A structure of the solenoidal 2D vector and 2-tensor fields given in a domain with the conformal Riemannian metric

The Helmholtz decomposition of a vector field on potential and solenoidal parts is much more natural from physical and geometric points of view then representations through the components of the vector in the Cartesian coordinate system of Euclidean space. The structure, representation through potentials and detailed decomposition for 2D symmetric m-tensor fields in a case of the Euclidean metric is known. For the Riemannian metrics similar results are known for vector fields. We investigate the properties of the solenoidal vector and 2-tensor two-dimensional fields given in the Riemannian domain with the conformal metric and establish the connections between the fields and metrics.

USING COMBINATORIAL MAPS FOR ALGORITHMS ON GRAPHS

The aim of this paper is to come back to a data structure representation of graph by permutations. This originated in the years 1960-1970 by contributions due to J. Edmonds [7], A. Jacques [11], W. Tutte [22] in order to consider the embedding of a graph in a surface as a combinatorial object. Some algebraic developments where suggested in [4] and [12]. It was also used for implementation in different situation, like planarity testing by H. de Fraysseix and P. Rosenstiehl [6], computer vision by G. Damiand and A. Dupas [5] or formal proofs by G. Gonthier [9].

Unusual Para-Substituent Effects on the Intramolecular Hydrogen Bond in Hydrazone-Based Switches: Insights from Chemical Landscape Analysis and DFT Calculations

Тhe adequacy of chemical property predictions strongly depends on the structure representation, including the proper treatment of the tautomeric and isomeric forms. A combination of an in-house developed open-source tool for automatic generation of tautomers, Ambit-Tautomer, based on H-atom shift rules and standard quantum chemical (DFT) calculations is used for a detailed investigation of the possible geometric isomers, conformers and tautomers of unsubstituted and para-substituted phenylhydrazones, systems with experimentally observed unusual para-substituent effects on the intramolecular hydrogen bond (IMHB) for E-isomers of the compounds. The computational results show that the energetically preferred E-isomers are characterized by stronger IMHBs than the corresponding Z-isomers. The HN–N=C–C=N molecular fragment in the E-configurations is less sensitive to the substitution effect than the HN–N=C–C=O fragment in the isomers with Z-configuration. A probable reason for this decreased sensitivity of E-isomers to phenyl ring substitution is the more efficient conjugation and charge distribution in the HN–N=C–C=N fragment.

Statistical Assessment of the Effects of Grain-Structure Representation and Micro-Properties on the Behavior of Bonded Block Models for Brittle Rock Damage Prediction

The ability to predict the mechanical behavior of brittle rocks using bonded block models (BBM) depends on the accuracy of the geometrical representation of the grain-structure and the applied micro-properties. This paper evaluates the capabilities of BBMs for predictive purposes using an approach that employs published micro-properties in combination with a Voronoi BBM that properly approximates the real rock grain-structure. The Wausau granite, with Unconfined Compressive Strength (UCS) of 226 MPa and average grain diameter of 2 mm, is used to evaluate the effectiveness of the predictive approach. Four published sets of micro-properties calibrated for granites with similar mineralogy to the Wausau granite are used for the assessment. The effect of grain-structure representation in Voronoi BBMs is analyzed, considering grain shape, grain size and mineral arrangement. A unique contribution of this work is the explicit consideration of the effect of stochastic grain-structure generation on the obtained results. The study results show that the macro-properties of a rock can be closely replicated using the proposed approach. When using this approach, the micro-properties have a greater impact on the realism of the predictions than the specific grain-structure representation. The grain shape and grain size representations have a minor effect on the predictions for cases that do not deviate substantially from the real average grain geometry. However, the stochastic effect introduced by the use of randomly-generated Voronoi grain-structures can be significant, and this effect should be considered in future studies.

Quasi-N4-Lattices

Within the Nelson family, two mutually incomparable generalizations of Nelson constructive logic with strong negation have been proposed so far. The first and more well-known, Nelson paraconsistent logic , results from dropping the explosion axiom of Nelson logic; a more recent series of papers considers the logic (dubbed quasi-Nelson logic ) obtained by rejecting the double negation law, which is thus also weaker than intuitionistic logic. The algebraic counterparts of these logical calculi are the varieties of N4-lattices and quasi-Nelson algebras . In the present paper we propose the class of quasi- N4-lattices as a common generalization of both. We show that a number of key results, including the twist-structure representation of N4-lattices and quasi-Nelson algebras, can be uniformly established in this more general setting; our new representation employs twist-structures defined over Brouwerian algebras enriched with a nucleus operator. We further show that quasi-N4-lattices form a variety that is arithmetical, possesses a ternary as well as a quaternary deductive term, and enjoys EDPC and the strong congruence extension property.

Ambiguous Sentence Processing in Translation

The goal of our research was to explore the possible online co-activation of both the target language (TL) syntactic structure representation and TL attachment strategies in translation, and to look over a possible interaction between both syntactic properties. To this purpose, Spanish (L1) – English (L2) bilinguals were instructed to read complex noun phrases with an ambiguous relative clause in Spanish to either repeat them in Spanish or translate them into English. The final word of the sentences and the syntactic congruency between the source language (SL) and TL syntactic structure were manipulated. The results revealed co-activation of both TL syntactic properties: participants interpreted sentences more accordingly to the TL preferred strategy (low attachment) in the reading for translation task, read congruent sentences faster, and used the TL preferred interpretation strategy in the congruent condition of the sentences more. These results indicated TL activation at different syntactic levels during comprehension of the SL in translation.