Software platforms for e-learning support various options for presenting educational content. One of the ways to organize and structure it is via so-called pedagogical patterns. They are a method for describing and sharing knowledge and practical experience. Pedagogical patterns are used to describe pedagogical situations that occur repeatedly in the learning process. In the context of e-learning systems, there are various approaches to digitalization of pedagogical patterns. The purpose of the paper is to show how to build instances of pedagogical patterns using e-learning pedagogical objects, which can be easily and conveniently used as models in an adaptive e-learning environment. An e-learning pedagogical object is an abstract concept that can be presented in the concrete form of an e-learning object, an e-learning methodological object, an e-learning object for monitoring and diagnostics or an e-learning object with learning outcomes. These objects are building blocks for constructing instances of pedagogical patterns. This paper thoroughly discusses the issue of creating instances of pedagogical patterns of the four types of e-learning pedagogical objects. The instance of a pedagogical pattern is meant to serve to create subsections of educational topics. The instances of the patterns built of e-learning objects are learning units that are used depending on the context of a particular pedagogical situation. The e-learning pedagogical objects and the pedagogical pattern instances are intended to be applied in an adaptive e-learning environment as teaching aids. Their theoretical models are applied in Moodle LMS in line with the tendency for software to assist and replace some of the teacher functions, while the teacher’s role is raised to a higher organizational, pedagogical and methodological level. Three instances of pedagogical patterns have been created through e-learning pedagogical objects: “Early Feedback”, “Feedback Sandwich” and “Consistent Metaphor” in LMS Moodle, which have been tested in the training course “Modeling of training courses in Moodle” during the autumn trimester of the academic year 2021/2022 at the Faculty of Mathematics and Informatics of Paisii Hilendarski University of Plovdiv, Bulgaria.

In recent years, there is rise in various human-computer interaction interfaces and automatic text translation services and frameworks. In this paper, we conduc

The article addresses the problem of accessibility of dynamic web content that is created when developing web pages and services. It discusses basic issues about the accessibility of digital objects and web page content. The aim of the article is to present a method for designing accessibility in the creation of dynamic web content in websites of Paisii Hilendarski Plovdiv University. The developed method is presented through the life cycle of its model, which is applied in parallel with the implementation of a software process in the renewal of the web infrastructure of the university. The method is built on standards, principles, guidelines, accessibility criteria, and techniques for creating and validating web content of the Web Accessibility Initiative. The main standards to which the method adheres are the Web Content Accessibility Guidelines and the Technical Specifications for Accessible Rich Internet Applications. It has been tested in the design and implementation of part of the web content of the web infrastructure of the university created after 2020, which is accessible through the main domain https://uni-plovdiv.bg and many of its sub-domains.

We study a class of wrapping operators acting on the space of formal languages over a fixed finite alphabet. The underlying space is equipped with a length-based ultrametric, in which two languages are close whenever they coincide on all sufficiently short words. We prove that every wrapping operator generated by a finite family of guards with positive total guard length is a contraction. As a consequence, Banach’s contraction principle yields existence and uniqueness of a fixed point for the corresponding recursive language equation, together with convergence of the Picard iteration from an arbitrary initial language. We also obtain an explicit quantitative estimate for the rate of convergence. This makes it possible to determine how many iterations are sufficient to recover the fixed point correctly on all words up to a prescribed length. Several examples illustrate the theory, including operators with different guard lengths and a case showing that convergence in the length-based ultrametric does not coincide with set-theoretic convergence. An application to recursive structures and document validation is also presented, including recursive data formats, abstract syntax trees, and a restricted fragment of JSON schemas. The results provide a formal foundation for validation together with explicit bounds for correctness on inputs of bounded length.

We study a class of wrapping operators acting on the space of formal languages over a fixed finite alphabet. The underlying space is equipped with a length-based ultrametric, in which two languages are close whenever they coincide on all sufficiently short words. We prove that every wrapping operator generated by a finite family of guards with positive total guard length is a contraction. As a consequence, Banach’s contraction principle yields existence and uniqueness of a fixed point for the corresponding recursive language equation, together with convergence of the Picard iteration from an arbitrary initial language. We also obtain an explicit quantitative estimate for the rate of convergence. This makes it possible to determine how many iterations are sufficient to recover the fixed point correctly on all words up to a prescribed length. Several examples illustrate the theory, including operators with different guard lengths and a case showing that convergence in the length-based ultrametric does not coincide with set-theoretic convergence. An application to recursive structures and document validation is also presented, including recursive data formats, abstract syntax trees, and a restricted fragment of JSON schemas. The results provide a formal foundation for validation together with explicit bounds for correctness on inputs of bounded length.