- Détails du magazine
- Format
- Magazine
- eISSN
- 2444-8656
- Première publication
- 01 Jan 2016
- Période de publication
- 2 fois par an
- Langues
- Anglais

#### Chercher

- Accès libre

Homoclinic and Heteroclinic Motions in Economic Models with Exogenous Shocks

Pages: 1 - 10

#### Résumé

In this study, we theoretically prove the presence of homoclinic and heteroclinic motions in the dynamics of economic models perturbed with exogenous shocks. An illustrative example based on the Kaldor model of the aggregate economy is presented.

#### Mots clés

- Exogenous shocks
- Homoclinic and heteroclinic motions
- Stable and unstable sets
- Kaldor model

#### MSC 2010

- 91G80
- 35A24
- 54H20

- Accès libre

Boundary value problems for fractional differential equation with causal operators

Pages: 11 - 22

#### Résumé

In this paper, we study the two-point boundary value problems for fractional differential equation with causal operator. By lower and upper solution method and the monotone iterative technique, some results for the extremal solution and quasisolutions are obtained. At last, an example is given to demonstrate the validity of assumptions and theoretical results.

#### Mots clés

- Fractional differential equation
- Causal operator
- Boundary value problems
- Lower and upper solution
- Extremal solution and quasisolutions.

#### MSC 2010

- 34B15
- 34A45

- Accès libre

Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas

Pages: 23 - 44

#### Résumé

In the paper there are presented and evaluated for effectiveness three methods of accuracy increase of fractional order derivatives and integrals computations for application with the Riemann-Liouville/Caputo formulas. They are based on the ideas of either transforming difficult integrand in the formulas to high-accuracy computations requirements of a applied method of numerical integration or adapting a numerical method of integration to handle with high-accuracy a difficult feature in the integrand. Additional accuracy gain is obtained by incorporating increased precision into computations. The actual accuracy improvement by applying presented methods is compared with the capabilities of wide range of available methods of integration.

#### Keywords and phrases

- Numerical Integration
- Fractional Order Derivatives and Integrals

#### MSC 2010

- 65-04
- 65K05
- 41-04
- 41A55

- Accès libre

Complex Network Theory and Its Application Research on P2P Networks

Pages: 45 - 52

#### Résumé

Advances in complex networks of Peer-to-Peer (P2P) networks were reviewed and summarized. The paper outlines some important topological properties such as degree, average path length and clustering coefficient at first, and then three kinds of most important network mechanism models are introduced, including random graph model, small world model and scale-free model. A simple description about research status for P2P networks based on complex networks is made from three aspects: positive research, network mechanism model, network broadcast and control. Some developing prospects of complex networks of P2P are pointed out finally. Complex network provides new ideas and methods to deal with many complex problems including P2P networks.

#### Keywords and phrases

- Complex network
- Peer to Peer network
- positive research
- network mechanism model

#### MSC 2010

- 68M10

- Accès libre

Friction Torque Behavior as a Function of Actual Contact Angle in Four-point-contact Ball Bearing

Pages: 53 - 64

#### Résumé

The friction is a key factor of rolling bearing performance, especially for those precision transmission fields. All the top rolling bearing manufactures provide their calculating models on friction torque. However, there is great difference between the calculation result and measured value. Two calculation methods on friction torque of four-point-contact ball bearing, considered different factors involving the calculation, are compared and researched for discovering the key influence factor. A specific test is development to verify the theoretical analysis and a precision control method on friction torque with lower cost in production is proposed.

#### Mots clés

- Friction torque
- ball bearing
- four-point-contact
- contact angle
- precision control

#### MSC 2010

- 00A69

- Accès libre

LAV Path Planning by Enhanced Fireworks Algorithm on Prior Knowledge

Pages: 65 - 78

#### Résumé

Path planning plays an extremely important role in the design of LAVs (Loitering Air Vehicles) to accomplish the air combat task fleetly and reliably. The planned path should ensure that LAVs reach the destination along the optimal path with minimum probability of being found and minimal consumed fuel. Traditional methods tend to find local best solutions due to the large search space. So it takes a lot of time and consumes a lot of computing resources. In this paper, a new young intelligent algorithm-fireworks algorithm is introduced, and EFWA (enhanced fireworks algorithm)-its enhanced version is used to find the optimal solution. At the same time, the battlefield prior knowledge is fully utilized to predict the existence space of the potential optimal trajectory. Greatly the search space reduced, plan planning efficiency is significantly improved. Path planning method effectiveness in this paper has further been improved compared with FACPSO. Moreover, the EFWA on prior knowledge performs well on the application of dynamic path planning when the threats cruise randomly than FAC-PSO.

#### Keywords and phrases

- FWA
- Threat Degree
- FAC-PSO
- Search Space

#### MSC 2010

- 68T42

- Accès libre

Centers: their integrability and relations with the divergence

Pages: 79 - 86

#### Résumé

This is a brief survey on the centers of the analytic differential systems in ℝ^{2}. First we consider the kind of integrability of the different types of centers, and after we analyze the focus–center problem, i.e. how to distinguish a center from a focus. This is a difficult problem which is not completely solved. We shall present some recent results using the divergence of the differential system.

#### Keywords and phrases

- Center problem
- integrability
- Poincaré–Liapunov constants
- divergence

#### MSC 2010

- 34C25
- 37G10
- 34A34
- 34C05

- Accès libre

Applications of the min-max symbols of multimodal maps

Pages: 87 - 98

#### Résumé

The min-max symbols generalize the kneading symbols in that they contain also information about the minimum or maximum character of the critical values and their iterates. Interestingly enough, this additional information can be obtained from the kneading symbols without further computation. In this paper we review some interesting applications of the min-max symbols. The applications chosen concern new expressions for the topological entropy of multimodal maps, as well as a numerical algorithm to compute it.

#### Keywords and phrases

- Multimodal maps
- min-max-symbols
- topological entropy
- numerical algorithm

#### MSC 2010

- 37B40
- 37E05
- 37B10
- 65Dxx

- Accès libre

Degree-based indices computation for special chemical molecular structures using edge dividing method

Pages: 99 - 122

#### Résumé

In computational chemistry, the molecular structures are modelled as graphs which are called the molecular graphs. In these graphs, each vertex represents an atom and each edge denotes covalent bound between atoms. It is shown that the topological indices defined on the molecular graphs can reflect the chemical characteristics of chemical compounds and drugs. In this paper, we report several degree based indices of some widely used chemical molecular structures by means of edge dividing technology.

#### Keywords and phrases

- Molecular graph
- degree-based index
- edge dividing approach

#### MSC 2010

- 05C15
- 05C07
- 05C35

- Accès libre

On the perturbed restricted three-body problem

Pages: 123 - 144

#### Résumé

In this survey paper we offer an analytical study regarding the perturbed planar restricted three-body problem in the case that the three involved bodies are oblate. The existence of libration points and their linear stability are explored under the effects of the perturbations in Coriolis and centrifugal forces. The periodic orbits around these points are also studied under these effects. Moreover, the elements of periodic orbits around these points are determined.

#### Keywords and phrases

- Restricted three-body problem
- Coriolis and centrifugal forces
- Oblateness
- Libration points
- Stability
- Periodic orbits

#### MSC 2010

- 70F05
- 37C27
- 37J30

- Accès libre

Overview of current techniques in remote data auditing

Pages: 145 - 158

#### Résumé

The emergence of cloud computing brings the infinite imagination space, both in individual and organizations, due to its unprecedented advantages in the IT history: on-demand self-service, ubiquitous network access, location independent resource pooling, rapid resource elasticity, usage-based pricing and transference of risk. Many of the individuals or organizations ease the pressure on their local data storage, and mitigate the maintenance overhead of local data storage by using outsource data to cloud. However, the data outsourcing is not absolutely safe in the cloud. In order to enhance the users’ confidence of the integrity of their outsource data in the cloud. To promote the rapid deployment of cloud data storage service and regain security assurances with outsourced data dependability, many scholars tend to design the Remote Data Auditing (RDA) technique as a new concept to enable public auditability for the outsourced data in the cloud. The RDA is a useful technique to ensure the correctness of the data outsourced to cloud servers. This paper presents a comprehensive survey on techniques of remote data auditing in cloud server. Recently, more and more remote auditing approaches are categorized into the three different classes, that is, replication-based, erasure coding-based, and network coding-based to present a taxonomy. This paper also aims to the explore major issues.

#### Keywords and phrases

- Cloud Computing
- cloud service
- data auditing
- network coding

#### MSC 2010

- 68P25
- 68P30

- Accès libre

Ontology optimization tactics via distance calculating

Pages: 159 - 174

#### Résumé

In this article, we propose an ontology learning algorithm for ontology similarity measure and ontology mapping in view of distance function learning techniques. Using the distance computation formulation, all the pairs of ontology vertices are mapped into real numbers which express the distance of their corresponding vectors. The more distance between two vertices, the smaller similarity between their corresponding concepts. The stabilities of our learning algorithm are defined and several bounds are yielded via stability assumptions. The simulation experimental conclusions show that the new proposed ontology algorithm has high efficiency and accuracy in ontology similarity measure and ontology mapping in certain engineering applications.

#### Keywords and phrases

- ontology
- similarity measure
- ontology mapping
- distance computation
- stability

#### MSC 2010

- 60J20
- 65L20

- Accès libre

Vertex PI_{v} Topological Index of Titania Carbon Nanotubes TiO _{2}(m,n)

_{v}

_{2}

Pages: 175 - 182

#### Résumé

A topological index of a graph G is a numeric quantity related to _{e=uv∈E(G)} [_{u}_{v}_{u}_{v}_{2}[

#### Keywords and phrases

- Molecular graph
- degree of vertex
- eccentricity of vertex
- PI index
- Titanian carbon Nanotube

#### MSC 2010

- 05C05
- 92E10

- Accès libre

Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Pages: 183 - 196

#### Résumé

Dynamic behaviour of contact impact forces in strongly nonlinear discontinuous vibroimpact system is studying. Contact impact force is one of the most significant vibroimpact system characteristics. We investigate the 2-DOF vibroimpact system by numerical parameter continuation method in conjunction with shooting and Newton-Raphson methods. We simulate the impact by nonlinear contact interactive force according to Hertz’s contact law. This paper is the continuation of the previous works [

#### Mots clés

- vibroimpact system
- discontinuous
- contact force
- Hertz’s law
- bifurcation, multiplier
- nonlinear
- stability

#### MSC 2010

- 37M20
- 65P30
- 65P40
- 70K43
- 70K50

- Accès libre

Jittering regimes of two spiking oscillators with delayed coupling

Pages: 197 - 206

#### Résumé

A system of two oscillators with delayed pulse coupling is studied analytically and numerically. The so-called jittering regimes with non-equal inter-spike intervals are observed. The analytical conditions for the emergence of in-phase and anti-phase jittering are derived. The obtained results suggest universality of the multi-jitter instability for systems with delayed pulse coupling.

#### Mots clés

- Pulse-coupled oscillators
- synchronization
- phase resetting curve
- delayed coupling
- jittering

#### MSC 2010

- 37L10
- 37L15

- Accès libre

A model for the operations to render epidemic-free a hog farm infected by the Aujeszky
disease

Pages: 207 - 228

#### Résumé

We present here a case study for modelling the control of the Aujeszky disease, in a farm declared virus-free. The model is validated on the available data. Simulations are performed to assess different containment strategies for the epidemic. Final recommendations indicate that a strict reduction of biohazards in the farrowing unit should be enforced. Also neglecting the third inoculation in the vaccination protocol leads to a sensible and quantifiable increase of the prevalence of the disease. The findings indicate that it is more important to keep biosafety at a high level in the farrowing unit rather than strive for the highest standards in the gestation unit. Also the importance of a properly implemented vaccination appears fundamental, and its absence can be quantified via our simulations.

#### Mots clés

- Data Analysis
- mathematical modelling
- simulations
- epidemics
- control measures

#### MSC 2010

- 92D30

- Accès libre

Multiple solutions of the Kirchhoff-type problem in R^{N}

^{N}

Pages: 229 - 238

#### Résumé

In this paper, we concern with a class of quasilinear Kirchhoff-type problem. By using the Ekeland’s Variational Principle and Mountain Pass Theorem, the existence of multiple solutions is obtained. Besides, we also take this problem as an example to give the main frame of using critical point theory to find the weak solutions of nonlinear partial differential equation.

#### Mots clés

- Mountain Pass Theorem
- Ekeland’s Variational Principle
- Kirchhoff-type problem
- () sequence

#### MSC 2010

- 35J62
- 58K05
- 58E05

- Accès libre

Vibrational resonance: a study with high-order word-series averaging

Pages: 239 - 246

#### Résumé

We study a model problem describing vibrational resonance by means of a high-order averaging technique based on so-called word series. With the technique applied here, the tasks of constructing the averaged system and the associated change of variables are divided into two parts. It is first necessary to build recursively a set of so-called

#### Mots clés

- High-order averaging
- vibrational resonance
- formal series

#### MSC 2010

- 34C29
- 34E05

- Accès libre

Computing Eccentric Version of Second Zagreb Index of Polycyclic Aromatic Hydrocarbons (PAHk)

Pages: 247 - 252

#### Résumé

A Recently, Ghorbani et. al. introduced the eccentric versions of first and second Zagreb indices called third and fourth Zagreb indices defined as_{3} (_{uv∊E}(_{4} (_{ν∊V(G)}^{2}, respectively, where _{k}

#### Mots clés

- Molecular graph
- Eccentricity
- Zagreb Indices
- Polycyclic Aromatic Hydrocarbons (PAHk)

#### MSC 2010

- 05C05
- 92E10

- Accès libre

Finite Element Analysis of Influence of Non-homogenous Temperature Field on Designed Lifetime of Spatial Structural Elements under Creep Conditions

Pages: 253 - 262

#### Résumé

The techniques of modeling of continual fracture process for spatial bodies under long-term static force loading condition in non-homogenous temperature field are presented. The scalar damage parameter is used to describe the material continual fracture process. A stress-strain problem solution made with semianalytic finite element method (SFEM). Results of lifetime determination of responsible parts are presented.

#### Mots clés

- long-term loading condition
- creep
- damage
- continual fracture
- lifetime
- spatial problem
- semianalytic finite element method (SFEM)

#### MSC 2010

- 74C10
- 74R99
- 74S05
- 74D10

- Accès libre

On the classical and nonclassical symmetries of a generalized Gardner equation

Pages: 263 - 272

#### Résumé

In this paper, we consider a generalized Gardner equation from the point of view of classical and nonclassical symmetries in partial differential equations. We perform a complete analysis of the symmetry reductions by using the similarity variables and the similarity solutions which allow us to reduce our equation into an ordinary differential equation. Moreover, we prove that the nonclassical method applied to the equation leads to new symmetries, which cannot be obtained by using the Lie classical method. Finally, we calculate exact travelling wave solutions of the equation by using the simplest equation method.

#### Mots clés

- Partial differential equations
- Symmetries
- Exact solutions

#### MSC 2010

- 35C07
- 35Q35
- 35Q40
- 76M60

- Accès libre

A Comparison between Integer and Fractional Order PD^{μ} Controllers for Vibration Suppression

^{μ}

Pages: 273 - 282

#### Résumé

Along the years, unwanted vibrations in airplane wings have led to passenger discomfort. In this study, the airplane wing is modeled as a cantilever beam on which active vibration suppression is tested. The paper details the tuning of both integer and fractional order Proportional Derivative type controllers based on constraints imposed in the frequency domain. The controllers are experimentally validated and the results prove once more the superiority of the fractional order control approach.

#### Mots clés

- Vibration Suppression
- PD controller
- Fractional Calculus
- Smart Beam

#### MSC 2010

- 93C80
- 26A33
- 58E25

- Accès libre

Computation of the fifth Geometric-Arithmetic Index for Polycyclic Aromatic Hydrocarbons PAH_{k}

_{k}

Pages: 283 - 290

#### Résumé

Let _{u}_{k}

#### Mots clés

- Molecular graphs
- chemical structures Polycyclic Aromatic Hydrocarbon (PAHk)
- enzenoid
- Topological indices
- fifth Geometric-Arithmetic Index

#### MSC 2010

- 05C05
- 92E10

- Accès libre

Redefined Zagreb indices of Some Nano Structures

Pages: 291 - 300

#### Résumé

In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and redefined Zagreb indices defined on molecular graph

#### Mots clés

- molecular graph
- redefined Zagreb index
- nanotube
- nanostar
- polyomino chain
- benzenoid series

#### MSC 2010

- 05C70

- Accès libre

Relative Equilibria in the 4-Vortex Problem Bifurcating from an Equilateral Triangle Configuration

Pages: 301 - 310

#### Résumé

We study the relative equilibria in the 4-vortex problem when two of vorticities are equal to 1, and the other two equal to

#### Mots clés

- n-vortex problem
- relative equilibria
- bifurcations of relative equilibria

#### MSC 2010

- 76F20
- 37C10