Dmitry S. Kulyabov
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  • Publications
    • Basic elements of the BibTeX file structure
    • Dual quaternion representation of points, lines and planes
    • Typesetting tables
    • Using NeuralPDE.jl to solve differential equations
    • Implementation of biquaternions in the Asymptote language. Supplements
    • The dual quaternion algebra and its implementation in Asymptote language
    • Abstract structure
    • Analytic projective geometry for computer graphics
    • Projective Geometric Algebra in Plane and Its Implementation in the Library Ganja.js
    • Statistical and density-based clustering techniques in the context of anomaly detection in network systems: A comparative analysis
    • Using generative artificial intelligence
    • Implementation of Analytic Projective Geometry for Computer Graphics
    • Symbolic Studies of Maxwell’s Equations in Space-Time Algebra Formalism
    • Numerical Integration of Highly Oscillatory Functions with and without Stationary Points
    • Application of the Chebyshev collocation method to solve boundary value problems of heat conduction
    • Author's ethics
    • IMRAD structure
    • Journal rubrics
    • Numerical solution of first-order exact differential equations by the integrating factor method
    • Solving the eikonal equation by the FSM method in Julia language
    • Symbolic-numeric approach for the investigation of kinetic models
    • Methodological derivation of the eikonal equation
    • Julia language features for processing statistical data
    • Asymptote-based scientific animation
    • Chebyshev collocation method for solving second order ODEs using integration matrices
    • Computer Algebra Tools for Geometrization of Maxwell's Equations
    • Geometric Algebra and Quaternion Techniques in Computer Algebra Systems for Describing Rotations in Eucledean Space
    • Implementation of Geometric Algebra in Computer Algebra Systems
    • Implementation of hyperbolic complex numbers in Julia language
    • Multistage collocation pseudo-spectral method for the solution of the first order linear ODE
    • Multistage pseudo-spectral method (method of collocations) for the approximate solution of an ordinary differential equation of the first order
    • Analytical-Numerical Implementation of Polyvector Algebra in Julia
    • Computer simulation of the stochastic RED algorithm
    • Implementation of an analytical-numerical approach to stochastization of one-step processes in the Julia programming language
    • Surrogate modeling assistant software
    • Computer Algebra in JULIA
    • Numerical integrating of highly oscillating functions: effective stable algorithms in case of linear phase
    • Using a Template Engine as a Computer Algebra Tool
    • Application of a numerical-analytical approach in the process of modeling differential equations in the Julia language
    • Comparative analysis of machine learning methods by the example of the problem of determining muon decay
    • Hybrid modelling of the RED algorithm in the Julia language
    • On improving the accuracy of the classification on imbalanced classes with machine learning
    • Paralinguistic model for emotions recognition with deep neural networks
    • The multi-model approach to the study of complex systems using the example of the RED active queue management algorithm
    • Hyperbolic numbers as Einstein numbers
    • Approaches to the implementation of generalized complex numbers in the Julia language
    • Languages for modeling the RED active queue management algorithms: Modelica vs. Julia
    • Skin cancer classification computer system development with deep learning
    • A Modular Extension for a Computer Algebra System
    • A Practical Approach to Testing Random Number Generators in Computer Algebra Systems
    • An Effective Stable Numerical Method for Integrating Highly Oscillating Functions with a Linear Phase
    • Deep Neural Networks for Emotion Recognition
    • Melanoma Detection Computer System Development with Deep Neural Networks
    • One-step Stochastization Methods for Open Systems
    • Practical Application of the Multi-model Approach in the Study of Complex Systems
    • Mathematical model of cavitation under the influence of a single stretching pulse
    • Numerical modeling of stationary pseudospin waves on a graphene monoatomic films
    • A new algorithm used the Chebyshev pseudospectral method to solve the nonlinear second-order Lienard differential equations
    • Structural Approach to the Deep Learning Method
    • Constrained Hamiltonian approach to the Maxwell theory
    • Essay on the study of the self-oscillating regime in the control system
    • Finslerian representation of the Maxwell equations
    • Numerical analysis of eikonal equation
    • Modeling RED algorithm modifications in the OpenModelica
    • Numerical solution of the problem of homogeneous nucleation in the liquid phase
    • Overview of social networks research software
    • Statistically significant performance testing of Julia scientific programming language
    • New Features in the Second Version of the Cadabra Computer Algebra System
    • Parametric study of the control system in the TCP network
    • Software Package Development for the Active Traffic Management Module Self-oscillation Regime Investigation
    • Statistically Significant Comparative Performance Testing of Julia and Fortran Languages in Case of Runge–Kutta Methods
    • The General Renovation as the Active Queue Management Mechanism. Some Aspects and Results
    • Pseudo-random number generator based on neural network
    • Software Package For The Active Queue Management Module Model Verification
    • Algorithm for Lens Calculations in the Geometrized Maxwell Theory
    • Automatic Code Generation for Stochastic Runge–Kutta Methods
    • Software Implementation of the Eikonal Equation
    • The Riemannian Geometry is not Sufficient for the Geometrization of the Maxwell's Equations
    • Functional Integral Approach to the Solution of a System of Stochastic Differential Equations
    • The Automation of Stochastization Algorithm with Use of SymPy Computer Algebra Library
    • Characteristics of Lost and Served Packets for Retrial Queueing System with General Renovation and Recurrent Input Flow
    • Implementing a Method for Stochastization of One-Step Processes in a Computer Algebra System
    • Issues in the Software Implementation of Stochastic Numerical Runge–Kutta
    • Regularized Computation of Oscillatory Integrals with Stationary Points
    • Simple Model of Nonlinear Spin Waves in Graphene Structures
    • The Methodology of Studying of Active Traffic Management Module Self-oscillation Regime
    • Two Formalisms of Stochastization of One-Step Models
    • The approach to investigation of the the regions of self-oscillations
    • Implementation Difficulties Analysis of Stochastic Numerical Runge-Kutta Methods
    • The Criteria for the Study of Occurrence of Self-Oscillation Mode of Active Traffic Management Module
    • Markov-modulated Arrival Processes and Their Application to the Analysis of Active Queue Management Algorithms
    • An Approach to Invistigate the Regions of Self-oscillations
    • Approaches to Stochastic Modeling of Wind Turbines
    • Implementation of Diagram Technique for Statistical Systems in Sympy
    • The Construction of the SDE for Modeling Wind Speed for Wind Power Plants
    • About Linearization of Active Traffic Management Module Model
    • Stochastic Modeling of Wind Turbines
    • Support for Parallel Computing in Julia Language
    • A Geometric Approach to the Lagrangian and Hamiltonian Formalism of Electrodynamics
    • Application of Functional Integrals to Stochastic Equations
    • Field Calculation for the Horn Waveguide Transition in the Single-Mode Approximation of the Cross-Sections Method
    • Geometrization of Maxwell's Equations in the Construction of Optical Devices
    • Guided Modes of a Planar Gradient Waveguide
    • Maxwell's Equations Instantaneous Hamiltonian
    • Modelica-based TCP simulation
    • Spinor Representation of Maxwell's Equations
    • The Survey on Markov-Modulated Arrival Processes and Their Application to the Analysis of Active Queue Management Algorithms
    • Diagram Representation for the Operator Approach of One-Step Processes Stochastization
    • Stable Algorithm of Integrating Rapidly Oscillating Functions
    • Waveguide Modes of a Planar Gradient Optical Waveguide
    • Operating System Plan9 as the Implementation of the GRID Ideology
    • Hybrid Simulation Of Active Traffic Management
    • Stochastization Of One-Step Processes In The Occupations Number Representation
    • Diagram Representation for the Stochastization of Single-Step Processes
    • Numerical and Analytical Modeling of Guided Modes of a Planar Gradient Waveguide
    • Operator Approach to the Master Equation for the One-Step Process
    • Operator Approach to the Master Equation for the One-Step Process
    • Spinor-Like Hamiltonian for Maxwellian Optics
    • Stochastic Runge–Kutta Software Package for Stochastic Differential Equations
    • The Stochastic Processes Generation in OpenModelica
    • Using two Types of Computer Algebra Systems to Solve Maxwell Optics Problems
    • Combinatorial and Operator Approaches to RED Modeling
    • Designing Installations for Verification of the Model of Active Queue Management Discipline RED in the GNS3
    • Operator Approach to the Master Equation for the One-Step Process
    • Quantum Field Theory Approach to the Analysis of One-Step Models
    • Spinor-Like Hamiltonian for Maxwellian Optics
    • The Method of Constructing Models of Peer to Peer Protocols
    • Waveguide Modes of a Planar Optical Waveguide
    • Integration of the computing cluster into the information system of facility
    • One-Step Stochastic Processes Simulation Software Package
    • Review of Julia programming language for scientific computing
    • A Naive Geometrization of Maxwell's Equations
    • Geometrization of Electromagnetic Waves
    • Symbolic Computation and p-adic Arithmetic
    • Tensor Computations in Computer Algebra Systems
    • The Method of Stochastization of One-Step Processes
    • Maxwell's Equations in Arbitrary Coordinate System
    • Application of stochastic differencial equations to model population systems
    • Getting the stochastic differential equations for multidimensional systems of birth-death
    • The System of Hamilton Equations for Normal Waves of the Electromagnetic Field in a Stratified Anisotropic Medium
    • An Application of Computer Algebra System Cadabra to Scientific Problems of Physics
    • Application of Two-Spinor Calculus in Quantum Mechanical and Field Calculations
    • Computer Realization of Regularized Method for a Wavefront Set Recovering on the Base of Hartmann Test with the Help of Analytical Calculations in Axiom CAS
    • Development of Click modules: DSRED and SDRED algorithms
    • Symbolic-numerical algorithm for constructing matrices stabilizing functional in the problem of restoring the surface
    • An application of computer algebra system CADABRA to quantum field and quantum mechanics problems
    • An application of two-spinors calculus to quantum field and quantum mechanics problems
    • Application of Computer Algebra System for stable diagnostic of optical surfaces using Zernike polynomials
    • Kink-like Configurations of Interacting Scalar, Electromagnetic, and Gravitational Fields
    • Stability of selfgraviting kink-like Solutions in Scalar Nonlinear Electrodynavics
  • Blog
    • 2025
      • Hugo. Researcher's website. Importing a list of publications
      • DCM. Journal rubrics
    • 2024
      • CEURART document verification
      • DCM. Author's Ethics
      • Reproducible Research
      • Contributor Roles
    • 2023
      • Emacs. Tabs
      • Saratov Fall Meeting Conference 2023
      • Tinkoff
      • SberBank
      • Books. Fiction
      • Kapanoglu, S. (2022): Street Coder. The rules to break and how to break them
      • BibTeX fields
      • BibTeX entry types
      • Update your Bitbucket Cloud SSH Host Keys
      • Books. History
      • RUDN University affiliation
      • Cisco vs Huawei Commands
      • L2TP over IPsec VPN client setup
      • LaTeX. What to read
      • RUDN University
    • 2021
      • BibTeX format
      • CEUR-WS conference repository
      • Installing TeXlive
      • Package manager for Windows. Chocolatey
      • Books. Programming
    • 2020
      • Happy Birthday
      • Vladimir Ilyich Lenin - 150 years
    • Migrating from livejournal to hexo
    • Stalin departed for a short while
    • 2022
    • 2026
  • Projects
    • Small utilities and scripts
    • Geometrization
    • LaTeX and environment
    • Machine learning
    • Relativity
  • Experience

Dual quaternion representation of points, lines and planes

2025-12-01·
Migran Nelsonovich Gevorkyan
,
Nikita A. Vishnevskiy
,
Kirill V. Didus
,
Anna Vladislavovna Korolkova
,
Dmitry Sergeevich Kulyabov
· 0 min read
URL DOI
Type
Journal article
Publication
Discrete and Continuous Models and Applied Computational Science
publications
Last updated on 2025-12-01
← Basic elements of the BibTeX file structure 2025-12-01
Typesetting tables 2025-10-01 →
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English
Русский

© 1986—2026 Dmitry S. Kulyabov. This work is licensed under CC BY 4.0

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