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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Leading order corrections to the quantum extremal surface prescription

We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Measurement of inclusive and leading subjet fragmentation in pp and Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

This article presents new measurements of the fragmentation properties of jets in both proton–proton (pp) and heavy-ion collisions with the ALICE experiment at the Large Hadron Collider (LHC). We report distributions of the fraction $z_r$ of transverse momentum carried by subjets of radius $r$ within jets of radius $R$. Charged-particle jets are reconstructed at midrapidity using the anti-$k_T$ algorithm with jet radius $R$ = 0.4, and subjets are reconstructed by reclustering the jet constituents using the anti-$k_T$ algorithm with radii $r$ = 0.1 and $r$ = 0.2. In proton–proton collisions, we measure both the inclusive and leading subjet distributions. We compare these measurements to perturbative calculations at next-to-leading logarithmic accuracy, which suggest a large impact of threshold resummation and hadronization effects on the $z_r$ distribution. In heavy-ion collisions, we measure the leading subjet distributions, which allow access to a region of harder jet frag- mentation than has been probed by previous measurements of jet quenching via hadron fragmentation distributions. The $z_r$ distributions enable extraction of the parton-to-subjet fragmentation function and allow for tests of the universality of jet fragmentation functions in the quark–gluon plasma (QGP). We find no significant modification of $z_r$ distributions in Pb–Pb compared to pp collisions. However, the distributions are also consistent with a hardening trend for $z_r$ < 0.95, as predicted by several jet quenching models. As $z_r$ → 1 our results indicate that any such hardening effects cease, exposing qualitatively new possibilities to disentangle competing jet quenching mechanisms. By comparing our results to theoretical calculations based on an independent extraction of the parton-to-jet fragmentation function, we find consistency with the universality of jet fragmentation and no indication of factorization breaking in the QGP.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Coherent gluon radiation: beyond leading-log accuracy

Abstract Results are presented for the medium-induced, soft coherent radiation spectrum for all 2 → 2 partonic channels in QCD, at leading-order inα s but beyond leading logarithmic accuracy. The general formula is valid in the full kinematic range of the underlying process, and reduces to previous results in special cases. The soft gluon radiation spectrum is expressed in terms of thecolor density matrixspecific to each channel, quantifying the entanglement between the color components of the 2 → 2 production amplitude. Beyond the leading logarithm, the spectrum depends explicitly on the off-diagonal elements of this matrix, owing to the soft gluon’s ability to probe the internal color structure of the parton pair.

Physics↗
DOE OSTI2026

Next-to-next-to-leading power corrections to unpolarized Semi-Inclusive Deep Inelastic Scattering

Semi-Inclusive Deep Inelastic Scattering (SIDIS) is a key tool for exploring the three-dimensional structure of the nucleon through Transverse Momentum Dependent parton distributions and fragmentation functions. While leading-power contributions to the SIDIS cross-section are well established, next-to-leading power (NLP) corrections of order 1/Q and next-to-next-to-leading power (NNLP) corrections of order 1/Q 2 to the hadronic tensor have only recently begun to be systematically investigated. These corrections are essential for reliable phenomenology and interpretation of modern high-precision data. In recent papers by one of the authors, NNLP corrections to the Drell-Yan process were derived using the rapidity factorization formalism. In the present work, we extend this approach to SIDIS and obtain analytic expressions for the unpolarized structure functions. We derive NNLP corrections that include convolutions of unpolarized distributions, f 1 , with unpolarized fragmentation functions, D 1 , and Boer-Mulders functions, ${h}_1^{\perp }$, with Collins fragmentation functions, ${H}_1^{\perp }$. We compare our results with previous formulations, provide numerical studies, confront our predictions with HERMES and COMPASS measurements, and present predictions for future experiments at Jefferson Lab and the Electron-Ion Collider.

deep inelastic scattering↗
DOE OSTI2022

Factorization for azimuthal asymmetries in SIDIS at next-to-leading power

Differential measurements of the semi-inclusive deep inelastic scattering (SIDIS) process with polarized beams provide important information on the three-dimensional structure of hadrons. Among the various observables are azimuthal asymmetries that start at subleading power, and which give access to novel transverse momentum dependent distributions (TMDs). Theoretical predictions for these distributions are currently based on the parton model rather than a rigorous factorization based analysis. Working under the assumption that leading power Glauber interactions do not spoil factorization at this order, we use the Soft Collinear Effective Theory to derive a complete factorization formula for power suppressed hard scattering effects in SIDIS. This yields generalized definitions of the TMDs that depend on two longitudinal momentum fractions (one of them only relevant beyond tree level), and a complete proof that only the same leading power soft function appears and can be absorbed into the TMD distributions at this order. We also show that perturbative corrections can be accounted for with only one new hard coefficient. Factorization formulae are given for all spin dependent structure functions which start at next-to-leading power. Prospects for improved subleading power predictions that include resummation are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

The pp → W(→ lν) + γ process at next-to-next-to-leading order

We present details of the calculation of the pp → W(→ lν)γ process at next-to-next-to-leading order in QCD, calculated using the jettiness slicing method. The calculation is based entirely on analytic amplitudes. Because of the radiation zero, the NLO QCD contribution from the gq channel is as important as the contribution from the Born $ q\overline{q} $ process, disrupting the normal counting of leading and sub-leading contributions. We also assess the importance of electroweak (EW) corrections, including the EW corrections to both the six-parton channel 0 →$ \overline{u} d\nu {e}^{+}\gamma g $ and the five-parton channel 0 →$ \overline{u} d\nu {e}^{+}\gamma $. Previous experimental results have been shown to agree with theoretical predictions, taking into account the large experimental errors. With the advent of run II data from the LHC, the statistical errors on the data will decrease, and will be competitive with the error on theoretical predictions for the first time. We present numerical results for $ \sqrt{s} $ = 7 and 13 TeV. Analytic results for the one-loop six-parton QCD amplitude and the tree-level seven-parton QCD amplitude are presented in appendices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate

In this work, we compute the next-to-leading order impact factor for inclusive dijet production in deeply inelastic electron-nucleus scattering at small x Bj . Our computation, performed in the framework of the Color Glass Condensate effective field theory, includes all real and virtual contributions in the gluon shock wave background of all-twist lightlike Wilson line correlators. We demonstrate explicitly that the rapidity evolution of these correlators, to leading logarithmic accuracy, is described by the JIMWLK Hamiltonian. When combined with the next-to-leading order JIMWLK Hamiltonian, our results for the impact factor improve the accuracy of the inclusive dijet cross-section to \( \mathcal{O} \) ( \( {\alpha}_s^2 \) ln( x f /x Bj )), where x f is a rapidity factorization scale. These results are an essential ingredient in assessing the discovery potential of inclusive dijets to uncover the physics of gluon saturation at the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

T-odd leading-twist quark TMDs at small x

We study the small-x asymptotics of the flavor non-singlet T-odd leading-twist quark transverse momentum dependent parton distributions (TMDs), the Sivers and Boer-Mulders functions. While the leading eikonal small-x asymptotics of the quark Sivers function is given by the spin-dependent odderon [1, 2], we are interested in revisiting the sub-eikonal correction considered by us earlier in [3]. We first simplify the expressions for both TMDs at small Bjorken x and then construct small-x evolution equations for the resulting operators in the large-N c limit, with N c the number of quark colors. For both TMDs, the evolution equations resum all powers of the double-logarithmic parameter α s ln 2 (1/x), where α s is the strong coupling constant, which is assumed to be small. Solving these evolution equations numerically (for the Sivers function) and analytically (for the Boer-Mulders function) we arrive at the following leading small-x asymptotics of these TMDs at large N c :$$ {\displaystyle \begin{array}{l}{f}_{1T}^{\perp NS}\left(x\ll 1,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left(x,{k}_T^2\right){\left(\frac{1}{x}\right)}^{3.4\sqrt{\frac{\alpha_s{N}_c}{4\pi }}}\\ {}{h}_1^{\perp \textrm{NS}}\left(x\ll 1,{k}_T^2\right)=C\left(x,{k}_T^2\right){\left(\frac{1}{x}\right)}^{-1}.\end{array}} $$ The functions C O (x,$ {k}_T^2 $), C 1 (x,$ {k}_T^2 $), and C(x,$ {k}_T^2 $) can be readily obtained in our formalism: they are mildly x-dependent and do not strongly affect the power-of-x asymptotics shown above. The function C O , along with the 1/x factor, arises from the odderon exchange. For the sub-eikonal contribution to the quark Sivers function (the term with C 1 ), our result shown above supersedes the one obtained in [3] due to the new contributions identified recently in [4].

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

All order factorization for virtual Compton scattering at next-to-leading power

We discuss all-order factorization for the virtual Compton process at next-to leading power (NLP) in the Λ QCD /Q and $\sqrt{-t}$/Q expansion (twist-3), both in the double deeply-virtual case and the single-deeply-virtual case. We use the soft-collinear efective theory (SCET) as the main theoretical tool. We conclude that collinear factorization holds in the double-deeply virtual case, where both photons are far of-shell. The agreement is found with the known results for the hard matching coefcients at leading order $α^0_s$, and we can therefore connect the traditional approach with SCET. In the single-deeply-virtual case, commonly called deeply virtual Compton scattering (DVCS), the contribution of non-target collinear regions complicates the factorization. These include momentum modes collinear to the real photon and (ultra)soft interactions between the photon-collinear and target-collinear modes. However, such contributions appear only for the transversely polarized virtual photon at the NLP accuracy and in fact it is the only NLP ~ (Λ QCD /Q) 1 ~ ( $\sqrt{-t}$/Q) 1 contribution in that case. We therefore conclude that the DVCS amplitude for a longitudinally polarized virtual photon, where the leading power ~ (Λ QCD /Q) 0 ~ ($\sqrt{-t}$/Q) 0 contribution vanishes, is free of non-target collinear contributions and the collinear factorization in terms of twist-3 GPDs holds in that case as well.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Effects of lead and lean in multi-axis directed energy deposition

Here, the present study examines the effect of varying laser incidence angles on textural, microstructural, and geometric characteristics of directed energy deposition (DED) processed materials, providing a more comprehensive outlook on participating laser-matter interaction phenomena and ultimately devising strategies to ameliorate print performance. In this study, single-layer, single-/multi-track specimens were processed to examine the effect of non-orthogonal angular configurations on bead morphology, microstructure, phase composition, and textural representation of DED-processed 316L stainless steel materials. It was observed that bead size decreased at increasing lead and lean angles. Asymmetry in the distribution of the bead morphology as a function of lead angle indicates better catchment for acute lead angle configurations over obtuse configurations. No significant differences in phase composition, texture, and microstructure were observed in moderate off-axis configurations. When the penetration depth for the deposits was below 20 μm, columnar structures dominated the microstructure of the deposited material. At deeper penetration depths, columnar and equiaxed structures were observed at the bead-substrate interface and center of the bead, respectively. Compared to powder-blown DED, wire-DED dilution profiles were found to be asymmetric in both orthogonal and non-orthogonal wire DED samples.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Effects of Isothermal Aging on the Thermal Expansion of Several Sn-Based Lead-Free Solder Alloys

In this paper, effects of high-temperature aging on the thermal expansion behavior of several lead-free alloys SAC305, SAC387, Sn-3.5Ag, SnCu, SN100C (SnCu-Ni-Ge) and SnCu-0.01Ge have been explored. The coefficients of thermal expansion (CTEs) of the alloys have been experimentally determined over the temperature range 30-150 °C after isothermal aging at 125 °C for up to 30 days (720 h). The CTE values of SAC305, SAC387 and Sn-3.5Ag increase by 8-16% after 30 days of aging, while the CTE values of SnCu, SnCu-Ge and SN100C solders increase by only 3-6%. The CTE evolution of lead-free solders can be explained by microstructural changes observed during isothermal aging, which causes coarsening of various phases of the solder. As the phases coarsen, dislocation movement proceeds with a consequent increase in the average interparticle distance. The observation of CTE increases during isothermal aging suggests potential reliability problems for lead-free solder joints subjected to long-term aging exposures at high temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Microstructural Evolution and Mechanical Behavior of Lead-Free Silicon Brass Manufactured by Low-Pressure Die Casting

Low-pressure die casting (LPDC) has been widely used to process aluminum and magnesium alloys; however, it has yet to be applied to manufacture brass alloys. This study investigates the microstructural evolution and mechanical behavior of a lead-free CuZnSiAl silicon brass via a variable-controlling approach on the basis of a faucet casting by LPDC. The manufactured silicon brass castings are predominantly composed of bcc β-CuZn(Si, Al) and minor fcc α-Cu(Zn, Si) solid solutions. The silicon brass castings also predominantly exhibit short rod-like or granular α phases, which distinctly differ from the acicular α morphology obtained by conventional gravity casting. The manufactured silicon brass castings which contain finer β grains and short rod-like or granular α phase exhibit superior mechanical properties. Their optimal mechanical properties—elongation of 15.0%, yield strength of 359.8 MPa, and ultimate tensile strength of 598.9 MPa—are far superior to those of the typical lead brass HPb59-1. The results obtained in this study provide insight into the manufacture and design of lead-free silicon brass castings by LDPC.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Disruption of LRRK2 in Zebrafish leads to hyperactivity and weakened antibacterial response

Highlights: • Disruption of LRRK2 in Zebrafish leads to hyperactivity at adult stage. • Neurological and immunological pathways are disrupted in LRRK2 mutant. • Disruption of LRRK2 in Zebrafish leads to a weakened antibacterial response. As a protein with complex domain structure and roles in kinase, GTPase and scaffolding, LRRK2 is believed to be an important orchestration node leading to several cascades of signal transduction rather than one specific pathway. LRRK2 variants were found to be associated with Parkinson's disease, Crohn's disease and leprosy. Here we disrupt LRRK2 in zebrafish and found hyperactivity rather than hypoactivity in adult zebrafish mutants. By RNA-seq we found genes involved in infectious disease and immunological disease were notably affected. Functional studies also revealed a weakened antibacterial response in LRRK2 mutant. This mutant can be further explored for revealing molecular mechanisms and modeling of LRRK2 related diseases.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Lead optimization and efficacy evaluation of quinazoline-based BET family inhibitors for potential treatment of cancer and inflammatory diseases

Extensive optimization of quinazoline-based lead 8 is described. The structure-activity relationship studies indicate the S-configuration is preferred for the phenylmorpholine substitution. Together with incorporation of a (2-hydroxyl-2-methylpropyl)pyrazole moiety at the 2-position leads to analogs with comparable potency and marked improvement in the pharmacokinetic profile over our previously reported lead compounds. Further in vivo efficacy studies in Kasumi-1 xenograft mouse model demonstrates that the selected inhibitors are well tolerated and highly efficacious in the inhibition of tumor growth. Additionally, the representative analog 19 also demonstrated significant improvement of arthritis severity in a collagen-induced arthritis (CIA) mouse model. These results indicate potential use of these quinazoline-based BET inhibitors for treatment of cancer and inflammatory diseases. Finally, a brief discussion of the co-crystallized structure of 19 with BRD4 (BD1) is also highlighted.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Stochastic boundary condition effects on supersonic leading edge blowing

The present manuscript studies the robustness of leading edge blowing for active control of the upstream bow shock and overall aerothermal characteristics of a supersonic airfoil subject to variability in the injection conditions. The injection boundary conditions were considered stochastic and their randomness was propagated to the flow topology and aerothermal quantities of interest by means of non-intrusive Polynomial Chaos Expansions. The evaluations needed to build these expansions were carried out via steady two-dimensional Reynolds-Averaged Navier Stokes simulations. Two different injection port sizes were considered, with the smallest promoting a Coanda effect that gives rise to non-symmetric flow topologies. The uncertain boundary conditions lead to significant variations in the flow topology, particularly at the injection exit and the bow shock position, with variations of up to 75% of the nominal value. Here this study identifies the key operating conditions to ensure the optimal application of leading-edge injection for active control of supersonic airfoils.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Blood lead levels and hypothalamic-pituitary-adrenal function in middle-aged individuals

Highlights: • We assessed cortisol secretions (CS) in adults aged 50–67 years. • We reported changes in CS in relation to blood lead levels. • At low-levels, lead does not impact the global trend of salivary CS. Experimental and epidemiological studies suggested that exposure to lead (Pb) may influence the hypothalamic-pituitary-adrenal (HPA) axis. However, previous studies have yielded mixed results. We evaluated changes in basal salivary cortisol levels and acute cortisol responsivity to psychological stress in relation with blood Pb levels (BPb), in Caucasian individuals 50–67 years of age. Data were collected through the Study of Genetics, Stress and Cognitive Development (2004–2006). Diurnal basal and stress-reactive salivary cortisol levels were collected and BPb levels were determined using inductively coupled plasma mass spectroscopy. A total of 65 participants were included in the current study. General linear mixed models were used to assess the association between BPb level and change in cortisol secretion over time, for diurnal basal pattern and stress-reactive pattern, respectively. The geometric mean BPb was 2.70 μg/dL (± 1.44) and two exposure groups were created based on the median value of 2.48 µg/dL. No difference in geometric mean of salivary cortisol (µg/dL) at awakening was observed between High and Low BPb groups (0.23 (± 0.11) vs 0.20 (± 0.11), p = 0.36). The overall pattern of change in both diurnal basal (from the awakening to bedtime) and reactive salivary cortisol (during the stress induction protocol) did not differ between groups. In these middle-aged and older adults, we concluded that Pb exposure, within the range observed in the current study, was associated with neither diurnal nor stress-reactive cortisol secretion. Further investigation with larger datasets are needed to confirm our observations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Lead exposure in young children over a 5-year period from urban environments using alternative exposure measures with the US EPA IEUBK model – A trial

Highlights: • IEUBK simulations of soil with petri dish dust (PDD), soil with handwipes, sweepings with PDD, sweepings with wipes. • Predicted blood lead levels (PbB) generally give good agreement with observed PbB in spite of differences in intake units for PDD and handwipes. • Analyses with dust loadings converted to concentration give higher predicted PbB. • Simulations on aggregated data for each child give similar results to age-stratified data. • Estimating house dust Pb from measured soil Pb concentrations (in the absence of measured house dust concentrations) results in over-prediction of PbB. The US Environmental Protection Agency (EPA) Integrated Exposure Uptake Biokinetic (IEUBK) model has been widely used to predict blood lead (PbB) levels in children especially around industrial sites. Exposure variables have strongly focussed on the major contribution of lead (Pb) in soil and interior dust to total intake and, in many studies, site-specific data for air, water, diet and measured PbB were not available. We have applied the IEUBK model to a comprehensive data set, including measured PbB, for 108 children monitored over a 5-year period in Sydney, New South Wales, Australia. To use this data set, we have substituted available data (with or without modification) for standard inputs as needed. For example, as an alternative measure for soil Pb concentration (μg/g), we have substituted exterior dust sweepings Pb concentration (μg/g). As alternative measures for interior dust Pb concentration (μg/g) we have used 1) 30-day cumulative petri dish deposition data (PDD) (as µg Pb/m{sup 2}/30days), or 2) hand wipe data (as μg Pb/hand). For comparison, simulations were also undertaken with estimates of dust Pb concentration derived from a prior regression of dust Pb concentration (μg/g) on dust Pb loading (μg/ft{sup 2}) as concentration is the unit specified for the Model. Simulations for each subject using observed data aggregated over the 5-year interval of the study, the most usual application of the IEUBK model, showed using Wilcoxon tests that there was a significant difference between the observed values and the values predicted by the Model containing soil with hand wipes (p < 0.001), and soil and PDD (p = 0.026) but not those for the other two sets of predictors, based on sweepings and PDD or sweepings and wipes. Overall, simulations of the Model using alternative exposure measures of petri dish dust (and possibly hand wipes) instead of vacuum cleaner dust and dust sweepings instead of soil provide predicted PbB which are generally consistent with each other and observed values. The predicted geometric mean PbBs were 2.17 ( ± 1.24) μg/dL for soil with PDD, 1.95 ( ± 1.17) μg/dL for soil with hand wipes, 2.36 ( ± 1.75) μg/dL for sweepings with PDD, and 2.15 ( ± 1.69) for sweepings with hand wipes. These results are in good agreement with the observed geometric mean PbB of 2.46 ( ± 0.99) μg/dL. In contrast to all other IEUBK model studies to our knowledge, we have stratified the data over the age ranges from 1 to 5 years. The median of the predicted values was lower than that for the observed values for every combination of age and set of measures; in some cases, the difference was statistically significant. The differences between observed and predicted PbB tended to be greatest for the soil plus wipes measure and for the oldest age group. Use of ‘default dust’ values calculated from the site-specific soil values, a common application of the IEUBK model, results in predicted PbB about 22% (range 0 to 52%) higher than those from soil with PDD data sets. Geometric mean contributions estimated from the Model to total Pb intake for a child aged 1–2 years was 0.09% for air, 42% for diet, 5.3% for water and 42% for soil and dust. Our results indicate that it is feasible to use alternative measures of soil and dust exposure to provide reliable predictions of PbB in urban environments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

Use of Chemical Inventory Accuracy Measurements as Leading Indicators

Chemical safety and lifecycle management (CSLM) is a process that involves managing chemicals and chemical information from the moment someone begins to order a chemical and lasts through final disposition(1). Central to CSLM is tracking data associated with chemicals which, for the purposes of this paper, is termed the chemical inventory. Examples of data that could be tracked include chemical identity, location, quantity, date procured, container type, and physical state. The reason why so much data is tracked is that the chemical inventory supports many functions. These functions include emergency management, which depends upon the data to more effectively plan for, and respond to, chemical accidents; environmental management that uses inventory information to aid in the generation of various federally-mandated and other regulatory reports; and chemical management that uses the information to increase the efficiency and safety with which chemicals are stored and utilized. All of the benefits of having an inventory are predicated upon having an inventory that is reasonably accurate. Because of the importance of ensuring one's chemical inventory is accurate, many have become concerned about measuring inventory accuracy. But beyond providing a measure of confidence in information gleaned from the inventory, does the inventory accuracy measurement provide any additional function? The answer is 'Yes'. It provides valuable information that can be used as a leading indicator to gauge the health of a chemical management system. In this paper, we will discuss: (1) what properties make leading indicators effective, (2) how chemical inventories can be used as a leading indicator, (3) how chemical inventory accuracy can be measured, what levels of accuracies should realistically be expected in a healthy system, and (4) what a subpar inventory accuracy measurement portends.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗