The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

The usefulness of ultrasound in the classification of chronic liver disease

Chronic Liver Disease is a progressive, most of the time asymptomatic, and potentially fatal disease. In this paper, a semi-automatic procedure to stage this disease is proposed based on ultrasound liver images, clinical and laboratorial data. In the core of the algorithm two classifiers are used: a k nearest neighbor and a Support Vector Machine, with different kernels. The classifiers were trained with the proposed multi-modal feature set and the results obtained were compared with the laboratorial and clinical feature set. The results showed that using ultrasound based features, in association with laboratorial and clinical features, improve the classification accuracy. The support vector machine, polynomial kernel, outperformed the others classifiers in every class studied. For the Normal class we achieved 100% accuracy, for the chronic hepatitis with cirrhosis 73.08%, for compensated cirrhosis 59.26% and for decompensated cirrhosis 91.67%.

Solubilities of C‑Tetraalkylcalix[4]resorcinarenes in SCCO2: experimental measurements, characterization, and correlation

The solubilities of two C-tetraalkylcalix[4]resorcinarenes, namely C-tetramethylcalix[4]resorcinarene and C-tetrapentylcalix[4]resorcinarene, in supercritical carbon dioxide (SCCO2) were measured in a flow-type apparatus at a temperature range from (313.2 to 333.2) K and at pressures from (12.0 to 35.0) MPa. The C-tetraalkylcalix[4]resorcinarenes were synthesized applying our optimized procedure and fully characterized by means of gel permeation chromatography, infrared and nuclear magnetic resonance spectroscopy. The solubilities of the C-tetraalkylcalix[4]resorcinarenes in SCCO2 were determined by analysis of the extracts obtained by HPLC with ultraviolet (UV) detection methodology adapted by our team. Four semiempirical density-based models, and the SoaveRedlichKwong cubic equation of state (SRK CEoS) with classical mixing rules, were applied to correlate the solubility of the calix[4]resorcinarenes in the SC CO2. The physical properties required for the modeling were estimated and reported.

Statistical classification of road pavements using near field vehicle rolling noise measurements

Low noise surfaces have been increasingly considered as a viable and cost-effective alternative to acoustical barriers. However, road planners and administrators frequently lack information on the correlation between the type of road surface and the resulting noise emission profile. To address this problem, a method to identify and classify different types of road pavements was developed, whereby near field road noise is analyzed using statistical learning methods. The vehicle rolling sound signal near the tires and close to the road surface was acquired by two microphones in a special arrangement which implements the Close-Proximity method. A set of features, characterizing the properties of the road pavement, was extracted from the corresponding sound profiles. A feature selection method was used to automatically select those that are most relevant in predicting the type of pavement, while reducing the computational cost. A set of different types of road pavement segments were tested and the performance of the classifier was evaluated. Results of pavement classification performed during a road journey are presented on a map, together with geographical data. This procedure leads to a considerable improvement in the quality of road pavement noise data, thereby increasing the accuracy of road traffic noise prediction models.

Partial classification of Lorenz knots: Syllable permutations of torus knots words

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.