Carnotaurus sastrei is an abelisaurid dinosaur from the Late Cretaceous of Argentina that has very reduced, but robust, forelimbs and derived hands with four digits, including a large, conical-shaped metacarpal IV lacking an articulation for a phalanx. The analysis presented in this work highlights a series of additional autapomorphies of C. sastrei. For example, the proximal phalanges are longer than the metacarpals in digits II and III, and digit III includes only one phalanx besides the ungual. The hand of Carnotaurus shares several features with those of Aucasaurus and Majungasaurus, but the hands of the latter genera also display autapomorphies, indicating that the diversity in abelisaurid hand structure is similar to the diversity of cranial protuberances of these dinosaurs.
It is known that any binary logic function (in binary logic) can be represented by at least one logic formula, however this is not always true for a ternary logic function (in ternary logic). A ternary logic function can be represented by at least one logic formula if and only if it satisfies a mathematical condition which is called regularity. Also, it is known that a fuzzy logic formula (in standard fuzzy logic) can be obtained by means of truth tables in ternary logic. This paper presents a method destined for extending a binary logic function into one (or more) ternary logic function(s) representable by at least one logic formula, and therefore, to obtain fuzzy logic formulas from a binary logic function.
Context: The bottleneck on interval type-2 fuzzy logic systems is the output processing when using Centroid Type-Reduction + Defuzzification (CTR+D method). Nie and Tan proposed an approximation to CTR+D (NT method). Recently, Mendel and Liu improved the NT method (INT method). Numerical examples (due to Mendel and Liu) exhibit the NT and INT methods as good approximations to CTR+D.Method: Normalization to the unit interval of membership function domains (examples and counterexample) and variables involved in the calculations for the three methods. Examples (due to Mendel and Liu) taken from the literature. Counterexample with piecewise linear membership functions. Comparison by means of error and percentage relative error.Results: NT vs. CTR+D: Our counterexample showed an error of 0.1014 and a percentage relative error of 30.53%. This is respectively 23 and 32 times higher than the worst case obtained in the examples. INT vs. CTR+D: Our counterexample showed an error of 0.0725 and a percentage relative error of 21.83%. This is respectively 363 and 546 times higher than the worst case obtained in the examples.Conclusions: NT and INT methods are not necessarily good approximations to the CTR+D method.
The ubiquity of radon in the subsurface, its ease of analytical detection in the field and its preferential partitioning in organic phases (i.e. non-aqueous phase organic contaminants or NAPLs) make it ideal for delineating subsurface organic contamination processes [1,2].This contribution presents the results of 4 field campaigns at a site affected by a dense NAPL (DNAPL). A total of 505 Rn determinations in soil air were obtained in successive blind sampling campaigns (i.e., no prior information was disclosed on the location of hot-spots or the extent of the contamination) and were subsequently used for surface mapping of Rn activity in soil air.The results of the 222 Rn-deficit technique were compared with direct information from boreholes and monitoring wells at the site. 222 Rn measurements correctly predicted the location of contaminated areas already identified by conventional characterization methods but also unveiled a large, previously overlooked DNAPL accumulation. These results indicate the ability of the 222 Rn-deficit technique to detect not only the presence of organic contaminants in the vadose zone (as described in previous publications [3,4], but also of dense free phases in the saturated zone.
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