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Volume 30 (2022): Issue 2 (May 2022)

Volume 30 (2022): Issue 1 (February 2022)

Volume 29 (2021): Issue 3 (November 2021)

Volume 29 (2021): Issue 2 (June 2021)

Volume 29 (2021): Issue 1 (March 2021)

Volume 28 (2020): Issue 3 (December 2020)

Volume 28 (2020): Issue 2 (July 2020)

Volume 28 (2020): Issue 1 (March 2020)

Volume 27 (2019): Issue 3 (December 2019)

Volume 27 (2019): Issue 2 (June 2019)

Volume 27 (2019): Issue 1 (March 2019)

Volume 26 (2018): Issue 3 (December 2018)

Volume 26 (2018): Issue 2 (July 2018)

Volume 26 (2018): Issue 1 (March 2018)

Volume 25 (2017): Issue 3 (December 2017)

Volume 25 (2017): Issue 2 (July 2017)

Volume 25 (2017): Issue 1 (January 2017)

Volume 24 (2016): Issue 3 (November 2016)

Volume 24 (2016): Issue 2 (June 2016)

Volume 24 (2016): Issue 1 (January 2016)

Volume 23 (2015): Issue 3 (November 2015)

Volume 23 (2015): Issue 2 (June 2015)

Volume 23 (2015): Issue 1 (January 2015)

Volume 22 (2014): Issue 3 (September 2014)

Volume 22 (2014): Issue 2 (June 2014)

Volume 22 (2014): Issue 1 (March 2014)

Volume 21 (2013): Issue 3 (November 2013)

Volume 21 (2013): Issue 2 (June 2013)

Volume 21 (2013): Issue 1 (March 2013)

Volume 20 (2012): Issue 3 (December 2012)

Volume 20 (2012): Issue 2 (June 2012)
Proceedings of the 10th International Workshop on Differential Geometry and its Applications

Volume 20 (2012): Issue 1 (May 2012)

Journal Details
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English

Search

Volume 30 (2022): Issue 2 (May 2022)

Journal Details
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English

Search

15 Articles
Open Access

A new existence results on fractional differential inclusions with state-dependent delay and Mittag-Leffler kernel in Banach space

Published Online: 02 Jun 2022
Page range: 5 - 24

Abstract

Abstract

In this manuscript the existence of the fractional-order functional differential inclusions [FFDI] with state-dependent delay [SDD] is investigated within the Mittag-Leffler kernel. We use both contractive and condensing maps to prove the existence of mild solutions through solution operator. Finally, an example is presented to illustrate the theoretical findings.

Keywords

  • A-B fractional-order derivative
  • mild solution
  • fixed point theorem

MSC 2010

  • Primary 26A33
  • Secondary 34A60
Open Access

Central and local limit theorems for the weighted Delannoy numbers

Published Online: 02 Jun 2022
Page range: 25 - 44

Abstract

Abstract

In this research we generalize our result for numbers satisfying the Delannoy triangle. We obtain a central limit theorem and a local limit theorem for weighted numbers of the triangle and establish the rate of convergence to the limiting (normal) distribution.

Keywords

  • Delannoy triangle
  • central limit theorem
  • local limit theorem
  • double generating function
  • triangular array

MSC 2010

  • Primary 05A15
  • 05A16
  • 60F05
  • Secondary 39A06
  • 39A14
Open Access

Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model

Published Online: 02 Jun 2022
Page range: 45 - 62

Abstract

Abstract

Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations. We will show that solitary wave solutions are recovered through a limiting process after the elliptic modulus of the Jacobi elliptic function cn that describes the periodic solutions for the self-focusing nonlinear Schrödinger model.

Keywords

  • NLS
  • self-focusing
  • defocusing
  • dispersive
  • nonlinearity
  • carrier waves
  • solution profile
  • envelope
  • cnoidal waves
  • solitary waves
  • surface gravity waves
  • sound waves
  • water-air interface
  • sonic layer depth

MSC 2010

  • Primary 33E05, 35Q55
  • Secondary 35Q53
Open Access

Negative clean rings

Published Online: 02 Jun 2022
Page range: 63 - 89

Abstract

Abstract

A ring is called negative clean if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.

In this paper, we develop the theory of the negative rings, with special emphasis on finding the clean matrices which have (or have not) clean negatives. Many explicit results are proved for 2 × 2 matrices and some hard to solve quadratic Diophantive equations are displayed.

Keywords

  • clean ring
  • negative clean ring
  • strongly clean element
  • 2 × 2 matrix

MSC 2010

  • Primary 16U99, 16U10, 15B33
  • Secondary 15B36, 16-04, 15-04
Open Access

Motion of Inextensible Quaternionic Curves and Modified Korteweg-de Vries Equation

Published Online: 02 Jun 2022
Page range: 91 - 101

Abstract

Abstract

Many curve evolutions have been determined which are integrable in recent times. The motion of curves can be defined by certain integrable equations including the modified Korteweg-de Vries. In this study, the quaternionic curves in 3 and 4-dimensional Euclidean spaces have been considered and the motions of inextensible quaternionic curves have been characterized by the modified Korteweg-de Vries (mKdV) equations. For this purpose, the basic concepts of the quaternions and quaternionic curves have been summarized. Then the evolutions of inextensible quaternionic curves with reference to the Frenet formulae have been obtained. Finally, the mKdV equations have been generated with the help of their evolutions

Keywords

  • Modified Korteweg-de Vries equation
  • quaternionic curve
  • evolution curve
  • inextensible curve

MSC 2010

  • Primary 53A04
  • Secondary 35Q53
Open Access

Characterization of second type plane foliations using Newton polygons

Published Online: 02 Jun 2022
Page range: 103 - 123

Abstract

Abstract

In this article we characterize the foliations that have the same Newton polygon that their union of formal separatrices, they are the foliations called of the second type. In the case of cuspidal foliations studied by Loray [Lo], we precise this characterization using the Poincaré-Hopf index. This index also characterizes the cuspidal foliations having the same process of singularity reduction that the union of its separatrices. Finally we give necessary and sufficient conditions when these cuspidal foliations are generalized curves, and a characterization when they have only one separatrix.

Keywords

  • foliation
  • second type foliation
  • Newton polygon

MSC 2010

  • Primary 32S65
  • Secondary 14H20
Open Access

Torsion subgroups of rational Mordell curves over some families of number fields

Published Online: 02 Jun 2022
Page range: 125 - 132

Abstract

Abstract

Mordell curves over a number field K are elliptic curves of the form y2 = x3 + c, where cK \ {0}. Let p ≥ 5 be a prime number, K a number field such that [K : ℚ] ∈ {2p, 3p}. We classify all the possible torsion subgroups E(K)tors for all Mordell curves E defined over ℚ when [K : ℚ] ∈ {2p, 3p}.

Keywords

  • Elliptic curves
  • Torsion group
  • Number fields

MSC 2010

  • Primary: 11G05, 11R16, 11R21
  • Secondary: 14H52
Open Access

Laplacian energy and first Zagreb index of Laplacian integral graphs

Published Online: 02 Jun 2022
Page range: 133 - 160

Abstract

Abstract

The set Si,n = {0, 1, 2, …, i − 1, i + 1, …, n − 1, n}, 1 ⩽ in, is called Laplacian realizable if there exists a simple connected undirected graph whose Laplacian spectrum is Si,n. The existence of such graphs was established by S. Fallat et all. In the present paper, we find the Laplacian energy and first Zagreb index of graphs whose Laplacian spectrum is Si,n.

Keywords

  • Laplacian matrix
  • Laplacian integral graphs
  • Laplacian energy
  • First zagreb index
  • Second zagreb index

MSC 2010

  • Primary 05C50, 15A18
  • Secondary 05C76, 05C90
Open Access

Properties of n-ary hypergroups relevant for modelling trajectories in HD maps

Published Online: 02 Jun 2022
Page range: 161 - 178

Abstract

Abstract

In the paper we show that trajectories used in HD maps of autonomous vehicles can be well modelled by means of n-ary hyperoperations and hypergroups. We investigate some properties of such hypergroups.

Keywords

  • autonomous driving
  • HD maps
  • hypergroup
  • -ary hypergroup
  • self-navigation

MSC 2010

  • Primary 20N20
  • 20N15
Open Access

A result of instability for two-temperatures Cosserat bodies

Published Online: 02 Jun 2022
Page range: 179 - 192

Abstract

Abstract

In our study we consider a generalized thermoelasticity theory based on a heat conduction equation in micropolar bodies. Specifically, the heat conduction depends on two distinct temperatures, the conductive temperature and the thermodynamic temperature. In our analysis, the difference between the two temperatures is clear and is highlighted by the heat supply. After we formulate the mixed initial boundary value problem defined in this context, we prove the uniqueness of a solution corresponding some specific initial data and boundary conditions. Also, if the initial energy is negative or null, we prove that the solutions of the mixed problem are exponentially instable.

Keywords

  • thermodynamic temperature
  • conductive temperature
  • micropolar bodies
  • uniqueness
  • exponential increasing
  • exponentially instable

MSC 2010

  • 74A15
  • 74A60
  • 74G40
  • 35A15
Open Access

Collectively Fixed Point Theory in the Compact and Coercive Cases

Published Online: 02 Jun 2022
Page range: 193 - 207

Abstract

Abstract

We present collectively fixed point results for multivalued maps which automatically generate analytic alternatives and minimax inequalities. As an application we consider equilbrium type problems for generalized games.

Keywords

  • Continuous selections
  • fixed point theory
  • analytic alternatives
  • minimax inequalities

MSC 2010

  • Primary 47H10
  • Secondary 54H25
Open Access

Algebraic Heun Operators with Tetrahedral Monodromy

Published Online: 02 Jun 2022
Page range: 209 - 230

Abstract

Abstract

Our work adds to the picture of second order differential operators with a full set of algebraic solutions, which we will call algebraic. We see algebraic Heun operators as pull-backs of algebraic hypergeometric operators via Belyi functions. We focus on the case when the hypergeometric one has a tetrahedral monodromy group. We find arithmetic conditions for the pull-back functions to exist. For each distribution of the singular points in the ramified fibers, we identify the minimal values of the exponent differences and we explicitly construct the dessin d’enfant corresponding to the pull-back function in the minimal cases. Then by allowing some parameters to vary, we find infinite families of such graphs, hence of Heun operators with tetrahedral monodromy.

Keywords

  • Algebraic solutions of differential equations
  • Belyi Functions
  • Dessins d’enfants
  • Planar graphs

MSC 2010

  • Primary 11G32, 34M15
  • Secondary 34M35, 05C10, 05C65, 33C99
Open Access

Sombor index of zero-divisor graphs of commutative rings

Published Online: 02 Jun 2022
Page range: 231 - 257

Abstract

Abstract

In this paper, we investigate the Sombor index of the zero-divisor graph of ℤn which is denoted by Γ(ℤn) for n ∈ {pα, pq, p2q, pqr} where p, q and r are distinct prime numbers. Moreover, we introduce an algorithm which calculates the Sombor index of Γ(ℤn). Finally, we give Sombor index of product of rings of integers modulo n.

Keywords

  • Topological indices
  • Sombor index
  • zero-divisor graph
  • vertex degree
  • algorithm

MSC 2010

  • Primary 13A70, 05C09, 05C07
  • Secondary 68R10, 05C25
Open Access

Solving Single Nesting Problem Using a Genetic Algorithm

Published Online: 02 Jun 2022
Page range: 259 - 272

Abstract

Abstract

Since the Bin Packing Problem (BPP) has application to industry and supply chain management problems (to mention only the most important ones), it attracted attention from its formulation. The Single Nesting Problem treated here is a particular case of this optimization problem, which different methods, mainly combinatorial, can solve. In this article, we propose using a genetic algorithm for solving the single nesting problem formulated in a previous article by the authors. The results comparisons prove that this approach is an excellent alternative to the combinatorial ones.

Keywords

  • Optimization
  • Combinatorics
  • Bin Packing Problem
  • Genetic Algorithms

MSC 2010

  • Primary 90C08, 90C59
  • Secondary: 68T20
Open Access

Ellipses surrounding convex bodies

Published Online: 02 Jun 2022
Page range: 273 - 282

Abstract

Abstract

If, for a double normal xx* of a convex body K, an ellipse Ex, x* is included in K, we say that E is surrounded by the boundary of K. If, instead, in the plane of E, K is included in the convex hull of E, then we say that E is surrounding K. In this paper we investigate surrounding and surrounded ellipses, particularly circles. We do this for arbitrary convex bodies, for polytopes, for convex bodies of constant width, and for most convex bodies (in the sense of Baire categories).

Keywords

  • Double normal
  • convex body of constant width
  • surrounded and surrounding ellipses

MSC 2010

  • Primary 52A15
15 Articles
Open Access

A new existence results on fractional differential inclusions with state-dependent delay and Mittag-Leffler kernel in Banach space

Published Online: 02 Jun 2022
Page range: 5 - 24

Abstract

Abstract

In this manuscript the existence of the fractional-order functional differential inclusions [FFDI] with state-dependent delay [SDD] is investigated within the Mittag-Leffler kernel. We use both contractive and condensing maps to prove the existence of mild solutions through solution operator. Finally, an example is presented to illustrate the theoretical findings.

Keywords

  • A-B fractional-order derivative
  • mild solution
  • fixed point theorem

MSC 2010

  • Primary 26A33
  • Secondary 34A60
Open Access

Central and local limit theorems for the weighted Delannoy numbers

Published Online: 02 Jun 2022
Page range: 25 - 44

Abstract

Abstract

In this research we generalize our result for numbers satisfying the Delannoy triangle. We obtain a central limit theorem and a local limit theorem for weighted numbers of the triangle and establish the rate of convergence to the limiting (normal) distribution.

Keywords

  • Delannoy triangle
  • central limit theorem
  • local limit theorem
  • double generating function
  • triangular array

MSC 2010

  • Primary 05A15
  • 05A16
  • 60F05
  • Secondary 39A06
  • 39A14
Open Access

Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model

Published Online: 02 Jun 2022
Page range: 45 - 62

Abstract

Abstract

Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations. We will show that solitary wave solutions are recovered through a limiting process after the elliptic modulus of the Jacobi elliptic function cn that describes the periodic solutions for the self-focusing nonlinear Schrödinger model.

Keywords

  • NLS
  • self-focusing
  • defocusing
  • dispersive
  • nonlinearity
  • carrier waves
  • solution profile
  • envelope
  • cnoidal waves
  • solitary waves
  • surface gravity waves
  • sound waves
  • water-air interface
  • sonic layer depth

MSC 2010

  • Primary 33E05, 35Q55
  • Secondary 35Q53
Open Access

Negative clean rings

Published Online: 02 Jun 2022
Page range: 63 - 89

Abstract

Abstract

A ring is called negative clean if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.

In this paper, we develop the theory of the negative rings, with special emphasis on finding the clean matrices which have (or have not) clean negatives. Many explicit results are proved for 2 × 2 matrices and some hard to solve quadratic Diophantive equations are displayed.

Keywords

  • clean ring
  • negative clean ring
  • strongly clean element
  • 2 × 2 matrix

MSC 2010

  • Primary 16U99, 16U10, 15B33
  • Secondary 15B36, 16-04, 15-04
Open Access

Motion of Inextensible Quaternionic Curves and Modified Korteweg-de Vries Equation

Published Online: 02 Jun 2022
Page range: 91 - 101

Abstract

Abstract

Many curve evolutions have been determined which are integrable in recent times. The motion of curves can be defined by certain integrable equations including the modified Korteweg-de Vries. In this study, the quaternionic curves in 3 and 4-dimensional Euclidean spaces have been considered and the motions of inextensible quaternionic curves have been characterized by the modified Korteweg-de Vries (mKdV) equations. For this purpose, the basic concepts of the quaternions and quaternionic curves have been summarized. Then the evolutions of inextensible quaternionic curves with reference to the Frenet formulae have been obtained. Finally, the mKdV equations have been generated with the help of their evolutions

Keywords

  • Modified Korteweg-de Vries equation
  • quaternionic curve
  • evolution curve
  • inextensible curve

MSC 2010

  • Primary 53A04
  • Secondary 35Q53
Open Access

Characterization of second type plane foliations using Newton polygons

Published Online: 02 Jun 2022
Page range: 103 - 123

Abstract

Abstract

In this article we characterize the foliations that have the same Newton polygon that their union of formal separatrices, they are the foliations called of the second type. In the case of cuspidal foliations studied by Loray [Lo], we precise this characterization using the Poincaré-Hopf index. This index also characterizes the cuspidal foliations having the same process of singularity reduction that the union of its separatrices. Finally we give necessary and sufficient conditions when these cuspidal foliations are generalized curves, and a characterization when they have only one separatrix.

Keywords

  • foliation
  • second type foliation
  • Newton polygon

MSC 2010

  • Primary 32S65
  • Secondary 14H20
Open Access

Torsion subgroups of rational Mordell curves over some families of number fields

Published Online: 02 Jun 2022
Page range: 125 - 132

Abstract

Abstract

Mordell curves over a number field K are elliptic curves of the form y2 = x3 + c, where cK \ {0}. Let p ≥ 5 be a prime number, K a number field such that [K : ℚ] ∈ {2p, 3p}. We classify all the possible torsion subgroups E(K)tors for all Mordell curves E defined over ℚ when [K : ℚ] ∈ {2p, 3p}.

Keywords

  • Elliptic curves
  • Torsion group
  • Number fields

MSC 2010

  • Primary: 11G05, 11R16, 11R21
  • Secondary: 14H52
Open Access

Laplacian energy and first Zagreb index of Laplacian integral graphs

Published Online: 02 Jun 2022
Page range: 133 - 160

Abstract

Abstract

The set Si,n = {0, 1, 2, …, i − 1, i + 1, …, n − 1, n}, 1 ⩽ in, is called Laplacian realizable if there exists a simple connected undirected graph whose Laplacian spectrum is Si,n. The existence of such graphs was established by S. Fallat et all. In the present paper, we find the Laplacian energy and first Zagreb index of graphs whose Laplacian spectrum is Si,n.

Keywords

  • Laplacian matrix
  • Laplacian integral graphs
  • Laplacian energy
  • First zagreb index
  • Second zagreb index

MSC 2010

  • Primary 05C50, 15A18
  • Secondary 05C76, 05C90
Open Access

Properties of n-ary hypergroups relevant for modelling trajectories in HD maps

Published Online: 02 Jun 2022
Page range: 161 - 178

Abstract

Abstract

In the paper we show that trajectories used in HD maps of autonomous vehicles can be well modelled by means of n-ary hyperoperations and hypergroups. We investigate some properties of such hypergroups.

Keywords

  • autonomous driving
  • HD maps
  • hypergroup
  • -ary hypergroup
  • self-navigation

MSC 2010

  • Primary 20N20
  • 20N15
Open Access

A result of instability for two-temperatures Cosserat bodies

Published Online: 02 Jun 2022
Page range: 179 - 192

Abstract

Abstract

In our study we consider a generalized thermoelasticity theory based on a heat conduction equation in micropolar bodies. Specifically, the heat conduction depends on two distinct temperatures, the conductive temperature and the thermodynamic temperature. In our analysis, the difference between the two temperatures is clear and is highlighted by the heat supply. After we formulate the mixed initial boundary value problem defined in this context, we prove the uniqueness of a solution corresponding some specific initial data and boundary conditions. Also, if the initial energy is negative or null, we prove that the solutions of the mixed problem are exponentially instable.

Keywords

  • thermodynamic temperature
  • conductive temperature
  • micropolar bodies
  • uniqueness
  • exponential increasing
  • exponentially instable

MSC 2010

  • 74A15
  • 74A60
  • 74G40
  • 35A15
Open Access

Collectively Fixed Point Theory in the Compact and Coercive Cases

Published Online: 02 Jun 2022
Page range: 193 - 207

Abstract

Abstract

We present collectively fixed point results for multivalued maps which automatically generate analytic alternatives and minimax inequalities. As an application we consider equilbrium type problems for generalized games.

Keywords

  • Continuous selections
  • fixed point theory
  • analytic alternatives
  • minimax inequalities

MSC 2010

  • Primary 47H10
  • Secondary 54H25
Open Access

Algebraic Heun Operators with Tetrahedral Monodromy

Published Online: 02 Jun 2022
Page range: 209 - 230

Abstract

Abstract

Our work adds to the picture of second order differential operators with a full set of algebraic solutions, which we will call algebraic. We see algebraic Heun operators as pull-backs of algebraic hypergeometric operators via Belyi functions. We focus on the case when the hypergeometric one has a tetrahedral monodromy group. We find arithmetic conditions for the pull-back functions to exist. For each distribution of the singular points in the ramified fibers, we identify the minimal values of the exponent differences and we explicitly construct the dessin d’enfant corresponding to the pull-back function in the minimal cases. Then by allowing some parameters to vary, we find infinite families of such graphs, hence of Heun operators with tetrahedral monodromy.

Keywords

  • Algebraic solutions of differential equations
  • Belyi Functions
  • Dessins d’enfants
  • Planar graphs

MSC 2010

  • Primary 11G32, 34M15
  • Secondary 34M35, 05C10, 05C65, 33C99
Open Access

Sombor index of zero-divisor graphs of commutative rings

Published Online: 02 Jun 2022
Page range: 231 - 257

Abstract

Abstract

In this paper, we investigate the Sombor index of the zero-divisor graph of ℤn which is denoted by Γ(ℤn) for n ∈ {pα, pq, p2q, pqr} where p, q and r are distinct prime numbers. Moreover, we introduce an algorithm which calculates the Sombor index of Γ(ℤn). Finally, we give Sombor index of product of rings of integers modulo n.

Keywords

  • Topological indices
  • Sombor index
  • zero-divisor graph
  • vertex degree
  • algorithm

MSC 2010

  • Primary 13A70, 05C09, 05C07
  • Secondary 68R10, 05C25
Open Access

Solving Single Nesting Problem Using a Genetic Algorithm

Published Online: 02 Jun 2022
Page range: 259 - 272

Abstract

Abstract

Since the Bin Packing Problem (BPP) has application to industry and supply chain management problems (to mention only the most important ones), it attracted attention from its formulation. The Single Nesting Problem treated here is a particular case of this optimization problem, which different methods, mainly combinatorial, can solve. In this article, we propose using a genetic algorithm for solving the single nesting problem formulated in a previous article by the authors. The results comparisons prove that this approach is an excellent alternative to the combinatorial ones.

Keywords

  • Optimization
  • Combinatorics
  • Bin Packing Problem
  • Genetic Algorithms

MSC 2010

  • Primary 90C08, 90C59
  • Secondary: 68T20
Open Access

Ellipses surrounding convex bodies

Published Online: 02 Jun 2022
Page range: 273 - 282

Abstract

Abstract

If, for a double normal xx* of a convex body K, an ellipse Ex, x* is included in K, we say that E is surrounded by the boundary of K. If, instead, in the plane of E, K is included in the convex hull of E, then we say that E is surrounding K. In this paper we investigate surrounding and surrounded ellipses, particularly circles. We do this for arbitrary convex bodies, for polytopes, for convex bodies of constant width, and for most convex bodies (in the sense of Baire categories).

Keywords

  • Double normal
  • convex body of constant width
  • surrounded and surrounding ellipses

MSC 2010

  • Primary 52A15

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