Balkan Journal of Applied Mathematics and Informatics
GOCE DELCEV UNIVERSITY - STIP, FACULTY OF COMPUTER SCIENCE
ANALYSIS OF THE MOVEMENT OF FLUCTUATIONS AND TRENDS OF THE GROSS DOMESTIC PRODUCT IN THE REPUBLIC OF NORTH MACEDONIA AND FORECASTS
In this paper, an analysis will be made of the movement of fluctuations and trends in the gross domestic product, in the period from 2000 to 2024 by quarter with current prices expressed in millions of denars in North Macedonia, using time series. The analysis will be done using the Python program. In the end, with the help of the previously prepared program and model, a prediction is made for the movement of trends and fluctuations in GDP in the period from 2024 to 2028.
Copyright (c) 2025 Balkan Journal of Applied Mathematics and Informatics
INTEGRATING AI AND CLOUD COMPUTING FOR EFFICIENT AUDIO ANALYSIS
Abstract. This paper propose a pipeline for sentiment analysis of audio inputs by using AI and techniques for speech recognition. A key aspect of our approach involves determining audio chunks based on silence detection and decibel height, allowing for more effective segmentation and analysis of the input data. These techniques will be instrumental in categorizing audio materials, enabling more organized and accessible content management. In the scope of this paper, we will compare and utilize several Python packages for audio detection, including Librosa, PyDub, and SoundFile, which offer various functionalities for audio analysis and manipulation. Additionally, we discuss the high computational demands associated with training and deploying of models, highlighting the potential cost barriers for many organizations. To address these challenges, we propose the use of cloud-based solutions, specifically AWS Spot Instances, Azure Spot VMs, and Google Cloud Preemptible VMs, which offer substantial cost savings for processing audio data. By leveraging these cloud resources, organizations can significantly reduce expenses while maintaining high performance in AI audio processing tasks.
STATE-OF-THE-ART COMPARISON OF MOBILESECURECOMM WITH MODERN SECURE COMMUNICATION PLATFORMS FOR TACTICAL OPERATIONS
Modern military and critical missions depend on secure, fast, and flexible communication systems that can perform reliably across various operational environments. Legacy platforms such as SINCGARS, EPLRS, and CERT-based emergency systems have offered foundational services, but they fall short when it comes to adapting to new threats, supporting modern data-intensive operations, or integrating with advanced technologies like artificial intelligence and quantum encryption. This paper presents a state-of-the-art comparison between existing secure communication platforms and a newly proposed system called MobileSecureComm. Designed for tactical operations, MobileSecureComm combines modular architecture, quantum-ready encryption, and AI-driven routing to meet the growing demands of modern warfare and emergency response scenarios. The paper draws from extensive literature covering secure mobile platforms, military-grade messaging systems, mobile edge computing, and real-world deployment models. Using simulation-based analysis, the study compares MobileSecureComm to 25 secure communication platforms in terms of latency, throughput, security, interoperability, and resilience. The results show that MobileSecureComm consistently achieves lower latency, higher data throughput, and stronger security safeguards than traditional platforms. It also offers seamless integration with NATO-compliant systems and the flexibility to scale across multi-domain operations. This paper highlights the importance of designing secure communication platforms that are not only technically advanced but also adaptable to changing threats and diverse mission requirements. MobileSecureComm provides a forward-looking solution that can help bridge the gap between existing systems and the future of tactical communication.
MONITORING OF AC MOTOR SPEED CONTROLLER PARAMETERS TO IoT NETWORK
Today's development of electronics mainly takes place in two directions. One direction is based on the technological development of semiconductor elements that will work in a larger current, voltage and frequency range. The other direction is based on the development of information bases and systems that will ensure the collection, visualization, processing and transport of process parameters. The first direction will enable applications in power electronics for higher powers and process speeds, and the second local and remote transmission of process data and their availability in intranet and internet networks. Taking this into account in the paper, an electronic system is designed and implemented that measures, stores and transmits the parameters of a 1-phase AC motor speed controller in an IoT network. The solution enables the visualization of input and output parameters locally on two LCD displays and remotely on an IoT device. A data log file is also provided for the measured values ​​on a local computer and on an IoT cloud computer.
AC motor controller, Integrated circuit, Data log file, Blynk cloud
DEEP LEARNING-BASED DETECTION AND CLASSIFICATION OF DOCUMENT ELEMENTS USING ROBOFLOW
Recent advances in deep learning have enabled significant improvements in document understanding and processing. This paper presents a workflow for detecting and classifying key document elements—paragraphs of text, tables, signatures, and stamps—using deep learning models implemented through the Roboflow platform. We address the unique challenges of document element detection, including complex spatial relationships, overlapping boundaries, and varying formats across different document types. Our methodology leverages Roboflow's comprehensive toolkit for dataset preparation, model training, and deployment, with particular attention to data augmentation techniques specific to document processing. The proposed system achieves robust detection and classification of document elements. Experimental results demonstrate the system's effectiveness in real-world applications. Our findings indicate that the proposed approach offers significant accuracy and efficiency of automated document processing, particularly in scenarios requiring the precise identification and extraction of structured and unstructured document components.
AUTOMATED DOOR STATE DETECTION USING DEEP LEARNING: A COMPUTER VISION APPROACH WITH ROBOFLOW PLATFORM
This paper presents a deep learning-based approach for automated door state detection, capable of classifying doors as open, closed, or semi-open. The implementation leverages the Roboflow platform for comprehensive image processing and model development workflow. Our methodology encompasses data collection, annotation, augmentation, and model training using state-of-the-art deep learning architectures. The system demonstrates robust performance in real-world scenarios, offering potential applications in building automation, security systems, and smart home technologies. This work contributes to the growing field of automated building monitoring by providing a practical solution for door state recognition that can be integrated into existing surveillance and security infrastructures.
GENERALIZATION OF APPLICATION OF FUNDAMENTAL LEMMA OF VARIATIONAL CALCULUS
Variational calculus studied methods for finding maximum and minimum values of functional. It has its inception in 1696 year by Johan Bernoulli with its glorious problem for the brachistochrone: to find a curve, connecting two points A and B , which does not lie in a vertical, so that heavy point descending on this curve from position A to reach position in for at least time. In functional analysis variational calculus takes the same space, as well as theory of maxima and minimum intensity in the classic analysis. In this paper we will prove a theorem for functional where proves that necessary condition for extreme of functional is the variation of functional is equal to zero.
SMART CITY: A REVIEW OF CURRENT DEVELOPMENTS AND IMPLEMENTATION OF SMART GRID TECHNOLOGY
To ensure better living standards for the population, it is necessary to develop smart cities that utilize modern technology and operational efficiency to facilitate daily life. The primary goal of implementing (or creating) a smart city is to maintain, balance, and continuously upgrade economic, social, and environmental resources while managing costs. Emphasis is placed on maximizing the use of natural resources through energy conservation (utilizing renewables), efficient water usage, time savings, land optimization, environmental quality, traffic management, and the extensive use of information and communication technology systems and services for effective management and their ongoing enhancement. This work aims to create improved functionality, smart connections, and better organization among people, while maximizing the use of natural resources, minimizing environmental pollution, and improving public health.
technology, natural resources, upgrading, green energy
This paper presents a comparative analysis of prominent BPMN (Business Process Model and Notation) tools, including Camunda, Bizagi Modeler, bpmn.io, ProcessMaker, and Lucidchart. We evaluate these tools based on key criteria such as features, functionality, usability, integration capabilities and cost. By examining their strengths and limitations, we aim to provide a comprehensive overview that assists organizations in selecting the most suitable tool for their business process modelling needs. The analysis includes practical insights into each tool's effectiveness in facilitating process design, simulation and execution, offering valuable guidance for practitioners and decision-makers.
BPMN tools, Camunda, Bizagi Modeler, bpmn.io, ProcessMaker, Lucidchart.
Copyright (c) 2024 Balkan Journal of Applied Mathematics and Informatics
Business Process Model and Notation (BPMN) and Unified Modeling Language (UML) are two widely adopted tools for modeling in business and software engineering respectively. This paper explores the use cases for both BPMN and UML tools, highlighting their respective applications, differences, and synergies. By examining their features and specific scenarios where each tool excels, this research provides insights into how organizations can effectively leverage these tools for optimal outcomes.
BPMN tools, UML tools, Camunda, Bizagi Modeler, Lucidchart, StarUML, Enterprise Architect, Visual Paradigm, ArgoUML;
ON THE INTERGRABILITY OF A SUBCLASS OF 2D MATRIX DIFFERENTIAL EQUATIONS
In this paper, the 2D matrix differential equations are considered. Under certain conditions, using the Rodrigues’ formula for these 2D matrix differential equations, a particular solution is obtained. Finally, this theory is supported by examples.
2D matrix differential equations, Rodrigues’ formula, integrability
MULTI-ACTION GRID AUTHENTICATION: A SECURE AND USABLE AUTHENTICATION SYSTEM FOR SMART TOUCH DEVICES
In the digital age, securing smart touch devices is of paramount importance to safeguard sensitive information. Traditional graphical password systems, while convenient, remain vulnerable to attacks such as shoulder surfing and smudge tracing. This paper introduces a novel multi-action grid authentication system that enhances security while preserving ease of use. The system allows users to authenticate by performing two actions—tapping and replacing—within a 3x3 grid. Through iterative development and testing, the method shows significant improvements in preventing common security threats while maintaining high user satisfaction. A thorough analysis of password space is also conducted, demonstrating the system's robust resistance to brute-force attacks. Our findings suggest that this multi-action approach offers a secure, efficient alternative to existing graphical password systems.
POSSIBILITIES FOR INSTALLATION OF PHOTOVOLTAIC SYSTEMS IN CATERING FACILITIES IN MACEDONIA
The energy crisis that swept across Europe and the resulting electricity price impact have highlighted the need for enhanced energy resilience. To mitigate future price fluctuations and unforeseen shocks, investments in photovoltaic (PV) systems are crucial. Hospitality establishments in Macedonia hold significant potential for reducing the country’s energy dependency and accelerating the energy transition. It is therefore essential to explore the feasibility of installing PV systems on these establishments and to assess the profitability of such investments. For an optimal analysis of PV system installation potential in the hospitality sector, data from the State Statistical Office, based on the 2021 census in Macedonia, were utilized. According to the census, there are a total of 1,006 hotels and restaurants in the country. This analysis presents the total potential installed capacity of PV systems on all hotels and restaurants in Macedonia, the predicted annual electricity generation from these systems, and the resulting avoided CO2 emissions. Since the intensity of solar radiation varies geographically, simulations were conducted for PV systems with an installed capacity of 40 kWp in each region: Vardar, Eastern, Southwestern, Southeastern, Pelagonia, Polog, Northeastern, and Skopje regions. These simulations were performed using the PV*SOL premium software, which leverages the Meteonorm database for solar radiation data to estimate annual electricity production from the PV systems. The analysis also includes case studies for a hotel and a restaurant, for which techno-economic analyses were conducted to evaluate the profitability of PV system installations.
photovoltaic systems, installed capacity, electricity generation, techno-economic analyses.
The science of digital forensics is an ever-changing and complex field which demands continuous advancements and development. It involves examining and extracting data from electronic devices which can consequently be used as digital evidence in the investigation of potential criminal activities. The forensic experts work tirelessly on finding new and improved tools which can make the research in the field more effective and the practical work of the examiners more productive. The processes and procedures are also constantly updated to follow the technological advances, in order to keep up with the trends lead by the manufacturers of electronic devices. The following research paper provides detailed description of the process of examination and extraction of data from mobile phones with android operating system. The detailed description explains the standardized procedures in stages, categorized in logical and chronological order to depict the work tasks of a digital forensic examiner. In addition to the theoretical explanation, this paper also offers practical examples of digital forensic examination. This practical examination was conducted to supports the key points of the elaborated research. Key words: digital forensics, mobile phone, android operating system
digital forensics, mobile phone, android operating system
APPLICATION OF CENTER OF GRAVITY METHOD FOR LOCATIONS OF FACILITIES
The facility location decision is a critical aspect of operations management, with transportation costs often serving as a primary consideration. The Center of Gravity (COG) method has emerged as a practical tool for its simplicity in estimating optimal facility locations. This paper provides a comprehensive review of the COG method, acknowledging its strengths as a quick approximation tool but also highlighting its limitations. We delve into the method's assumptions, notably the uniformity of transportation costs, and discuss its application in dynamic and complex environments. Furthermore, we advocate for a holistic approach to facility location decisions, incorporating factors such as market competition, legal constraints, and environmental sustainability. To address these complexities, we propose the integration of advanced tools and techniques, including optimization algorithms, geographical information systems (GIS), and machine learning. By embracing a more sophisticated analytical framework, organizations can make informed decisions that align with broader business objectives, ensuring that facility locations are strategically chosen beyond the narrow focus on transportation costs. This paper aims to guide practitioners and researchers in navigating the intricacies of facility location planning, emphasizing the importance of a nuanced and advanced approach.
DETERMINATION OF ALGEBRAIC POINTS OF LOW DEGREE ON A FAMILY CURVES
Let n be a positive integer. The purpose of this paper is to determine explicitly algebraic points of low degree over Q on the family curves of affine equation y3n=x4n-1. An algebraic point of degree at most 2 is called an algebraic point of low degree. The essential tools for this determination are the theorem of Chevalley-Weil, cyclotomic polynomials, rational morphisms between these curves and the special Picard curve of affine equation y3=x4-1.
EXIBITION PRAMETRIC FAMILY OF ALGEBRIC POINTS OF GIVEN DEGREE ON THE AFFINE EQUATION CURVE: −y2 = x6 − 20x3 − 8
We give an explicit parametric family of algebraic points of given degree on Q over the affine equation curve: -y2 = x6 - 20x3 - 8. These curves are described by Nils BRUIN in [1], who showed that the MordellWeill group is finite and explained the generators of the torsion group for this curve.
IMPLEMENTATION OF SCADA SYSTEM FOR REMOTE MONITORING AND POWER METERING IN RF AND IoT NETWORKS
This paper represents the results of the development, design, and practical implementation of the SCADA monitoring power meter system. This power meter system is implemented in RF and IoT networks.The solution has been tasked with collecting, measuring, storing, and visualizing energydata (voltage, current, power, energy, reactive power, reactive energy, and power factor), as well as appropriate process data in two remote industrial plants. In the first plant, the first energy measuring point marked as the MASTER station is located, and in the second plant, the second energy measuring point marked as the SLAVE station is located. The SCADA monitoring system is built into the MASTER station. The SLAVE station is connected by RF (radio frequency connection) to the MASTER station. In the MASTER and SLAVE stations, two microcomputers and energy measurement units as well as appropriate RF modules are installed. The microcomputer in the MASTER station is serially connected to the IoT microcomputer for the transfer of measurement data in the Internet network. The solution provides visualization, data log file, and transfer to the IoT network of the energy and process data from the two measuring points.
SCADA, Smart Power Meter, RF Network, Data log file, IoT network
SOLUTION TO THE CATENARY PROBLEM BY APPLYING THE FUNDAMENTAL LEMMA OF VARIATIONAL CALCULUS
In this paper, we will prove a theorem for functional where prove that necessary condition for extreme of functional is the variation of functional is equal to zero and we will give an example of its application, to the catenary problem.
extreme, functional, variation, condition, catenary
AUTONOMOUS SOLUTIONS FOR DESIGN AND IMPLEMENTATION OF MODULAR STRUCTURES
Our objective with this paper is to analyze and explore emerging autonomous solutions for designing and implementing modular structures. Modular structures have been in use since the 1950s, so the concept is not new to us. Historically, the popularity of modular structures peaked following catastrophic natural disasters or wars, in areas that required rapid rebuilding. However, modular construction somewhat fell out of favor afterward. Nowadays, its popularity is resurging, becoming a notable trend once again. The robots employed in modular construction offer distinct advantages over those used in traditional construction, with streamlined tasks and enhanced efficiency. In this paper, we plan to analyze drones, loaders, cranes, and worker bots. These robots will serve various roles, including observation, construction, organization, and excavation. Furthermore, we aim to integrate these robots with cutting-edge technologies such as artificial intelligence, augmented and virtual reality, the internet of things, cloud services, and building information modeling - BIM.
Modular construction, Autonomous robots, Drones, Artificial intelligence, IoT
MODELLING A MASS-SPRING SYSTEM USING A SECOND-ORDER HOMOGENEOUS LINEAR ORDINARY DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS
In this paper, a mass-spring system is considered. The system is modelled using a second-order homogeneous linear (ODE) with constant coefficients. Using this model, the behaviour of the system is studied. The most significant factor, the value of the damping, determines whether the case occurs: no damping, underdamping, critical damping, or overdamping. Each case is mathematically analysed to get particular parameters that impact how the motion system performs. The obtained solution, which demonstrates the behaviour of the system in a diagram plot of a displacement-time graph and a phase plane graph, is graphically presented in MATLAB software.
Mass, damping coefficient, spring constant, modelling, energy
SCADA PROCESS VARIABLES MONITIORING INTEGRATED IN RF NETWORK
In this paper results fromt the developed design and practical implementation of the SCADA system are represented. The solution collects, measures, stores and displays the process data in an industrial plant. The SCADA system includes IoT RF communication between MASTER and SLAVE stations. Some of the hardware sensors and components are installed in SLAVE station and some in MASTER station. The communication between the SLAVE and MASTER stations is ensured by a microcomputer and RF modules.
SCADA, RF Network, Master and slave stations, Data log file
AUTOMATED PROCESSING LINE FOR EFFICIENT SORTING OF WASTE RECYCLABLE MATERIALS
This paper is considering the implementation of a modern automated processing line designed to enhance the efficiency of waste material sorting. With a focus on delivering products of optimal quality and quantity within defined timeframes, the research uses a comprehensive methodology integrating advanced automation techniques. Through an examination of the complex dynamics inherent in sorting processes, the research not only addresses fundamental challenges in waste management understanding but also highlights positive environmental outcomes and promotes ecological integrity. The integration of automated systems not only aims to improve productivity and staff working conditions but also aligns with the imperative of promoting a more ecologically sustainable environment. The architectural layout of the facility is strategically organized into two specialized zones, including the reception area for waste intake and sorting and preprocessing section utilizing advanced technologies. These identified zones collectively form the backbone of the facility’s infrastructure, ensuring a systematic and effective approach to waste management.
Robotic automation, waste management, sorting, RVM, deep learning, artificial intelligence
CAN CHATGPT BE USED FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS
In this research we have conducted empirical study to evaluate the capabilities of OpenAI’s chat bot ChatGPT for automated software code generation and programming numerical methods for solving various types of differential equations. We have tested the ChatGPT for analytical as well as numerical solution of first and second order ordinary differential equations. Obtained results suggest that ChatGPT is a promising AI tool for programming numerical algorithms and solving differential equations. However, there are still some limitations and challenges of using AI for numerical solution generation, related to the potential biases in the algorithm, as well as need for large amount of high-quality training data. However, as AI technology continues to develop, it is likely that the use of AI for programming will become more prevalent and effective in the future.
ChatGPT, Ordinary Differential Equations (ODE), Artificial Intelligence (AI).
Copyright (c) 2023 Balkan Journal of Applied Mathematics and Informatics
COMPARATIVE ANALYSIS OF STANDARDS AND METHODOLOGIES FOR MANAGEMENT OF INFORMATION-SECURITY RISKS OF TECHNICAL AND ELECTRONIC SYSTEMS OF THE CRITICAL INFRASTRUCTURE
Information security is a priority at the national and world level, which results with the need to define certain security violations with the ultimate goal of successfully preventing information breaches, and with that quickly and successfully remediating the consequences. In a cyber-war scenario, the energy and financial sectors are considered as the most critical to national security. The identification of key weaknesses, risks and potential exposure to cyber threats in energy systems, as well as the creators of cyber incidents, can be performed based on the perception of possible cyber-attack scenarios. At the world level, there are several models for assessing and managing security risk (ISO/IEC 27001, NIST 800-53, COBIT, OCTAVE Allegro, etc.) and therefore the main goal of this research is to sublimate and compare the values of the most frequently used methodologies, which will enable the selection of the best model for the successful prevention of information breaches and the quick and successful remediation of the consequences. This paper will analyze the application of current standards and methodologies for managing information-security risks in the elements of CI, assessment of the level of application of standards and methodologies in the institutions, which are part of CI, as well as determining a way to improve the management of current information security risks.
security risk assessment methodology, security risk management, ICT-Infrastructure, security incidents, computer incidents, protection, cyberspace, cloud system, Intelligent Electronic Devices, Industrial Control Systems, Supervisory Control and Data Acquisition, Distribution Control Systems.
Tuberculosis (TB) is a highly contagious infectious disease caused by the bacterium Mycobacterium tuberculosis. It primarily affects the lungs but can also affect other parts of the body. TB poses a significant global health burden, with millions of new cases and deaths reported each year. Understanding the spread of tuberculosis and evaluating control measures are crucial for effective disease management. The SEIR model is a commonly used mathematical framework for studying the spread of infectious diseases. It divides the population into four compartments: Susceptible (S), Exposed (E), Infectious (I), and Recovered (R). In the case of tuberculosis, an additional compartment for the number of deaths (D) is included. The model tracks the flow of individuals between these compartments over time.
Tuberculosis, SEIR model, simulation, differential equations
GANTT CHART AS A PROJECT MANAGEMENT TOOL THAT REPRESENTS A CLUTCH HUB MANUFACTURING PROCESS
The purpose of the research in this paper is to present a clutch hub manufacturing process via Gantter, a Gantt chart-based project management software. The Gantt chart is one of the most used planning and controlling tools in project management today and can be called a main and very important tool of management. It allows the creation and edition of project plans through the implementation of defined activities, their durations, relationships between the activities, appropriate resources, and possible risks. This paper is an example that shows how the logic embedded in projects can be based on real manufacturing processes and applied to a project management tool in order to achieve the goals of the project.
Resource, risk, schedule, manufacturing operation, machine.
IMPACT OF CUTTING CONDITIONS ON THE LOAD ON SERVO MOTORS AT A CNC LATHE IN THE PROCESS OF TURNING A CLUTCH HUB
The purpose of the research in this paper is to investigate the impact of cutting conditions on the load on servo motors at a three-axis computer numerically controlled (CNC) Hitachi Seiki Seicos lathe. The analysed parameters (cutting speed, feed, and depth of cut) play a crucial role in the turning process. It is significant that each cutting condition directly alters the value of the load on the power system and has a significant effect on cutting forces, which in turn affect the load on the servo motors at the CNC lathe during the process.
Cutting speed, feed, depth of cut, workpiece, motion, asynchronous.
PROGRAMING PLC CONTROLLER WITH LADDER DIAGRAM
In this paper are consider one industrial process and consider about the automation of that industrial process. In automation the most important part is the controller. The controller is actually the brain of the process, and it regulates the switching on and off of all the elements involved in the process itself. The controllers that are used in industrial automation are called programmable logic controllers (PLC controllers). With example is showed how the PLC controller can be programed with Ladder Diagram. PLC programming involves creating a set of instructions that govern the behavior of a PLC to control machinery and processes. These instructions are written using specialized software tools and are executed in a sequential manner. The primary objectives of PLC programming are to ensure the safe and efficient operation of automated systems, maintain process accuracy, and facilitate quick responses to changing conditions.
Analysis of the usage of mobile devices as distributed tools for patient health monitoring and remote patient data acquisition
The COVID-19 pandemic raised the need for telemedicine systems. Wearable and mobile devices are often a crucial part of those systems. In accordance with current research, this paper presents an analysis of some means, sensors and devices for remote patient health monitoring which can be combined together to form a complete patient health monitoring system. A few ways of measuring the health parameters are described. Focusing on the benefits offered by contemporary technology towards more complete use of telemedicine potential, this paper also reviews topics from the field of biomedical engineering.