Hristina Kulina

We study guarded recursive operators on spaces of formal languages equipped with weighted first-disagreement ultrametrics generated by arbitrary decreasing depth profiles. We show that all admissible profiles preserve the same compact complete finite-depth topology while producing substantially different quantitative contraction behavior. A uniform decay profile is introduced to measure the relative decrease of metric weights under guarded disagreement shifts. We determine the exact Lipschitz modulus of canonical guarded contexts and prove that the same decay quantity is the optimal universal Lipschitz coefficient for finite guarded wrapping operators with a prescribed minimal guard length. This leads to an exact universal Banach contractivity criterion and to a sharp guard-length threshold separating uniformly contractive and nonuniform regimes. Independently of Banach contractivity, positive guardedness is shown to guarantee a unique fixed language, global Picard convergence, and explicit finite-depth stabilization for every admissible weight profile. Representative geometric, stretched-exponential, polynomial, and block-structured profiles illustrate all possible finite and infinite decay-threshold regimes.

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 article examines the impact of students’ prior experience with English on their academic success in a university English course. The study is based on a survey conducted among students majoring in Computer Science, Business Information Technology (BIT), and Software Technology and Design (STD) at the Faculty of Mathematics and Informatics (FMI), University of Plovdiv, at the beginning of their general English language course. We focus on students’ self-assessed language competence at the start of the course and examine how these self-assessments correspond to their actual test results. Using high-performance machine learning methods, we identify background factors that influence academic achievement, including the number of years spent learning English, the type of high school attended, and informal exposure to English. The findings aim to support more effective and tailored approaches to teaching English in technical and scientific disciplines.

This study presents an integrated framework for forecasting the USD/JPY exchange rate using ensemble machine learning techniques – CART-Ensembles and Arcing. The analysis employs monthly macroeconomic data from October 1987 to April 2025. Key predictive variables include differentials in interest rates, inflation, unemployment, and government bond yields between the United States and Japan. After a preliminary time-series analysis and feature selection, ensemble models were developed for four distinct time periods. Each model performs step-by-step forecasts up to four months ahead (January–April 2025), achieving exceptionally high predictive accuracy, with coefficients of determination (R²) above 0.98 and mean absolute percentage errors (MAPE) below 1%. The results demonstrate that combining macroeconomic fundamentals with advanced ensemble learning methods significantly enhances the accuracy, robustness, and reliability of exchange rate forecasting. These findings provide policymakers and investors with a robust analytical tool for anticipating short-term currency fluctuations under varying macroeconomic conditions.

This article examines the impact of students’ prior experience with English on their academic success in an English course at university. The study is based on a survey conducted with students majoring in Computer Science, Business Information Technology (BIT), and Software Technology and Design (STD) at the Faculty of Mathematics and Informatics (FMI), University of Plovdiv, at the beginning of their general English language course. We focus on students’ self-assessed language competence at the start of the course and examine how these self-assessments correspond to their actual test results. Using high-performance machine learning methods, we identify background factors that influence academic achievement, including the number of years spent learning English, the type of high school attended, and informal exposure to English. The findings aim to support more effective and tailored approaches to teaching English in technical and scientific disciplines.

Tocopherols, due to their antioxidant properties, are valuable compounds in the food and pharmaceutical industries. The present study compares the glyceride oil content and tocopherol profile of seeds of 49 plant species from 39 families of Bulgarian wild flora to identify their potential industrial and nutritional applications. The oils were extracted using the Soxhlet apparatus, and the tocopherol and tocotrienol composition was established by high-performance liquid chromatography (HPLC). Hierarchical cluster analysis was performed to group the plants based on their tocopherol profile. The results show high variability in the content of glyceride oils (ranging from 0.5% to 40.6%) and tocopherol profiles among species, even among plants within the same family. Four clusters were identified, each of which was characterized by the dominance of one of the tocopherol or tocotrienol isomers, i.e., α-tocopherol or γ-tocopherol, and reflected the chemical diversity of the examined plants. The statistical analysis confirmed that tocopherols and tocotrienols are significant factors influencing cluster grouping. The results reflect natural variability among species grown under field conditions, influenced by both genetic and environmental factors. This study provides valuable preliminary information for identifying wild species with promising tocopherol profiles for future functional research.

We unify a known technique used for fixed points and coupled, tripled and N-tupled fixed points for weak monotone maps, i.e., maps that exhibit monotone properties for each of their variables. We weaken the classical contractive condition in partially ordered metric spaces by requiring it to hold only for a sequence of successive iterations, generated by the considered map, provided that it is a monotone one. We show that some known results are a direct consequence of the main result. The introduced technique shows that the partial order in the constructed Cartesian space is induced by both the partial order in the considered metric space and by the monotone properties of the investigated maps. We illustrate the main result, which is applied to solve a nonlinear matrix equation, following key ideas from Berzig, Duan & Samet. We present an illustrative example. We comment that a similar approach can be used to solve systems of nonlinear matrix equations.

Using the deep result of Ran & Reunrings, we generalize existing results for tripled fixed points. In contrast to the previously known results for tripled fixed points of maps with or without the mixed monotone property in partially ordered complete metric spaces, we demonstrate that it is possible to obtain results for the existence and uniqueness of such points for arbitrary maps with a type of monotonicity, with the partial ordering in the Cartesian product arising from the maps itself. We prove theorems that ensure the existence and uniqueness for tripled fixed points for maps with different types of monotone properties. We obtain sufficient conditions for the existence and uniqueness of systems of three nonlinear matrix equations. The obtained results are illustrated by solving systems of matrix equations.