Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “High angular resolution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 919 records · Page 51

Joint 3D-Wind Retrievals with Stereoscopic Views from MODIS and GOES

Atmospheric motion vectors (AMVs), derived by tracking patterns, represent the winds in a layer characteristic of the pattern. AMV height (or pressure), important for applications in atmospheric research and operational meteorology, is usually assigned using observed IR brightness temperatures with a modeled atmosphere and can be inaccurate. Stereoscopic tracking provides a direct geometric height measurement of the pattern that an AMV represents. We extend our previous work with multi-angle imaging spectroradiometer (MISR) and GOES to moderate resolution imaging spectroradiometer (MODIS) and the GOES-R series advanced baseline imager (ABI). MISR is a unique satellite instrument for stereoscopy with nine angular views along track, but its images have a narrow (380 km) swath and no thermal IR channels. MODIS provides a much wider (2330 km) swath and eight thermal IR channels that pair well with all but two ABI channels, o e ring a rich set of potential applications. Given the similarities between MODIS and VIIRS, our methods should also yield similar performance with VIIRS. Our methods, as enabled by advanced sensors like MODIS and ABI, require high-accuracy geographic registration in both systems but no synchronization of observations. AMVs are retrieved jointly with their heights from the disparities between triplets of ABI scenes and the paired MODIS granule. We validate our retrievals against MISR-GOES retrievals, operational GOES wind products, and by tracking clear-sky terrain. We demonstrate that the 3D-wind algorithm can produce high-quality AMV and height measurements for applications from the planetary boundary layer (PBL) to the upper troposphere, including cold-air outbreaks, wildfire smoke plumes, and hurricanes.

Carr, James L.↗

Infrared spectroscopy of star formation in galaxies

The Brackett alpha and beta lines with 7.2 seconds angular and 350 km/s velocity resolution were observed in 11 infrared-bright galaxies. From these measurements extinctions, Lyman continuum fluxes, and luminosities due to OB stars were derived. The galaxies observed to date are NGC3690, M38, NGC 5195, Arp 220, NGC 520, NGC660, NGC1614, NGC 3079, NGC 6946, NGC 7714, and Maffei 2, all of which were suggested at some time to be starburst ogjects. The contributions of OB stars to the luminosities of these galaxies can be quantified from the measurements and range from insignificant to sufficient to account for the total energy output. The OB stellar luminosities observed are as high as 10 to the 12th solar luminosities in the galaxy NGC 1614. It is noteworthy that star formation can play very different roles in the infrared energy output of galaxies of similar luminosity, as for example Arp 220 and NGC 1614. In addition to probing the star formation process in these galaxies, the Brackett line measurements, when compared to radio and infrared continuum results, have revealed some unexpected and at present imperfectly understood phenomena: in some very luminous sources the radio continuum appears to be suppressed relative to the infrared recombination lines; in many galaxies there is a substantial excess of 10 micron flux over that predicted from simple models of Lyman alpha heating of dust if young stars are the only significant energy source.

Beck, Sara C.↗

Extraction of soil and vegetation parameters from high resolution bi-directional reflectance spectra

High spectral resolution reflectance spectra were collected over a semi-desert grassland at both dry and wet season periods. Spectral reflectance measurements were made from several viewing angles at both low and high solar zenith angles. A mixture model was used to separate and extract green vegetation from dry/dead vegetation and soil. The extracted vegetation signal varied greatly with view and sun angle variations such that off-nadir viewing and illuminating angles resulted in the highest vegetation loadings. These variations were normalized with cosine functions for both sun and view angle. These results offer a methodology for standardizing multi-temporal and multi-angular satellite measurements of vegetation activity.

Huete, A. R.↗

Formation Control for the Maxim Mission.

Over the next twenty years, a wave of change is occurring in the spacebased scientific remote sensing community. While the fundamental limits in the spatial and angular resolution achievable in spacecraft have been reached, based on today's technology, an expansive new technology base has appeared over the past decade in the area of Distributed Space Systems (DSS). A key subset of the DSS technology area is that which covers precision formation flying of space vehicles. Through precision formation flying, the baselines, previously defined by the largest monolithic structure which could fit in the largest launch vehicle fairing, are now virtually unlimited. Several missions including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), and the Stellar Imager will drive the formation flying challenges to achieve unprecedented baselines for high resolution, extended-scene, interferometry in the ultraviolet and X-ray regimes. This paper focuses on establishing the feasibility for the formation control of the MAXIM mission. The Stellar Imager mission requirements are on the same order of those for MAXIM. This paper specifically addresses: (1) high-level science requirements for these missions and how they evolve into engineering requirements; (2) the formation control architecture devised for such missions; (3) the design of the formation control laws to maintain very high precision relative positions; and (4) the levels of fuel usage required in the duration of these missions. Specific preliminary results are presented for two spacecraft within the MAXIM mission.

Luquette, Richard J.↗

Formation Control for the MAXIM Mission

Over the next twenty years, a wave of change is occurring in the space-based scientific remote sensing community. While the fundamental limits in the spatial and angular resolution achievable in spacecraft have been reached, based on today s technology, an expansive new technology base has appeared over the past decade in the area of Distributed Space Systems (DSS). A key subset of the DSS technology area is that which covers precision formation flying of space vehicles. Through precision formation flying, the baselines, previously defined by the largest monolithic structure which could fit in the largest launch vehicle fairing, are now virtually unlimited. Several missions including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), and the Stellar Imager will drive the formation flying challenges to achieve unprecedented baselines for high resolution, extended-scene, interferometry in the ultraviolet and X-ray regimes. This paper focuses on establishing the feasibility for the formation control of the MAXIM mission. MAXIM formation flying requirements are on the order of microns, while Stellar Imager mission requirements are on the order of nanometers. This paper specifically addresses: (1) high-level science requirements for these missions and how they evolve into engineering requirements; and (2) the development of linearized equations of relative motion for a formation operating in an n-body gravitational field. Linearized equations of motion provide the ground work for linear formation control designs.

Luquette, Richard J.↗

Airborne Trajectory Management for Urban Air Mobility

Urban Air Mobility (UAM) has captured the imagination of the public and the aviation industry for someday soon moving people and goods through and around metropolitan areas using Unmanned Aircraft Systems (UAS) that are electrically powered, environmentally friendly, and autonomously operated. Significant investment and rapid development of vehicles for this activity is taking place, with package delivery services already beginning in some areas. However, the ability to manage thousands of these vehicles safely in a congested urban area presents a challenge unprecedented in air traffic management. Initial studies of this problem led by NASA under the UAS Traffic Management (UTM) initiative have primarily focused on geo-fencing and centralized reservation of airspace for individual flights. This paper proposes an extension of UTM using a de-centralized approach employing airborne surveillance, self-separation, and a minimized “design separation” approach to permit the optimization and safety of each flight in very high traffic densities and close proximities. The concept employs Airborne Trajectory Management (ABTM) principles and a novel new concept for variable separation criteria to manage the angular velocity of a passing vehicle, thus eliminating the "startle factor" and perceived hazard of very close operations. ABTM also accomplishes most of the services required for safe planning and execution of normal flights and recovery from abnormal or emergency operations while accommodating conventional piloted flights using the current air traffic control paradigm. The environment for UAM operations is described along with the proposed means for autonomous, tactical separation of the vehicles. Sample geometries of traffic conflicts and resolutions are shown and the airspace definitions, rules for flight within them, and additions and exemptions to the rules for these flights are listed and explained.

Cotton, William↗

Spatiotemporal sampling of near-petahertz vortex fields

Measuring the field of visible light with high spatial resolution has been challenging, as many established methods only detect a focus-averaged signal. Here, we introduce a near-field method for optical field sampling that overcomes that limitation by employing the localization of the enhanced near-field of a nanometric needle tip. A probe field perturbs the photoemission from the tip, which is induced by a pump pulse, generating a field-dependent current modulation that can easily be captured with our electronic detection scheme. The approach provides reliable characterization of near-petahertz fields. We show that not only the spiral wavefront of visible femtosecond light pulses carrying orbital angular momentum (OAM) can be resolved but also the field evolution with time in the focal plane. Additionally, our method is polarization sensitive, which makes it applicable to vectorial field reconstruction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

OGLE-2016-BLG-0156: Microlensing Event with Pronounced Microlens-parallax Effects Yielding a Precise Lens Mass Measurement

We analyze the gravitational binary-lensing event OGLE-2016-BLG-0156, for which the lensing light curve displays pronounced deviations induced by microlens-parallax effects. The light curve exhibits three distinctive widely separated peaks and we find that the multiple-peak feature provides a very tight constraint on the microlens-parallax effect, enabling us to precisely measure the microlens parallax . All the peaks are densely and continuously covered from high-cadence survey observations using globally located telescopes and the analysis of the peaks leads to the precise measurement of the angular Einstein radius . From the combination of the measured and , we determine the physical parameters of the lens. It is found that the lens is a binary composed of two M dwarfs with masses M(1) = 0.18 ± 0.01 M(⊙) and M(2) = 0.16 ± 0.01 M(⊙) located at a distance D(L) = 1.35 ± 0.09 kpc. According to the estimated lens mass and distance, the flux from the lens comprises an important fraction, ~25%, of the blended flux. The bright nature of the lens combined with the high relative lens-source motion, μ = 6.94 ± 0.50 mas/yr, suggests that the lens can be directly observed from future high-resolution follow-up observations.

Youn Kil Jung↗

Lynx x-ray microcalorimeter

Lynx is an x-ray telescope, one of four large satellite mission concepts currently being studied by NASA to be a flagship mission. One of Lynx’s three instruments is an imaging spectrometer called the Lynx x-ray microcalorimeter (LXM), an x-ray microcalorimeter behind an x-ray optic with an angular resolution of 0.5 arc sec and ∼2 sq. m of area at 1 keV. The LXM will provide unparalleled diagnostics of distant extended structures and, in particular, will allow the detailed study of the role of cosmic feedback in the evolution of the Universe. We discuss the baseline design of LXM and some parallel approaches for some of the key technologies. The baseline sensor technology uses transition-edge sensors, but we also consider an alternative approach using metallic magnetic calorimeters. We discuss the requirements for the instrument, the pixel layout, and the baseline readout design, which uses microwave superconducting quantum interference devices and high-electron mobility transistor amplifiers and the cryogenic cooling requirements and strategy for meeting these requirements. For each of these technologies, we discuss the current technology readiness level and our strategy for advancing them to be ready for flight. We also describe the current system design, including the block diagram, and our estimate for the mass, power, and data rate of the instrument.

Simon R. Bandler↗

Sensor technology for advanced space missions

The capability and applications of two sensors, Spatial, High-Accuracy, Position-Encoding Sensor (SHAPES) and Fiber Optics Rotation Sensor (FORS), for advanced missions are discussed. The multiple target, 3-D position sensing capability of SHAPES meets a critical technology need for many developing applications. A major milestone of the SHAPES task was completed on schedule on May 30, 1986, by demonstrating simultaneous ranging to eight moving targets at a rate of 10 measurements per second. The range resolution to static target was shown to be 25 microns. SHAPES scheduled technology readiness will support the sensor needs of a number of early users. The next phase in the development of SHAPES is to incorporate an angular measurement CCD to provide the full 3-dimensional sensing. A flight unit design and fabrication can be complete by FY89. FORS, with its significant improvement over present technology in lifetime, performance, weight, power, and recurrent cost, will be an important technology for future space systems. Technology readiness will be demonstrated with a FORS brassboard with fully integrated IO chips by FY88. The unique capability of miniature remote sensing heads, connected to a central system, will open up new areas in control and stability of large space structures. This application requires additional study.

Nerheim, N. M.↗

A New Method to Use Chandra Data to Resolve the X-Ray Halos Around Point Sources and Its Application to Cygnus X-1

The excellent angular resolution, good energy resolution and broad energy band make Chandra ACIS the best instrument for studying the X-ray halos around some galactic x-ray point sources caused by the dust scattering of X-rays in the interstellar medium, but direct images of bright sources of b r i g h t sources obtained with ACIS usually from severe pile- UP - Making use of the fact that an isotropic image could be reconstructed from it's projection on any direction, we can reconstruct the images of the X-ray halos from data obtained with the regular HETGS and/or the CC mode. With the reconstructed high resolution images, we can probe the X-ray halos as close as 1 arcsecond to their associated point sources.

Yao, Y.↗

Derivation of Improved Surface and TOA Broadband Fluxes Using CERES-derived Narrowband-to-Broadband Coefficients

Satellites can provide global coverage of a number of climatically important radiative parameters, including broadband (BB) shortwave (SW) and longwave (LW) fluxes at the top of the atmosphere (TOA) and surface. These parameters can be estimated from narrowband (NB) Geostationary Operational Environmental Satellite (GOES) data, but their accuracy is highly dependent on the validity of the narrowband-to-broadband (NB-BB) conversion formulas that are used to convert the NB fluxes to broadband values. The formula coefficients have historically been derived by regressing matched polarorbiting satellite BB fluxes or radiances with their NB counterparts from GOES (e.g., Minnis et al., 1984). More recently, the coefficients have been based on matched Earth Radiation Budget Experiment (ERBE) and GOES-6 data (Minnis and Smith, 1998). The Clouds and the Earth's Radiant Energy Budget (CERES see Wielicki et al. 1998)) project has recently developed much improved Angular Distribution Models (ADM; Loeb et al., 2003) and has higher resolution data compared to ERBE. A limited set of coefficients was also derived from matched GOES-8 and CERES data taken on Topical Rainfall Measuring Mission (TRMM) satellite (Chakrapani et al., 2003; Doelling et al., 2003). The NB-BB coefficients derived from CERES and the GOES suite should yield more accurate BB fluxes than from ERBE, but are limited spatially and seasonally. With CERES data taken from Terra and Aqua, it is now possible to derive more reliable NB-BB coefficients for any given area. Better TOA fluxes should translate to improved surface radiation fluxes derived using various algorithms. As part of an ongoing effort to provide accurate BB flux estimates for the Atmospheric Radiation Measurement (ARM) Program, this paper documents the derivation of new NB-BB coefficients for the ARM Southern Great Plains (SGP) domain and for the Darwin region of the Tropical Western Pacific (DTWP) domain.

Khaiyer, Mandana M.↗

Morphology and Kinematics of Filaments in the Serpens and Perseus Molecular Clouds

We present H(exp 13)CO(exp +) (J= 1-0) and HNC (J= 1-0) maps of regions in Serpens South, Serpens Main, and NGC 1333 containing filaments. We also observe the Serpens regions using H(exp 13)CN (J= 1-0). These dense gas tracer molecular line observations carried out with CARMA have an angular resolution of approximately 7", a spectral resolution of approximately 0.16 km s (exp -1), and a sensitivity of 50-100 mJy beam (exp -1). Although the large-scale structure compares well with the Herschel dust continuum maps, we resolve finer structure within the filaments identified by Herschel. The H(exp 13)CO(exp +) emission distribution agrees with the existing CARMA diazenylium(exp +) (J= 1-0) maps, so they trace the same morphology and kinematics of the filaments. The H(exp 13)CO(exp +) maps additionally reveal that many regions have multiple structures partially overlapping in the line of sight. In two regions, the velocity differences are as high as 1.4 km s(exp -1). We identify eight filamentary structures having typical widths of 0.03 - 0.08 pc in these tracers. At least 50% of the filamentary structures have distinct velocity gradients perpendicular to their major axis, with average values in the range of 4-10 km s(exp -1) pc (exp -1). These findings are in support of the theoretical models of filament formation by 2D inflow in the shock layer created by colliding turbulent cells. We also find evidence of velocity gradients along the length of two filamentary structures; the gradients suggest that these filaments are inflowing toward the cloud core.

Dhabal, Arnab↗

Mission Overview and Status IGARSS Conference

The Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission is a strategic climate continuity mission that was defined in the 2010 document Responding to the Challenge of Climate and Environmental Change: NASA’s Plan for Climate-Centric Architecture for Earth Observations and Applications from Space (referred to as the “Climate Initiative”). Scheduled for launch in January 2024, the PACE mission represents NASA’s next investment in ocean biology, clouds, and aerosol data records [1]. PACE will extend the high quality ocean ecological, ocean biogeochemical, cloud, and aerosol particle data records begun by NASA in the 1990s, building on the exceptional heritages of the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS), the Moderate Resolution Imaging Spectroradiometer (MODIS), the Multi-angle Imaging SpectroRadiometer (MISR), and the Visible Infrared Imaging Radiometer Suite (VIIRS). The PACE project office at NASA’s GSFC is responsible for the satellite development, launch and operations. The NASA Headquarters PACE Program Science office is responsible for supporting the science data processing system and assembling competed community science teams, which will include field-based vicarious calibration and data product validation efforts to support the PACE Project Science team. The mission is planned for launch into a Sun synchronous polar orbit at 676.5 km with an inclination of 98 degrees and a 1 pm local ascending node crossing time. The PACE observatory is comprised of three instruments, an Ocean Color Instrument (OCI) and two polarimeters, the Hyper-Angular Rainbow Polarimeter 2 (HARP2) and the Spectro-Polarimeter for Exploration (SPEXone). The OCI is the primary instrument on the observatory and is being developed at Goddard Space Flight Center (GSFC). The OCI is a hyperspectral scanning radiometer designed to measure spectral radiances from the ultraviolet to shortwave infrared (SWIR) to enable advanced ocean color and heritage cloud and atmospheric aerosol science [2]. The HARP2 and SPEXone are complimentary instruments on the PACE observatory, acquired outside of GSFC. The HARP2 is multi-spectral, wide swath (supporting atmospheric correction of OCI), and hyper-angular, with capabilities for cloud science that exceed what is capable from OCI alone. The SPEXone is narrow swath, multi-angular, and hyperspectral, with capabilities for atmospheric aerosol science that exceed what can be accomplished with OCI. NASA Headquarters directed the mission development to be guided by a Design-to-Cost (DTC) process. All elements of the mission, other than the cost, are in the DTC trade space. At the heart of the DTC process are the mission studies, performed across all the mission elements. The mission studies were used to define appropriate approaches within and across elements while maximizing science capabilities at a high cost confidence. Mission baseline requirements development is also embedded within the DTC process, as these requirements were not established at the onset of the mission concept development. Baseline mission requirements are a product of the mission studies and are defined by the project office as part of the DTC process. At the time of this writing, OCI, HARP2 and SPEXone are integrated onto the PACE spacecraft, creating the PACE observatory. The instruments and spacecraft subsystems are undergoing combined functional performance testing in preparation for observatory-level environmental testing prior to shipment to the launch site. Here, we will provide an update on science capabilities and observatory readiness for its early 2024 launch.

remote sensing↗

Ultra-Low Noise Laser and Optical Frequency Comb-Based Timing System for the Event Horizon Explorer (EHE) Mission

Very Long Baseline Interferometry (VLBI) requires a highly stable time reference and synchronization system to maintain coherence between observations recorded independently at multiple stations – for example, the array of ground-based radio telescopes that comprise the Event Horizon Telescope (EHT). Instability in the time reference or inaccuracy in the synchronization impacts phase conference and reduces the performance of the VLBI system. For space-based telescopes like the Event Horizon Explorer (EHE) mission, the precision timing system must meet the size, weight, and power (SWaP) constraints of the spacecraft platform and be capable of operating in the space environment. The EHE mission is a proposed extension to the EHT that can improve the angular and time resolution of observations by enabling longer interferometric baselines than are possible on the Earth and sampling a wide range of Fourier spatial frequencies throughout the orbital motion. In this effort, we demonstrate the performance of one option for the EHE mission: the use of a space-qualified, ultra-low noise laser developed as part of the Laser Interferometer Space Antenna (LISA) mission as the timing reference, and an optical frequency comb to transfer the stability of this laser to the microwave regime for instrumentation use. We describe the implementation of the microwave down-conversion, in which the LISA cavity-stabilized laser is locked to a self-referenced optical frequency comb to divide the optical frequency down to 100 MHz. The phase noise of the 100 MHz signal is measured and validated using a phase noise analyzer that is referenced to a separate laboratory ultra-stable laser system. We present the results of this experiment, which demonstrates that the performance of this system meets the EHE requirement: a relative frequency error of 1e-14 from 1 to 30 seconds.

Hannah Tomio↗

Latest Progress on the Gamma-Ray Imager/Polarimeter for Solar Flares (GRIPS)

We present the latest progress on building the balloon-borne Gamma-Ray Imager/Polarimeter for Solar flares (GRIPS) instrument, including testing and calibration of the detectors and development of the imaging and aspect systems. A continental-US test flight is slated for fall 2012. GRIPS will provide a near-optimal combination of high-resolution imaging, spectroscopy, and polarimetry of solar-flare gamma-ray/hard X-ray emissions from approx.20. keV to > approx.10 MeV. The spectrometer/polarimeter consists of sixteen 3D position-sensitive germanium detectors (3D-GeDs), where each energy deposition is individually recorded with an energy resolution of a few keV FWHM and a spatial resolution to within <0.1 cu mm. Imaging is accomplished by a single multi-pitch rotating modulator (MPRM), a 2.5-cm thick tungsten-alloy grid with pitches that range quasi-continuously from 1 to 13 mm. With the MPRM situated 8 meters from the spectrometer, this instrument will provide excellent image quality and unparalleled angular resolution at gamma-ray energies (12.5 arcsec FWHM), sufficient to separate the 2.2 MeV footpoint sources for almost all flares. Polarimetry is accomplished by analyzing the anisotropy of reconstructed Compton scattering in the 3D-GeDs (i.e. as an active scatterer), with an estimated minimum detectable polarization of a few percent at 150-650 keV in an X-class flare. GRIPS will address questions relevant to particle acceleration and energy release that ha-.e been raised by recent solar flare observations, such as: What causes the spatial separation between energetic electron producing hard X-rays and energetic ions producing gamma-ray lines? How anisotropic are the accelerated electrons, and why do relativistic electron dominate in the corona? How does the composition of accelerated and ambient material vary with space and time, and why?

Shih, Albert Y.↗

Precision Epoch of Reionization Studies with Next-Generation CMB Experiments

Future arcminute resolution polarization data from ground-based Cosmic Microwave Background (CMB) observations can be used to estimate the contribution to the temperature power spectrum from the primary anisotropies and to uncover the signature of reionization near l = 1500 in the small angular-scale temperature measurements. Our projections are based on combining expected small-scale E-mode polarization measurements from Advanced ACTPol in the range 300 < l < 3000 with simulated temperature data from the full Planck mission in the low and intermediate l region, 2 < l < 2000. We show that the six basic cosmological parameters determined from this combination of data will predict the underlying primordial temperature spectrum at high multipoles to better than 1% accuracy. Assuming an efficient cleaning from multi-frequency channels of most foregrounds in the temperature data, we investigate the sensitivity to the only residual secondary component, the kinematic Sunyaev-Zel'dovich (kSZ) term. The CMB polarization is used to break degeneracies between primordial and secondary terms present in temperature and, in effect, to remove from the temperature data all but the residual kSZ term. We estimate a 15 sigma detection of the di use homogeneous kSZ signal from expected AdvACT temperature data at l > 1500, leading to a measurement of the amplitude of matter density fluctuations, sigma 8, at 1% precision.

Precision↗

High Resolution Photoelectron Spectroscopy of the Acetyl Anion

High-resolution photoelectron spectra of cryogenically cooled acetyl anions (CH 3 CO - ) obtained using slow photoelectron velocity-map imaging are reported. The high resolution of the photoelectron spectrum yields a refined electron affinity of 0.4352 ± 0.0012 eV for the acetyl radical as well as the observation of a new vibronic structure that is assigned based on ab initio calculations. Three vibrational frequencies of the neutral radical are measured to be 1047 ± 3 cm -1 (ν 6 ), 834 ± 2 cm -1 (ν 7 ), and 471 ± 1 cm -1 (ν 8 ). Here this work represents the first experimental measurement of the ν 6 frequency of the neutral. The measured electron affinity is used to calculate a refined value of 1641.35 ± 0.42 kJ mol -1 for the gas-phase acidity of acetaldehyde. Analysis of the photoelectron angular distributions provides insight into the character of the highest occupied molecular orbital of the anion, revealing a molecular orbital with strong d-character. Additionally, details of a new centroiding algorithm based on finite differences, which has the potential to decrease data acquisition times by an order of magnitude at no cost to accuracy, are provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗