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Ultra regular covering space and its automorphism group

Sang-Eon Han (2010)

International Journal of Applied Mathematics and Computer Science

In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces...

Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing

Olga Drblíková (2007)

Kybernetika

This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient...

Uses of new sensitivity and DAE solving methods in SmartMOBILE for verified analysis of mechanical systems

Ekaterina Auer, Wolfram Luther (2009)

International Journal of Applied Mathematics and Computer Science

Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the input data. The program SmartMOBILE enhances the existing MSS MOBILE with verified techniques to provide a guarantee that the obtained results are correct and measure the influence of data uncertainty. In this paper, we outline the main features and functionalities...

Using Discourse Context to Interpret Object-Denoting Mathematical Expressions

Wolska, Magdalena, Grigore, Mihai, Kohlhase, Michael (2011)

Towards a Digital Mathematics Library. Bertinoro, Italy, July 20-21st, 2011

We present a method for determining the context-dependent denotation of simple object-denoting mathematical expressions in mathematical documents. Our approach relies on estimating the similarity between the linguistic context within which the given expression occurs and a set of terms from a flat domain taxonomy of mathematical concepts; one of 7 head concepts dominating a set of terms with highest similarity score to the symbol’s context is assigned as the symbol’s interpretation. The taxonomy...

Using fuzzy relational databases to represent agricultural and environmental information. An example within the scope of olive cultivation in Granada.

Juan Manuel Serrano, M.ª Amparo Vila, Víctor Aranda, Gabriel Delgado (2001)

Mathware and Soft Computing

A query system for several types of users and for information retrieval about olive cultivation and its environmental support in the province of Granada (Spain) is introduced. The system is based on fuzzy data and is flexible. The main problems which this model solves are those relating to uncertain and imprecise data processing (as in the case of environmental and cultivation information), spatial and punctual data representation, and fusion of cultivation-resulting and scientific-experimental...

Using genetic feature selection for optimizing user profiles.

Henrik Legind Larsen, Nicolás Marín, María José Martín-Bautista, M. Amparo Vila (2000)

Mathware and Soft Computing

Most of the techniques used in text classification are determined by the occurrences of the words (terms) appearing in the documents, combined with the user feedback over the documents retrieved. However, in our model, the most relevant terms will be selected from a previous fuzzy classification given by the genetic algorithm guided by the user feedback, but using techniques from Machine Learning. A feature selection process is carried out through a Genetic Algorithm in order to find the most discriminatory...

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