SEARCH · Engineering Papers

Results for “pseudo measurement”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

All sources NASA NTRS DOE OSTI

NASA NTRS1994

Progress In Incompressible Pump Flow Calculations

Steady and unsteady flows for propulsion systems are efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard kappa - epsilon model equations. The resulting computer code is applied to the flow analysis inside an advanced rocket pump impeller in steadily rotating reference frames. Numerical results are compared with experimental measurements. The effects of exit and shroud cavities with the leak-age flow are investigated. Time-accurate incompressible Navier-Stokes formulation with the overlapped grid scheme capability was evaluated by using MIT flapping foil experiment. The grid dependency, turbulence model effects, and the effect of order of differencing were investigated. Numerical results were compared against experimental data. The resulting procedure were applied to unsteady flapping foil calculations. Two upstream NACA 0025 foils perform high frequency synchronized motion and generate unsteady flow conditions to the downstream larger stationary foil. Comparison between unsteady experimental data and numerical results from two different moving boundary procedures will be presented.

Kiris, Cetin↗

NASA NTRS2006

Chill Down Process of Hydrogen Transport Pipelines

A pseudo-steady model has been developed to predict the chilldown history of pipe wall temperature in the horizontal transport pipeline for cryogenic fluids. A new film boiling heat transfer model is developed by incorporating the stratified flow structure for cryogenic chilldown. A modified nucleate boiling heat transfer correlation for cryogenic chilldown process inside a horizontal pipe is proposed. The efficacy of the correlations is assessed by comparing the model predictions with measured values of wall temperature in several azimuthal positions in a well controlled experiment by Chung et al. (2004). The computed pipe wall temperature histories match well with the measured results. The present model captures important features of thermal interaction between the pipe wall and the cryogenic fluid, provides a simple and robust platform for predicting pipe wall chilldown history in long horizontal pipe at relatively low computational cost, and builds a foundation to incorporate the two-phase hydrodynamic interaction in the chilldown process.

Mei, Renwei↗

NASA NTRS2004

Results of the Magnetometer Navigation (MAGNAV)lnflight Experiment

The Magnetometer Navigation (MAGNAV) algorithm is currently running as a flight experiment as part of the Wide Field Infrared Explorer (WIRE) Post-Science Engineering Testbed. Initialization of MAGNAV occurred on September 4, 2003. MAGNAV is designed to autonomously estimate the spacecraft orbit, attitude, and rate using magnetometer and sun sensor data. Since the Earth's magnetic field is a function of time and position, and since time is known quite precisely, the differences between the computed magnetic field and measured magnetic field components, as measured by the magnetometer throughout the entire spacecraft orbit, are a function of the spacecraft trajectory and attitude errors. Therefore, these errors are used to estimate both trajectory and attitude. In addition, the time rate of change of the magnetic field vector is used to estimate the spacecraft rotation rate. The estimation of the attitude and trajectory is augmented with the rate estimation into an Extended Kalman filter blended with a pseudo-linear Kalman filter. Sun sensor data is also used to improve the accuracy and observability of the attitude and rate estimates. This test serves to validate MAGNAV as a single low cost navigation system which utilizes reliable, flight qualified sensors. MAGNAV is intended as a backup algorithm, an initialization algorithm, or possibly a prime navigation algorithm for a mission with coarse requirements. Results from the first six months of operation are presented.

Thienel, Julie K.↗

NASA NTRS2001

New tracking implementation in the Deep Space Network

As part of the Network Simplification Project, the tracking system of the Deep Space Network is being upgraded. This upgrade replaces the discrete logic sequential ranging system with a system that is based on commercial Digital Signal Processor boards. The new implementation allows both sequential and pseudo-noise types of ranging. The other major change is a modernization of the data formatting. Previously, there were several types of interfaces, delivering both intermediate data and processed data (called 'observables'). All of these interfaces were bit-packed blocks, which do not allow for easy expansion, and many of these interfaces required knowledge of the specific hardware implementations. The new interface supports four classes of data: raw (direct from the measuring equipment), derived (the observable data), interferometric (multiple antenna measurements), and filtered (data whose values depend on multiple measurements). All of the measurements are reported at the sky frequency or phase level, so that no knowledge of the actual hardware is required. The data is formatted into Standard Formatted Data Units, as defined by the Consultative Committee for Space Data Systems, so that expansion and cross-center usage is greatly enhanced.

ranging↗

DOE OSTI2023

$\Sigma (1385)^{\pm }$ resonance production in Pb–Pb collisions at $\sqrt{s_{\textrm{NN}}} = 5.02$ TeV

Hadronic resonances are used to probe the hadron gas produced in the late stage of heavy-ion collisions since they decay on the same timescale, of the order of 1–10 fm/c, as the decoupling time of the system. In the hadron gas, (pseudo)elastic scatterings among the products of resonances that decayed before the kinetic freeze-out and regeneration processes counteract each other, the net effect depending on the resonance lifetime, the duration of the hadronic phase, and the hadronic cross sections at play. In this context, the Σ(1385) ± particle is of particular interest as models predict that regeneration dominates over rescattering despite its relatively short lifetime of about 5.5 fm/c. The first measurement of the Σ(1385) ± resonance production at midrapidity in Pb–Pb collisions at $\sqrt{s_{NN}}$=5.02 TeV with the ALICE detector is presented in this Letter. The resonances are reconstructed via their hadronic decay channel, Λπ, as a function of the transverse momentum (p T ) and the collision centrality. The results are discussed in comparison with the measured yield of pions and with expectations from the statistical hadronization model as well as commonly employed event generators, including PYTHIA8/Angantyr and EPOS3 coupled to the UrQMD hadronic cascade afterburner. None of the models can describe the data. For Σ(1385) ± , a similar behaviour as K*(892) 0 is observed in data unlike the predictions of EPOS3 with afterburner.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Measurement of $\nu_\mu$ CC Interactions With Two-Proton Final State in MINERvA

This dissertation presents a measurement of charged–current (CC) muon–neutrino interactions with exactly two protons and no pions in the final state (CC~$2p\,0\pi$), using data collected by the MINERvA detector in the NuMI medium–energy beam at Fermilab. Such two–proton topologies are a sensitive probe of nuclear dynamics in the few–GeV regime, including multi–nucleon correlations (npnh, notably $2p2h$) and intranuclear final–state interactions (FSI) such as pion absorption and nucleon rescattering. A precise experimental characterization of these processes is essential both for neutrino–interaction theory and for reducing systematic uncertainties in oscillation experiments that rely on accurate modeling of neutrino–nucleus interactions. Events are selected by requiring a $\nu_\mu$ CC interaction with a reconstructed $\mu^-$ and two proton tracks originating from a common vertex in MINERvA’s finely segmented scintillator tracker, with no reconstructed mesons. Muon charge and momentum are constrained by matching to the MINOS Near Detector, while proton identification exploits energy–loss profiles and stopping–proton features. Backgrounds from pion–producing channels that enter the signal region through FSI or reconstruction effects are constrained with data–driven sidebands (Michel–electron and isolated–cluster “blob” samples) and tuned via a simultaneous fit across signal and sideband regions. To correct detector resolution and acceptance effects, the analysis employs iterative Bayesian unfolding with extensive validation: statistical pseudo–experiments, and robustness checks against generator systematic “universes” and additional strong shape warps. Single–differential cross sections are reported for three observables tailored to the two–proton final state: the opening–angle cosine $\cos\!\left(\theta_{pp}\right)$, the leading–proton momentum, and the subleading–proton momentum. Systematic uncertainties include contributions from neutrino flux, interaction modeling (e.g., npnh and resonance parameters, pion FSI), and detector response (calibration, reconstruction efficiencies). The resulting distributions provide targeted constraints on the interplay of multi–nucleon dynamics and FSI that shape CC~$2p\,0\pi$ final states on hydrocarbon. Comparisons to modern GENIE–based simulations highlight kinematic regions where model components require refinement. These measurements thus inform generator tuning and improve the reliability of neutrino–energy reconstruction strategies for current and future long–baseline oscillation programs.

Syrotenko, Vladyslav S. [Tufts U.]↗

NASA NTRS2011

Operational Parameters, Considerations, and Design Decisions for Resource-Constrained Ion Trap Mass Spectrometers

Mass spectrometers are increasingly finding applications in new and unique areas, often in situations where key operational resources (i.e. power, weight and size) are limited. One such example is the Mars Organic Molecule Analyzer (MOMA). This instrument is a joint venture between NASA and the European Space Agency (ESA) to develop an ion trap mass spectrometer for chemical analysis on Mars. The constraints on such an instrument are significant as are the performance requirements. While the ideal operating parameters for an ion trap are generally well characterized, methods to maintain analytical performance with limited power and system weight need to be investigated and tested. Methods Experiments have been performed on two custom ion trap mass spectrometers developed as prototypes for the MOMA instrument. This hardware consists of quadrupole ion trap electrodes that are 70% the size of common commercial instrumentation. The trapping RF voltage is created with a custom tank circuit that can be tuned over a range of RF frequencies and is driven using laboratory supplies and amplifiers. The entire instrument is controlled with custom Lab VIEW software that allows a high degree of flexibility in the definition of the scan function defining the ion trap experiment. Ions are typically generated via an internal electron ionization source, however, a laser desorption source is also in development for analysis of larger intact molecules. Preliminary Data The main goals in this work have been to reduce the power required to generate the radio frequency trapping field used in an ion trap mass spectrometer. Generally minimizing the power will also reduce the volume and mass of the electronics to support the instrument. In order to achieve optimum performance, commercial instruments typically utilize RF frequencies in the 1 MHz range. Without much concern for power usage, they simply generate the voltage required to access the mass range of interest. In order to reduce the required RF voltage (and power), operation of the ion trap at lower RF frequencies has been investigated. Surprisingly, the performance of the instrument has only been slightly degraded at RF frequencies all the way down to 500 kHz. Mass resolution is relatively stable to this point and depending on the resonant ejection point used, the peak intensity is also quite stable. To date only masses up to m/z 200 have been fully investigated, however, additional studies are planned to verify the performance with higher mass ions. The lower frequency and voltage should reduce the pseudo potential well depth, eventually affecting the trapping efficiency of the instrument -- effect that could manifest itself in significantly limiting the mass range of trapped ions. Other methods to reduce the RF power while maintaining analytical performance are also under investigation. This includes ion ejection at lower q(sub z) values to access a given mass with a lower RF voltage. The loss of mass resolution at lower q(sub eject) points has been measured and current work is underway to leverage scan speed and the use of non-linear resonances in order to counter this trend. The overall trap performance under this range of operating conditions will be presented with a goal of identifying what trade-offs are acceptable.

Danell, Ryan M.↗

NASA NTRS2003

Software Searches for Better Spacecraft-Navigation Models

ADAPT is a computer program that searches for better mathematical models for spacecraft navigation. The task of tuning trajectory-determination models for interplanetary navigation is complex, requiring an intensive search of multiple dynamical and nondynamical models that yield trajectory solutions with minimal errors. By automating the search, ADAPT eases the task of human analysts and enables them to consider wider ranges of potential solutions. ADAPT uses genetic algorithms to search a range of relevant parameters in a user-selected design space to arrive at values for those parameters that best fit the measured spacecraft-tracking data. The user s guide for ADAPT reviews the theoretical basis of the program and presents two example applications. One example is that of selecting a solar-radiation model for the Mars Pathfinder (MPF) mission using MPF tracking data and an extended Kalman filter from prior spacecraft-navigation software. The second example is of the use of tracking data from the Stardust spacecraft mission combined with a pseudo-epoch-state batch filter and an empirical small-forces model to find improved impulse models for use during Stardust attitude adjustments.

Ely, Todd↗

DOE OSTI2025

Charm and bottom hadrons in hot hadronic matter

Heavy quarks, and the hadrons containing them, are excellent probes of the QCD medium formed in high-energy heavy-ion collisions, as they provide essential information on the transport properties of the medium and how quarks color-neutralize into hadrons. Large theoretical and phenomenological efforts have been dedicated thus far to assess the diffusion of charm and bottom quarks in the quark–gluon plasma and their subsequent hadronization into heavy-flavor (HF) hadrons. However, the fireball formed in heavy-ion collisions also features an extended hadronic phase, and therefore any quantitative analysis of experimental observables needs to account for the rescattering of charm and bottom hadrons. This is further reinforced by the presence of a QCD cross-over transition and the notion that the interaction strength is maximal in the vicinity of the pseudo-critical temperature. We review existing approaches for evaluating the interactions of open HF hadrons in a hadronic heat bath and the pertinent results for scattering amplitudes, spectral functions and transport coefficients. While most of the work to date has focused on D -mesons, we also discuss excited states as well as HF baryons and the bottom sector. Both the HF hadro-chemistry and bottom observables will play a key role in future experimental measurements. We also conduct a survey of transport calculations in heavy-ion collisions that have included effects of hadronic HF diffusion and assess its impact on various observables.

effective field theories↗

DOE OSTI2025

Spectral emission characteristics near 646 nm and plasma properties of laser-induced plasma of gaseous uranium hexafluoride

We present a detailed investigation of the temporal evolution of line and continuum emissions in laser-induced breakdown spectroscopy (LIBS) of gaseous uranium hexafluoride (UF 6 ), focusing on the spectral region near 646 nm. Spectral emission features, signal-to-background ratios (SBRs) of selected uranium lines, and spectral linewidths were examined under varying UF 6 pressures (15–60 Torr) and laser pulse energies (10–60 mJ). Higher pressures and pulse energies enhanced continuum emission and reduced SBRs but did not cause significant spectral congestion. Additional studies with the use of different laser systems, including nanosecond-pulsed Nd:YAG lasers (at fundamental and various harmonics) and a femtosecond-pulsed Ti:sapphire laser, revealed long-lived plasma continua in all cases. This persistent continuum is attributed to a pseudo-continuum from overlapping molecular emissions, as its intensity scales linearly with electron number density, deviating from the expected quadratic dependence of classical ion–electron interactions for free-free and free-bound continuum emission. Based on plasma persistence time, SBR, U II/U I intensity ratios, and electronic excitation temperature, no fundamental advantage was found for femtosecond-pulsed lasers over conventional nanosecond-pulsed ones for UF 6 enrichment assay with direct LIBS measurement.

Laser-induced breakdown spectroscopy↗

NASA NTRS1992

Incompressible viscous flow computations for the pump components and the artificial heart

A finite difference, three dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. Here, equations are solved in steadily rotating reference frames by using the steady state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two.

Kiris, Cetin↗

NASA NTRS1989

A practical approach for minimum time control of the Spacecraft Control Laboratory Experiment (SCOLE), appendix A

The Space COntrol Laboratory Experiment (SCOLE) is a challenge for control engineering applications. This is a result of the system dynamics, the available measurement information, the actuator capabilities and finally the specified performance requirements set. Results on the use of Model Reference Adaptive Control were reported. In view of the necessity for rapid response, this work deals with an optimal control formulation, with a minimum time requirement and constrained input. A mathematical statement of the problem is presented. The time optimal control formulation is presented and the reasons that make such an approach not promising are discussed. As a result, a pseudo time-optimal control algorithm is discussed. The proposed approach is tested to see if it satisfies the design specifications, and finally a discussion and suggestions for further research are provided.

Kaufman, H.↗

NASA NTRS2001

Computationally efficient control allocation

A computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed. The control allocation problem is that of distributing the effort of redundant control effectors to achieve some desired set of objectives. The problem is deemed linear if control effectiveness is affine with respect to the individual control effectors. The optimal solution is that which exploits the collective maximum capability of the effectors within their individual physical limits. Computational efficiency is measured by the number of floating-point operations required for solution. The method presented returned optimal solutions in more than 90% of the cases examined; non-optimal solutions returned by the method were typically much less than 1% different from optimal and the errors tended to become smaller than 0.01% as the number of controls was increased. The magnitude of the errors returned by the present method was much smaller than those that resulted from either pseudo inverse or cascaded generalized inverse solutions. The computational complexity of the method presented varied linearly with increasing numbers of controls; the number of required floating point operations increased from 5.5 i, to seven times faster than did the minimum-norm solution (the pseudoinverse), and at about the same rate as did the cascaded generalized inverse solution. The computational requirements of the method presented were much better than that of previously described facet-searching methods which increase in proportion to the square of the number of controls.

Durham, Wayne↗

DOE OSTI2021

Dark initial state radiation and the kinetic mixing portal

Data from Planck measurements of the cosmic microwave background (CMB) place important constraints on models with light dark matter (DM) and light mediators especially when both lie in the mass range below ~ 1 GeV. In models involving kinetic mixing where the dark photon acts as the mediator, these constraints are easily satisfied and the appropriate DM relic density achievable if the DM is, e.g., a complex scalar, where p-wave annihilation occurs, or is the lighter component of a split pseudo-Dirac state where co-annihilation dominates. In both of these cases, although higher order in the dark gauge coupling, g D , the corresponding annihilation processes including dark photon initial state radiation (ISR) will be dominantly s-wave with essentially temperature independent cross sections. The rates for these dark ISR associated processes, though not yielding cross sections large enough to contribute to the relic density, can still run into possible conflicts with the bounds arising from the CMB. In this paper we perform a preliminary study of the present and potential future constraints that the CMB imposes on the parameter spaces for both of these scenarios due to the existence of this dark ISR. Further analyses of the effects of dark ISR in DM annihilation is clearly warranted.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Amplified Mesoscale and Submesoscale Variability and Increased Concentration of Precipitation under Global Warming over Western North America

Abstract Cold-season precipitation statistics in simulations from the storm-resolving WRF Model at 6-km and 1-h resolution over western North America are analyzed. Pseudo–global warming future simulations for the 2041–80 period, constrained by GCMs under the RCP8.5 scenario, are compared to the 1981–2020 historical simulation. The analysis focuses on the dynamical properties of precipitation time series at subdaily scales and on the morphology of storms. The statistical distribution of precipitation intensities in each pixel of the simulation domain is characterized through nonparametric statistical indicators: frequency of wet hours, mean wet-hour precipitation intensity, and Gini coefficient as a measure of the temporal concentration of the precipitation volume. Additionally, the temporal and spatial Fourier power spectra of precipitation time series and precipitation fields are analyzed. The half-power period (HPP) and half-power wavelength (HPW) are defined as spectral measures of the characteristic scales of precipitation’s temporal and spatial patterns. The results show statistically significant increases in the mean wet-hour precipitation intensity and in the Gini coefficient in 99% of the pixels, indicating that the seasonal precipitation volume becomes more concentrated within a smaller number of hours with higher precipitation intensity. The statistics of change in the frequency of wet hours are more contrasted across the simulation domain. The changes are also reflected in the power spectra, which show the spatial and temporal variability increasing proportionally more with finer spatial and temporal scales and the HPW and HPP decreasing. These projected changes are expected to have consequences, not only in terms of hydrologic impacts but also in terms of the predictability of precipitation patterns. Significance Statement The precipitation characteristics of winter storms over the western United States and southwestern Canada are analyzed in future climate simulations for the 2041–80 period. As compared to present-day climate, the most intense parts of the storms are projected to produce a higher rainfall volume, with increased concentration over smaller areas and shorter time intervals. The propensity of rainfall intensity to vary rapidly over time will be enhanced in the future according to the simulations. These model predictions imply an increased risk of rapid flooding in small basins. They also suggest that predicting several hours ahead the time and location at which a storm will produce maximum rainfall may become more challenging in the future.

Climate change↗

NASA NTRS1999

Flame Spread Across Liquids: Experimental Results

The goal of our research on flame spread across a pool of liquid fuel is the quantitative identification of the mechanisms that control the rate and nature of flame spread when the initial temperature of the liquid pool is below the fuel's flash point temperature. Besides numerous experiments in drop towers and 1 g laboratories, we have flown five microgravity (mu-g) experiments on sounding rockets. As described in earlier papers, the first three flights examined the effect of forced opposed airflow over a 2.5 cm deep x 2 cm wide x 30 cm long pool of 1-butanol in mu-g. It was found that the flame spread is much slower and steadier than in 1 g where flame spread has a pulsating character. It was speculated that the flame spread in mu-g resembled the character of pseudo-uniform spread in 1 g; Ito et al later confirmed this conclusively in 1 g experiments. Much of the mu-g flame is also farther from the surface, dimmer, and with less soot, when compared to the 1 g flame. Three-dimensional liquid-phase flow patterns that control the liquid preheating were discovered in both 1 g and mu-g. Our numerical model, restricted to two dimensions, had predicted faster, pulsating flame spread in mu-g for opposed airflow. In examining the differences in the dimensionality of the model and experiment, it was noted that the experiment allowed gas expansion in the lateral direction (across the width of the pool), for which the model could not account. Such lateral expansion could reduce the expansion in the forward and upward directions. Because only these latter directions could be modeled, it was decided to artificially reduce the gas thermal expansion in the predictions. When this was done, satisfactory agreement could be obtained between the predicted and observed spread rates and the steadiness of the spread in microgravity. In 1 g, however, the predicted flame spread character also changed to pseudo-uniform, which disagreed with our 1 g experiments where the spread is pulsating. It was then speculated that gas-phase buoyant flow might oppose the lateral gas expansion, so that the 1 g experiments retained their pulsating flame spread character. If this speculation was valid, a difference in lateral gas expansion should be observable when comparing 1 g and mu-g experiments. Specifically, it was anticipated that greater flow divergence caused by lateral expansion would be measured in mu-g in the absence of a buoyant flow directed towards the flame.

Ross, H. D.↗

DOE OSTI2020

Effect of Heterogeneities on the Reaction-zone of a Propagating Detonation Wave

Reactive burn models for propagating detonation waves in an explosive are based on the ZND (Zel'dovich-Von Neumann-Doring) theory. A key property of the ZND theory, which leads to self-sustaining detonation waves, is a sonic point relative to the front in the reaction zone. Moreover, burn models assume the explosive is a homogeneous material. This assumption is used for plastic-bonded explosives, even though they are heterogeneous materials. The heterogeneities are accounted for only with an empirical burn rate. Furthermore, the reaction-zone width can be less than the length scale of heterogeneities. This raises the question of the effect of heterogeneities on the reaction zone. In particular, whether the reaction zone can be steady and have a well defined sonic point. To examine this question we focus on PBX 9501 since there is data on the grain-binder heterogeneities and on the reaction-zone velocity time history of a steady planar detonation wave. Using pseudo-mesoscale 1-D simulations, we examine the effect of a detonation wave transversing explosive and binder segments of random length. The simulations show that the reaction zone is quasi-steady with only short wavelength small amplitude variations in the detonation wave pressure and speed. The main effect of the heterogeneities is to introduce noise in the pressure and velocity fields that propagates into the Taylor wave behind the detonation. This is consistent with the scatter in the reaction-zone measurements for PBX 9501.

42 ENGINEERING↗

DOE OSTI2021

A Bayesian analysis of classical shadows

Abstract The method of classical shadows proposed by Huang, Kueng, and Preskill heralds remarkable opportunities for quantum estimation with limited measurements. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations—such as high-fidelity ground truth states—which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.

97 MATHEMATICS AND COMPUTING↗