Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics
The Annual of Sofia University “St. Kliment Ohridski”. Faculty of Mathematics and Informatics is the first scientific Bulgarian journal, founded in 1904, devoted initially to pure and applied mathematics and mechanics, and later also to computer sciences.
Sofia Universty "St. Kliment Ohridski". Faculty of Mathematics and Informatics
A characterisation of the rate of approximation of the Baskakov-Kantorovich operator
We characterise the $K$-functional that was previously shown to describe the rate of approximation of the Baskakov-Kantorovich operator in the $L_p$-spaces with the weight $(1+x)^\gamma$ with $\gamma\le 0$. The characterisation uses the Ditzian-Totik moduli of smoothness.
Copyright (c) 2025 Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics
Notes on two definite quadrature formulae of order three
In two recent papers from 2017 and 2018 two definite quadrature formulae of order three were obtained which are modifications of the compound trapezium and midpoint quadrature rules, respectively. The criteria applied to the construction of these definite quadrature formulae is minimization of their error constants through the usage of appropriate formulae for numerical differentiation. In this note, we show that the aforementioned definite quadrature formulae also meet another criteria for optimality. For integrands having a continuous third derivative with a permanent sign, we present another error estimates, which are easier to evaluate and in many cases provide better error bounds.
A short note on a weighted Opial-type inequality
This paper establishes new weighted Opial-type inequalities by employing recent advances in weighted Hardy inequalities. Our approach builds upon results of Nikolov and Uluchev and develops inequalities for both single and two functions.
On the connection between fixed point theorems on metric spaces with graphs and $\mathbb{P}$ sets
The Banach contraction principle is one of the most famous and applied results in recent mathematical history. Due to its utility, plenty of generalizations have been established. One of them considers a contraction principle on metric spaces with graphs, while another confines the contraction principle to pairs of elements inside a $\mathbb{P}$ set, a generalization of partial orders. In this work we examine the similarities of both approaches, establishing the connection between theorems of metric spaces with graphs and metric spaces with $\mathbb{P}$ sets and restating results from one approach to the other and vice versa.
Two properties of the partial theta function
For the partial theta function $\theta(q,z):=\sum_{j=0}^{\infty}q^{j(j+1)/2}z^j$, $q$, $z\in\mathbb{C}$, $|q|<1$, we prove that its zero locus is connected. This set is smooth at every point $(q^{\flat},z^{\flat})$ such that $z^{\flat}$ is a simple or double zero of $\theta(q^{\flat},.)$. For $q\in (0,1)$, $q\to 1^-$ and $a\geq e^{\pi}$, there are $o(1/(1-q))$ and $(\ln(a/e^{\pi}))/(1-q)+o(1/(1-q))$ real zeros of $\theta(q,.)$ in the intervals $[-e^{\pi},0)$ and $[-a,-e^{-\pi}]$ respectively (and none in $[0,\infty)$). For $q\in (-1,0)$, $q\to -1^+$ and $a\geq e^{\pi/2}$, there are $o(1/(1+q))$ real zeros of $\theta(q,.)$ in the interval $[-e^{\pi/2},e^{\pi/2}]$ and $(\ln(a/e^{\pi/2})/2)/(1+q)+o(1/(1+q))$ in each of the intervals $[-a,-e^{\pi/2}]$ and $[e^{\pi /2},a]$.
A new reducibility result for minihypers in finite projective geometries
In this paper, we prove a new reducibility result for minihypers in projective geometries over finite fields. It is further used to characterize the minihypers with parameters $(70,22)$ in $PG(4,3)$. The latter can be used to attack the existence problem for some hypothetical ternary Griesmer codes of dimension 6.
Some applications of the functions of the system $\Gamma_{\mathcal{B}_s}$ to the theory of the uniformly distributed sequences
The authors use the $\mathcal{B}_s$-adic functions constructed in Cantor systems to show some of their applications to the theory of the uniformly distributed sequences. The notions of multidimensional modified integrals from these functions are introduced. The following results - the LeVeque's inequality, the Koksma's formula, the Erdős-Turán-Koksma's inequality and the integral Weyl's criterion, are presented in the terms of the introduced integrals.
function system $\Gamma_{\mathcal{B}_s}$
Large Language Models: A tool for solving mathematical problems in high school
Mathematics learning resources have evolved from static textbooks to collaborative online forums and conversational artificial intelligence (AI) tools. This evolution reflects students’ ongoing demand for clarity, adaptability, and accessible support. While traditional textbooks offered privacy, they limited flexibility. Online forums, such as Yahoo! Answers, Math Stack Exchange, and Mathematika.bg, enabled collaborative problem-solving, but they required public participation. Large language models (LLMs), including ChatGPT, now offer private, adaptive "comfort mode" interactions, combining the autonomy of self-study with the responsiveness of a personal tutor. The potential of LLMs to support mathematics education in Bulgaria is examined through a dual approach in this study: (1) eleven models solving problems from the Bulgarian National External Assessment (NEA) for 10th grade are empirically evaluated, and (2) practicing mathematics teachers enrolled in a Master program are qualitatively observed. Model performance was evaluated based on accuracy, methodological alignment with the national curriculum, and linguistic appropriateness. The findings indicate that, although several models, such as Mistral (22B) and DeepSeek R1, achieved perfect accuracy, they often used solution strategies that deviated from national standards. Locally fine-tuned models (e.g., BgGPT) demonstrated stronger curriculum alignment and the use of precise Bulgarian mathematical terminology. Teacher feedback revealed recognition of AI's potential for personalized student support, as well as caution toward integration, reflecting a preference to retain creative and methodological control. The study concludes that three conditions are necessary for successful AI integration in mathematics education: mathematical accuracy, adherence to curriculum-specific methods, and linguistically precise explanations. Large language models (LLMs) can complement, but not replace, the teacher's role when deliberately embedded in the continuum of educational resources, from books to forums to conversational AI.
An approach for ecological water bodies' environment modeling
The study presents an approach for modeling ecological water bodies' protection in order to support the transformation of agricultural land surrounding water springs into woodlands. Google Earth Pro was chosen for its enhanced capability to import Geographic Information System (GIS) data. It enables the measurement of ground area, radius, and circumference, along with the creation of high-resolution screenshots and offline videos for sharing. SketchUp, a 3D modeling tool, offers various drawing applications and features an extensive online library of free model assemblies. The combined use of these tools allows the creation of file formats that can be accessed in Google Earth Pro for virtual presentations. The efficacy of the proposed approach was illustrated using data from two springs located in the region of North Macedonia, which are utilized for bottled water.
Building mental health resources: the human-centered interaction design implemented in me_HeLi-D platform
This paper analyzes user feedback on the Moodle-based digital mental health literacy platform developed under the Erasmus+ project "me_HeLi-D: Mental Health Literacy and Diversity. Enhancing Mental Health and Resilience through digital Resources for Youth" (me_HeLi-D). The platform aimed to provide interactive mental health literacy content, and supported by user feedback contribute for engagement and improve learning outcomes. A mixed-methods approach, combining structured surveys and open-ended comments, was used to collect data on user experiences. Feedback was systematically categorized into general comments, module-specific critiques, and technical issues. Analysis helped identify recurring issues related to navigation, content accessibility, and technical difficulties with multimedia components, particularly with the multimedia functionality. Inconsistencies like the lack of availability for a "back to course" option confused users, and duplicated titles in some modules created additional navigational obstacles. Technical issues, such as the multimedia functionality, made content engagement difficult. These findings underscore the critical importance of user-centered design principles in developing effective digital learning environments. The study highlights the need for rigorous testing across diverse devices and operating systems to ensure accessibility and functionality. Furthermore, the feedback emphasizes the demand for more interactive learning experiences, suggesting that incorporating active learning strategies can enhance engagement and knowledge retention. Recommendations for platform revisions include addressing navigation inconsistencies, improving multimedia functionality, and incorporating interactive elements to promote active learning. This study contributes to the growing body of knowledge on best practices for designing and evaluating digital mental health literacy interventions and emphasizes the iterative nature of development based on continuous user feedback.
Almost zero and high $\omega$-Turing degrees
We show that the class of the high degrees is definable in the terms of the almost zero degrees in the local substructure of the $\omega$-Turing degrees. Namely, we prove that a degree is high if and only if it bounds all almost zero degrees.
On the error bounds of the Gauss-type quadrature formulae associated with spaces of parabolic and cubic spline functions with double equidistant knots
In two papers from 1995 P.~Köhler and G. Nikolov showed that Gauss-type quadrature formulae associated with spaces of spline functions with equidistant knots are asymptotically optimal in certain Sobolev classes of functions. In particular, Gauss-type quadratures associated with the spaces of spline functions of degree $r-1$ with double equispaced knots are asymptotically optimal definite quadrature formulae of order $r$ when $r$ is even, and it is conjectured that the asymptotical optimality property persists also in the case of odd $r$. For $r=3,\,4$, these quadrature formulae have been constructed by G. Nikolov, who also proved estimates for their error constants. The aim of this note is to refine the estimates for the error constant in the case $r=3$, and to point out to some error estimates in both cases $r=3$ and $r=4$, which are easier to evaluate and could be sharper than those which involve the uniform norm of the $r$-th derivative of the integrand.
Peano representation of linear functionals
Iordan Iordanov passed away unexpectedly on October 3, 2021. His loss is deeply felt by the academic community and friends around the world. The current work provides an overview of his academic career and achievements and surveys his research in mathematics, economics and finance.
Copyright (c) 2024 Annual of Sofia University “St. Kliment Ohridski”. Faculty of Mathematics and Informatics
Exploring software engineering knowledge domains
Software engineering, as the primary value-based process, is influenced by the culture a given company establishes, formal and informal procedures, and technological improvements introduced during the implementation. Having this in mind it could be articulated further how these innovative methods could result in best practices, communication flows, strong-bonded teams, and successful projects. By adding an organisational domain to the model, the relationships between management's organizational aspects and technological development approaches are discussed. This paper aims to explore and classify the software engineering domains in order to facilitate the process of managing knowledge within ICT companies. Based on a literature overview, a model is proposed which combines the multiple perspectives for adopting knowledge management practices more efficiently.
Digital hologram denoising by filtering in the hologram plane using the Hilbert-Huang transform
Image quality degradation is one of the main problems in Digital Holography. A novel method for noise reduction based on the Hilbert-Huang transform is introduced that reduces the normalized contrast and partially removes the DC-term. It is successfully applied in the hologram plane and requires a single hologram to function. The method causes no reduction in spatial resolution. Moreover, it can be combined with existing noise-filtering methods to improve image quality even further.
CAPEC is an effort coordinated by MITRE Corporation. Its aim is attack pattern database structured in taxonomies. CAPEC is available as XML document from its project site. CAPEC structure and content are under permanent change and development. It is still not mature database but may be never will. CAPEC, CWE, and CVE are databases devoted to attacks, weaknesses, and vulnerabilities. They refer each other forming a knowledge ecosystem in cybersecurity area. Traditional approach for knowledge presentation as information does not work well with conceptualizations under dynamics of this ecosystem and particularly of CAPEC. In this paper, an alternative approach to CAPEC knowledge presentation is proposed, as ontology. First, CAPEC structure and content are discussed and then ontology structure is introduced. CAPEC as ontology opens doors to ``open world'' concept that is more adequate to ecosystem dynamics. CAPEC ontology is programmatically generated from CAPEC database. CAPEC ontology generator in implemented in Python.
Social media data mining for exploring readers’ literary interests
Digital humanities have become a booming field of study thanks to the application of computer and information science methods to the humanities and the accumulation of large-scale digital resources. The use of data mining techniques and quantitative methods is expanding and starting to dominate the domain of literary studies, focusing not only on the study of the text itself but also on the study of social influences and preferences of the readers. By analysing social network data from VK, the most popular Russian platform, the study investigates which authors and literary works resonate most with users. To analyse the quotations, we created a framework which combines tools for extracting and cleaning data, named entity recognition and finally, corpus analysis; this framework can be applied to other datasets to compare and expand our findings. We also noted that within the information behaviour research domain, such studies of sharing among communities are not yet very popular. The study showcases the importance of employing advanced computational tools in humanities research. The obtained quantitative results are subjected to a critical analysis, which can serve as a basis for humanitarian understanding based on data. The compelling findings of this pilot study confirm opportunities for further research using more advanced quantitative methodologies, as well as broadening the scope of criteria that potentially influence the formation of reading preferences, such as level of education, pop-culture trends, social environment, etc. Additionally, it sheds light on the underexplored domain of community building in social media networks, calling for broader research into information behaviour and online community dynamics.
The integrability of the generalized Hamiltonian system
This paper reviews the generalized Hamiltonian system and its connection to contact transformations. The generalized Hamiltonian system is related to Herglotz variational principle in the same way in which the Hamiltonian system is related to the classical variational principle. We prove a criterion for the integrability of the generalized Hamiltonian system in terms of a complete set of first integrals, and a method of generating such first integrals. These results are due to Gustav Herglotz.
The present article studies the finite Zariski tangent spaces to an affine variety $X$ as linear codes, in order to characterize their typical or exceptional properties by global geometric conditions on $X$. We provide procedures for optimizing one of the parameters length, dimension or minimum distance of a single code by families of tangent codes.
No zeros of the partial theta function in the unit disk
We prove that for $q\in (-1,0)\cup (0,1)$, the partial theta function $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ has no zeros in the closed unit disk.
Exchange of occupational health assessment summaries based on the EN 13606 standard
The globalization of world economy stimulates large number of people to search abroad for better employment opportunities. This is the reason to consider the exchange of occupational health assessment summary (OHAS) content from cross-border view point. It is a problem of larger social-significance than the cross-border exchange for International Patient Summary (IPS). While the IPS dataset is well studied in the framework of an international standard, the OHAS remains rather insufficiently explored in the existing literature. This paper proposes a novelty systematic approach to provide a practicable solution to this problem by ensuring semantic interoperability in the exchange of OHAS. It starts by presenting a description of the use case for cross-border exchange. Next, the OHAS dataset is defined on the basis of exploring common data requirements the national legislation of EU countries. The final step of this approach is the design of an EN~13606 archetype of OHAS satisfying all the requirements for semantic interoperability in the exchange of clinical data. Further on, the static, non-volatile and reusable information model of OHAS is used to create EN~13606 instances that are valid with respect to the Reference model and the datatypes of this standard. Finally, this paper demonstrates the software implementation of basic activities in the OHAS use case in a fully functional web application, where the EN~13606 instances are managed by means of a native XML database.
The International Conference on Information Systems, Embedded Systems, and Intelligent Applications (ISESIA) 2023 was held in Sofia, Bulgaria, from May 26 to May 27, 2023. You can access detailed information about the event at ISESIA's official website https://isesia.fmi.uni-sofia.bg/.
Copyright (c) 2023 Annual of Sofia University “St. Kliment Ohridski”. Faculty of Mathematics and Informatics
Modeling and clinical data exchange in registration of infectious disease cases
The registration of communicable disease cases aims to limit their prevalence. The Ordinance on the Procedure for Registration, Notification and Reporting on Communicable Diseases, issued by the Ministry of Health, determines the rules for the implementation of the registration procedure in Bulgaria. Currently, this information is communicated by phone, email or on paper, and then the data is manually re-entered. This significantly complicates the exchange of information between health care participants. In addition, valuable information to produce reports noting disease prevalence levels is lost or fragmented. This paper aims to resolve these problems by the means of information technologies and ensure efficient storage, processing and management of data registration for patients with communicable diseases. The business process for the implementation has been studied in detail. The main roles, resources and sequence of activities at each stage of the application of the regulation have been determined. A relational database model is created for centralized storage, processing and management of data for registered patients and their contacts. An algorithm is developed and implemented for the automated determination of cases based on the symptoms of each disease specified in the regulation. ICD-10 is used, thus, creating the possibility of exchanging the collected data with international centers for tracking the spread of the disease. A three-tier application is created where web services perform the activities of registration, communication and reporting of communicable cases. The obtained results were tested with real data, consulted with experts from the health inspections and demonstrate the advantages of the developed software for fulfilling the requirements of the provisions in national legislation.
Enterprise data and semantic modelling: conceptual model of information technology incident management
Knowledge management methods and their efficient implementation across the organization determine sound and resilient management of processes. This paper studies the semantic integration of enterprise data sources essential to service management processes. Implementing a semantic layer within the enterprise architecture uses various tools, methods, and techniques. The semantic conceptual model unifies and implements intelligent integration of multiple data sources across the enterprise, achieving consistency and more accessible interpretation. Specifically, we draw our attention to incident and problem management within enterprises. We propose an ontology - a conceptual model for the incident management process. The incident ontology presented as an intelligent data integration layer component aims to achieve operational excellence. Besides, this ontology is a fundamental part of the proactive process in problem management. An ontology as a logic-based system supports integrity validation. It infers new, no explicitly modeled facts in the problem domain, thus helping experts better analyze and understand the problem. We discuss the conducted experiment results with the proposed in this article conceptual model using the enterprise knowledge graph platform. It can be perceived as a framework for a query-answering system with components, including ontology schema, data mapping, and classification methods for data graph enrichment.
An improved Bulgarian natural language processing pipeline
In this paper, we present a language pipeline for processing Bulgarian language data. The pipeline consists of the following steps: tokenization, sentence splitting, part-of-speech tagging, dependency parsing, named entity recognition, lemmatization, and word sense disambiguation. The first two components are based on rules and lists of words specific to the Bulgarian language, while the rest of the components use machine learning algorithms trained on universal dependency data and pretrained word vectors. The pipeline is implemented in the Python library spaCy (https://spacy.io/) and achieves significant results on all the included subtasks. The pipeline is open source and is available on Github (https://github.com/melaniab/spacy-pipeline-bg/) for use by researchers and developers for a variety of natural language processing and text analysis tasks.
Increase digital health literacy with the practical implementation of an e-learning system according to WCAG compliance standards
Individuals with cognitive difficulties (CD) have very limited access to appropriate learning resources. Their unique individual needs and requirements prevent them from accessing traditional online formal and informal learning methods, and resources are usually inadequate. We develop an e-learning platform with health content as an opportunity for all to increase digital health literacy, including people with cognitive disabilities. The paper aims to present some feature's settings important for people with a wide range of cognitive disabilities.
Frequency modulated signal standing out by stochastic resonance effect
In this paper, the phenomenon which is known as stochastic resonance is considered to the signal processing application. Signal standing out with the presence of noise is considered to be one of the basic problems of telecommunication and radioengineering. The stochastic resonance effect is shown to provide significant improvement of some characteristics of the information signal, such as power gain, and noise dispersion at the system output at a certain optimal noise level. In the present article, Minimum Shift Keying signal mixed with Gaussian white noise has been studied using stochastic resonance effect. Noise coefficient, which is one of the quantitative characteristics of noise immunity is calculated and investigated.
CAPEC is an effort coordinated by MITRE Corporation. Its aim is attack pattern database structured in taxonomies. CAPEC is available as XML document from its project site. CAPEC structure and content are under permanent change and development. It is still not mature database but may be never will. CAPEC, CWE, and CVE are databases devoted to attacks, weaknesses, and vulnerabilities. They refer each other forming a knowledge ecosystem in cybersecurity area. Traditional approach for knowledge presentation as information does not work well with conceptualizations under dynamics of this ecosystem and particularly of CAPEC. In this paper an alternative approach to CAPEC knowledge presentation is proposed, as ontology. First, CAPEC structure and content are discussed and then ontology structure is introduced. CAPEC as ontology opens doors to ``open world'' concept that is more adequate to ecosystem dynamics.
Machine learning for biomedical-focus on brain signals
There is a growing interest in machine learning (ML) in this decade. This growing interest is accelerated by cheaper computing power and low-cost memory. Thus, large amount of data can be stored, processed and analyzed efficiently. Machine learning has used in brain machine systems (BMS) system that converts brain impulses into messages or commands. In this paper we propose an EEG-based BMS with the focus on evoked potential. An average classification accuracy of 95% was attained among nine participants. With a rate of 4 flashes per second implemented, selecting one of four possibilities takes 5 s, resulting in an information transfer rate of 24 bits/min. Also, brain computer interfacing using oscillatory activity was measured. The results show that after around 5 h of co-adaptive training over many days, the average 3-class accuracy of the Linear Discriminant Analysis committee classifier reached about 80%, with a false positive rate for motor imagery recognition of around 17%.
Copyright (c) 2023 Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics
Preprocessing techniques for brain mri scans: a comparative analysis for radiogenomics applications
In this study, we aim to investigate the use of preprocessing techniques on brain magnetic resonance imaging (MRI) scans for the prediction of Methylguanine-DNA methyltransferase methylation (MGMT) status in glioma patients. MGMT methylation is a biomarker that has been linked to treatment response and prognosis in glioma. We review several studies that have applied preprocessing techniques to brain MRI scans, along with molecular genetic information, for this purpose. The preprocessing techniques include but are not limited to image registration, normalization, brain extraction, and tumor segmentation. We compare the effectiveness of the techniques used in these studies and evaluate the performance of each technique in terms of accuracy, computational efficiency and other parameters. Our goal is to identify the most effective preprocessing techniques for radiogenomics applications and to determine the potential of these techniques for improving the accuracy of predictions in brain MRI scans by combining different types of data. The results of this study have the potential to serve as a basis for the development of more accurate and efficient imaging-based diagnostic tools for glioma patients, and to improve the understanding of the relationship between imaging and genomics in glioma.