate the partition function, the energy and the free energy, the moments of the position, the corrections due to quantum effects and higher terms of the potential, the specific heat and the thermal expansion. An anharmonic approximative approach, based on the self-consistent potential of the used method, is developed also. We apply these two approaches to the study of the thermoelastic properties of a one dimensional system (krypton). It is demonstrated that the approximate approach is very effective when dealing with pairwise potentials of positive second derivative. The Lennard-Jones potential is used in our calculations.

One-photon excitation in the e-H collision in the presence of a laser field.

We consider the one-photon excitation of atomic hydrogen by electron impact in the presence of a homogeneous monochromatic linearly polarized electric field as a model for the radiation field of the laser. In the framework of the approximative approach of Faisal and Rahman (in {ital Fifth} {ital International} {ital Conference} {ital on} {ital Atomic} {ital Physics}, edited by R. Marrus, M. H. Prior, and H. A. Stutgart (University of California, Berkeley, 1976), p. 49), suited for high-energy electrons, we present an analytic expression for the transition amplitude to an arbitrary {ital nlm} state, in terms of hypergeometric Gauss and Appell {ital F}{sub 1} functions, together with the numerical results for excitation to the {ital n}=4 states.

Remarks on Approximation Methods in Degree Theory

An approximative approach to a generalized theory of the topological mapping degree is presented. Some new wide classes of operators acting in Banach spaces, which include $A$-proper mappings of Petryshyn, are introduced and studied from the viewpoint of the homotopic properties of the topological degree. The results are applied in some existence aspects of abstract nonlinear equations.

Remarks on approximation methods in degree theory

An approximative approach to a generalized theory of the topological mapping degree is presented. Some new wide classes of operators acting in Banach spaces, which include A A -proper mappings of Petryshyn, are introduced and studied from the viewpoint of the homotopic properties of the topological degree. The results are applied in some existence aspects of abstract nonlinear equations.

Third-order Nonlinear Dissipative Oscillator with an Initial Squeezed State

Abstract The statistical properties of radiation passing through a nonlinear medium modelled as a third-order nonlinear dissipative oscillator interacting with squeezed light have been investigated. Whereas the photon statistics, being insensitive to the nonlinearity, are determined exactly, an approximative approach has been adopted in the description of squeezing in order to involve fluctuations. As a consequence of the general treatment, new results for a damped linear oscillator with initial squeezed light are provided.

A theorem of large deviations for the generalized student ratio

We prove a theorem of large deviations which provides a multiplicative variant of Welch's approximative approach [1] to interval estimation of a given linear function of the means of several normal populations with unknown parameters.

The application of the space-charge model to the permeability properties of charged microporous membranes

In the recent past the space-charge model (Morrison, F. A., and Osterle, J. F., J. Chem. Phys. 43, 2111 (1965)) has been extensively used for predicting electrokinetic transport coefficients of charged microcapillary pores. With respect to the other transport coefficients, e.g., the reflection coefficient σ, the solute permeability ω, and the electric transport number t i , this model has played a minor part up to now. In this paper these quantities are evaluated as functions of electrolyte concentrations, pore radius, and density of the pore wall charge. Instead of the method usually followed of solving the Poisson-Boltzmann equation numerically, an approximative analytical approach (Levine, S., Marriott, J. R., Neale, G., and Epstein, N., J. Colloid Interface Sci. 52, 136 (1975)) has been chosen. As a result analytical expressions for σ and ω are formulated. For the regime of low electrolyte concentrations explicit equations are presented in which these quantities are expressed in terms of the pore radius and the charge density of the pore wall for a z 1–z 2 electrolyte. The theoretically predicted behavior of the coefficients is compared with experimental data obtained from osmotic measurements with an aqueous solution of sodium chloride and weakly charged Nuclepore membranes.

Large deviations in a linear model with nuisance parameters

The well-known approximative approach of Welch to the problem of Studentization in testing a linear hypothesis [B. L. Welch, Biometrika,34, 28 (1947)] admits a number of generalizations. One of them is connected with considering linear models in which the weights of the observations are nuisance parameters and another is related to the construction of multiplicative analogues of Welch's approach in the sense given this term in the work of O. V. Shalaevskii [Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,79, 88 (1978)]. In the present paper such a multiplicative analogue is constructed for a general linear model with unknown weights.