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DOE OSTI2023

Characterization of Infrequent Samples from The Concentration, Storage, And Transfer Facility: Leak Detection Box (LDB) Drain Cell Sample: February 26, 2023, Sample

Savannah River Mission Completion Engineering (SRMC-E) requested that the Savannah River National Laboratory (SRNL) analyze the Concentration, Storage, and Transfer Facility (CSTF) samples from the following Tank Farm areas: the sump encasement, catch tank, drain cell, and waste tank annulus. In general, these CSTF samples will be analyzed on an infrequent basis and analyses will include detection for total beta/gamma activities, total alpha activity, free hydroxide, and pH measurements. This report presents characterization results for the leak detection box (LDB) February 26, 2023, drain cell sample. The sample was clear and colorless with no visible particulates. The results are measurements for total gamma, total alpha, total beta, free hydroxide, pH, and density. These analyses were performed in triplicate. A summary of the average analytical results for the LDB sample includes the following. The directly measured pH for the LDB February 26, 2023 "as-received" drain cell sample range was 7.12-7.16, and the free hydroxide concentration was <0.02 M. The density of the "as-received" drain cell sample determined at 25 °C was 1.02±0.00 g/mL. The total alpha activity for the LDB February 26, 2023, sample is reported as a less than value (Upper Limit) because of possible spectral interferences. Thus, the total alpha activity averaged <3.52E+02 dpm/mL. This value is less than 4.83E+03 dpm/mL, which is the procedural limit for non-waste determination. The total beta activity in the LDB February 26, 2023, drain cell sample is above the instrument detection limits and average 9.76E+03±5.94E+02 dpm/mL. The total beta activity in the LDB February 26, 2023, drain cell sample is above he instrument detection limits and averaged 7.76E+03±5.94E+02 dpm/mL. The average measured cesium-137 activity (dominant beta emitter) in the LDB February 26, 2023, drain cell sample is 7.76E+03±2.35E+02 dpm/mL. The corresponding Ba-137m (dominant gamma emitter) activity, calculated as 94.6% of the Cs-137 values, is 7.34E+03±2.23E+02 dpm/mL. The total empirical activity of the beta and gamma emitting (represented by the sum of total beta and Ba-137m activities) averaged 1.71E+04±8.18E+02 dpm/mL. This value is less than 8.69E+05 dpm/mL, which is the procedural limit for non-waste determination.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Characterization of Infrequent Samples from the Concentration, Storage, and Transfer Facility: Leak Detection Box (LDB) Drain Cell Sample: May 15, 2023, Sample

Savannah River Mission Completion Engineering (SRMC-E) requested that the Savannah River National Laboratory (SRNL) analyze the Concentration, Storage, and Transfer Facility (CSTF) samples from the following Tank Farm areas: the sump encasement, catch tank, drain cell, and waste tank annulus. In general, these CSTF samples will be analyzed on an infrequent basis and analyses will include detection for total beta/gamma activities, total alpha activity, free hydroxide, and pH measurement. SRMC-E corresponded with SRNL to obtain the final results through memo SRNL-L3120-2023-00013. This report presents characterization from results for the leak detection box (LDB) May 15, 2023, drain cell sample. The sample was clear and colorless with no visible particulates. The results are measurements for total gamma, total alpha, total beta, free hydroxide, pH, and density. These analyses were performed in triplicate. A summary of the average analytical results for the LDB sample includes the following. The measured pH for the LDB May 15, 2023 "as-received" drain cell sample range was 6.60-6.89, and the free hydroxide concentration as expected, based upon the pH, was <0.02 M. The average measured density of the "as-received" drain cell sample determined at 22 °C was 1.022±0.001 g/mL. the average measured total alpha activity for the LDB May 15, 2023, sample was 3.04E+02±1.13E+01. This value is less than 4.83E+03 dpm/mL, which is the procedural limit for non-waste determination. The total empirical activity of the beta and gamma emitting (represented by by the sum of total beta and B-137 m activities) averaged to 1.83+04±1.07E+03 dpm/mL. This value is less than 8.69E+05 dpm/mL, which is the procedural limit for non-waste determination.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Characterization of Infrequent Samples from the Concentration, Storage, and Transfer Facility: F-Area Pump Pit 3 (FPP-3) Sump Sample: December 2021 Sample

In December 2021, SRR-E sent an ~185 mL sample identified as FPP-3 from a F-Area pump pit sump to SRNL for analysis. The sample was pale yellow in color and contained a small amount of suspended solids visually estimated to be less than 1% by volume. SRNL analysis indicated that the sample contained 4.4 E+05 dpm/mL Cs-137, 6.2 E+05 dpm/mL total beta activity, 9.3 E+02 dpm/mL beta activity following cesium removal, and below detectable levels of alpha activity following cesium removal. In addition, the sample contained 0.015 M free OH- and 947 μg total organic carbon/mL.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Characterization of Infrequent Samples from the Concentration, Storage, and Transfer Facility: H-Area Diversion Box 7 (HDB-7) Sump Sample: December 2021 Sample

In December 2021, SRR-E sent an ~250 mL sample identified as HDB-7 from an H-Area diversion box sump to SRNL for analysis. The sample was clear and colorless and free from any solids. SRNL analysis indicated that the sample contained 2.97E+05 dpm/mL Cs-137, 3.74E+05 dpm/mL total beta activity, 1.04E+03 dpm/mL beta activity following cesium removal, and below detectable levels of alpha activity and alpha activity following cesium removal. In addition, the pH of the sample was 7.32, free hydroxide concentration was 2.09E-07 M, and the density was 0.991 g/mL.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Characterization of Infrequent Samples from the Concentration, Storage, and Transfer Facility: H-Area Diversion Box 7 (HDB-7) Sump Sample: January 2022 Samples

Savannah River Remediation Engineering (SRR-E) requested that the Savannah River National Laboratory (SRNL) analyze the Concentration, Storage, and Transfer Facility (CSTF) samples from the following Tank Farm areas: the sump encasement, catch tank, drain cell, and waste tank annulus. In general, these CSTF samples will be analyzed on an infrequent basis and analyses will include detection for total beta/gamma, total alpha activities, density, free hydroxide, and pH measurements. This report presents characterization results for the H-Area diversion box 7 sump (HDB-7) 07 January 2022 and 18 January 2022 samples. The samples were clear and colorless and free from any solids. The results are measurements for total gamma, total alpha, total beta, density, free hydroxide, and pH.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Characterization of Infrequent Samples from the Concentration, Storage, and Transfer Facility: H-Area Diversion Box 1 (HDB-1) Sump Sample: January 25, 2022 Sample

Savannah River Remediation Engineering (SRR-E) requested that the Savannah River National Laboratory (SRNL) analyze the Concentration, Storage, and Transfer Facility (CSTF) samples from the following Tank Farm areas: the sump encasement, catch tank, drain cell, and waste tank annulus. In general, these CSTF samples will be analyzed on an infrequent basis and analyses will include detection for total beta/gamma, total alpha activities, density, free hydroxide, and pH measurements. This report presents characterization results for the H-Area diversion box 1 sump (HDB-1) January 2022 sample. The sample was slightly brown with a small amount of suspended fine particulates visually estimated to be less than 1% by volume. The results are measurements for total gamma, total alpha, total beta, density, free hydroxide, and pH.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Characterization of Infrequent Samples from the Concentration, Storage, and Transfer Facility: Leak Detection Box (LDB) Drain Cell Sample: February 09, 2022 Sample

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Characterization of Infrequent Samples from the Concentration, Storage, and Transfer Facility: Leak Detection Box (LDB) Drain Cell Sample: August 04, 2022 Sample

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

A Comparison of Groundwater Sampling Technologies, Including Passive Diffusion Sampling, for Radionuclide Contamination - 20205

Using traditional high-flow purge methods for long-term water quality monitoring of deep groundwater wells can be expensive, affect contaminant migration, and produce excessive volumes of discharge water that can be difficult to manage. The use of low-flow pumping methods and depth discrete bailers (DDBs) can reduce the cost of sampling deep groundwater wells. In general, using different pumping methods to obtain reproducible and representative groundwater can be challenging. Passive diffusion samplers (PDSs) have successfully been used in long-term monitoring for volatile organic compounds, major ions, and trace-elements, but application has been limited for stable and radioactive isotopes. Beginning in 2018, the United States Geological Survey (USGS) conducted three sampling events to test the ability of PDSs and DDBs to obtain reproducible and representative groundwater samples. The sampled well is completed in a regional, permeable carbonate aquifer and is one in a set of wells that have historically been used for tritium tracer testing. All samples were obtained at 180 m (590 ft) below land surface (bls) in a 13.97 cm (5.5 inch) uncased well that has a total depth of 202 m (662 ft) bls. The first sampling event deployed a regenerated cellulose dialysis membrane (RCDM) PDS for 14 days with deionized water as the blank. The second sampling event deployed a RCDM for 27 days also with deionized water as the blank. The third sampling event deployed a Dual Membrane (DM) PDS for 65 days using a blank of tritium-dead carbonate water. The DM PDS was used to assess the effect of longer term deployment on tritium concentrations and address whether or not the PDSs reached equilibrium with ambient groundwater. The day after each of the three passive samplers were retrieved a DDB was used to obtain discrete non-integrated groundwater samples. For each DDB sampling day, the bailer was lowered into the well 10 consecutive times to determine if the water chemistry changed from the first to the last bailed sample. Quality assurance samples including blanks and duplicates were obtained during all three sampling events. All blank waters had tritium concentrations less than 21±33 pCi/L. Major ion (e.g. calcium, chloride, sodium, and sulfate) results were compared between all samples obtained with RCDM and DDB. Major ion concentrations showed a coefficient of variation of less than 6% between all RCDM and DDB samples; however, the coefficient of variation between the different deployment times and the two different methods for trace-element concentrations was much larger, particularly for manganese (82%), lead (41%), and zinc (33%). Stable isotope values were compared between the RCDM and DDB samples. The DDB sample results all fell within analytical uncertainty and were considered representative of the formation groundwater. The stable isotope values from the RCDM samples indicated that a longer deployment time was necessary to gain equilibrium and to obtain representative groundwater samples. Tritium results from groundwater samples obtained from the RCDM, DM, and DDB indicate that groundwaters obtained with PDSs produced tritium concentrations 2 to 3 times higher (between 1,426 and 3,060±87 pCi/L) than groundwaters obtained with a DDB (479 to 1,219±51 pCi/L). The longer the passive diffusion samplers were deployed, the higher the tritium concentration, suggesting that equilibrium with tritium was not reached within a 27-day deployment. DDB samples showed tritium results declining from the first to the last bailed sample for all three sampling events. This research suggests that tritium results from groundwater samples obtained from PDSs are more reproducible than samples obtained from DDBs. Also, PDSs likely do not accumulate isotopes of water but rather equilibrate with the ambient groundwater. On the other hand, both PDSs and DDBs were able to provide representative groundwater samples for major ions and have the potential to produce representative groundwater samples for stable isotopes of water (δD and δ{sup 18}O). Utilizing the most effective method for sampling groundwater is important for long-term groundwater monitoring. Quantifying the ability of passive diffusion groundwater samplers to obtain representative radioactive chemistry samples will help determine if these methods can be a useful alternative to pumping and purging wells for long-term monitoring. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2026

SPRUCE: Peat Core Sample Collection Metadata, Marcell Experimental Forest, Minnesota, August 2024

This data set contains metadata associated with peat core samples collected from the Spruce and Peatland Responses Under Changing Environments (SPRUCE) experiment in August 2024. This sample metadata contains no analytical results and is a reference for analytical datasets. To ensure accessibility and discoverability, each sample was assigned an International Generic Sample Number (IGSN), a persistent identifier, using System for Earth and Extraterrestrial Sample Registration (SESAR). These samples were used for downstream analysis by multiple teams of researchers the results of which will be reported separately. This dataset contains one data file in comma separate (.csv) format. Additional metadata are provided: one data dictionary and a file-level metadata file in comma separate (.csv) format and a user guide in PDF (*.pdf) format. An aliquot of most samples is stored at Oak Ridge National Laboratory and may be available for further analysis. Access this collection event on SESAR https://doi.org/10.58052/IEJ9B00VQ. To inquire about obtaining archived samples for analysis, reach out using the Contact Sample Owner form located on the bottom of the landing page in SESAR. Note: Only dried and ground material from C Cores are available for new analysis.

Birkebak, Joshua [ORNL] (ORCID:0009000955611494)↗

DOE OSTI2024

Apollo Next Generation Sample Analysis (ANGSA): an Apollo Participating Scientist Program to Prepare the Lunar Sample Community for Artemis

As a first step in preparing for the return of samples from the Moon by the Artemis Program, NASA initiated the Apollo Next Generation Sample Analysis Program (ANGSA). ANGSA was designed to function as a low-cost sample return mission and involved the curation and analysis of samples previously returned by the Apollo 17 mission that remained unopened or stored under unique conditions for 50 years. These samples include the lower portion of a double drive tube previously sealed on the lunar surface, the upper portion of that drive tube that had remained unopened, and a variety of Apollo 17 samples that had remained stored at -27 °C for approximately 50 years. ANGSA constitutes the first preliminary examination phase of a lunar “sample return mission” in over 50 years. It also mimics that same phase of an Artemis surface exploration mission, its design included placing samples within the context of local and regional geology through new orbital observations collected since Apollo and additional new “boots-on-the-ground” observations, data synthesis, and interpretations provided by Apollo 17 astronaut Harrison Schmitt. ANGSA used new curation techniques to prepare, document, and allocate these new lunar samples, developed new tools to open and extract gases from their containers, and applied new analytical instrumentation previously unavailable during the Apollo Program to reveal new information about these samples. Most of the 90 scientists, engineers, and curators involved in this mission were not alive during the Apollo Program, and it had been 30 years since the last Apollo core sample was processed in the Apollo curation facility at NASA JSC. There are many firsts associated with ANGSA that have direct relevance to Artemis. ANGSA is the first to open a core sample previously sealed on the surface of the Moon, the first to extract and analyze lunar gases collected in situ, the first to examine a core that penetrated a lunar landslide deposit, and the first to process pristine Apollo samples in a glovebox at -20 °C. All the ANGSA activities have helped to prepare the Artemis generation for what is to come. The timing of this program, the composition of the team, and the preservation of unopened Apollo samples facilitated this generational handoff from Apollo to Artemis that sets up Artemis and the lunar sample science community for additional successes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Data Trend Shifts Induced by Method of Concentration for Trace Metals in Seawater: Automated Online Preconcentration vs Borohydride Reductive Coprecipitation of Nearshore Seawater Samples for Analysis of Ni, Cu, Zn, Cd, and Pb via ICP-MS

This research compares performance, reproducibility, and detection limits of ambient seawater analysis for trace metals using both borohydride reductive co-precipitation and an automated chelation column (seaFAST™ 2) co-preconcentration for matrix interferent elimination on total and dissolved grab samples in nearshore to marine waters, over a broad concentration range, prior to ICP-MS injection. A move to an online preconcentration method both minimizes sample preparation, and eliminates correction errors when accounting for trace impurities in precipitated samples, induced via reagents. The reproducability of the online preconcentration method described, coupled with low blanks and method detection limits (MDLs), demonstrates an effective move to an automated procedure using ethylenediaminetriacetic and iminodiacetate acid chelation exchange resin and multi-analyte determination via ICP-MS for total and dissolved Ni, Cu, Zn, Cd, and Pb in marine water samples. Average CASS-5 recoveries using the online preconcentration method (n=9) were 109±7%, 104±5%, 103±7%, 101±3%, and 86±8% respectively. The MDLs obtained from the automated method for Ni, Cu, Zn, Cd and Pb were 3.3, 1.8, 13.5, 4, and 10 times lower, respectively, than for the Borohydride method. There were statistically significant differences between the methods for CASS-5 recoveries of Ni, Cu, Zn (p < 0.0001), and Pb (p = 0.0024). Comparison of methods gave high concordance (rC = 0.90) between methods for total and dissolved Ni, Cu, Zn, and Pb, and total Cd.

seaFAST, borohydride, seawater, Ethylenediaminetet↗

DOE OSTI2019

Size Selectivity of Sampling Gears Used to Sample Kokanee

Abstract Kokanee Oncorhynchus nerka provide valued recreational fisheries and also serve as a prey resource for economically, socially, and ecologically important fishes. As such, management of kokanee is a major focus of natural resource agencies. Kokanee are typically monitored using midwater trawls, but the interpretation of data collected using midwater trawls is difficult due to the unknown size selectivity of the gear. We sought to assess the length selectivity of midwater trawls by comparing estimates obtained from midwater trawls with estimates obtained from gill nets adjusted for size selectivity. Experimental curtain gill nets and midwater trawls were used in conjunction to sample kokanee in seven lentic systems in Idaho. The size selectivity of gill nets was estimated by accounting for the probability of encounter and the probability of retention. Estimates of size selectivity were then used to adjust the length distribution of fish sampled in gill nets. The adjusted length distribution of fish sampled in gill nets was compared with estimates obtained from midwater trawls to identify potential size selectivity of midwater trawls. A pattern of size selectivity was apparent for both sampling techniques. The average length of kokanee sampled with midwater trawls was 111 mm; whereas, kokanee sampled with gill nets had a mean length of 235 mm. Our results suggest experimental gill nets are useful for common sampling of kokanee (e.g., trend monitoring) because the gear is less size selective than midwater trawls and is adjustable for size selectivity. However, midwater trawls are likely the best gear for addressing questions associated with early life history. Overall, our results provide a better understanding of gill-net and midwater trawl selectivity and ultimately improve the ability to sample and manage the species.

Klein, Zachary B.↗

DOE OSTI2021

Searching For Transiting Planets Around Halo Stars. I. Sample Selection and Validation

By measuring the elemental abundances of a star, we can gain insight into the composition of its initial gas cloud—the formation site of the star and its planets. Planet formation requires metals, the availability of which is determined by the elemental abundance. In the case where metals are extremely deficient, planet formation can be stifled. To investigate such a scenario requires a large sample of metal-poor stars and a search for planets therein. This paper focuses on the selection and validation of a halo star sample. We select ~17,000 metal-poor halo stars based on their Galactic kinematics, and confirm their low metallicities ([Fe/H] < -0.5), using spectroscopy from the literature. Furthermore, we perform high-resolution spectroscopic observations using LBT/PEPSI and conduct detailed metallicity ([Fe/H]) analyses on a sample of 13 previously-known halo stars that also have hot kinematics. We can use the halo star sample presented here to measure the frequency of planets and to test planet formation in extremely metal-poor environments. The result of the planet search and its implications will be presented and discussed in a companion paper by Boley et al.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

13 C-Isotope-Assisted Assessment of Metabolic Quenching During Sample Collection from Suspension Cell Cultures

Metabolomics and fluxomics are core approaches to directly profile and interrogate cellular metabolism in response to various genetic or environmental perturbations. In order to accurately measure the abundance and isotope enrichment of intracellular metabolites, cell culture samples must be rapidly harvested and cold-quenched to preserve the in vivo metabolic state of the cells at the time of sample collection. When dealing with suspension cultures, this process is complicated by the need to separate the liquid culture media from cellular biomass prior to metabolite extraction. Here, we examine the efficacy of several commonly used metabolic quenching methods, using the model cyanobacterium Synechocystis sp. PCC 6803 as an example. Multiple 13 C-labeled compounds, including 13 C-bicarbonate, 13 C-glucose and 13 C-glutamine, were used as tracers during the sample collection and cold-quenching process to assess the extent of metabolic turnover after cells were harvested from culture flasks. We show that the combination of rapid filtration followed by 100% cold (–80°C) methanol quenching exhibits the highest quenching efficiency, while mixing cell samples with a partially frozen 30% methanol slurry (–24°C) followed by centrifugation is slightly less effective at quenching metabolism but enables less laborious sample processing. By contrast, rapidly mixing the cells with a saline ice slurry (~0°C) is less effective as indicated by high isotope-labeling rates after sample harvest, while mixing the cells with 60% cold methanol (–65°C) prior to centrifugation causes significant metabolite loss. Furthermore, this study demonstrates a rigorous, quantitative, and broadly applicable method for assessing the metabolic quenching efficacy of protocols used for sample collection in metabolomics and fluxomics studies.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Characterization of Tank 11H samples from tank closure cesium removal (TCCR) Batch 3 - intermediate and final samples

Savannah River Remediation (SRR) is currently operating the Tank Closure Cesium Removal (TCCR) process to remove 137 Cs from tank waste supernate using an ion exchange process. The TCCR unit processes dissolved salt from Tank 10H through a series of ion exchange columns containing crystalline silicotitanate (CST) and the effluent is then discharged to Tank 11H. Four interim samples pulled from Tank 11H during and just after the completion of processing of Batch 3 through the TCCR process have been analyzed for 137 Cs activity and density. The 137 Cs activity was found to decrease with each subsequent sample, which is consistent with the addition of decontaminated solution to Tank 11H. When compared to the expected composition from mixing the Tank 10H Batch 3 feed with the material already present in Tank 11H, the bulk chemical composition was as expected. A corrosion control sample collected from Tank 11H in June 2020 showed changes in the chemical composition and 137 Cs activity when compared to the composition measured at the end of Batch 2 processing. As there were no additions made to the tank during this period, these changes were attributed to leaching of the solids present in Tank 11H. Revision 1 of this report contains additional analyses of the fourth interim sample including inductively coupled plasma – mass spectrometry (ICP-MS) results and activities of other radionuclides. These results are consistent with the previously reported results, showing leaching from the Tank 11H heel. Notably, the 90 Sr activity was about 2.7x higher than calculated from a mixture of the original Tank 11H supernate and the Tank 10H supernate as treated by TCCR, suggesting additional leaching of Sr from the Tank 11H heel solids. In addition, Revision 1 includes analysis results for the Batch 3 Post-Production surface and variable depth samples collected in October of 2020. The Post-Production surface sample was similar in composition to the fourth interim surface sample, except for the increased Cs-137 and oxalate concentrations that were presumably associated with leaching of the Tank 11H heel solids.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2025

Development and Demonstration of a Prototype Molten Salt Sampling System

Molten salt reactors (MSRs) offer potential operability and safety advantages when compared to commercial light water reactors (LWRs). However, operating experience with MSRs is sparse in comparison to what exists for LWRs. Further, the chemical and isotopic composition of the fuel and/or coolant salt is dynamic and difficult to characterize continuously, posing potential safety, operability, and safeguards unknowns that need to be addressed. A molten salt sampling system (MSSS) is regarded as a necessary subsystem within first generation MSRs used to obtain samples of salt for chemical and isotopic analysis in support of the need to monitor and control salt composition during operation. The MSSS is being developed using the Safety-in-Design (SiD) methodology, which incorporates incremental integration of safety analysis into the design process. The MSSS conceptual design emerging from the application of the early stages of the SiD methodology consists of a sample collection system and its housing, a freeze port, and inert gas control and delivery systems. This article describes the prototypes developed to test the functions of these MSSS subsystems, presents the results of testing in both dry and molten salt environments (including reliability data collection performed in accordance with the principles of SiD and the development of a semiquantitative fault tree model), and summarizes the opportunities for future design and testing enhancements based on the results of prototype testing.

molten salt reactor↗

DOE OSTI2020

The Combination of Rejection Sampling with Biased Probability Density Sampling (with Special Comments on MCNP "Cookie Cutter" Rejection)

Sampling from biased probability densities and rejection sampling are both very common Monte Carlo techniques. As far as I know, the combination of sampling from a biased density and rejection sampling has not been developed. This note develops the theory for sampling from a biased density and then accepting or rejecting that sampling.

97 MATHEMATICS AND COMPUTING↗