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Discrete and Continuous Models and Applied Computational Science
Scopus
ISSN 2658-4670 · Peoples’ Friendship University of Russia (RUDN University) · 209 articles in the index
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Journal Article
On the classical Volterra spectral equation
We study the characterizations of the classical Volterra operator based on a simple relation between its singular numbers and the eigenvalues of its imaginary part on \( L^2[0,1] \).
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Journal Article
About one method of approximate solution of the first boundary value problem for the fractional diffusion equation
Background This article focuses on a rapidly developing area of fractional calculus that describes anomalous diffusion. Since the correct form of the fractional-order equation describing anomalous diffusion - remains an open question, the authors use examples of models based on fractional diffusion…
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Journal Article
Stochastic representation of quantum mechanics and entangled solitons
Background Using the Einstein's idea on particles-solitons, the stochastic representation of the wave function as a large sum of solitons with random phases is suggested. Purpose To illustrate the main idea of the stochastic representation, let us recall the lectures by N. Wiener on nonlinear…
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Journal Article
A queueing-inventory model for energy-constrained UAV base stations in non-terrestrial networks
Unmanned aerial vehicle base stations are envisioned as key enablers of sixth-generation non-terrestrial networks, offering on-demand aerial coverage for remote areas, mass events, and emergency scenarios; however, their operational continuity is fundamentally limited by finite onboard battery…
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Journal Article
On quadratic transformations of the Fano plane
The importance of studying quadratic Cremona transformations over algebraically non-closed fields for the theory of Kahan difference schemes for dynamical systems with a quadratic right-hand side is discussed. Cremona transformations of the projective plane over a Galois field of size 2, i.e., the…
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Journal Article
Efficient Polyp Segmentation and Classification with YOLO11-SAM3 and LoRA
Purpose To develop and experimentally evaluate an autonomous computer-aided diagnosis (CADx) system for colonoscopy that integrates polyp segmentation with binary histological classification (adenoma/non-adenoma) while maintaining computational efficiency for near real-time clinical deployment…
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Journal Article
Development of the malicious traffic detection system for mobile applications security
Background: The rapid increase in cyberattacks targeting infrastructure, enterprises, and individual users through mobile devices has created an urgent need for effective intrusion detection systems. Traditional signature-based methods are inadequate against zero-day vulnerabilities and advanced…
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Journal Article
Calculation of modified Hamiltonian in Sage
The algebraic properties of difference approximations of Hamiltonian systems are investigated. Symplectic schemes exactly preserve linear and quadratic integrals by virtue of Cooper's theorem, but not the total mechanical energy of nonlinear systems. However, it is known that instead of energy…
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Journal Article
On the behavior of orbits of Vanhaecke system on integral surfaces
In the 1990s, P. Vanhecke described a Hamiltonian system with two degrees of freedom and a polynomial Hamiltonian integrable in Abelian functions of two variables. This system provides a convenient example of an integrable system (in the sense of Liouville) in which integral curves are wound on a…
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Journal Article
ISO rules for typesetting mathematics
Using ISO standards for mathematical notation is important for improving the quality of scientific paper presentation. This article describes the key requirements of ISO standards for mathematical notation. It also provides recommendations for the notation of differential operators.
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Journal Article
Modeling authorship attribution for short texts under training corpus degradation
Attributing authorship of short texts is a complex task, and its accuracy heavily depends on the quality and quantity of training data. In many practical scenarios, however, this data is subject to degradation. This study examines how two specific types of degradation - textual corruption and…
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Journal Article
A model of cumulative advantage for conference dynamics
This paper attempts to modify the standard Verhulst model to describe the dynamics of scientific conferences taking into account cumulative advantage.
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Journal Article
Solution of the one-dimensional Schrödinger equation for a heterostructure with a triangular potential function by the power series method
In the work by the power series method the one-dimensional Schrödinger equation is solved with a triangular potential function which is applied in various modern heterostructures, in particular for GaAs and the others. By varying available parameters it is possible to obtain the desired precision…
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Journal Article
The waiting time extremal index in GI/G/1 system
In this paper the conditions to compare the extremal index of the stationary waiting time in the $M/G/1$ and $GI/M/1$ systems are obtained. These conditions include exponential asymptotic behaviour of waiting time tail and the order in failure rates for the interarrival intervals and for the…
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Journal Article
Usage of polynomial representation of numbers for approximate homomorphic encryption
\emph {Introduction} In the modern world of computers and networks the idea of expanding of personal computer resources with the help of cloud storages and computation looks more and more lucrative. However, usage of these resources may endanger data being processed. In last twenty years several…
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Journal Article
On a finite-difference scheme defining a birational non-quadratic map between time layers
The article considers reversible difference schemes for dynamical systems based on the system doubling method proposed by V.N. Abrashin and S.N. Sytova. The method duplicates the original variables, leading to an extended system whose finite-difference approximation defines a birational map between…
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Journal Article
Dual quaternion representation of geometrical motion in 3D space
\emph {Background} In a previous article we discussed the use of dual quaternions for modeling points, lines and planes and solving standard geometric problems. This article is a logical continuation and reveals the use of dual quaternions to describe isometries of three-dimensional space. \emph…
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Journal Article
Physical dimensional quantities typesetting
The siunitx package is designed for typographically correct and consistent typesetting of physical quantities (numbers with units of measurement) in LaTeX documents. It automates formatting according to the rules of the International System of Units (SI), eliminating the need to manually manage…
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Journal Article
Simulation of the evacuation of passengers and crew from aircraft during a fire on the ground
Background. Currently, incidents, including fires on board of aircrafts during takeoff and landing, are becoming more frequent. To address this issue, we introduce new models of fire propagation dynamics and the evacuation process for aircraft passengers, accounting for their physical interactions…
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Journal Article
Interaction of relativistic electrons with intense electromagnetic fields: ponderomotive\,effect, acceleration,\,refraction,\,reflection, dependence\,on\,initial\,conditions
The rigorous theory and characterization of charged-particle dynamics in high-intensity electromagnetic fields are fundamental for the development of advanced plasma-based applications. Accurate analytical models must bridge the gap between smoothed trajectories and exact particle motion to…