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At least 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Net Radiative Effects of Dust in the Tropical North Atlantic Based on Integrated Satellite Observations and in Situ Measurements

In this study, we integrate recent in situ measurements with satellite retrievals of dust physical and radiative properties to quantify dust direct radiative effects on shortwave (SW) and longwave (LW) radiation (denoted as DRESW and DRELW, respectively) in the tropical North Atlantic during the summer months from 2007 to 2010. Through linear regression of the CERES-measured top-of atmosphere (TOA) flux versus satellite aerosol optical depth (AOD) retrievals, we estimate the instantaneous DRESW efficiency at the TOA to be -49+/-7.1 W/sq.m AOD(exp -1) and -36+/-4:8W/sq.m AOD(exp -1) based on AOD from MODIS and CALIOP, respectively. We then perform various sensitivity studies based on recent measurements of dust particle size distribution (PSD), refractive index, and particle shape distribution to determine how the dust microphysical and optical properties affect DRE estimates and its agreement with the above-mentioned satellite-derived DREs. Our analysis shows that a good agreement with the observation-based estimates of instantaneous DRESW and DRELW can be achieved through a combination of recently observed PSD with substantial presence of coarse particles, a less absorptive SW refractive index, and spheroid shapes. Based on this optimal combination of dust physical properties we further estimate the diurnal mean dust DRE(sub SW) in the region of -10W/sq.m at TOA and -26W/sq.m at the surface, respectively, of which ~30% is canceled out by the positive DRE(sub LW). This yields a net DRE of about -6:9 and -18.3 W/sq.m at TOA and the surface, respectively. Our study suggests that the LW flux contains useful information on dust particle size, which could be used together with SW observations to achieve a more holistic understanding of the dust radiative effect.

Song, Qianqian↗
NASA NTRS1999

Multitaper Spectral Analysis and Wavelet Denoising Applied to Helioseismic Data

Estimates of solar normal mode frequencies from helioseismic observations can be improved by using Multitaper Spectral Analysis (MTSA) to estimate spectra from the time series, then using wavelet denoising of the log spectra. MTSA leads to a power spectrum estimate with reduced variance and better leakage properties than the conventional periodogram. Under the assumption of stationarity and mild regularity conditions, the log multitaper spectrum has a statistical distribution that is approximately Gaussian, so wavelet denoising is asymptotically an optimal method to reduce the noise in the estimated spectra. We find that a single m-upsilon spectrum benefits greatly from MTSA followed by wavelet denoising, and that wavelet denoising by itself can be used to improve m-averaged spectra. We compare estimates using two different 5-taper estimates (Stepian and sine tapers) and the periodogram estimate, for GONG time series at selected angular degrees l. We compare those three spectra with and without wavelet-denoising, both visually, and in terms of the mode parameters estimated from the pre-processed spectra using the GONG peak-fitting algorithm. The two multitaper estimates give equivalent results. The number of modes fitted well by the GONG algorithm is 20% to 60% larger (depending on l and the temporal frequency) when applied to the multitaper estimates than when applied to the periodogram. The estimated mode parameters (frequency, amplitude and width) are comparable for the three power spectrum estimates, except for modes with very small mode widths (a few frequency bins), where the multitaper spectra broadened the modest compared with the periodogram. We tested the influence of the number of tapers used and found that narrow modes at low n values are broadened to the extent that they can no longer be fit if the number of tapers is too large. For helioseismic time series of this length and temporal resolution, the optimal number of tapers is less than 10.

Komm, R. W.↗
DOE OSTI2024

An introduction to Spent Nuclear Fuel decay heat for Light Water Reactors: a review from the NEA WPNCS

This paper summarized the efforts performed to understand decay heat estimation from existing spent nuclear fuel (SNF), under the auspices of the Working Party on Nuclear Criticality Safety (WPNCS) of the OECD Nuclear Energy Agency. Needs for precise estimations are related to safety, cost, and optimization of SNF handling, storage, and repository. The physical origins of decay heat (a more correct denomination would be decay power) are then introduced, to identify its main contributors (fission products and actinides) and time-dependent evolution. Due to limited absolute prediction capabilities, experimental information is crucial; measurement facilities and methods are then presented, highlighting both their relevance and our need for maintaining the unique current full-scale facility and developing new ones. The third part of this report is dedicated to the computational aspect of the decay heat estimation: calculation methods, codes, and validation. Different approaches and implementations currently exist for these three aspects, directly impacting our capabilities to predict decay heat and to inform decision-makers. Finally, recommendations from the expert community are proposed, potentially guiding future experimental and computational developments. One of the most important outcomes of this work is the consensus among participants on the need to reduce biases and uncertainties for the estimated SNF decay heat. If it is agreed that uncertainties (being one standard deviation) are on average small (less than a few percent), they still substantially impact various applications when one needs to consider up to three standard deviations, thus covering more than 95% of cases. The second main finding is the need of new decay heat measurements and validation for cases corresponding to more modern fuel characteristics: higher initial enrichment, higher average burnup, as well as shorter and longer cooling time. Similar needs exist for fuel types without public experimental data, such as MOX, VVER, or CANDU fuels. A third outcome is related to SNF assemblies for which no direct validation can be performed, representing the vast majority of cases (due to the large number of SNF assemblies currently stored, or too short or too long cooling periods of interest). A few solutions are possible, depending on the application. For the final repository, systematic measurements of quantities related to decay heat can be performed, such as neutron or gamma emission. This would provide indications of the SNF decay heat at the time of encapsulation. For other applications (short- or long-term cooling), the community would benefit from applying consistent and accepted recommendations on calculation methods, for both decay heat and uncertainties. This would improve the understanding of the results and make comparisons easier.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

A differentiable perturbation-based weak lensing shear estimator

Upcoming imaging surveys will use weak gravitational lensing to study the large-scale structure of the Universe, demanding sub-per cent accuracy for precise cosmic shear measurements. We present a new differentiable implementation of our perturbation-based shear estimator (fpfs), using jax, which is publicly available as part of a new suite of analytic shear algorithms called anacal. This code can analytically calibrate the shear response of any non-linear observable constructed with the fpfs shapelets and detection modes utilizing autodifferentiation (ad), generalizing the formalism to include a family of shear estimators with corrections for detection and selection biases. Using the ad capability of jax, it calculates the full Hessian matrix of the non-linear observables, which improves the previously presented second-order noise bias correction in the shear estimation. As an illustration of the power of the new anacal framework, we optimize the effective galaxy number density in the space of the generalized shear estimators using an LSST-like galaxy image simulation for the 10 yr LSST. For the generic shear estimator, the magnitude of the multiplicative bias |m| is below 3 × 10 –3 (99.7 per cent confidence interval), and the effective galaxy number density is improved by 5 per cent. We also discuss some planned future additions to the anacal software suite to extend its applicability beyond the fpfs measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1985

Estimating the weight of generally configured dual wing systems

Formulas available for the weight estimation of monoplane wings cannot be said to be appropriate for the estimation of generally configured dual wing systems. In the present paper a method is described which simultaneously generates a structural weight estimate and a fully stressed, quasi-optimal structure for a model of a dual wing system. The method is fast and inexpensive. It is ideally suited to preliminary design. To illustrate the method, a dual wing system and a conventional wing system are sized. Numerical computation is shown to be suitably fast for both cases and, for both cases, convergence to a final configuration is shown to be quite rapid. To illustrate the validity of the method, a conventional wing is sized and its weight obtained by the present method is compared to its weight determined by a reputable weight estimation formula. The results are shown to be very close.

Cronin, D. L.↗
DOE OSTI2025

Estimating time in quantum chaotic systems and black holes

We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation". Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time values. Intuitively, it should become increasingly difficult to estimate the precise value of time by making measurements on the state. We use a quantity called the Fisher information from quantum metrology to quantify the minimum uncertainty in estimating time. Due to unitarity, the uncertainty in the time estimate does not grow with time if we have access to optimal measurements on the full system. Restricting the measurements to act on a small subsystem or to have low computational complexity leads to results expected from equilibration, where the time uncertainty becomes large at late times. With optimal measurements on a subsystem larger than half of the system, we regain the ability to estimate the time very precisely, even at late times. Hawking's calculation for the reduced density matrix of the black hole radiation in semiclassical gravity contradicts our general predictions for unitary quantum chaotic systems. Hawking's state always has a large uncertainty for attempts to estimate the time using the radiation, whereas our general results imply that the uncertainty should become small after the Page time. This gives a new version of the black hole information loss paradox in terms of the time estimation task. By restricting to simple measurements on the radiation, the time uncertainty becomes large. This indicates from a new perspective that the observations of computationally bounded agents are consistent with the semiclassical effective description of gravity.

Black holes↗
DOE OSTI2020

Exotic Meson Photoproduction at GlueX – Search for the hybrid candidate Y

Understanding the hadron spectrum is one of the primary goals of non-perturbative QCD. Many predictions have experimentally been confirmed, others still remain under experimental investigation. Of particular interest is how gluonic excitations give rise to states with constituent glue. One class of such states are hybrid mesons that are predicted by theoretical models and Lattice QCD calculations. Searching for and understanding the nature of these states is a primary physics goal of the GlueX experiment at the CEBAF accelerator at Jefferson Lab. A search for a JPC = 1-- hybrid meson candidate, the Y (2175), in phi(1020)pi+pi+ and phi(1020)f0(980) channels in photoproduction on a proton target has been conducted. A first measurement of non-resonant phi(1020)pi+pi+ and phi(1020)f0(980) total cross sections in photoproduction has been performed. An upper limit on the resonance production cross section for the Y (2175) -> phi(1020)pi+pi+ and Y (2175) -> phi(1020)f0(980) channels are estimated. Since the analysis essentially depends on the quality of the charged kaon identification, also an optimization of particle identification through an improvement of the energy loss estimation in the CDC by a truncated mean method has been investigated.

Hamdi, Abdennacer↗
DOE OSTI2020

RouteE: A Vehicle Energy Consumption Prediction Engine

The emergence of connected and automated vehicles and smart cities technologies create the opportunity for new mobility modes and routing decision tools, among many others. To achieve maximum mobility and minimum energy consumption, it is critical to understand the energy cost of decisions and optimize accordingly. The Route Energy prediction model (RouteE) enables accurate estimation of energy consumption for a variety of vehicle types over trips or sub-trips where detailed drive cycle data are unavailable. Applications include vehicle route selection, energy accounting and optimization in transportation simulation, and corridor energy analyses, among others. The software is a Python package that includes a variety of pre-trained models from the National Renewable Energy Laboratory (NREL). However, RouteE also enables users to train custom models using their own data sets, making it a robust and valuable tool for both fast calculations and rigorous, data-rich research efforts. The pre-trained RouteE models are established using NREL’s Future Automotive Systems Technology Simulator paired with approximately 1 million miles of drive cycle data from the Transportation Secure Data Center, resulting in energy consumption behavior estimates over a representative sample of driving conditions for the United States. Validations have been performed using on-road fuel consumption data for conventional and electrified vehicle powertrains. Transferring the results of the on-road validation to a larger set of real-world origin-destination pairs, it is estimated that implementing the present methodology in a green-routing application would accurately select the route that consumes the least fuel 90% of the time. The novel machine learning techniques used in RouteE make it a flexible and robust tool for a variety of transportation applications.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Risk-Adaptive Experimental Design for High-Consequence Systems: LDRD Final Report

Constructing accurate statistical models of critical system responses typically requires an enormous amount of data from physical experiments or numerical simulations. Unfortunately, data generation is often expensive and time consuming. To streamline the data generation process, optimal experimental design determines the 'best' allocation of experiments with respect to a criterion that measures the ability to estimate some important aspect of an assumed statistical model. While optimal design has a vast literature, few researchers have developed design paradigms targeting tail statistics, such as quantiles. In this project, we tailored and extended traditional design paradigms to target distribution tails. Our approach included (i) the development of new optimality criteria to shape the distribution of prediction variances, (ii) the development of novel risk-adapted surrogate models that provably overestimate certain statistics including the probability of exceeding a threshold, and (iii) the asymptotic analysis of regression approaches that target tail statistics such as superquantile regression. To accompany our theoretical contributions, we released implementations of our methods for surrogate modeling and design of experiments in two complementary open source software packages, the ROL/OED Toolkit and PyApprox.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2017

Impact of Archeomagnetic Field Model Data on Modern Era Geomagnetic Forecasts

A series of geomagnetic data assimilation experiments have been carried out to demonstrate the impact of assimilating archeomagnetic data via the CALS3k.4 geomagnetic field model from the period between 10 and 1590 CE. The assimilation continues with the gufm1 model from 1590 to 1990 and CM4 model from 1990 to 2000 as observations, and comparisons between these models and the geomagnetic forecasts are used to determine an optimal maximum degree for the archeomagnetic observations, and to independently estimate errors for these observations. These are compared with an assimilation experiment that uses the uncertainties provided with CALS3k.4. Optimal 20 year forecasts in 1990 are found when the Gauss coefficients up to degree 3 are assimilated. In addition we demonstrate how a forecast and observation bias correction scheme could be used to reduce bias in modern era forecasts. Initial experiments show that this approach can reduce modern era forecast biases by as much as 50 percent.

Tangborn, Andrew↗
NASA NTRS2012

Application of an Optimal Tuner Selection Approach for On-Board Self-Tuning Engine Models

An enhanced design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented in this paper. It specific-ally addresses the under-determined estimation problem, in which there are more unknown parameters than available sensor measurements. This work builds upon an existing technique for systematically selecting a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. While the existing technique was optimized for open-loop engine operation at a fixed design point, in this paper an alternative formulation is presented that enables the technique to be optimized for an engine operating under closed-loop control throughout the flight envelope. The theoretical Kalman filter mean squared estimation error at a steady-state closed-loop operating point is derived, and the tuner selection approach applied to minimize this error is discussed. A technique for constructing a globally optimal tuning parameter vector, which enables full-envelope application of the technology, is also presented, along with design steps for adjusting the dynamic response of the Kalman filter state estimates. Results from the application of the technique to linear and nonlinear aircraft engine simulations are presented and compared to the conventional approach of tuner selection. The new methodology is shown to yield a significant improvement in on-line Kalman filter estimation accuracy.

Simon, Donald L.↗
DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗
NASA NTRS2003

Optimal Observations for Variational Data Assimilation

An important aspect of Ocean state estimation is the design of an observing system that allows the efficient study of climate aspects in the ocean. A solution of the design problem is presented here in terms of optimal observations that emerge as nondimensionalized singular vectors of the modified data resolution matrix. The actual computation is feasible only for scalar quantities in the limit of large observational errors. In the framework of a lo resolution North Atlantic primitive equation model it is demonstrated that such optimal observations when applied to determining the strength of the volume and heat transport across the Greenland-Scotland ridge, perform significantly better than traditional section data. On seasonal to inter-annual time-scales optimal observations are located primarily along the continental shelf and information about heat-transport, wind stress and stratification is being communicated via boundary waves and advective processes. On time-scales of about a month, sea surface height observations appear to be more efficient in reconstructing the cross-ridge heat transport than hydrographic observations. Optimal observations also provide a tool for understanding how the ocean state is effected by anomalies of integral quantities such as meridional heat transport.

Koehl, Armin↗
DOE OSTI2024

A Cohesive Deep Drilling Field Strategy for LSST Cosmology

The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will image billions of astronomical objects in the wide–fast–deep primary survey and in a set of minisurveys including intensive observations of a group of deep drilling fields (DDFs). The DDFs are a critical piece of three key aspects of the LSST Dark Energy Science Collaboration (DESC) cosmological measurements: they provide a required calibration for photometric redshifts (photo- z ) and weak gravitational lensing (WL) measurements and they directly contribute to cosmological constraints from the most distant Type Ia supernovae (SNe Ia). We present a set of cohesive DDF strategies fulfilling science requirements relevant to DESC and following the guidelines of the Survey Cadence Optimization Committee. We propose a method to estimate the observing strategy parameters and we perform simulations of the corresponding surveys. We define a set of metrics for each science case to assess the performance of the proposed observing strategies. We show that the most promising results are achieved with deep rolling surveys characterized by two sets of fields: ultradeep fields ( z ≲ 1.1) observed at a high cadence with a large number of visits over a limited number of seasons, and deep fields ( z ≲ 0.7), observed with a cadence of ~3 nights for 10 yr. These encouraging results should be confirmed with realistic simulations using the LSST scheduler. A DDF budget of ~8.5% is required to design observing strategies satisfying all the cosmological requirements. A lower DDF budget leads to surveys that either do not fulfill the photo- z /WL requirements or are not optimal for SN Ia cosmology.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Spatial distributions of X CO 2 seasonal cycle amplitude and phase over northern high-latitude regions

Satellite-based observations of atmospheric carbon dioxide (CO 2 ) provide measurements in remote regions, such as the biologically sensitive but undersampled northern high latitudes, and are progressing toward true global data coverage. Recent improvements in satellite retrievals of total column-averaged dry air mole fractions of CO 2 (X CO 2 ) from the NASA Orbiting Carbon Observatory 2 (OCO-2) have allowed for unprecedented data coverage of northern high-latitude regions, while maintaining acceptable accuracy and consistency relative to ground-based observations, and finally providing sufficient data in spring and autumn for analysis of satellite-observed X CO 2 seasonal cycles across a majority of terrestrial northern high-latitude regions. Here, we present an analysis of X CO 2 seasonal cycles calculated from OCO-2 data for temperate, boreal, and tundra regions, subdivided into 5° latitude by 20° longitude zones. We quantify the seasonal cycle amplitudes (SCAs) and the annual half drawdown day (HDD). OCO-2 SCAs are in good agreement with ground-based observations at five high-latitude sites, and OCO-2 SCAs show very close agreement with SCAs calculated for model estimates of X CO 2 from the Copernicus Atmosphere Monitoring Services (CAMS) global inversion-optimized greenhouse gas flux model v19r1 and the CarbonTracker2019 model (CT2019B). Model estimates of X CO 2 from the GEOS-Chem CO 2 simulation version 12.7.2 with underlying biospheric fluxes from CarbonTracker2019 (GC-CT2019) yield SCAs of larger magnitude and spread over a larger range than those from CAMS, CT2019B, or OCO-2; however, GC-CT2019 SCAs still exhibit a very similar spatial distribution across northern high-latitude regions to that from CAMS, CT2019B, and OCO-2. Zones in the Asian boreal forest were found to have exceptionally large SCA and early HDD, and both OCO-2 data and model estimates yield a distinct longitudinal gradient of increasing SCA from west to east across the Eurasian continent. In northern high-latitude regions, spanning latitudes from 47 to 72° N, longitudinal gradients in both SCA and HDD are at least as pronounced as latitudinal gradients, suggesting a role for global atmospheric transport patterns in defining spatial distributions of X CO2 seasonality across these regions. GEOS-Chem surface contact tracers show that the largest X CO 2 SCAs occur in areas with the greatest contact with land surfaces, integrated over 15–30d. The correlation of X CO 2 SCA with these land surface contact tracers is stronger than the correlation of X CO 2 SCA with the SCA of CO 2 fluxes or the total annual CO 2 flux within each 5° latitude by 20° longitude zone. This indicates that accumulation of terrestrial CO 2 flux during atmospheric transport is a major driver of regional variations in X CO 2 SCA.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Tritium Breeding Ratio Evaluation of Solid Breeder Concepts for the FESS-FNSF

This paper presents a parametric study of the Fusion Energy System Studies-Fusion Nuclear Science Facility’s (FNSF’s) tritium breeding performance for several solid breeder concepts, neutron multiplying materials, and blanket materials, assuming volume fractions based on the most recent FNSF design as a realistically representative fusion facility. In this study, we initially surveyed the tritium breeding ratio (TBR) of several solid breeder concepts by employing a simplified but efficient one-dimensional (1-D) infinite cylinder reduced-order model (ROM). Parametric studies were performed with the ROMs for the full range of breeder-to-multiplier ratios to identify the optimum mixture compositions for each breeder type that would lead to a maximum TBR. These optimized breeder-multiplier combinations were then homogenized with FNSF blanket component materials to estimate their impacts on the TBR. Subsequently, as a validation step for the optimal designs, TBR calculations were performed using a more realistic modified 1-D ROM with inner and outer breeding regions, as well as with a fully detailed 22.5-deg three-dimensional (3-D) sector of the FNSF to assess the impact of geometry details on the TBR. The differences between the two 1-D models were negligible, while the ROMs were able to correctly predict trends and identify the maximum and minimum TBR cases, as well as show consistent biases relative to the results produced by the full 3-D, 22.5-deg sector for specific breeder/multiplier combinations. Solid breeder concepts such as Li 2 O, Li 4 SiO 4 , and Li 8 ZrO 6 outperformed all others in this study in terms of TBR performance when combined with all the neutron multiplier materials selected. Here, an underlying goal of this study was to develop and improve rapid and reliable ROMs to aid designers during parametric optimizations of highly complex and computationally expensive fusion models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Solar-Thermal Ammonia Production Via a Nitride Looping Cycle [Slides]

Solar Thermal Ammonia Production has the potential to synthesize ammonia in a green, renewable process that can greatly reduce the carbon footprint left by conventional Haber-Bosch reaction. Ternary nitrides in the family A 3 B x N (A=Co, Ni, Fe; B=Mo; x=2,3) have been identified as a potential candidate for NH 3 production. Experiments with Co 3 Mo 3 N in Ammonia Synthesis Reactor demonstrate cyclable NH 3 production from bulk nitride under pure H 2 . Production rates were fairly flat in all the reduction steps with no evident dependence on the consumed solid-state nitrogen, as would be expected from catalytic Mars-van Krevelen mechanism. Material can be re-nitridized under pure N 2 . Bulk nitrogen per reduction step average between 25 – 40% of the total solid-state nitrogen. Selectivity to NH 3 stabilized at 55 – 60% per cycle. Production rates (NH 3 and N 2 ) become apparent above 600 °C at P(H 2 ) = 0.5 – 2 bar. Optimal point of operation to keep selectivity high without compromising NH 3 rates currently estimated at 650 °C and 1.5 - 2 bar. The next steps are to optimize production rates, examine effect of N 2 addition in NH 3 synthesis reaction, and test additional ternary nitrides.

14 SOLAR ENERGY↗
NASA NTRS1972

Optimal filter design subject to output delobe constraints

The design of filters for detection and estimation in radar and communications systems is considered, with inequality constraints on the maximum output sidelobe levels. A constrained optimization problem in Hilbert space is formulated, incorporating the sidelobe constraints via a partial ordering of continuous functions. Generalized versions (in Hilbert space) of the Kuhn-Tucker and Duality Theorems allow the reduction of this problem to an unconstrained one in the dual space of regular Borel measures. A convergent algorithm is presented for computational solution of the dual problem.

Fortmann, T. E.↗