- 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

#### On the Method of Inverse Mapping for Solutions of Coupled Systems of Nonlinear Differential Equations Arising in Nanofluid Flow, Heat and Mass Transfer

Pages: 1 - 14

#### Résumé

Very recently, Liao has invented a Directly Defining Inverse Mapping Method (MDDiM) for nonlinear differential equations. Liao’s method is novel and can be used for solving several problems arising in science and engineering, if we can extend it to nonlinear systems. Hence, in this paper, we extend Liao’s method to nonlinear-coupled systems of three differential equations. Our extension is not limited to single, double or triple equations, but can be applied to systems of any number of equations.

#### Mots clés

- Method of directly defining the inverse mapping
- Nonlinear systems
- Nanofluid
- Brownian motion
- Stretching surface
- analytical methods
- Homotopy analysis method

#### MSC 2010

- 34A25
- 34A34
- 34B15
- 65L10
- 76D10

Accès libre

#### A global solution for a reaction-diffusion equation on bounded domains

Pages: 15 - 22

#### Résumé

In the literature, it has been proved the existence of a pullback global attractor for reaction-diffusion equation on a bounded domain and under some conditions, a uniform bound on the dimension of its sections. Using those results and putting a bound on the diameter of the domain, we proved that the pullback global attractor consists only of one global solution. As an application to this result, a bounded perturbation of Chafee-Infante equation has been studied.

#### Mots clés

- non-autonomous reaction-diffusion equation
- pullback global attractor
- fractal dimension
- Chafee-Infante equation

#### MSC 2010

- 35B40
- 35B41
- 35B45
- 35K57
- 37L30

Accès libre

#### Perfect phase-coded pulse trains generated by Talbot effect

Pages: 23 - 32

#### Résumé

A perfect phase sequence is a finite and ordered set of constant-amplitude complex numbers whose periodic autocorrelation vanishes at any non-zero time shift. They find multiple applications in science an engineering as phase-coded waveforms, where the sequence defines the relative phases within a burst of electromagnetic or acoustic pulses. We show how a physical propagation effect, the so-called fractional Talbot phenomenon, can be used to generate pulse trains coded according to these sequences. The mathematical description of this effect is first reviewed and extended, showing its close relationship with Gauss perfect phase sequences. It is subsequently shown how it leads to a construction of Popović’s Generalized Chirp-Like (GCL) sequences. Essentially, a set of seed pulses with prescribed amplitude and phase levels, cyclically feeds a linear and dispersive medium. At particular values of the propagation length, multiple pulse-to-pulse interference induced by dispersion passively creates the sought-for pulse trains composed of GCL sequences, with the additional property that its repetition rate has been increased with respect to the seed pulses. This observation constitutes a novel representation of GCL sequences as the result of dispersive propagation of a seed sequence, and a new route for the practical implementation of perfect phase-coded pulse waveforms using Talbot effect.

#### Keywords and phrases

- Perfect sequences
- Phase sequences
- CAZAC sequences
- Talbot effect

#### MSC 2010

- 42-XX
- 65T50
- 11Z05
- 94A14
- 78A45

Accès libre

#### Revan and hyper-Revan indices of Octahedral and icosahedral networks

Pages: 33 - 40

#### Résumé

Let _{1}(_{G}_{G}_{2}(_{G}_{G}_{1}(_{G}_{G}^{2} and _{2}(_{G}_{G}^{2}. In this paper, we compute the first and second kind of Revan and hyper-Revan indices for the octahedral and icosahedral networks.

#### Mots clés

- Revan index
- hyper-Revan
- Octahedral
- Icosahedral
- Networks

#### MSC 2010

- 05C05
- 05C07
- 05C35

Accès libre

#### Peristaltic slip flow of a Bingham fluid in an inclined porous conduit with Joule heating

Pages: 41 - 54

#### Résumé

The present study deals with simultaneous effects of Joule heating and slip on peristaltic flow of a Bingham fluid in an inclined tapered porous channel with elastic walls. The closed form solutions for the stream function, the velocity and the temperature fields are obtained. The effects of the physical parameters on the flow characteristics are presented through graphs for both slip and no-slip cases. In addition, the performance of the temperature is studied with and without Joule heating effects. Moreover, the trapping phenomenon is analysed. The size of the trapped bolus increases with increasing values of the slip parameter and decreasing values of the magnetic, the permeability and the yield stress parameters. The present results are compared with the available results in the literature and our results agree well with the available results for some special cases.

#### Mots clés

- MHD peristaltic slip flow
- Joule heating
- Bingham fluid
- inclined porous channel

#### MSC 2010

- 76A05
- 76Z05

Accès libre

#### Analysis of models for viscoelastic wave propagation

Pages: 55 - 96

#### Résumé

We consider the problem of waves propagating in a viscoelastic solid. For the material properties of the solid we consider both classical and fractional differentiation in time versions of the Zener, Maxwell, and Voigt models, where the coupling of different models within the same solid are covered as well. Stability of each model is investigated in the Laplace domain, and these are then translated to time-domain estimates. With the use of semigroup theory, some time-domain results are also given which avoid using the Laplace transform and give sharper estimates. We take the time to develop and explain the theory necessary to understand the relation between the equations we solve in the Laplace domain and those in the time-domain which are written using the language of causal tempered distributions. Finally we offer some numerical experiments that highlight some of the differences between the models and how different parameters effect the results.

#### Mots clés

- Hyperbolic PDE
- viscoelasticity
- Laplace transforms
- semigroups of operators
- stability analysis
- fractional derivatives

#### MSC 2010

- 35B35
- 35L05
- 46F12
- 65M60
- 65J08
- 74B99

Accès libre

#### Perturbation analysis of a matrix differential equation ẋ = ABx

Pages: 97 - 104

#### Résumé

Two complex matrix pairs (^{−1}^{−1}^{−1}^{−1}^{−1}

#### Mots clés

- Contragredient equivalence
- Miniversal deformation
- Perturbation

#### MSC 2010

- 15A21
- 93D13

Accès libre

#### Research on relationship between tourism income and economic growth based on meta-analysis

Pages: 105 - 114

#### Résumé

In recent years, with the rapid growth of Chinese economy, the domestic tourism industry has gradually formed. Many scholars on the relationship between the tourism income and economic growth has carried on the empirical research and the most found that tourism income promote economic growth. The study uses the method of meta-analysis to study the relationship between tourism income and economic growth in major cities, and then analyzes the relationship between domestic tourism income and economic growth. Through literature retrieval, extract contains 409 sample sizes 21 valid documents, it is found that the tourism income and economic growth significantly correlated, analyzing the relation between the two different methods and no significant influence on the relation between regional differences. This study provides a way to promote economic growth.

#### Mots clés

- Tourism income
- Economic growth
- Meta-analysis

#### MSC 2010

- 91B42

Accès libre

#### Simulation analysis of resource-based city development based on system dynamics: A case study of Panzhihua

Pages: 115 - 126

#### Résumé

Resources and the environment have always been the two important natural factors that affect people’s lives. In recent years, the problem of resources and the environment has increasingly become an important issue that people are concerned about. This study discusses the use and consumption of energy and the impact of environmental pollution on economic development under sustainable economic development. This paper takes Panzhihua as an example to analyze the impact of energy and environment on the economy, and proposes solutions to improve economic development, which is of strategic significance for the future development of Panzhihua City. In this paper, the system dynamics method is used to decompose the Panzhihua large-scale system into three parts and carry out modeling and simulation to explore the connection between them. Based on the data from 2007 to 2015 in Panzhihua City, simulations have been carried out to obtain qualitative and quantitative analysis of certain simulation curves of the energy-environment-economy 3E system (hereinafter referred to as 3E system) from 2007 to 2030 to ascertain the future development pattern of Panzhihua City. The results show that when the 3E system is a coordinated development model, economic development and environmental protection have a good development trend at the same time, which is applicable to the future development of Panzhihua City. This model has good reference suggestions and application prospects for urban development. We want to give Panzhihua City the following suggestions: (1) Continue to focus on the secondary industry and increase competitiveness. (2) Increase the investment funds in environmental protection and achieve sustainable economic development.

#### Mots clés

- dynamical systems
- mathematical model and city development

#### MSC 2010

- 03C65

Accès libre

#### Attractors for a nonautonomous reaction-diffusion equation with delay

Pages: 127 - 150

#### Résumé

In this paper, we discuss the existence and uniqueness of solutions for a non-autonomous reaction-diffusion equation with delay, after we prove the existence of a pullback 𝒟-asymptotically compact process. By a priori estimates, we show that it has a pullback 𝒟-absorbing set that allow us to prove the existence of a pullback 𝒟-attractor for the associated process to the problem.

#### Mots clés

- pullback attractors
- nonclassical reaction-diffusion equations
- critical exponent
- delay term

#### MSC 2010

- 35B41
- 35B40
- Secondary 37L30
- 35Q35

Accès libre

#### Design of Gravity Assist trajectory from Earth to Jupiter

Pages: 151 - 160

#### Résumé

The goal of this paper is to find a combination of conical trajectories, using gravitational assisted maneuvers (swing-by), which perform the transfer from a nearby of the departure planet (Earth) to the vicinity of the arrival planet (Jupiter), making a closest approaches with Mars (flyby) to reduce the fuel consumption for the journey. A detailed description of the mission from Earth— Mars—Jupiter, that used this technique is presented. The table of flyby dates, altitudes of closest approaches is also included. A methodology known as the Patched Conics was used, where the trajectory is divided into three parts:

Departure phase, inside of the sphere of influence of the departure planet,

Heliocentric phase, during the journey between the planets,

Arrival phase, inside the sphere of influence of the arrival planet.

#### Mots clés

- Interplanetary trajectories
- Gravity Assist
- Flyby
- Departure and arrival trajectories

#### MSC 2010

- Primary: 70F15
- Secondary: 70M20

Accès libre

#### Some Improvements on Relativistic Positioning Systems

Pages: 161 - 166

#### Résumé

We make some considerations about Relativistic Positioning Systems (RPS). Four satellites are needed to position a user. First of all we define the main concepts. Errors should be taken into account. Errors depend on the Jacobian transformation matrix. Its Jacobian is proportional to the tetrahedron volume whose vertexes are the four tips of the receiver-satellite unit vectors. If the four satellites are seen by the user on a circumference in the sky, then, the Jacobian and the tetrahedron volume vanish. The users we consider are spacecraft. Spacecraft to be positioned cannot be close to a null Jacobian satellites-user configuration. These regions have to be avoided choosing an appropriate set of four satellites which are not seen too close to the same circumference in the sky. Errors also increase as the user spacecraft separates from the emission satellite region, since the tetrahedron volume decreases.We propose a method to autonomously potion a user-spacecraft which can test our method. This positioning should be compared with those obtained by current methods. Finally, a proposal to position a user-spacecraft moving far from Earth, with suitable devices (autonomous), is presented.

#### Mots clés

- Astronomy and Astrophysics
- Mathematical Physics
- General Relativity
- Relativistic Positioning Systems
- Numerical Methods

#### MSC 2010

- 35Q85
- 37M99
- 83C05

Accès libre

#### A new computational algorithm for the solution of second order initial value problems in ordinary differential equations

Pages: 167 - 174

#### Résumé

In this article, we propose a new computational method for second order initial value problems in ordinary differential equations. The algorithm developed is based on a local representation of theoretical solution of the second order initial value problem by a non-linear interpolating function. Numerical examples are solved to ensure the computational performance of the algorithm for both linear and non-linear initial value problems. From the results we obtained, the algorithm can be said computationally efficient and effective.

#### Mots clés

- Absolute Stability
- Finite difference approximations
- Initial Value Problems
- Maximum Absolute Error
- Nonlinear IVP

#### MSC 2010

- 65L10
- 65L12

Accès libre

#### Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

Pages: 175 - 186

#### Résumé

In term of the global random attractors theory, global dynamics of nonlinear stochastic heat conduction driven by multiplicative white noise with a variable coefficient are investigated numerically. It is shown that global 𝒟-bifurcation, secondary global 𝒟-bifurcation and complex dynamical behavior occur in motion of the system with increasing the intensity of linear component in the heat source. Furthermore, the results obtained here indicate that Hasudorff dimension which is relevant to global Lyapunov exponent can be used to describe global dynamics of the associated system qualitatively.

#### Mots clés

- nonlinear stochastic heat conduction
- global dynamics
- random invariant measure
- Hausdorff dimension
- global Lyapunov exponent

Accès libre

#### The Triaxiality Role in the Spin-Orbit Dynamics of a Rigid Body

Pages: 187 - 208

#### Résumé

We study the roto-orbital dynamics of a uniform sphere and a triaxial body by means of a radial intermediary, which defines a 2-DOF Hamiltonian system. Our analysis is carried out by using variables referred to the total angular momentum. Its validity and applicability is assessed numerically by experiments comprising three different scenarios; analysis of the triaxiality, eccentricity and altitude. They show that there is a range of parameters and initial conditions for which the radial distance and the slow angles are estimated accurately, even after one orbital period. On the contrary, fast angles deteriorates as the triaxiality grows. We also include the study of the relative equilibria, finding constant radius solutions filling 4-D and lower dimensional tori. These families of relative equilibria include some of the classical ones reported in the literature and some new types. For a number of scenarios the relation between the triaxiality and the inclination connected with relative equilibria are given.

#### Mots clés

- Rotational and orbital dynamics
- gravity-gradient
- intermediary
- relative equilibria

#### MSC 2010

- 70F05
- 70F15

Accès libre

#### New and Modified Eccentric Indices of Octagonal Grid O^{m}_{n}

^{m}

_{n}

Pages: 209 - 228

#### Résumé

The eccentricity _{u}

#### Mots clés

- Degree
- Eccentricity
- Ediz eccentric connectivity index
- modified eccentric connectivity index
- modified eccentric connectivity polynomial (, )
- octagonal grid

#### MSC 2010

- Primary: 05C12
- 05C90

Accès libre

#### Noether’s theorems of variable mass systems on time scales

Pages: 229 - 240

#### Résumé

This paper deals with the Noether’s theory for variable mass system on time scales. The calculus on time scales unifies and extends variable mass system continuous model and discrete model into a single theory. Firstly, Hamilton’s principle of the variable mass system on time scales is given. Secondly, based on the quasi-invariance of the Hamilton’s action under a group of infinitesimal transformations, Noether’s theorem and its inverse theorem of the variable mass system on time scales are presented. Finally, two examples are given to illustrate the applications of the results.

#### Mots clés

- variable mass system
- Noether’s theorem
- time scale

#### MSC 2010

- Primary: 46F12
- 65R10

Accès libre

#### Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation

Pages: 241 - 254

#### Résumé

In this paper we study a (2+1)-dimensional coupling system with the Korteweg-de Vries equation, which is associated with non-semisimple matrix Lie algebras. Its Lax-pair and bi-Hamiltonian formulation were obtained and presented in the literature. We utilize Lie symmetry analysis along with the (

#### Mots clés

- (2+1)-dimensional coupling system with the Korteweg-de Vries equation
- Lie symmetries
- (′/)–expansion method
- travelling wave solutions, conservation laws

#### MSC 2010

- 35C07
- 35L65

Accès libre

#### Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

Pages: 255 - 264

#### Résumé

In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems.

#### Mots clés

- Split step method
- Semi-linear Parabolic equation
- Galerkin-Chebyshev spectral method
- Galerkin-Chebyshev pseudo spectral method
- Poisson-Boltzman model

#### MSC 2010

- 365M70
- 35K58
- 65N06
- 65N12

Accès libre

#### Reckoning of the Dissimilar Topological indices of Human Liver

Pages: 265 - 276

#### Résumé

The molecular topological indices as validly demonstrated its high performance in the discovery and design of new drugs. The goal of this paper is to study the structurally constructed a graph model of human Liver using graph operator. After the construction, nurtured the model using various topological indices. Also, established a diagnosis defect in the human Liver. Basically, considered structure of Liver can divide into healthy Liver and affected Liver. In this case study the topological indices are used in describe the structure of Liver using graph operator. Constructed model can be useful further in the medical field for any diagnosis with special care.

#### Mots clés

- Liver Structure
- double graph
- first and second Zagreb
- Harmonic index
- Randic index
- Symmetric division deg index
- Atom-Bond connectivity () index
- Geometric-Arithmetic () index

#### MSC 2010

- AMS Subject Classification: 05C05
- 05C12
- 05C75

Accès libre

#### Wall Properties and Slip Consequences on Peristaltic Transport of a Casson Liquid in a Flexible Channel with Heat Transfer

Pages: 277 - 290

#### Résumé

In this paper, the peristaltic wave propagation of a Non-Newtonian Casson liquid in a non-uniform (flexible)channel with wall properties and heat transfer is analyzed. Long wavelength and low Reynolds number approximations are considered. Analytical solution for velocity, stream function and temperature in terms of various physical parameters is obtained. The impact of yield stress, elasticity, slip and non-uniformity parameters on the peristaltic flow of Casson liquidare observed through graphs and discussed. The important outcome is that an increase in rigidity, stiffness and viscous damping force of the wall results in the enhancement of the size and number of bolus formed in the flow pattern.

#### Mots clés

- Peristaltic wave
- wall effects
- rigidity
- casson liquid
- heat transfer

#### MSC 2010

- 7605

Accès libre

#### Effects of second-order slip and drag reduction in boundary layer flows

Pages: 291 - 302

#### Résumé

In this paper, boundary layer flow over a moving flat plate with second-order velocity slip, injection and applied magnetic field is analyzed. The governing partial differential equations are converted in to a nonlinear ordinary differential equation through an appropriate similarity transformation. The resulting nonlinear equation is solved via homotopy analysis method (HAM). Errors ranging from 10^{–7} to 10^{–10} are reported for a relatively few terms. The effects of the pertinent parameters on the velocity and the shear stress are presented graphically and discussed. In the absence of magnetic field and the two slip parameters, the results are found to be in excellent agreement with the available results in the literature. It is expected that the results obtained will not only provide useful information for industrial applications but also complement the earlier works.

#### Mots clés

- Second-order slip
- drag reduction
- boundary-layer flow
- homotopy analysis method

#### MSC 2010

- 65L10
- 76D10

Accès libre

#### Acousto-optic modulation in ion implanted semiconductor plasmas having SDDC

Pages: 303 - 310

#### Résumé

The present paper is aimed to the exploration of acousto-optic (AO) modulational amplification in ion implanted semiconductors. The AO modulational process has been treated as a four wave parametric mixing process and the effective third-order acousto-optic susceptibility characterizing the instability process has been deduced. By considering that the origin of modulational interaction lies in the third order AO susceptibility arising from the nonlinear induced current density and using the coupled mode theory, an analytical investigation of an intense laser beam in a strain dependent dielectric constant (SDDC) semiconductor crystal is presented. We found a significant change in threshold and gain characteristics with changes in charge imbalance parameter. The presence of colloidal grains (CGs) plays an effective role in changing the threshold intensity and effective gain constant.

Accès libre

#### A finite difference method for a numerical solution of elliptic boundary value problems

Pages: 311 - 320

#### Résumé

In this article, we have considered for numerical solution of a Poisson and Laplace equation in a domain. we have presented a novel finite difference method for solving the system of the boundary value problems subject to Dirichlet boundary conditions. We have derived the solution of the Poisson and Laplace equations in a two-dimensional finite region. We present numerical experiments to demonstrate the efficiency of the method.

#### Mots clés

- Elliptic equations
- finite difference method
- finite region
- maximum absolute error
- Poison and Laplace equations

#### MSC 2010

- 65N06

#### Résumé

In this paper we introduce the walk polynomial to find the number of walks of different lengths in a simple connected graph. We also give the walk polynomial of the bipartite, star, wheel, and gear graphs in closed forms.

#### Mots clés

- Walk
- Walk polynomial
- Adjacency matrix
- Bipartite graph
- Gear graph

#### MSC 2010

- 05C31
- 05C30