- Détails du magazine
- Format
- Magazine
- eISSN
- 1844-0835
- Première publication
- 17 May 2013
- Période de publication
- 1 fois par an
- Langues
- Anglais

#### Chercher

- Accès libre

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

Pages: 5 - 24

#### Résumé

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.

#### Mots clés

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

#### MSC 2010

- Primary 26A33
- Secondary 34A60

- Accès libre

Central and local limit theorems for the weighted Delannoy numbers

Pages: 25 - 44

#### Résumé

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.

#### Mots clés

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

#### MSC 2010

- Primary 05A15
- 05A16
- 60F05
- Secondary 39A06
- 39A14

- Accès libre

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

Pages: 45 - 62

#### Résumé

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.

#### Mots clés

- 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

#### Résumé

A ring is called

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.

#### Mots clés

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

#### MSC 2010

- Primary 16U99, 16U10, 15B33
- Secondary 15B36, 16-04, 15-04

- Accès libre

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

Pages: 91 - 101

#### Résumé

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

#### Mots clés

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

#### MSC 2010

- Primary 53A04
- Secondary 35Q53

- Accès libre

Characterization of second type plane foliations using Newton polygons

Pages: 103 - 123

#### Résumé

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 [

#### Mots clés

- foliation
- second type foliation
- Newton polygon

#### MSC 2010

- Primary 32S65
- Secondary 14H20

- Accès libre

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

Pages: 125 - 132

#### Résumé

Mordell curves over a number field ^{2} = ^{3} + _{tors} for all Mordell curves

#### Mots clés

- Elliptic curves
- Torsion group
- Number fields

#### MSC 2010

- Primary: 11G05, 11R16, 11R21
- Secondary: 14H52

- Accès libre

Laplacian energy and first Zagreb index of Laplacian integral graphs

Pages: 133 - 160

#### Résumé

The set _{i,n}_{i,n}_{i,n}

#### Mots clés

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

#### MSC 2010

- Primary 05C50, 15A18
- Secondary 05C76, 05C90

- Accès libre

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

Pages: 161 - 178

#### Résumé

In the paper we show that trajectories used in HD maps of autonomous vehicles can be well modelled by means of

#### Mots clés

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

#### MSC 2010

- Primary 20N20
- 20N15

- Accès libre

A result of instability for two-temperatures Cosserat bodies

Pages: 179 - 192

#### Résumé

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.

#### Mots clés

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

#### MSC 2010

- 74A15
- 74A60
- 74G40
- 35A15

- Accès libre

Collectively Fixed Point Theory in the Compact and Coercive Cases

Pages: 193 - 207

#### Résumé

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.

#### Mots clés

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

#### MSC 2010

- Primary 47H10
- Secondary 54H25

- Accès libre

Algebraic Heun Operators with Tetrahedral Monodromy

Pages: 209 - 230

#### Résumé

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.

#### Mots clés

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

#### MSC 2010

- Primary 11G32, 34M15
- Secondary 34M35, 05C10, 05C65, 33C99

- Accès libre

Sombor index of zero-divisor graphs of commutative rings

Pages: 231 - 257

#### Résumé

In this paper, we investigate the Sombor index of the zero-divisor graph of ℤ_{n}_{n}^{α}, pq, p^{2}_{n}

#### Mots clés

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

#### MSC 2010

- Primary 13A70, 05C09, 05C07
- Secondary 68R10, 05C25

- Accès libre

Solving Single Nesting Problem Using a Genetic Algorithm

Pages: 259 - 272

#### Résumé

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.

#### Mots clés

- Optimization
- Combinatorics
- Bin Packing Problem
- Genetic Algorithms

#### MSC 2010

- Primary 90C08, 90C59
- Secondary: 68T20

#### Résumé

If, for a double normal ^{*} of a convex body ^{*} is included in

#### Mots clés

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

#### MSC 2010

- Primary 52A15