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At least 703 records · Page 39

On relaxations of the max k -cut problem formulations

Here, a tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max k-cut problem is a fundamental combinatorial optimization problem with multiple notorious mixed integer optimization formulations. In this paper, we explore four existing mixed integer optimization formulations of the max k-cut problem. Specifically, we show that the continuous relaxation of a binary quadratic optimization formulation of the problem is: (i) stronger than the continuous relaxation of two mixed integer linear optimization formulations and (ii) at least as strong as the continuous relaxation of a mixed integer semidefinite optimization formulation. We also conduct a set of experiments on multiple sets of instances of the max k-cut problem using state-of-the-art solvers that empirically confirm the theoretical results in item (i). Furthermore, these numerical results illustrate the advances in the efficiency of global non-convex quadratic optimization solvers and more general mixed integer nonlinear optimization solvers. As a result, these solvers provide a promising option to solve combinatorial optimization problems. Our codes and data are available on GitHub.

97 MATHEMATICS AND COMPUTING↗

Search for K + decays to a muon and invisible particles

The NA62 experiment at CERN reports searches for K + → μ + N and K + → μ + ν X decays, where N and X are massive invisible particles, using the 2016–2018 data set. The N particle is assumed to be a heavy neutral lepton, and the results are expressed as upper limits of O ( 10 - 8 ) of the neutrino mixing parameter | U μ 4 | 2 for N masses in the range 200–384 MeV/ c 2 and lifetime exceeding 50 ns. The X particle is considered a scalar or vector hidden sector mediator decaying to an invisible final state, and upper limits of the decay branching fraction for X masses in the range 10–370 MeV/ c 2 are reported for the first time, ranging from O ( 10 - 5 ) to O ( 10 - 7 ) . An improved upper limit of 1.0 × 10 - 6 is established at 90% CL on the K + → μ + ν ν ν ¯ branching fraction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Production of Λ and $K^{0}_{S}$ in jets in p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV and pp collisions at $\sqrt{s}$ =7 TeV

The production of Λ baryons and $K^{0}_{S}$ mesons (V 0 particles) was measured in p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV and pp collisions at $\sqrt{s}$ = 7 TeV with ALICE at the LHC. The production of these strange particles is studied separately for particles associated with hard scatterings and the underlying event to shed light on the baryon-to-meson ratio enhancement observed at intermediate transverse momentum (p T ) in high multiplicity pp and p–Pb collisions. Hard scatterings are selected on an event-by-event basis with jets reconstructed with the anti-k T algorithm using charged particles. The production of strange particles associated with jets $p^{ch}_{T,}$ jet > 10 and $p^{ch}_{T,}$ jet > 20 GeV/c in p–Pb collisions, and with jet $p^{ch}_{T,}$ jet > 10 GeV/c in pp collisions is reported as a function of p T . Its dependence on angular distance from the jet axis, R(V 0 , jet), for jets with $p^{ch}_{T,}$ jet > 10 GeV/c in p–Pb collisions is reported as well. The p T -differential production spectra of strange particles associated with jets are found to be harder compared to that in the underlying event and both differ from the inclusive measurements. In events containing a jet, the density of the V 0 particles in the underlying event is found to be larger than the density in the minimum bias events. The Λ/$K^{0}_{S}$ ratio associated with jets in p–Pb collisions is consistent with the ratio in pp collisions and follows the expectation of jets fragmenting in vacuum. On the other hand, this ratio within jets is consistently lower than the one obtained in the underlying event and it does not show the characteristic enhancement of baryons at intermediate p T often referred to as “baryon anomaly” in the inclusive measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Impact of recent ENDF nuclear data update, high initial enrichment and high burnup fuel on critical experiments applicability determination via the integral index c k for burnup credit validation

In 2012, NUREG/CR-7109 reported on the validation of burnup credit calculations involving major and minor actinides and major fission products which was investigated for pressurized and boiling water reactor (PWR and BWR) fuel enrichments up to 5 wt% 235 U and assembly-average burnups up to 60 GWd/MTU. Recently, there has been interest in increasing the maximum enrichment used in PWR fuel as high as 8 wt% 235 U and correspondingly increasing the maximum assembly-average burnups to approximately 75 GWd/MTU. These proposed increases in enrichment and burnup necessitate reinvestigation of the validation basis for k eff calculations for this expanded application space. Additionally, the 2012 study was performed by using the Evaluated Nuclear Data File (ENDF)/B-VII.0 nuclear data with the SCALE 6 covariance library, and the effects of using the newly released ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear data and covariance libraries should be evaluated. In this work, published in NUREG/CR-7309 in 2025, the validation assessment was performed consistently with NUREG/CR-7109: modeling irradiated fuel assemblies in the Generic Burnup Credit (GBC)-32 cask defined in NUREG/CR-6747. The TSUNAMI-3D sequence was used to generate sensitivity data for the application model, and the data were compared with sensitivity data from select benchmark models. The integral parameter c k is the metric of similarity used in this study and is consistent with NUREG/CR-7109, where a c k value in excess of 0.8 indicates sufficient similarity for use in validation. A new set of benchmark experiments with sensitivity data has been assembled for this effort. The number of experiments with available sensitivity data is now 2,104, compared to 474 in NUREG/CR-7109. This increase was facilitated by the efforts of the Nuclear Energy Agency to generate sensitivity data for a majority of the experiments in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook to supplement the data available in the Oak Ridge National Laboratory (ORNL) Verified, Archived Library of Inputs and Data (VALID). The complete set of benchmarks considered here includes experiments for low-enriched uranium (LEU), intermediate enriched uranium (IEU), and a mixture of uranium and plutonium (MIX) from the ICSBEP Handbook and VALID, as well as ORNL models of the Haut Taux de Combustion (HTC) experiments and other potentially relevant models not included in VALID. The updated similarity study shows that none of the extended burnup and higher enrichment combinations considered show a significant decrease in the number of potentially applicable experiments, meaning sufficient critical experiments exist for the validation of BUC criticality safety calculations, with initial enrichments up to 8 wt% 235 U and burnups up to 80 GWd/MTU. Additionally, both the ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear data libraries can be used for validation since the number of critical experiments applicable for validation increases for most cases with the most recent nuclear data compared to the previous one. As in previous BUC validation studies, the French HTC experiments are the most similar in a majority of the application cases studied, especially from representative discharge burnups ranging from 40 to 80 GWd/MTU. In conclusion, these results match the conclusions presented in NUREG/CR-7109 regarding validation of the primary actinides in BUC analyses.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

MXene-Derived Potassium-Preintercalated Bilayered Vanadium Oxide Nanostructures for Cathodes in Nonaqueous K-Ion Batteries

Bilayered vanadium oxides (BVOs) are promising cathode materials for beyond-Li-ion batteries due to their tunable chemistries and high theoretical capacities. However, the large size of beyond-Li + ions limits electrochemical cycling and rate capability of BVO electrodes. Recent reports of MXene-derived BVOs with nanoscale flower-like morphology have shown improved electrochemical stability at high rates up to 5C in nonaqueous lithium-ion batteries. Here, we report how morphological stabilization can lead to improved rate capability in potassium-ion batteries (PIBs) through the synthesis and electrochemical characterization of MXene-derived K-preintercalated BVOs (MD-KVOs), which were derived from two V 2 CT x precursor materials prepared using two different etching protocols. We show that the etching conditions affect the surface chemistry of the MXene, which plays a role in the MXene-to-oxide transformation process. MXene derived from a milder etchant transformed into a nanoflower MD-KVO with two-dimensional (2D) nanosheet petals (KVO-DMAE) while a more aggressive etchant produced a MXene that transformed into a MD-KVO with one-dimensional (1D) nanorod morphology (KVO-CMAE). Electrochemical cycling of the produced MD-KVOs after drying at 200 °C under vacuum (KVO-DMAE-200 and KVO-CMAE-200) in PIBs showed that electrochemical stability of MD-KVO at high rates improved through the morphological stabilization of 2D particles combined with the control of interlayer water and K + ion content. Structure refinement of KVO-DMAE-200 further corroborates the behavior observed during K + ion cycling, connecting structural and compositional characteristics to the improved rate capability. This work demonstrates how proper synthetic methodology can cause downstream effects in the control of structure, chemical composition, and morphology of nanostructured layered oxide materials, which is necessary for development of future materials for beyond-Li-ion battery technologies.

25 ENERGY STORAGE↗

Large magnetic anisotropy of a decorated spin-chain system K 2 Co 3 (MoO 4 ) 3 (OH) 2

The magnetic structure of K 2 Co 3 (MoO 4 ) 3 (OH) 2 is studied in detail. The material has a half-sawtooth one-dimensional (1-D) structure containing two unique Co 2+ ions, one in the chain backbone and one on the apex of the sawtooth creating a series of isosceles triangles along the b-axis. These triangles can be a source of magnetic frustration. The ability to grow large single crystals enables detailed magnetic measurements with the crystals oriented in a magnetic field along the respective axes. It has a Curie–Weiss temperature θ CW of 5.3(2) K with an effective magnetic moment of 4.8(3)μ B /Co. The material is highly anisotropic with a sharp antiferromagnetic ordering transition at 7 K with a metamagnetic transition at 2 kOe. Neutron diffraction was used to determine the magnetic structure and revealed a magnetic structure with canted spins along the backbone of the chain while spins along the sawtooth caps maintained a colinear orientation, arranging antiferromagnetically relative to the backbone spins. In conclusion, the parallel chains arrange antiferromagnetically relative to each other along the c-axis and ferromagnetically along the a-axis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Translational diffusion in supercooled water at and near the glass transition temperature—136 K

The properties of amorphous solid water at and near the calorimetric glass transition temperature, T g , of 136 K have been debated for years. One hypothesis is that water turns into a “true” liquid at T g (i.e., it becomes ergodic) and exhibits all the characteristics of an ergodic liquid, including translational diffusion. A competing hypothesis is that only rotational motion becomes active at T g , while the “real” glass transition in water is at a considerably higher temperature. To address this dispute, we have investigated the diffusive mixing in nanoscale water films, with thicknesses up to ∼100 nm, using infrared (IR) spectroscopy. The experiments used films that were composed of at least 90% H 2 O with D 2 O making up the balance and were conducted under conditions where H/D exchange was essentially eliminated. Because the IR spectra of multilayer D 2 O films (e.g., thicknesses of ∼3–6 nm) embedded within thick H 2 O films are distinct from the spectrum of isolated D 2 O molecules within H 2 O, the diffusive mixing of (initially) isotopically layered water films could be followed as a function of annealing time and temperature. The results show that water films with total thicknesses ranging from ∼20 to 100 nm diffusively mixed prior to crystallization for temperatures between 120 and 144 K. The translational diffusion had an Arrhenius temperature dependence with an activation energy of 40.8 ± 3.5 kJ/mol, which indicates that water at and near T g is a strong liquid. The measured diffusion coefficient at 136 K is 6.25 ± 1.4 × 10 −21 m 2 /s.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Charge disproportionation in the spin-liquid candidate κ – ( ET ) 2 Cu 2 ( CN ) 3 at 6 K revealed by Cu 63 NQR measurements

The spin-liquid candidate κ – ( ET ) 2 Cu 2 ( CN ) 3 [ET: bis(ethylenedithio)tetrathiafulvalene] does not exhibit magnetic ordering down to a very low temperature, but shows a mysterious anomaly at 6 K. The origin of the so-called 6-K anomaly is still under debate. We carried out nuclear quadrupole resonance (NQR) measurements on the copper sites of the insulating layers, which are sensitive to the charge dynamics unlike conventional spin- 1 / 2 nuclear magnetic resonance (NMR). The main finding of this Rapid Communication is that the observation of a sharp peak behavior in the nuclear spin-lattice relaxation rate T 1 – 1 of Cu 63 NQR at 6 K while T 1 – 1 of both C 13 and H 1 NMR show no clear anomaly. This behavior can be understood as a second-order phase transition related to charge disproportionation in the ET layers.

36 MATERIALS SCIENCE↗

Oxygen K -edge X-ray absorption spectra of liquids with minimization of window contamination

We report oxygen K-edge X-ray absorption spectroscopy is used routinely to study a range of solid materials. However, liquid samples are studied less frequently at the oxygen K-edge due to the combined challenges of high-vacuum conditions and oxygen contamination of window materials. A modular sample holder design with a twist-seal sample containment system that provides a simple method to encapsulate liquid samples under high-vacuum conditions is presented. This work shows that pure silicon nitride windows have lower oxygen contamination than both diamond- and silicon-rich nitride windows, that the levels of oxygen contamination are related to the age of the windows, and provides a protocol for minimizing the background oxygen contamination. Acid-washed 100 nm-thick silicon nitride windows were found to give good quality oxygen K-edge data on dilute liquid samples.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Fungal organic acid uptake of mineral-derived K is dependent on distance from carbon hotspot

Fungal mineral weathering regulates the bioavailability of inorganic nutrients from mineral surfaces to organic matter and increase the bioavailable fraction of nutrients. Such weathering strategies are classified as biomechanical or biochemical. In the case of fungal uptake of mineral nutrients through biochemical weathering, it is widely hypothesized that uptake of inorganic nutrients occurs through organic acid chelation, but such processes have not been directly visualized. This is in part due to challenges in probing the complex and heterogeneous soil environment. Here, using an epoxy-based, mineral-doped soil micromodel platform, which emulates soil mineralogy and porosity, we visualize the molecular mechanisms of mineral weathering. Mass spectrometry imaging revealed differences in the distribution of fungal exudates, citric acid, and tartaric acid on the soil micromodels in presence of minerals. Citric acid was detected closer to the nutrient-rich inoculation point, whereas tartaric acid was highly abundant away from inoculation point. This suggested that the organic acid exuded by the fungi depended on the proximity from the carbon-rich organic substrate at the point of inoculation. Using a combination of X-ray fluorescence and X-ray near edge structure analysis, we identified citric acid- and tartaric acid-bound K within fungal hyphae networks grown in the presence of minerals. Combined, our results provide direct evidence that fungi uptake and transport mineral derived nutrient organic acid chelation. The results of this study provided unprecedented visualization of fungal uptake and transport of K + , while resolving the indirect weathering mechanism of fungal K uptake from mineral interfaces.

59 BASIC BIOLOGICAL SCIENCES↗

Performing k eff Validation of As-Loaded Criticality Safety Calculations Using UNF-ST&DARDS: Applicable Experiment Selection

The general method for performing validation of as loaded criticality safety calculations using UNF ST&DARDS is presented in a paper by Clarity, which includes a description of the UNF-ST&DARDS system. Proof-of-principle analyses were performed in the summer of 2019 for MPC-32 dual purpose canisters (DPCs) containing pressurized water reactor (PWR) fuel assemblies. Summaries of these results are presented in this and a companion paper for this conference. The current paper describes the TSUNAMI-IP calculations performed to select applicable experiments for validation of 11 MPC-32 DPCs. The companion paper discusses the TSUNAMI-3D calculations used to generate sensitivity data to support the experiment selections discussed here. Experiment selection is based on the sensitivity/uncertainty (S/U) methods used to validate criticality safety calculations of as-loaded DPCs containing pressurized water reactor (PWR) spent nuclear fuel (SNF). This process has been demonstrated and is summarized in this paper. The approach is similar to that used in NUREG/CR-7109, which provides an approach for validation of PWR burnup credit (BUC), including major and minor actinides and major fission products. The premise of S/U-based validation is that applicable experiments—those having a similar bias to a given application system—will have similar sensitivities for each isotope and reaction in the two systems. It is assumed that cross sections with larger uncertainties are more likely to contain data errors which contribute to the bias. The integral index c k thus propagates the system sensitivities with the nuclear covariance data to calculate a correlation coefficient representing the similarity of the two systems. In this work, a c k value of 0.8 or higher is interpreted as identifying an experiment with sufficient similarity for use in validation. This paper presents a brief summary of the characteristics of the 11 MPC-32 DPCs used in the proof of-principle analysis for as-loaded criticality safety calculation validation and an overview of the critical experiment suite with which each of these DPC models was compared. A summary and discussion of c k results is also presented, followed by conclusions and a discussion of future work to be performed for validation of UNF ST&DARDS as-loaded criticality safety calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Hot Hydride Superconductivity Above 550 K

The search for room temperature superconductivity has accelerated in the last few years driven by experimentally accessible theoretical predictions that indicated alloying dense hydrogen with other elements could produce conventional superconductivity at high temperatures and pressures. These predictions helped inform the synthesis of simple binary hydrides that culminated in the discovery of the superhydride LaH 10 with a superconducting transition temperature T c of 260 K at 180 GPa. We have now successfully synthesized a metallic La-based superhydride with an initial T c of 294 K. When subjected to subsequent thermal excursions that promoted a chemical reaction to a higher order system, the Tc onset was driven irreversibly to 556 K. X-ray characterization confirmed the formation of a distorted LaH 10 based backbone that suggests the formation of ternary or quaternary compounds with substitution at the La and/or H sites. The results provide evidence for hot superconductivity, aligning with recent predictions for higher order hydrides under pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Phage K gp102 Drives Temperature-Sensitive Antibacterial Activity on USA300 MRSA

There is widespread interest in using obligately lytic bacteriophages (“phages”) to treat human bacterial infections. Among Staphylococcus aureus infections, the USA300 lineage is a frequent cause of invasive disease. We observed that phage K, a model S. aureus myophage, exhibits temperature-sensitive growth on USA300 strains, with the wild-type phage providing poorer growth suppression in broth and forming smaller and fainter plaques at 37 °C vs. 30 °C. We isolated 65 mutants of phage K that had improved plaquing characteristics at 37 °C when compared to the parental phage. In all 65 mutants, this phenotype was attributable to loss-of-function (LoF) mutations in gp102, which encodes a protein of unknown function that has homologs only among the Herelleviridae (SPO1-like myophages infecting gram-positive bacteria). Additional experiments with representative mutants consistently showed that the temperature-sensitive plaque phenotype was specific to USA300 MRSA strains and that Gp102 disruption was correlated with improved suppression of bacterial growth in broth and improved antibacterial activity in a mouse model of upper respiratory tract infection. The same genotype and in vitro phenotypes could be replicated in close relatives of phage K. Gp102 disruption did not have a detectable effect on adsorption but did delay cell culture lysis relative to wild-type under permissive infection conditions, suggesting that gp102 conservation might be maintained by selective pressure for more rapid replication. Expression of gp102 on a plasmid was toxic to both an MSSA and a USA300 MRSA strain. Molecular modeling predicts a protein with two helix-turn-helix domains that displays some similarity to DNA-binding proteins such as transcription factors. While its function remains unclear, gp102 is a conserved gene that is important to the infection process of Kayvirus phages, and it appears that the manner in which USA300 strains defend against them at 37 °C can be overcome by gp102 LoF mutations.

59 BASIC BIOLOGICAL SCIENCES↗

A Catalog of Distance Determinations for the LAMOST DR8 K Giants in the Galactic Halo

We present a catalog of distances for 19,544 K giants drawn from Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) DR8. Most of them are located in the halo of the Milky Way up to ~120 kpc. There are 15% K giants without Sloan Digital Sky Survey (SDSS) photometry, for which we supplements with Pan-STARRS1 (PS1) photometry calibrated to SDSS photometric system. The possible contamination of the red clumps/horizontal branch are removed according to metallicities and colors before the distance determination. Combining the LAMOST spectroscopic metallicities with the SDSS/PS1 photometry, we estimate the absolute magnitudes in the SDSS r band, the distance moduli, and the corresponding uncertainties through an Bayesian approach devised by Xue et al. for the Sloan Extension for Galactic understanding and exploration halo K giants. The typical distance precision is about 11%. The stars in the catalog lie in a region of 4–126 kpc from the Galactic center, of which with 6320 stars beyond 20 kpc and 273 stars beyond 50 kpc, forming the largest spectroscopic sample of distant tracers in the Milky Way halo so far.

79 ASTRONOMY AND ASTROPHYSICS↗

In vitro Ca-45/++/ uptake and exchange by otoconial complexes in high and low K/+/Na/+/ fluids

Recently, data have been accumulating to indicate that saccular and utricular otoconial complexes of the gravity receptor organs are dynamic and interact constantly with their environment. This study investigates the possibility that the ionic composition of the surrounding fluid influences calcium ion binding and release, and explores the importance of the K(+)/Na(+) ratio. Two in-vitro methods were developed, the first of which employed artificial endolymph and perilymph while ionically balanced fluids in which only the K(+)/Na(+) was altered were used in the second. The ability of rat complexes to take up Ca-45(++) during incubation with these fluids was assessed using liquid scintillation spectrometry. In vitro uptake of Ca-45(++) was greater in fluids with a high K(+)/Na(+) ratio than in fluids in which the ratio was low. The ability of the complexes to take up Ca-45(++) appeared to decline with age.

Ross, M. D.↗

Geochemical comparison of K-T boundaries from the Northern and Southern Hemispheres

Closely spaced (cm-scale) traverses through the K-T boundary at Stevns Klint (Denmark), Woodside Creek (New Zealand) and a new Southern Hemisphere site at Richards Bay (South Africa) were subjected to trace element and isotopic (C, O, Sr) investigation. Intercomparison between these data-sets, and correlation with the broad K-T database available in the literature, indicate that the chemistry of the boundary clays is not globally constant. Variations are more common than similarities, both of absolute concentrations, and interelement ratios. For example, the chondrite normalized platinum-group elements (PGE) patterns of Stevns Klint are not like those of Woodside Creek, with the Pt/Os ratios showing the biggest variation. These differences in PGE patterns are difficult to explain by secondary alteration of a layer that was originally chemically homogeneous, especially for elements of such dubious crustal mobility as Os and Ir. The data also show that enhanced PGE concentrations, with similar trends to those of the boundary layers, occur in the Cretaceous sediments below the actual boundary at Stevns Klint and all three the New Zealand localities. This confirms the observations of others that the geochemistry of the boundary layers apparently does not record a unique component. It is suggested that terrestrial processes, eg. an extended period of Late Cretaceous volcanism can offer a satisfactory explanation for the features of the K-T geochemical anomaly. Such models would probably be more consistent with the observed stepwise, or gradual, palaeontological changes across this boundary, than the instant catastrophe predicated by the impact theory.

Tredous, M.↗

K-distribution and polarimetric terrain radar clutter

A multivariate K-distribution is proposed to model the statistics of fully polarimetric radar data from earth terrain with polarizations HH, HV, VH, and VV. In this approach, correlated polarizations of radar signals, as characterized by a covariance matrix, are treated as the sum of N n-dimensional random vectors; N obeys the negative binomial distribution with a parameter alpha and mean N-bar. Subsequently, an n-dimensional K-distribution, with either zero or nonzero mean, is developed in the limit of infinite N-bar or illuminated area. The probability density function (PDF) of the K-distributed vector normalized by its Euclidean norm is independent of the parameter alpha and is the same as that derived from a zero-mean Gaussian-distributed random vector.

Yueh, S. H.↗

Ca II H and K measurements made at Mount Wilson Observatory, 1966-1983

Summaries are presented of the photoelectric measurements of stellar Ca II H and K line intensity made at Mount Wilson Observatory during the years 1966-1983. These results are derived from 65,263 individual observations of 1296 stars. For each star, for each observing season, the maximum, minimum, mean, and variation of the instrumental H and K index 'S' are given, as well as a measurement of the accuracy of observation. A total of 3110 seasonal summaries are reported. Factors which affect the ability to detect stellar activity variations and accurately measure their amplitudes, such as the accuracy of the H and K measurements and scattered light contamination, are discussed. Relations are given which facilitate intercomparison of 'S' values with residual intensities derived from ordinary spectrophotometry, and for converting measurements to absolute fluxes.

Duncan, Douglas K.↗