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Real Functions, Dynamical Systems and Applications

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Volume 77 (2020): Edition 1 (December 2020)

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Real Functions, Dynamical Systems and their Applications

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Applied Mathematics'19

Volume 74 (2019): Edition 1 (December 2019)
Real Functons, Ideals, Measurable Functions, Functional Equations

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Number Theory, Algebra and Cryptology '18

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Volume 70 (2017): Edition 1 (September 2017)

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Special Edition: Real Functions ’16, Real Functions, Density Topologies, Porosity

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Volume 66 (2016): Edition 1 (June 2016)
Edition title: Applied Mathematics ’16

Volume 65 (2016): Edition 1 (March 2016)
Real Functions '15 — Measure Theory, Real Functions, General Topology. Editors: J. Borsík, 2016.

Volume 64 (2015): Edition 1 (September 2015)
Number Theory and Cryptology ’15

Volume 62 (2015): Edition 1 (March 2015)
Special Edition Title: Real Functions ’14

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Special Edition Title: Applied Mathematics ‘14

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Special Edition Title: Cryptology ’14

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Special Edition Title: Number Theory ‘14

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Real Functions ‘13 Real Functions, Topology, Real and Functional Analysis, Locally Convex Spaces

Volume 57 (2013): Edition 1 (December 2013)
Cryptology

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Number Theory

Volume 55 (2013): Edition 1 (August 2013)

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Differential and Difference Equations and Applications ‘2012

Volume 53 (2012): Edition 1 (December 2012)
TATRACRYPT ‘12

Volume 52 (2012): Edition 1 (August 2012)

Volume 51 (2012): Edition 1 (April 2012)
PROBASTAT ‘11

Volume 50 (2011): Edition 1 (December 2011)
Applied Mathematics and Informatics

Volume 49 (2011): Edition 1 (August 2011)
Real Functions ‘10

Volume 48 (2011): Edition 1 (April 2011)
Differential and Difference Equations and Applications 2010

Volume 47 (2010): Edition 1 (December 2010)
CCEC ‘09

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Real Functions ‘09

Volume 45 (2010): Edition 1 (April 2010)
NILCRYPT ‘10

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Real Function ’08 Functional Equation, Measures, Integration and Harmonic Analysis

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Differential and Difference Equations and Applications 2008

Volume 42 (2009): Edition 1 (April 2009)
Real Function ‘07

Détails du magazine
Format
Magazine
eISSN
1338-9750
Première publication
12 Nov 2012
Période de publication
3 fois par an
Langues
Anglais

Chercher

Volume 80 (2021): Edition 3 (December 2021)

Détails du magazine
Format
Magazine
eISSN
1338-9750
Première publication
12 Nov 2012
Période de publication
3 fois par an
Langues
Anglais

Chercher

7 Articles
Accès libre

Oscillation Results for Third-Order Quasi-Linear Emden-Fowler Differential Equations with Unbounded Neutral Coefficients

Publié en ligne: 01 Jan 2022
Pages: 1 - 14

Résumé

Abstract

Some new oscillation criteria are obtained for a class of thirdorder quasi-linear Emden-Fowler differential equations with unbounded neutral coefficients of the form (a(t)(z(t))α)+f(t)yλ(g(t))=0,\[(a(t){(z(t))^\alpha })' + f(t){y^\lambda }(g(t)) = 0,\] where z(t) = y(t) + p(t)y(σ(t)) and α, λ are ratios of odd positive integers. The established results generalize, improve and complement to known results.

Mots clés

  • quasi-linear
  • neutral differential equation
  • Emden-Fowler differential equation
  • oscillation
Accès libre

A Quintic Spline Collocation Method for Solving Time-Dependent Convection-Diffusion Problems

Publié en ligne: 01 Jan 2022
Pages: 15 - 34

Résumé

Abstract

In this paper, we develop a new numerical algorithm for solving a time dependent convection-diffusion equation with Dirichlet’s type boundary conditions. The method comprises the horizontal method of lines for time integration and (θ-method, θ ∈ [1/2, 1] (θ = 1 corresponds to the backward Euler method and θ = 1/2 corresponds to the Crank-Nicolson method) to discretize in temporal direction and the quintic spline collocation method. The convergence analysis of proposed method is discussed in detail, and it justified that the approximate solution converges to the exact solution of orders Ot + h3) for the backward Euler method and Ot2 + h3) for the Crank-Nicolson method, where Δt and h are mesh sizes in the time and space directions, respectively. It is also shown that the proposed method is unconditionally stable. This scheme is applied on some test examples, the numerical results illustrate the efficiency of the method and confirm the theoretical behaviour of the rates of convergence. Results shown by this method are in good agreement with the known exact solutions. The produced results are also more accurate than some available results given in the literature.

Mots clés

  • convection-diffusion equation
  • -method
  • quintic
  • spline collocation method
  • convergence
Accès libre

Solving Nonlinear Volterra-Fredholm Integral Equations using an Accurate Spectral Collocation Method

Publié en ligne: 01 Jan 2022
Pages: 35 - 52

Résumé

Abstract

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both L and weighted L2 norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods.

Mots clés

  • Jacobi collocation methods
  • convergence analysis
  • spectral methods
  • nonlinear Volterra-Fredholm integral equations
Accès libre

Finite Volume Schemes for the Affine Morphological Scale Space (Amss) Model

Publié en ligne: 01 Jan 2022
Pages: 53 - 70

Résumé

Abstract

Finite volume (FV) numerical schemes for the approximation of Affine Morphological Scale Space (AMSS) model are proposed. For the scheme parameter θ, 0 ≤ θ ≤ 1 the numerical schemes of Crank-Nicolson type were derived. The explicit (θ = 0), semi-implicit, fully-implicit (θ = 1) and Crank-Nicolson (θ = 0.5) schemes were studied. Stability estimates for explicit and implicit schemes were derived. On several numerical experiments the properties and comparison of the numerical schemes are presented.

Mots clés

  • affine morphological scale space
  • finite volume scheme
  • explicit
  • semi-implicit
  • fully-implicit
  • Crank-Nicolson schemes
  • stability estimates
  • error
  • EOC
  • CPU time
Accès libre

What was the River Ister in the Time of Strabo? A Mathematical Approach

Publié en ligne: 01 Jan 2022
Pages: 71 - 118

Résumé

Abstract

We introduce a novel method for map registration and apply it to transformation of the river Ister from Strabo’s map of the World to the current map in the World Geodetic System. This transformation leads to the surprising but convincing result that Strabo’s river Ister best coincides with the nowadays Tauernbach-Isel-Drava-Danube course and not with the Danube river what is commonly assumed. Such a result is supported by carefully designed mathematical measurements and it resolves all related controversies otherwise appearing in understanding and translation of Strabo’s original text. Based on this result, we also show that Strabo’s Suevi in the Hercynian Forest corresponds to the Slavic people in the Carpathian-Alpine basin and thus that the compact Slavic settlement was there already at the beginning of the first millennium AD.

Mots clés

  • Strabo
  • Geographica
  • historical map registration
  • affine transformation
  • Laplace equation
  • finite difference method
  • Slavic ethnogenesis
  • history of Central Europe
Accès libre

Improvement and Handling of the Segmentation Model with an Inflation Term

Publié en ligne: 01 Jan 2022
Pages: 119 - 134

Résumé

Abstract

The use of balloon models to address the problems of “snakes” based models was introduced by Laurent D. Cohen. This paper presents a geodesic active contours model with a modified external force term that includes a balloon model. This balloon model makes the segmentation surface to behave like a balloon inflated by the external forces. In this paper, we show an automatic way to control the behaviour of the external force with respect to the segmentation evolution. The external forces, comprised of edge and inflation terms, push the segmentation surface to edges, while curvature regularizes the evolution. As segmentation evolves, the influence of the applied inflation force is determined by how close we are to the edges. With this setup, the initial segmentation does not need to be close to the object’s edges, instead it is inflated by the balloon model towards the edges. Closer to the edges, the influence of the inflation force is adjusted accordingly. The force’s influence is completely turned off when the evolution is stable (reached the edges), then only the curvature and edge information is used to evolve the segmentation.

This approach solves the issues associated with inclusion of balloon model. These issues are that the inflation force can overpower forces from weak edges, or they can cause the contour to be slightly larger than the actual minima. We present examples of the improved model for segmentation of human bladder images. Weak edges are more prevalent in medical images, and the automated handling of the inflation forces gives promising results for this kind of images.

Mots clés

  • geodesic active contours
  • balloon model
  • estimation
  • curve fitting
  • curve smoothing
Accès libre

A Fractional Order Delay Differential Model for Survival of Red Blood Cells in an Animal: Stability Analysis

Publié en ligne: 01 Jan 2022
Pages: 135 - 144

Résumé

Abstract

In this paper, we analyse stability of survival of red blood cells in animal fractional order model with time delay. Results have been illustrated by numerical simulations.

Mots clés

  • red blood cell
  • stability
  • time-delay
  • fractional differential equation
  • Caputo fractional derivative
7 Articles
Accès libre

Oscillation Results for Third-Order Quasi-Linear Emden-Fowler Differential Equations with Unbounded Neutral Coefficients

Publié en ligne: 01 Jan 2022
Pages: 1 - 14

Résumé

Abstract

Some new oscillation criteria are obtained for a class of thirdorder quasi-linear Emden-Fowler differential equations with unbounded neutral coefficients of the form (a(t)(z(t))α)+f(t)yλ(g(t))=0,\[(a(t){(z(t))^\alpha })' + f(t){y^\lambda }(g(t)) = 0,\] where z(t) = y(t) + p(t)y(σ(t)) and α, λ are ratios of odd positive integers. The established results generalize, improve and complement to known results.

Mots clés

  • quasi-linear
  • neutral differential equation
  • Emden-Fowler differential equation
  • oscillation
Accès libre

A Quintic Spline Collocation Method for Solving Time-Dependent Convection-Diffusion Problems

Publié en ligne: 01 Jan 2022
Pages: 15 - 34

Résumé

Abstract

In this paper, we develop a new numerical algorithm for solving a time dependent convection-diffusion equation with Dirichlet’s type boundary conditions. The method comprises the horizontal method of lines for time integration and (θ-method, θ ∈ [1/2, 1] (θ = 1 corresponds to the backward Euler method and θ = 1/2 corresponds to the Crank-Nicolson method) to discretize in temporal direction and the quintic spline collocation method. The convergence analysis of proposed method is discussed in detail, and it justified that the approximate solution converges to the exact solution of orders Ot + h3) for the backward Euler method and Ot2 + h3) for the Crank-Nicolson method, where Δt and h are mesh sizes in the time and space directions, respectively. It is also shown that the proposed method is unconditionally stable. This scheme is applied on some test examples, the numerical results illustrate the efficiency of the method and confirm the theoretical behaviour of the rates of convergence. Results shown by this method are in good agreement with the known exact solutions. The produced results are also more accurate than some available results given in the literature.

Mots clés

  • convection-diffusion equation
  • -method
  • quintic
  • spline collocation method
  • convergence
Accès libre

Solving Nonlinear Volterra-Fredholm Integral Equations using an Accurate Spectral Collocation Method

Publié en ligne: 01 Jan 2022
Pages: 35 - 52

Résumé

Abstract

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both L and weighted L2 norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods.

Mots clés

  • Jacobi collocation methods
  • convergence analysis
  • spectral methods
  • nonlinear Volterra-Fredholm integral equations
Accès libre

Finite Volume Schemes for the Affine Morphological Scale Space (Amss) Model

Publié en ligne: 01 Jan 2022
Pages: 53 - 70

Résumé

Abstract

Finite volume (FV) numerical schemes for the approximation of Affine Morphological Scale Space (AMSS) model are proposed. For the scheme parameter θ, 0 ≤ θ ≤ 1 the numerical schemes of Crank-Nicolson type were derived. The explicit (θ = 0), semi-implicit, fully-implicit (θ = 1) and Crank-Nicolson (θ = 0.5) schemes were studied. Stability estimates for explicit and implicit schemes were derived. On several numerical experiments the properties and comparison of the numerical schemes are presented.

Mots clés

  • affine morphological scale space
  • finite volume scheme
  • explicit
  • semi-implicit
  • fully-implicit
  • Crank-Nicolson schemes
  • stability estimates
  • error
  • EOC
  • CPU time
Accès libre

What was the River Ister in the Time of Strabo? A Mathematical Approach

Publié en ligne: 01 Jan 2022
Pages: 71 - 118

Résumé

Abstract

We introduce a novel method for map registration and apply it to transformation of the river Ister from Strabo’s map of the World to the current map in the World Geodetic System. This transformation leads to the surprising but convincing result that Strabo’s river Ister best coincides with the nowadays Tauernbach-Isel-Drava-Danube course and not with the Danube river what is commonly assumed. Such a result is supported by carefully designed mathematical measurements and it resolves all related controversies otherwise appearing in understanding and translation of Strabo’s original text. Based on this result, we also show that Strabo’s Suevi in the Hercynian Forest corresponds to the Slavic people in the Carpathian-Alpine basin and thus that the compact Slavic settlement was there already at the beginning of the first millennium AD.

Mots clés

  • Strabo
  • Geographica
  • historical map registration
  • affine transformation
  • Laplace equation
  • finite difference method
  • Slavic ethnogenesis
  • history of Central Europe
Accès libre

Improvement and Handling of the Segmentation Model with an Inflation Term

Publié en ligne: 01 Jan 2022
Pages: 119 - 134

Résumé

Abstract

The use of balloon models to address the problems of “snakes” based models was introduced by Laurent D. Cohen. This paper presents a geodesic active contours model with a modified external force term that includes a balloon model. This balloon model makes the segmentation surface to behave like a balloon inflated by the external forces. In this paper, we show an automatic way to control the behaviour of the external force with respect to the segmentation evolution. The external forces, comprised of edge and inflation terms, push the segmentation surface to edges, while curvature regularizes the evolution. As segmentation evolves, the influence of the applied inflation force is determined by how close we are to the edges. With this setup, the initial segmentation does not need to be close to the object’s edges, instead it is inflated by the balloon model towards the edges. Closer to the edges, the influence of the inflation force is adjusted accordingly. The force’s influence is completely turned off when the evolution is stable (reached the edges), then only the curvature and edge information is used to evolve the segmentation.

This approach solves the issues associated with inclusion of balloon model. These issues are that the inflation force can overpower forces from weak edges, or they can cause the contour to be slightly larger than the actual minima. We present examples of the improved model for segmentation of human bladder images. Weak edges are more prevalent in medical images, and the automated handling of the inflation forces gives promising results for this kind of images.

Mots clés

  • geodesic active contours
  • balloon model
  • estimation
  • curve fitting
  • curve smoothing
Accès libre

A Fractional Order Delay Differential Model for Survival of Red Blood Cells in an Animal: Stability Analysis

Publié en ligne: 01 Jan 2022
Pages: 135 - 144

Résumé

Abstract

In this paper, we analyse stability of survival of red blood cells in animal fractional order model with time delay. Results have been illustrated by numerical simulations.

Mots clés

  • red blood cell
  • stability
  • time-delay
  • fractional differential equation
  • Caputo fractional derivative

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