Maximum likelihood method for fitting a sum of exponentials to experimental data
Maximum likelihood method for fitting sum of expotentials to experimental data
STATISTICAL PROBABILITY↗
SEARCH · Search NASA
Results for “EXPONENTIAL FUNCTION”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Estimation of the parameters in exponential decontamination models
Parameter estimation in exponential decontamination models
PROBABILITY THEORY↗
Light from reflection nebulae. IV - Scattering by silicate grains
UBV colors and polarization models for reflection nebulae based on Mie scattering functions for exponential size distribution of silicate particles
Hanner, M. S.↗
X-ray study of solar plage regions and a small flare.
The O VII and Ne IX resonance line and 5 keV continuum emission of a small solar flare are interpreted on the basis of a model in which the emission measure of the region is an exponentially decreasing function of temperature. Good agreement with all three sets of data is obtained - a result not possible on the basis of an isothermal approximation. The change in the emission of the flare over a two minute interval appears to be consistent with a simple cooling of the region. Computation of the contribution function versus temperature for each emission indicates that each predominantly comes from a physically separate volume within the feature. The emission measure distribution for the flare is distinctly flatter than that of five plage regions which tend to have similar slopes and which are in turn flatter than the general corona.
Acton, L. W.↗
Computer-controlled environmental test systems - Criteria for selection, installation, and maintenance.
Applications for presently marketed, new computer-controlled environmental test systems are suggested. It is shown that capital costs of these systems follow an exponential cost function curve that levels out as additional applications are implemented. Some test laboratory organization changes are recommended in terms of new personnel requirements, and facility modification are considered in support of a computer-controlled test system. Software for computer-controlled test systems are discussed, and control loop speed constraints are defined for real-time control functions. Suitable input and output devices and memory storage device tradeoffs are also considered.
Chapman, C. P.↗
A nonlinear theory of cosmic ray pitch angle diffusion in homogeneous magnetostatic turbulence
A plasma strong turbulence, weak coupling, theory is applied to the problem of cosmic ray pitch angle scattering in magnetostatic turbulence. The theory used is a rigorous generalization of Weinstock's resonance-broadening theory and contains no ad hoc approximations. A detailed calculation is presented for a model of slab turbulence with an exponential correlation function. The results agree well with numerical simulations. The rigidity dependence of the pitch angle scattering coefficient differs from that found by previous researchers. The differences result from an inadequate treatment of particle trajectories near 90 deg pitch angle in earlier work.
Goldstein, M. L.↗
A nonlinear theory of cosmic-ray pitch-angle diffusion in homogeneous magnetostatic turbulence
A plasma strong turbulence, weak coupling, theory is applied to the problem of cosmic-ray pitch-angle scattering in magnetostatic turbulence. The theory used is a rigorous generalization of Weinstock's 'resonance broadening' theory and contains no ad hoc approximations. A detailed calculation is presented for a model of 'slab' turbulence with an exponential correlation function. The results agree well with numerical simulations. The rigidity dependence of the pitch-angle scattering coefficient differs from that found by previous researchers. The differences result from an inadequate treatment of particle trajectories near 90 deg pitch angle in earlier work.
Goldstein, M. L.↗
Some MACSYMA program for solving difference equations
A set of MACSYMA programs are described for finding closed form solutions to linear recurrence relations in equations having either constant or variable coefficients. In the homogenous case, a polymonial equation is obtained and the solution to the recurrence relation can be written as a linear combination of the roots of the polynomial. Exponential generating functions are used to solve variable coefficient relations. Taking successive derivatives and using the recurrence relation, an ordinary differential equation is obtained. Expanding the solution to the differential equation in a Taylor series, shows that the nth term of the series is the solution to the recurrence relation. For second order recurrences, a check is made for those that can be solved in terms of Bessel functions.
Ivie, J.↗
Coding for optical channels with photon-counting
The problem of coding for Pierce's recent model for optical communications is studied. It was concluded that for any positive rate rho (measured in nats per photon), the best code of length n has an error probability bounded by an exponentially decaying function of n. Explicit practical schemes are shown for rho less than or = to 1; and evidence is given that rho approximating 1 may be the practical limit for optical communication.
Mceliece, R. J.↗
The C IV 1550 profile in type 1 Seyfert galaxies
The paper presents C IV 1550 A line profiles for the type 1 Seyfert galaxies NGC 5548, Mrk 509, NGC 7469, and MCG-2-58-22. Several line broadening mechanisms and theoretical line profiles are considered, and random motion of discrete clouds is ruled out. A spherical ensemble of discrete clouds with steady outflow or inflow produces a logarithmic profile, but does not account for the highly extended wings. A spherical ensemble with ballistic outflow produces a profile of the first exponential integral function, and fits the observed profile to the continuum level. Although C IV profiles favor the ballistic model, both Mrk 509 and NGC 7469 have significant asymmetry, and Balmer lines with a higher optical depth show higher asymmetry and redshift than all four galaxies.
Wu, C.-C.↗
Engineering calculations for communications satellite systems planning
Progress is reported on a computer code to improve the efficiency of spectrum and orbit utilization for the Broadcasting Satellite Service in the 12 GHz band for Region 2. It implements a constrained gradient search procedure using an exponential objective function based on aggregate signal to noise ratio and an extended line search in the gradient direction. The procedure is tested against a manually generated initial scenario and appears to work satisfactorily. In this test it was assumed that alternate channels use orthogonal polarizations at any one satellite location.
Martin, C. H.↗
Optimal design and use of retry in fault tolerant real-time computer systems
A new method to determin an optimal retry policy and for use in retry of fault characterization is presented. An optimal retry policy for a given fault characteristic, which determines the maximum allowable retry durations to minimize the total task completion time was derived. The combined fault characterization and retry decision, in which the characteristics of fault are estimated simultaneously with the determination of the optimal retry policy were carried out. Two solution approaches were developed, one based on the point estimation and the other on the Bayes sequential decision. The maximum likelihood estimators are used for the first approach, and the backward induction for testing hypotheses in the second approach. Numerical examples in which all the durations associated with faults have monotone hazard functions, e.g., exponential, Weibull and gamma distributions are presented. These are standard distributions commonly used for modeling analysis and faults.
Lee, Y. H.↗
Finite difference simulations of seismic scattering Implications for the propagation of short-period seismic waves in the crust and models of crustal heterogeneity
Synthetic seismographs that were obtained by the finite difference method are presently applied to the study of elastic and acoustic wave scattering in two-dimensional media with random spatial variations in seismic velocity. The seismograms are analyzed to determine the variation in travel times and waveforms across arrays of receivers. The random media with Gaussian and exponential correlation functions considered differ in the spectral falloff of their velocity fluctuations at wavelengths smaller than 2pi times the correlation distance. It is found that alternative models of crustal heterogeneity can be tested by improved measurements of the frequency dependence of the crustal Q at frequencies greater than about 1 Hz, assuming that scattering is responsible for most of the attenuation at such frequencies.
Frankel, A.↗
SMM observation of a cosmic gamma-ray burst from 20 keV to 100 MeV
The Solar Maximum Mission gamma-ray spectrometer has detected an intense gamma-ray burst that occurred on August 5, 1984. The burst originated from a source in the constellation Hydra and lasted about 45 s. Its integral fluence at 20 keV was 0.003 erg/sq cm. Spectral evolution similar to other bursts detected by SMM was observed. The overall shape of the spectrum from 20 keV to 100 MeV, on timescales as short as 2 s, is relatively constant. This shape can be fitted by the sum of an exponential-type function and a power law. There is no evidence for narrow or broadened emission lines.
Share, G. H.↗
Reliable algorithm for modal decomposition
This paper describes a reliable, general algorithm for modal decomposition in real arithmetic and its use in analyzing and synthesizing control logic for linear dynamic systems. The numerical difficulties are described associated with computing the Jordan canonical form when the system has repeated, or nearly repeated, eigenvalues. A new algorithm is described that satisfactorily solves these numerical difficulties. The relation and extension to related numerical analysis research are discussed to clarify the reliability of the techniques. Finally, its implementation as a practical modal decomposition method for efficiently computing the matrix exponential, transfer functions, and frequency response is also described.
Walker, Robert A.↗
ETARA PC version 3.3 user's guide: Reliability, availability, maintainability simulation model
A user's manual describing an interactive, menu-driven, personal computer based Monte Carlo reliability, availability, and maintainability simulation program called event time availability reliability (ETARA) is discussed. Given a reliability block diagram representation of a system, ETARA simulates the behavior of the system over a specified period of time using Monte Carlo methods to generate block failure and repair intervals as a function of exponential and/or Weibull distributions. Availability parameters such as equivalent availability, state availability (percentage of time as a particular output state capability), continuous state duration and number of state occurrences can be calculated. Initial spares allotment and spares replenishment on a resupply cycle can be simulated. The number of block failures are tabulated both individually and by block type, as well as total downtime, repair time, and time waiting for spares. Also, maintenance man-hours per year and system reliability, with or without repair, at or above a particular output capability can be calculated over a cumulative period of time or at specific points in time.
Hoffman, David J.↗
Separability of spatiotemporal spectra of image sequences
The spatiotemporal power spectrum was calculated of 14 image sequences in order to determine the degree to which the spectra are separable in space and time, and to assess the validity of the commonly used exponential correlation model found in the literature. The spectrum was expanded by a Singular Value Decomposition into a sum of separable terms and an index was defined of spatiotemporal separability as the fraction of the signal energy that can be represented by the first (largest) separable term. All spectra were found to be highly separable with an index of separability above 0.98. The power spectra of the sequences were well fit by a separable model. The power spectrum model corresponds to a product of exponential autocorrelation functions separable in space and time.
Eckert, Michael P.↗
Measurements of strain at plate boundaries using space based geodetic techniques
We have used the space based geodetic techniques of Satellite Laser Ranging (SLR) and VLBI to study strain along subduction and transform plate boundaries and have interpreted the results using a simple elastic dislocation model. Six stations located behind island arcs were analyzed as representative of subduction zones while 13 sites located on either side of the San Andreas fault were used for the transcurrent zones. The length deformation scale was then calculated for both tectonic margins by fitting the relative strain to an exponentially decreasing function of distance from the plate boundary. Results show that space-based data for the transcurrent boundary along the San Andreas fault help to define better the deformation length scale in the area while fitting nicely the elastic half-space earth model. For subduction type bonndaries the analysis indicates that there is no single scale length which uniquely describes the deformation. This is mainly due to the difference in subduction characteristics for the different areas.
Robaudo, Stefano↗