Dimiter Prodanov
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View article: Elastic Curves and Euler–Bernoulli Constrained Beams from the Perspective of Geometric Algebra
Elastic Curves and Euler–Bernoulli Constrained Beams from the Perspective of Geometric Algebra Open
Elasticity is a well-established field within mathematical physics, yet new formulations can provide deeper insight and computational advantages. This study explores the geometry of two- and three-dimensional elastic curves using the forma…
View article: Elastic Curves and Euler-Bernoulli Constrained Beams from the Perspective of Geometric Algebra
Elastic Curves and Euler-Bernoulli Constrained Beams from the Perspective of Geometric Algebra Open
Elasticity is a well-established field within mathematical physics, yet new formulations can provide deeper insight and computational advantages. This study explores the geometry of two- and three-dimensional elastic curves using the forma…
View article: Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras
Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras Open
Clifford algebras are an active area of mathematical research having numerous applications in mathematical physics and computer graphics, among many others. This paper demonstrates algorithms for the computation of characteristic polynomia…
View article: Topology of Locally and Non-Locally Generalized Derivatives
Topology of Locally and Non-Locally Generalized Derivatives Open
This article investigates the continuity of derivatives of real-valued functions from a topological perspective. This is achieved by the characterization of their sets of discontinuity. The same principle is applied to Gateaux derivatives …
View article: Geometric Nature of the Turánian of Modified Bessel Function of the First Kind
Geometric Nature of the Turánian of Modified Bessel Function of the First Kind Open
This work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starliken…
View article: Topology of Locally and Non-Locally Generalized Derivatives
Topology of Locally and Non-Locally Generalized Derivatives Open
The article investigates the continuity of derivatives of real-valued functions from a topological perspective. This is achieved by the characterization of their sets of discontinuity. The same principle is applied to Gateaux derivatives a…
View article: Geometric Nature of the Turánian of Modified Bessel Function of the First Kind
Geometric Nature of the Turánian of Modified Bessel Function of the First Kind Open
This work explores the geometric properties of the Turanian of the modified Bessel function of the first Kind (TMBF). By using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starli…
View article: Exponential series approximation of the SIR epidemiological model
Exponential series approximation of the SIR epidemiological model Open
Introduction The SIR (Susceptible-Infected-Recovered) model is one of the simplest and most widely used frameworks for understanding epidemic outbreaks. Methods A second-order dynamical system for the R variable is formulated using an infi…
View article: Fractal Calculus to Derive Fractal Frenet Equations for Fractal Curves
Fractal Calculus to Derive Fractal Frenet Equations for Fractal Curves Open
This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a mea…
View article: Finite Representations of the Wright Function
Finite Representations of the Wright Function Open
The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wri…
View article: Finite Representations of theWright Function
Finite Representations of theWright Function Open
The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wri…
View article: Examples for CGI2023
Examples for CGI2023 Open
Examples for CGI2023. Calculations are described in the paper "Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras".
View article: Examples for CGI2023
Examples for CGI2023 Open
Examples for CGI2023. Calculations are described in the paper "Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras".
View article: Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras
Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras Open
The power of Clifford or, geometric, algebra lies in its ability to represent geometric operations in a concise and elegant manner. Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into non-com…
View article: Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras
Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras Open
The power of Clifford or, geometric, algebra lies in its ability to represent geometric operations in a concise and elegant manner. Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into non-com…
View article: Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras
Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras Open
The power of Clifford or, geometric, algebra lies in its ability to represent geometric operations in a concise and elegant manner. Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into non-com…
View article: Examples for CGI2023
Examples for CGI2023 Open
Examples for CGI2023. Calculations are described in the paper "Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras".
View article: Examples for CGI2023
Examples for CGI2023 Open
Examples for CGI2023. Calculations are described in the paper "Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras".
View article: Computation of the Wright function from its integral representation
Computation of the Wright function from its integral representation Open
The Wright function arises in the theory of the fractional differential equations. It is a very general mathematical object having diverse connections with other special and elementary functions. The Wright function provides a unified trea…
View article: The Wright function -- hypergeometric representation and symbolical evaluation
The Wright function -- hypergeometric representation and symbolical evaluation Open
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides …
View article: The Wright function – hypergeometric representation and symbolical evaluation
The Wright function – hypergeometric representation and symbolical evaluation Open
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides …
View article: Fractional Taylor Expansions and Derivative Regularization
Fractional Taylor Expansions and Derivative Regularization Open
Power series expansions are useful in approximation theory and mathematical physics. The manuscript presents several types of fractional Taylor expansions of sufficiently smooth functions. This is achieved by employing an incremental regul…
View article: The Active Segmentation Platform for Microscopic Image Classification and Segmentation
The Active Segmentation Platform for Microscopic Image Classification and Segmentation Open
Image segmentation still represents an active area of research since no universal solution can be identified. Traditional image segmentation algorithms are problem-specific and limited in scope. On the other hand, machine learning offers a…
View article: Manual segmentation and classification dataset
Manual segmentation and classification dataset Open
The archive contains 2 datasets for the Special issue "Neuroinformatics and Signal Processing" https://www.mdpi.com/journal/brainsci/special_issues/Neuroinformatics_Signal A segmentation dataset demonstrating Active Segmentation. The image…
View article: Manual segmentation dataset
Manual segmentation dataset Open
A dataset demonstrating Active Segmentation. The image is taken from the ISIBI 2012 dataset. Dataset for the Special issue "Neuroinformatics and Signal Processing" https://www.mdpi.com/journal/brainsci/special_issues/Neuroinformatics_Signal
View article: Manual segmentation and classification dataset
Manual segmentation and classification dataset Open
The archive contains 2 datasets for the Special issue "Neuroinformatics and Signal Processing" https://www.mdpi.com/journal/brainsci/special_issues/Neuroinformatics_Signal A segmentation dataset demonstrating Active Segmentation. The image…