A method is developed to investigate the additive structure of data that (a) may be measured at the nominal, ordinal or cardinal levels, (b) may be obtained from either a discrete or continuous source, (c) may have known degrees of imprecision, or (d) may be obtained in unbalanced designs. The method also permits experimental variables to be measured at the ordinal level. It is shown that the method is convergent, and includes several previously proposed methods as special cases. Both Monte Carlo and empirical evaluations indicate that the method is robust.

A new procedure is discussed which fits either the weighted or simple Euclidian model to data that may (a) be defined at either the nominal, ordinal, interval or ratio levels of measurement; (b) have missing observations; (c) be symmetric or asymmetric; (d) be conditional or unconditional; (e) be replicated or unreplicated; and (f) be continuous or discrete. Various special cases of the procedure include the most commonly used individual differences multidimensional scaling models, the familiar nonmetric multidimensional scaling model, and several other previously undiscussed variants.

The procedure optimizes the fit of the model directly to the data (not to scalar products determined from the data) by an alternating least squares procedure which is convergent, very quick, and relatively free from local minimum problems.

The procedure is evaluated via both Monte Carlo and empirical data. It is found to be robust in the face of measurement error, capable of recovering the true underlying configuration in the Monte Carlo situation, and capable of obtaining structures equivalent to those obtained by other less general procedures in the empirical situation.

Rice herbicide drift poses a significant challenge in California, where rice fields are near almond, pistachio, and walnut orchards. This research was conducted as part of a stewardship program for a newly registered rice herbicide and specifically aimed to compare the onset of foliar symptoms resulting from simulated florpyrauxifen-benzyl drift with residues in almond, pistachio, and walnut leaves at several time points after exposure. Treatments were applied to one side of the canopy of 1- and 2-yr-old trees at 1/100X and 1/33X of the florpyrauxifen-benzyl rice field use rate of 29.4 g ai ha–1 in 2020 and 2021. Symptoms were observed 3 d after treatment (DAT) for pistachio and 7 DAT for almond and walnut, with peak severity at approximately 14 DAT. While almond and walnut symptoms gradually dissipated throughout the growing season, pistachio still had symptoms at leaf out in the following spring. Leaf samples were randomly collected from each tree for residue analysis at 7, 14, and 28 DAT. At 7 DAT with the 1/33X rate, almond, pistachio, and walnut leaves had florpyrauxifen-benzyl at 6.06, 5.95, and 13.12 ng g–1 fresh weight (FW) leaf, respectively. By 28 DAT, all samples from all crops treated with the 1/33X drift rate had florpyrauxifen-benzyl at less than 0.25 ng g–1 FW leaf. At the 1/100X rate, pistachio, almond, and walnut residues were 1.78, 2.31, and 3.58 ng g–1 FW leaf at 7 DAT, respectively. At 28 DAT with the 1/100X rate, pistachio and almond samples had florpyrauxifen-benzyl at 0.1 and 0.04 ng g–1 FW leaf, respectively, but walnut leaves did not have detectable residues. Together, these data suggest that residue analysis from leaf samples collected after severe symptoms may substantially underestimate actual exposure due to the relatively rapid dissipation of florpyrauxifen-benzyl in nut tree foliage.

A procedure based on loss of weight after selective dissolution analysis (SDA) and washing with (NH4)2CO3 was developed for estimating the noncrystalline material content of soils derived from widely different parent materials. After extracting with 0.2 N ammonium-oxalate or boiling 0.5 N NaOH solutions, samples were washed with 1 N (NH4)2CO3 to remove excess dissolution agents and to prevent sample dispersion. The amount of noncrystalline material removed from the sample by the extracting solution was estimated by weighing the leached products dried to constant weight at 110°C. The results match closely with those obtained by chemical analyses of the dissolution product and assignment of the appropriate water. The proposed weight-loss method is less time-consuming than the chemical method, and no assumptions need be made concerning sample homogeneity or water content of the noncrystalline material.

Extractions of whole soil and dispersed clay fractions indicated that noncrystalline material determinations on the clay fractions underestimated the noncrystalline material content for whole soils from 0 to 34%. Acid ammonium oxalate was found to be a much more selective extractant for noncrystalline materials than NaOH.

We investigate whether ordinary quantification over objects is an extensional phenomenon, or rather creates non-extensional contexts; each claim having been propounded by prominent philosophers. It turns out that the question only makes sense relative to a background theory of syntax and semantics (here called a grammar) that goes well beyond the inductive definition of formulas and the recursive definition of satisfaction. Two schemas for building quantificational grammars are developed, one that invariably constructs extensional grammars (in which quantification, in particular, thus behaves extensionally) and another that only generates non-extensional grammars (and in which quantification is responsible for the failure of extensionality). We then ask whether there are reasons to favor one of these grammar schemas over the other, and examine an argument according to which the proper formalization of deictic utterances requires adoption of non-extensional grammars.

Illite polytype quantification allows the differentiation of diagenetic and detrital illite components. In Paleozoic shales from the Illinois Basin, we observe 3 polytypes: 1Md, 1M and 2M1. 1Md and 1M are of diagenetic origin and 2M1 is of detrital origin. In this paper, we compare experimental X-ray diffraction (XRD) traces with traces calculated using WILDFIRE© and quantify mixtures of all 3 polytypes, adjusting the effects of preferred orientation and overlapping peaks. The broad intensity (“illite hump”) around the illite 003, which is very common in illite from shales, is caused by the presence of 1Md illite and mixing of illite polytypes and is not an artifact of sample preparation or other impurities in the sample. Illite polytype quantification provides a tool to extrapolate the K/Ar age and chemistry of the detrital and diagenetic end-members by analysis of different size fractions containing different proportions of diagenetic and detrital illite polytypes.

The quantification of the relative mineralogical composition of clay mixtures by powder X-ray diffraction or chemical mass balance methods has been severely hampered by a lack of representative standards. The recent development of elemental mass balance models that do not require standards for all minerals in the mixture may help circumvent this problem. These methods, which are based on the numerical optimization of systems of non-linear equations using the Marquardt algorithm, show promise for mineral quantification. The objective of this study is to make a preliminary assessment of the accuracy of these methods and to compare them to linear models that require standards for all mineral phases. Methods 1 and 2 are based on weighted average solutions to simultaneous linear equations solved for single samples with known standards. Solutions were achieved by a matrix decomposition algorithm and the Marquardt algorithm, respectively. Methods 3 and 4 are based on a set of simultaneous non-linear equations with reduced non-linearity solved by least squares optimization based on the Marquardt algorithm for multiple samples. Illite and halloysite compositions were fixed in Method 3, only the halloysite composition was fixed in Method 4. All models yielded relative weight fractions of the three mineral components; additionally, Methods 3 and 4 yielded compositions of smectite, and smectite and illite, respectively. Ten clay mixtures with varying proportions of the <0.2 μm size fraction of three different reference clays (Wyoming bentonite, Fithian illite, and New Bedford halloysite) were prepared gravi-metrically and analyzed by inductively coupled plasma-atomic emission spectroscopy. Accuracy of the four methods was evaluated by comparing the known mineralogical compositions of the mixtures with those predicted by the models. Relative errors of 5 and 10% (randomly +/-) were imposed on the elemental composition of the smectite standard to simulate errors due to lack of good standards. Not surprisingly, the accuracy of Methods 1 and 2 decreased rapidly with increasing error. Because Methods 3 and 4 optimized for the smectite composition and only used it for an initial guess, they were unaffected by the level of introduced error. They accurately quantified the mineralogical compositions of the mixtures and the elemental compositions of smectite, and smectite and illite, respectively.

The rapid phase quantification method using X-ray diffraction (XRD) with a position-sensitive detector (PSD), outlined by Cressey and Schofield (1996), has been extended to facilitate mineral phase quantification of clay-bearing samples. In addition, correction factors for differences in matrix absorption effects have been calculated and applied. The method now enables mudrock mineralogy to be quantified rapidly and efficiently. Using this approach overcomes many of the problems hitherto associated with the quantitative analysis of clay minerals, in particular the effects of preferred orientation of crystallites and variable sample-area irradiation, that make the task of quantification extremely difficult by conventional Bragg-Brentano scanning diffractometry.

Allophane is a very fine-grained clay mineral which is especially common in Andosols. Its importance in soils derives from its large reactive surface area. Owing to its short-range order, allophane cannot be quantified by powder X-ray diffraction (XRD) directly. It is commonly dissolved from the soil by applying extraction methods. In the present study the standard extraction method (oxalate) was judged to be unsuitable for the quantification of allophane in a soil/clay deposit from Ecuador, probably because of the large allophane content (>60 wt.%). This standard extraction method systematically underestimated the allophane content but the weakness was less pronounced in samples with small allophane contents. In the case of allophane-rich materials, the Rietveld XRD technique, using an internal standard to determine the sum of X-ray amorphous phases, is recommended if appropriate structural models are available for the other phases present in the sample. The allophane (+imogolite) content is measured by subtracting the amount of oxalate-soluble phases (e.g. ferrihydrite). No correction would be required if oxalate-soluble Fe were incorporated in the allophane structure. The present study, however, provides no evidence for this hypothesis. Mössbauer and scanning electron microscopy investigations indicate that goethite and poorly ordered hematite are the dominant Fe minerals and occur as very fine grains (or coatings) being dispersed in the cloud-like allophane aggregates.

Allophane is known to adsorb appreciable amounts of water, depending on ambient conditions. The mass fraction of the sample attributed to this mineral thus changes accordingly; the choice of a reference hydration state is, therefore, a fundamental factor in the quantification of allophane in a sample. Results from the present study revealed that (1) drying at 105ºC produced a suitable reference state, and (2) water adsorption has no effect on quantification by XRD analysis.

Thirty six bentonite samples from 16 different locations were examined in order to demonstrate the applicability of a new Rietveld description approach for quantitative phase analysis. X-ray diffraction patterns of the bulk material were obtained and analyzed by the Rietveld method. The samples contain up to ten different minerals, with dioctahedral smectite as the major component. A model for turbostratic disorder of smectites was formulated inside a structure-description file of the Rietveld program BGMN. The quality of the refinements was checked using an internal standard mineral (10.0 or 20.0 wt.% corundum) and by cross-checking results with X-ray fluorescence (XRF) data. The corundum content was reproduced with only small deviations from the nominal values. A comparison of the chemical composition obtained by XRF and the composition as re-calculated from quantitative Rietveld results shows a satisfactory agreement, although X-ray amorphous components such as volcanic glasses were not considered. As a result of this study, the Rietveld method combined with the new structure model for turbostratic disorder has proven to be a suitable method for routine quantitative analysis of bentonites with smectites as the dominant clay minerals.

Reflectance spectroscopy is a rapid and non-destructive method that can be used to detect organic compounds in geologic samples over a wide range of spatial scales that includes outcrops, hand samples, drill cores, and planetary surfaces. In order to assess the viability of this technique for quantification of organics and aliphatic compounds in particular, the present study examines how clay mineralogy, water content, and albedo influence the strength of organic absorptions in near-infrared (NIR) reflectance spectra. The effects of clay structure and water content are evaluated using kaolinite, smectite (montmorillonite), and a mixed-layer illite-smectite as starting materials. Absorption strengths for C—H absorptions are compared to known total organic carbon (TOC) values using both reflectance spectra and single scattering albedo (SSA) spectra derived from a Hapke radiative transfer model. A linear relationship was observed between band depth and TOC for each sample suite, but strong albedo variation led to non-unique trends when band depths were calculated from reflectance spectra. These effects were minimized by conversion to SSA, for which band depth-TOC trends were similar for all mixture suites regardless of albedo or hydration level, indicating that this approach may be more broadly applicable for clay and organic-bearing samples. Extrapolation of band depth-TOC trends for the synthetic mixtures suggested a very conservative lower limit of detection of <1 wt.% TOC, but preliminary results for natural organic-bearing shales indicated that detection limits may be an order of magnitude lower.

This paper presents a language, Alda, that supports all of logic rules, sets, functions, updates, and objects as seamlessly integrated built-ins. The key idea is to support predicates in rules as set-valued variables that can be used and updated in any scope, and support queries using rules as either explicit or implicit automatic calls to an inference function. We have defined a formal semantics of the language, implemented a prototype compiler that builds on an object-oriented language that supports concurrent and distributed programming and on an efficient logic rule system, and successfully used the language and implementation on benchmarks and problems from a wide variety of application domains. We describe the compilation method and results of experimental evaluation.