Hristo Hristov

This article presents the development of a web application for automated translation of TXT, DOCX, and PDF documents, built with Next.js/React and integrated with OpenAI LLM models. The study investigates the influence of the sampling parameters temperature and Top-P (nucleus sampling) on translation quality between Bulgarian and English. Translation experiments were conducted on a bilingual corpus of popular-science and biographical texts, analysing effects on verb tense, lexical choice, word order, and output stability. Proper tuning of these parameters allows control over style and lexical richness without compromising reliability, and the trends remain relevant in newer model versions.

We study positive–negative guarded systems of language equations over a fixed finite alphabet. The ambient space is the complete ultrametric space of all formal languages equipped with a length-based distance, where two languages are close whenever they agree on all words up to a sufficiently large length. The systems considered here contain both positive recursive dependencies and negative dependencies expressed through language complements. To handle this mixed structure, we introduce a suitable product order on pairs of languages and prove that the associated system operator has the weak monotone property. We show that the complement is an isometry for the length-based ultrametric and establish a signed wrapping estimate for guarded positive and negative language terms. These estimates lead to an ordered contraction principle for comparable pairs. As a consequence, the canonical lower and upper Picard iterations converge to the same limit, which is the unique fixed pair of the system. We also derive an explicit convergence rate and a finite-depth certification result: after a prescribed number of iterations, the approximants agree with the fixed-point semantics on all words below a given length. Additional symmetry assumptions are shown to force the unique fixed pair to be diagonal, reducing the system to a single language equation. Finally, we discuss an application to trace-based policies for tool-using AI agents. In this interpretation, finite executions of an agent are represented as words over an alphabet of observable tool-events, and the two components of the fixed point provide a stable semantics for policy-defined admissible and risky trace classes. The resulting framework gives a mathematically certified method for finite-depth analysis of recursive trace-based policies based on ultrametric fixed-point techniques.

We study positive–negative guarded systems of language equations over a fixed finite alphabet. The ambient space is the complete ultrametric space of all formal languages equipped with a length-based distance, where two languages are close whenever they agree on all words up to a sufficiently large length. The systems considered here contain both positive recursive dependencies and negative dependencies expressed through language complements. To handle this mixed structure, we introduce a suitable product order on pairs of languages and prove that the associated system operator has the weak monotone property. We show that complement is an isometry for the length-based ultrametric and establish a signed wrapping estimate for guarded positive and negative language terms. These estimates lead to an ordered contraction principle for comparable pairs. As a consequence, the canonical lower and upper Picard iterations converge to the same limit, which is the unique fixed pair of the system. We also derive an explicit convergence rate and a finite-depth certification result: after a prescribed number of iterations, the approximants agree with the fixed-point semantics on all words below a given length. Additional symmetry assumptions are shown to force the unique fixed pair to be diagonal, reducing the system to a single language equation. Finally, we discuss an application to trace-based policies for tool-using AI agents. In this interpretation, finite executions of an agent are represented as words over an alphabet of observable tool-events, and the two components of the fixed point provide a stable semantics for policy-defined admissible and risky trace classes. The resulting framework gives a mathematically certified method for finite-depth analysis of recursive trace-based policies based on ultrametric fixed-point techniques.

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.

This study examines the problem of the lack of an integrated model for the sustainable development of a YouTube channel tailored to a specific target audience. Under conditions of algorithmically driven visibility on the YouTube platform, content creators are faced with the need to combine analytical, content-related, and managerial factors within a unified strategic framework. The article aims to develop a practically applicable model that integrates audience analysis, content optimization, video structuring, SEO practices, and systematic analysis of data from YouTube Analytics. Methodologically, the study combines an analysis of scholarly literature, an analysis of active YouTube channels, the dynamics of channel development, and the interpretation of behavioral metrics. The proposed framework is designed to support the improvement of key behavioral indicators such as watch time, audience retention, and click-through rate by aligning content strategy with audience behavior and platform recommendation dynamics. In this sense, the model provides a structured basis for sustainable organic channel development.

The present article examines the conceptualization of a model for building a digital business ecosystem through design and implementation of an e-platforms’ network that integrates software services within PropTech Bulgaria as an international organization. “Business Model Archetypes” as a conceptual framework is being applied to the real business case of PropTech Bulgaria, thus clearly showcasing how different business models (BM) correspond to respective e-platforms starting from the basic BMs like product, service, and commerce; developing into combined BM forms such as subscription, marketplace, and brokerage. The system architecture is implemented through a modular approach, led by the understanding that strategies, knowledge, and technologies change over time. As a natural consequence, transaction points change as well. Having a modular structure presupposes a bigger number of transaction points. Currently, there is no communication among separate modules through data transfer. The study advances a practically applicable model for developing a resilient international PropTech ecosystem, i.e., the most complex business model archetype.

The article presents an approach and software tool aimed at achieving quality, accessible, and sustainable education. The approach is based on reusable learning objects—educational video materials that can be repeatedly used and adapted for different languages and audiences. The proposed learning model uses quality learning resources (regardless of their language) and integrates them into courses and educational processes, regardless of the language proficiency of the learners. The approach relies on the integration of subtitle translation technologies into educational video resources, aiming to overcome language barriers in education. The software tool, AI Subtitle Translator, is developed using artificial intelligence (AI) and offers automated subtitle translation. It utilizes OpenAI models (GPT-4o and GPT-4.5) to provide translation services. The workflow, architecture, implementation, and operational scenario of the software tool are also presented. The discussed approach serves as a solution to enhance accessibility to global educational content. By combining reusable learning objects with AI Subtitle Translator, effective education without language constraints is ensured.

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