Rational solitons of wave resonant-interaction models

Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear Schrödinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied under the condition that the solutions have rational, or mixed rational-exponential, dependence on coordinates. Our algebraic construction relies on the use of nilpotent matrices and their Jordan form. We systematically search for all bounded rational (mixed rational-exponential) solutions and find a broad family of such solutions of the three wave resonant interaction equations

Results of the ontology alignment evaluation initiative 2019

The Ontology Alignment Evaluation Initiative (OAEI) aims at comparing ontology matching systems on precisely defined test cases. These test cases can be based on ontologies of different levels of complexity (from simple thesauri to expressive OWL ontologies) and use different evaluation modalities (e.g., blind evaluation, open evaluation, or consensus). The OAEI 2019 campaign offered 11 tracks with 29 test cases, and was attended by 20 participants. This paper is an overall presentation of that campaign

A complete classification of spatial relations using the Voronoi-based nine-intersection model

In this article we show that the Voronoi-based nine-intersection (V9I) model proposed by Chen et al. (2001, A Voronoi-based 9-intersection model for spatial relations. International Journal of Geographical Information Science, 15 (3), 201-220) is more expressive than what has been believed before. Given any two spatial entities A and B, the V9I relation between A and B is represented as a 3 × 3 Boolean matrix. For each pair of types of spatial entities that is, points, lines, and regions, we first show that most Boolean matrices do not represent a V9I relation by using topological constraints and the definition of Voronoi regions. Then, we provide illustrations for all the remaining matrices. This guarantees that our method is sound and complete. In particular, we show that there are 18 V9I relations between two areas with connected interior, while there are only nine four-intersection relations. Our investigations also show that, unlike many other spatial relation models, V9I relations are context or shape sensitive. That is, the existence of other entities or the shape of the entities may affect the validity of certain relations. © 2013 Taylor & Francis

Discovery of topological constraints on spatial object classes using a refined topological model

In a typical data collection process, a surveyed spatial object is annotated upon creation, and is classified based on its attributes. This annotation can also be guided by textual definitions of objects. However, interpretations of such definitions may differ among people, and thus result in subjective and inconsistent classification of objects. This problem becomes even more pronounced if the cultural and linguistic differences are considered. As a solution, this paper investigates the role of topology as the defining characteristic of a class of spatial objects. We propose a data mining approach based on frequent itemset mining to learn patterns in topological relations between objects of a given class and other spatial objects. In order to capture topological relations between more than two (linear) objects, this paper further proposes a refinement of the 9-intersection model for topological relations of line geometries. The discovered topological relations form topological constraints of an object class that can be used for spatial object classification. A case study has been carried out on bridges in the OpenStreetMap dataset for the state of Victoria, Australia. The results show that the proposed approach can successfully learn topological constraints for the class bridge, and that the proposed refined topological model for line geometries outperforms the 9-intersection model in this task

Immobile Water Content and Mass Exchange Coefficient of a Field Soil

Determining the preferential flow characteristics of a soil is important because agrichemicals can contaminate groundwater via preferential flow pathways. A model that predicts solute transport due to preferential flow is the mobile-immobile solute transport model, which partitions the total water content (θ, m3 m−3) into a mobile fraction (θm) and an immobile fraction (θim). Recently, an in situ method was proposed for determining the mobile-immobile model parameters of θim and mass exchange coefficient (α) between the fractions by using a tension infiltrometer to apply a series of four fluorobenzoate tracers. The objective of this study was to test the in situ technique at 47 sites along a transect in a ridge-till corn (Zea mays L.) field of Nicollet soil (fine-loamy, mixed, mesic Aquic Hapludoll). The immobile fraction (θim /θ) ranged from 0.394 to 0.952 with a median of 0.622. The mass exchange coefficient ranged from 0.000237 to 0.00481 min−1 with a median of 0.00123 min−1. These values are similar in magnitude and range to values reported by other investigators, and they follow the same relationships. The values of θim/θ and α along the transect indicated no obvious spatial trends or spatial correlations. Significant linear correlations did exist between α and soil water flux, α and θim, and θ and θim

Spatiotemporal data as the foundation of an archaeological stratigraphy extraction and management system

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