Vestnik (series: physical-mathematical and natural sciences), №1/2026

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СОДЕРЖАНИЕ 

MATHEMATICS AND COMPUTER SCIENCE

Tsirunyan V.D.  Integer Linear Programming Model for Investigating Near-Interval Edge-Colorings of Complete Bipartite Graphs PDF📥

ABSTRACT. A proper edge-coloring of a graph 𝐺 is a mapping 𝛼: 𝐸(𝐺) → ℕ such that 𝛼(𝑒) ≠ 𝛼(𝑒′) for every pair of adjacent edges 𝑒 and 𝑒′ in 𝐺. If 𝛼 is a proper edge-coloring of 𝐺 and 𝑣 ∈ 𝑉(𝐺), then 𝑆𝐺 (𝑣, 𝛼) denotes the set of colors appearing on edges incident to 𝑣. A proper edge-coloring 𝛼 of a graph 𝐺 with colors 1, … ,𝑡 is called a near-interval 𝑡-coloring if all colors are used, and for each vertex 𝑣 ∈ 𝑉(𝐺), 𝑆𝐺 (𝑣, 𝛼) is an interval of integers with no more than one gap. If a graph 𝐺 has such a coloring, the minimum number of colors in a near-interval coloring of a graph 𝐺 is denoted by 𝑤1 (𝐺). It is known that all complete bipartite graphs admit near-interval colorings. In this paper, we propose an integer linear programming (ILP) model to determine or bound the parameter 𝑤1 (𝐾𝑚,𝑛) (𝑚, 𝑛 ∈ ℕ) for complete bipartite graphs.
Keywords: proper edge-coloring, near-interval coloring, interval coloring, complete bipartite graph, integer linear programming. 

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Mikaelyan H.V.  General Bounds on Edge-Chromatic Sums of Graphs PDF📥

ABSTRACT. Proper edge-coloring of a graph is a mapping from its edges to natural numbers so that adjacent edges receive different numbers (colors). The edge-chromatic sum of the graph is the minimum sum of the colors on all edges among all proper edge-colorings of the graph. This work aims to find lower and upper bounds of the edge-chromatic sum parameter of graphs. Two lower and two upper bounds are obtained, they are compared with some existing results. It is also shown that both bounds are efficient for certain classes of graphs and for each bound there are graphs, for which it is more efficient than the other one.
Keywords: edge-chromatic sum, proper edge-coloring. 

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Sahakyan V. Visual Relative Localization for GNSS-Free Control of UAV Swarm PDF📥

ABSTRACT. Operation of UAV formations in GNSS-denied environments requires alternative sources of position information that can be integrated directly into the flight-control loop. This paper presents a leader–follower approach in which GNSS isreplaced for follower UAVs using visual relative localization computed onboard a single leader platform. The leader estimates the relative three-dimensional positions of follower UAVs using monocular vision and injects these estimates into the followers’ PX4 flight controllers through the external-vision interface. The followers rely exclusively on the injected relative position measurements for state estimation and closed-loop position control, without using GNSS or performing onboard localization. The proposed system is fully onboard, requires no external infrastructure, and is implemented using an open-source ROS 2–PX4 software stack. The approach is evaluated in a multi-UAV software-in-the-loop simulation under GNSS-denied conditions. Two experiments are conducted: nominal formation flight to assess steady-state behavior, and a leader velocity sweep to analyze the effect of increased dynamic excitation on tracking accuracy. Results show stable follower position control using relative localization alone, with bounded error across the tested operating range, demonstrating the feasibility of visual relative localization as a practical GNSS replacement for leader–follower UAV formations.
Keywords: GNSS-denied navigation; UAV formations; leader–follower architecture; visual relative localization; PX4 autopilot. 

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Avagyan T., Movsisyan H., Aslanyan H.  Solidity Compiler Version Detection from Source Code  PDF📥

ABSTRACT. This paper presents a method and an implementation of a tool, that finds the compiler version from the source code for the language Solidity. The approach uses regular expressions on its base, which ensures high performance compared to other methods based on the abstract syntax tree. Experimental evaluation on real-life projects has demonstrated its effectiveness, and the comparison with an existing tool has demonstrated its performance and accuracy. The developed tool demonstrates a performance increase of six times over the existing alternative solution; its precision reaches 100% (compared to 88.41%), while its recall is 98.77% (compared to 79.04%). 
Keywords: blockchain, code analysis, compilers. 

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Melkonyan V., Smbatyan M., Sardaryan A.  Automated Detection and Analysis of Projectile Impacts Using Computer Vision  PDF📥

ABSTRACT. This paper presents a software system for the automated real-time detection, stabilization, and analysis of projectile impacts in video sequences. The system utilizes a model to identify the region of interest automatically. Impact events are identified through a multi-method approach that combines the inter-frame transformation magnitudes, background subtraction, and contour analysis within a defined mask. The system outputs annotated frames marking the precise impact location and calculates its coordinates relative to the center of the target.
Keywords: lmpact Detection, Computer Vision, Optical Flow, Video Stabilization, Background Subtraction.

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Tumanyan H., Kirakosyan L.  A Software-Defined Radio Approach to LoRa-Based Сommunication for Unmanned Aerial Vehicles  PDF📥

ABSTRACT. As Unmanned Aerial Vehicles (UAVs) continue to expand their operational reach, the critical need for highly resilient, long-distance data links has driven significant interest in Low Power Wide Area Network (LPWAN) technologies. LoRa modules are commonly used for UAV telemetry; however, they typically operate on a fixed frequency channel, which makes the communication link vulnerable to jamming, whereas SDR-based systems can mitigate this issue by changing the operating frequency. SDRs offer incredible flexibility, allowing us to dynamically change frequencies to avoid active RF jamming and create custom, wideband channels that standard chips cannot support. Using BladeRF 2.0 micro xA4 SDRs and custom GNU Radio processing, we built a continuous, Frequency Division Duplex (FDD) LoRa link. By artificially expanding the bandwidth to 3 MHz and placing the uplink and downlink on entirely separate frequency bands, the system effortlessly handles the data flow required by Ground Control Stations. This design preserves the ruggedness of LoRa's Chirp Spread Spectrum while eliminating traditional bottlenecks, easily supporting MAVLink v2 encryption overhead, and entirely removing turnaround delays. Real-world flight tests with a Raspberry Pi 5 companion computer confirmed the system's stability, maintaining a flawless, low-latency connection at 400 meters using only the SDR's unamplified native power.
Keywords: Software-Defined Radio (SDR), Unmanned Aerial Vehicles (UAV), LoRa, Telemetry, BladeRF.

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Khachatryan G., Melkonyan V., Avanyan A., Hovhannisyan O.  Object Re-Detection in Aerial Imagery Captured by Uavs  PDF📥

ABSTRACT. Object re-detection in aerial imagery is a critical task for surveillance systems, search and rescue operations, and environmental monitoring. Objects that have previously appeared in a frame may disappear due to occlusions, viewpoint changes, or temporal gaps between frames. The ability to re-detect such objects significantly enhances the reliability of aerial observation systems. This work proposes a method for object re-detection in aerial images captured by unmanned aerial vehicles (UAVs). The method involves scanning new frames to find the object most similar to the previously lost one, using visual similarity. To improve robustness against distortions, the approach includes image preprocessing techniques and clustering to narrow the search area. The re-detection system incorporates a matching algorithm that compares the visual features of the lost object with potential candidates in subsequent frames. The effectiveness of the proposed approach is validated through experiments on real aerial image datasets, demonstrating successful object re-detection under varying conditions of background, scale, and lighting.
Keywords: object re-detection; aerial images; unmanned aerial vehicles.

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Movsisyan H.,  Aslanyan H.  Research and development of methods for source and binary code matching PDF📥

ABSTRACT. This paper addresses the problem of matching source code with its corresponding executable functions in the absence of debugging and symbol information. We present Pigaios++, an enhanced tool built upon the Pigaios framework. Key improvements include the integration of preliminary library function matching mechanisms and the introduction of new metrics, such as function signature comparison and library call analysis. Furthermore, a method is proposed to improve matching precision by analyzing the positional context of functions relative to already identified pairs. To evaluate the effectiveness of the tool, an automated test generation algorithm was developed. Experimental results conducted on the GNU Coreutils suite demonstrate that these modifications improved the average precision by 14.15% and recall by 10.3% compared to the baseline implementation.
Keywords: code matching, static matching, vulnerability analysis.

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Surmenelyan K., Aramyan A., Hovhannisyan O., Smbatyan М., Poghosyan V., Malajyan A.  Synthetic Data Generation Pipeline for Remote Sensing Tasks Based on Unreal ENGINE 5 PDF📥

ABSTRACT. This paper presents a synthetic data generation pipeline for remote sensing tasks implemented in Unreal Engine 5. The approach is based on procedural modeling of urban environments, stochastic object placement with geometric and semantic constraints, and simulation of virtual camera parameters. Annotations are generated automatically from the 3D scene and include 2D bounding boxes and semantic masks. The proposed pipeline ensures consistency between rendered images and annotations and enables scalable generation of training data for computer vision tasks in remote sensing.
Keywords: synthetic data, Unreal Engine, data annotation, remote sensing.
 

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PHYSICAL AND TECHNICAL SCIENCES  

Sivolenko E., Pinamyan M., Hovhannisyan B. Research and Modeling of Frequency-Modulated continuous waves (LFM, FMCW) in Software-Defined Radio Systems based on Open Tools PDF📥

ABSTRACT. This paper examines frequency-modulated continuous-wave (FMCW) radar technology, which is widely used in modern measurement radar systems. The primary focus is on the software implementation of an FMCW radar using a software-defined radio (SDR) platform based on USRP hardware and the GNU Radio development environment. The objective of the study is to obtain a functional implementation of an FMCW radar using the block-based architecture of GNU Radio and to experimentally validate its principal radar performance characteristics. FMCW signal generation, reflected signal modeling, and digital signal processing are implemented in this work. The experimental investigation is aimed at analyzing the spectral characteristics of the processed signals. It is shown that the software-defined approach provides high flexibility in configuring the parameters of the LFM (chirp) signal and enables efficient investigation of the influence of bandwidth, frequency sweep duration, and sampling rate on measurement results. The obtained results confirm the applicability of GNU Radio and USRP as a universal experimental platform for the study of FMCW radar systems and can be used in the development of automotive radars, collision avoidance systems, and other short-range radar applications. 
Keywords: Software-defined radio (SDR), functional principles of radar technologies, GNU Radio, digital signal processing (DSP).  

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Hovhannisyan S., Sivolenko E. Investigation and Implementation of a Multi-Frequency Continuous Wave Radar Using SDR Systems in an Open-Source Environment and the PYTHON Programming Toolkit PDF📥

ABSTRACT. Radar systems are classified according to the type of transmitted probing signal, including continuous-wave (CW), frequency-modulated continuous-wave (FMCW), stepped-frequency continuous-wave (SFCW), and pulsed radars. The choice of signal determines the system architecture and the methods used for processing the reflected signals. In this work, a multi-frequency continuous-wave (MFCW) radar is considered, which is based on the use of a set of discrete frequencies to estimate the target range from the phase relationships of the reflected signals. Compared with conventional CW and FMCW approaches, MFCW provides increased informational content with moderate implementation complexity and is well suited for experimental studies. The implementation of the MFCW radar is carried out using software-defined radio (SDR) based on the GNU Radio environment and the specialized gr-radar library designed for radar signal processing. The gr-radar toolkit provides ready-made blocks for signal generation, phase processing, and range estimation, enabling realtime signal processing and accelerating system prototyping. To improve the signal-to-noise ratio, matched filtering is applied within the utilized software framework. This approach ensures efficient detection of reflected signals with relatively low computational cost, which is particularly important for SDR-based radar implementations.
Keywords: GNU Radio, USRP, radar, MFCW, gr-radar.

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BIOLOGICAL SCIENCES

Tumoyan J. Biocompatible Silver Nanoparticles as Promising ANTICANCER Agents  PDF📥

ABSTRACT. Oncological diseases remain one of the leading global health challenges, with continuously increasing incidence and mortality rates, thereby driving the search for novel, effective, and safe therapeutic agents. Against the backdrop of the rapid development of nanotechnologies, particular interest has been directed toward nanoparticles with unique physicochemical properties that enable targeted effects on tumor cells and modulation of intracellular processes. Among these, silver nanoparticles (AgNPs) are considered promising anticancer agents due to their pronounced cytotoxic, pro-apoptotic, and antiproliferative properties. In recent years, significant attention has been devoted to elucidating the molecular mechanisms underlying their biological activity, including the generation of reactive oxygen and nitrogen species (ROS and RNS), mitochondrial dysfunction, caspase activation, modulation of key signaling pathways, biopolymer denaturation, and inhibition of tumor neoangiogenesis, including suppression of HIF-1α/VEGF-dependent pathways. Biogenic (“green”) synthesis of silver nanoparticles not only improves the biocompatibility of AgNPs but also enables the incorporation of biologically active phytocomponents, thereby enhancing their antiproliferative and pro-apoptotic potential. Moreover, AgNPs demonstrate pronounced synergistic effects with chemotherapeutic agents, contributing to the overcoming of multidrug resistance and improving treatment efficacy. This review also addresses the limitations associated with potential toxicity, tissue accumulation, and the sensitivity of nanoparticle properties to size, shape, and coating type. Current strategies aimed at improving the safety and targeting of AgNPs are discussed, including biogenic synthesis and surface functionalization. Despite significant progress, the clinical application of AgNPs remains limited due to an incomplete understanding of their pharmacokinetics, biotransformation, and toxicity. 
Keywords: oncology, nanotechnology, silver nanoparticles, anticancer activity, molecular mechanisms.

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