Volumen 1 (2016): Heft 1 (January 2016)

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.

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.

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.

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.

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.

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.

This is a brief survey on the centers of the analytic differential systems in ℝ². 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.

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.

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.

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.

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.

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.

A topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The Padmakar-Ivan (PI) index of a graph G is defined as PI(G) = Σ_e=uv∈E(G) [n_u + n_v], where n_u is the number of edges of G lying closer to v than u, analogously n_v. In this paper, we compute the vertex PI index of Titania carbon Nanotubes TiO₂[m,n].

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 [1,2]. We have determined the instability zones and bifurcations points for loading curves [1] and frequency-amplitude response [2] under variation of excitation amplitude and frequency. In this paper we investigate the behaviour of contact forces at bifurcation points particularly at discontinuous bifurcation points where set-valued Floquet multipliers cross the unit circle by jump that is their moduli becoming more than unit by jump. It is phenomenon unique for nonsmooth systems with discontinuous right-hand side. We observe also the contact forces increase at nT -periodical multiple impacts regimes. We also learn the change of contact forces behaviour when the impact between system bodies became the soft one due the change of system parameters.

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.

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.

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.

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 word basis functions and, after that, all the required manipulations involve only scalar coefficients that are computed by means of simple recursions. As distinct from the situation with other approaches, with word-series, high-order averaged systems may be derived without having to compute the associated change of variables. In the system considered here, the construction of high-order averaged systems makes it possible to obtain very precise approximations to the true dynamics.

A Recently, Ghorbani et. al. introduced the eccentric versions of first and second Zagreb indices called third and fourth Zagreb indices defined asM₃ (G) = Σ_uv∊E(G) (ε (u) + ε (ν)) and M₄ (G) = Σ_ν∊V(G)ε (ν)², respectively, where ε (ν)is the eccentricity of the vertex ν. In this paper, we compute the closed formula for third Zagreb index of Polycyclic Aromatic Hydrocarbons (PAH_k).

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.

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.

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.

Let G be a simple connected graph. The geometric-arithmetic index of G is defined as GA1(G)=∑uν∈E(G)2d(u)d(ν)d(u)+d(ν)$\begin{array}{} G{A_1}\left( G \right) = {\sum\nolimits _{u\nu \in E(G)}}\frac{{2\sqrt {d(u)d(\nu)} }}{{d(u) + d(\nu)}} \end{array}$, where d(u) represents the degree of the vertex u in the graph G. Recently, Graovac defined the fifth version of geometric-arithmetic index of a graph G as GA5(G)=∑uν∈E(G)2SνSuSν+Su$\begin{array}{} G{A_5}\left( G \right) = {\sum\nolimits _{u\nu \in E(G)}}\frac{{2\sqrt {{S_\nu}{S_u}} }}{{{S_\nu} + {S_u}}} \end{array}$, where S_u is the sum of degrees of all neighbors of vertex u in the graph G. In this paper, we compute the fifth geometric arithmetic index of Polycyclic Aromatic Hydrocarbons (PAH_k).

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 G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of redefined Zagreb indices for certain important chemical structures like nanotube and nanostar. As supplement, the redefined Zagreb indices of polyomino chain and benzenoid series are manifested.

We study the relative equilibria in the 4-vortex problem when two of vorticities are equal to 1, and the other two equal to m are enough small. We prove that for m > 0 there is a unique concave kite relative equilibria. We also prove that there is a unique convex planar relative equilibria having two pairs of equal vorticities located at the adjacent vertices of the configuration and it is an isosceles trapezoid.