Volume 4 (2019): Issue 1 (January 2019)

Dynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation".

In this work, we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations. We establish existence and uniqueness of solution in the case of non-Lipschitz coefficients.

The objectives in each construction process can be multiple. However, the constructions have to be carried out under some restrictions concerning price and terms. They constitute some strategic and interdependent goals. In other words, “time is money”. Several papers support that seasonal effects influence the execution rate of construction. Thus, most of them try to improve the forecasts by evaluating and joining them to the planning, although always measuring their influence indirectly. In this paper, we suggest a methodology to directly measure the influence of the seasonal factors as a whole over the earned value of construction. Additionally, we apply it to a certain case study regarding the subsidised housing of public promotion in the Castilla-La Mancha region (Spain). It is worth mentioning that our results are clarified: we have calculated the average monthly production for each month a year with respect to the annual monthly mean. Moreover, the differences regarding the average monthly production we have contributed are quite significant, and hence they have to be taken into account for each earned value forecast so that a project becomes reliable.

In this study, numerical solutions of the fractional Harry Dym equation are investigated. Linearization techniques are utilized for non-linear terms existing in the fractional Harry Dym equation. The error norms L₂ and L_∞ are computed. Stability of the finite difference method is studied with the aid of Von Neumann stabity analysis.

The use of complex dynamics tools in order to deepen the knowledge of qualitative behaviour of iterative methods for solving non-linear equations is a growing area of research in the last few years with fruitful results. Most of the studies dealt with the analysis of iterative schemes for solving non-linear equations with simple roots; however, the case involving multiple roots remains almost unexplored. The main objective of this paper was to discuss the dynamical analysis of the rational map associated with an existing class of iterative procedures for multiple roots. This study was performed for cases of double and triple multiplicities, giving as a conjecture that the wideness of the convergence regions of the multiple roots increases when the multiplicity is higher and also that this family of parametric methods includes some specially fast and stable elements with global convergence.

In this paper, We give a generalization the resut of Roger B. Nelsen, by giving a closed form expression for x =[a0,a1,⋯,ak,b1,⋯bm¯],$\left[ {{a}_{0}},{{a}_{1}},\cdots ,{{a}_{k}},\overline{{{b}_{1}},\cdots {{b}_{m}}} \right],$

The dimensionless groups that govern the Davis and Raymond non-linear consolidation model, and its extended versions resulting from eliminating several restrictive hypotheses, were deduced. By means of the governing equations nondimensionalization technique and introducing the characteristic time concept, both in terms of settlement and pressures, was obtained (for the most general model) that the average degree of settlement only depends on the dimensionless time while the average degree of pressure dissipation does it, additionally, on the loading ratio. These results allowed the construction of universal curves expressing the solutions of the unknowns of interest in a direct and simple way.

The control of insect pests in agriculture is essential for food security. Chemical controls typically damage the environment and harm beneficial insects such as pollinators, so it is advantageous to identify targetted biological controls. Since predators are often generalists, pathogens or parasitoids are more likely to serve the purpose. Here, we model a fungal pathogen of aphids as a potential means to control of these important pests in cereal crops. Typical plant herbivore pathogen models are set up on two trophic levels, with dynamic variables the plant biomass and the uninfected and infected herbivore populations. Our model is unusual in that (i) it has to be set up on three trophic levels to take account of fungal spores in the environment, but (ii) the aphid feeding mechanism leads to the plant biomass equation becoming uncoupled from the system. The dynamical variables are therefore the uninfected and infected aphid population and the environmental fungal concentration. We carry out an analysis of the dynamics of the system. Assuming that the aphid population can survive in the absence of disease, the fungus can only persist (and control is only possible) if (i) the host grows sufficiently strongly in the absence of infection, and (ii) the pathogen transmission parameters are sufficiently large. If it does persist the fungus does not drive the aphid population to extinction, but controls it below its disease-free steady state value, either at a new coexistence steady state or through oscillations. Whether this control is sufficient for agricultural purposes will depend on the detailed parameter values for the system.

Researching different solutions of nonlinear models has been interesting in different fields of science and application. In this study, we investigated different solutions of fourth-order nonlinear Ablowitz– Kaup–Newell–Segur wave equation. We have used the sine-Gordon expansion method (SGEM) during this research. We have given the 2D, 3D, and contour graphs acquired from the values of the solutions obtained using strong SGEM.

In this work, we deal with a backward stochastic differential equation driven by two mutually independent fractional Brownian motions (with Hurst parameter greater than 1/2). We establish the existence and uniqueness of the solution in the case of non-Lipschitz condition on the generator. The stochastic integral used throughout the paper is the divergence-type integral.

The present paper deals with the study of a D-homothetic deformation of an extended generalized ϕ-recurrent (LCS)_2n+1-manifolds their geometrical properties are discussed. Finally, we construct an example of an extended generalized ϕ-recurrent (LCS)₃-manifolds that are neither ϕ-recurrent nor generalized ϕ-recurrent under such deformation is constructed.

In this paper, a powerful sine-Gordon expansion method (SGEM) with aid of a computational program is used in constructing a new hyperbolic function solutions to one of the popular nonlinear evolution equations that arises in the field of mathematical physics, namely; longren-wave equation. We also give the 3D and 2D graphics of all the obtained solutions which are explaining new properties of model considered in this paper. Finally, we submit a comprehensive conclusion at the end of this paper.

This paper deals with a class of backward stochastic differential equation driven by two mutually independent fractional Brownian motions. We essentially establish existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.

In this paper, we introduce the concept of dual skew Heyting almost distributive lattices (dual skew HADLs) and characterise it in terms of dual HADL. We define an equivalence relation θ on a dual skew HADL L and prove that θ is a congruence relation on the equivalence class [x]θ so that each congruence class is a maximal rectangular subalgebra and the quotient [y]θ/θ is a maximal lattice image of [x]θ for any y ∈ [x]θ. Moreover, we show that if the set PI (L) of all the principal ideals of an ADL L with 0 is a dual skew Heyting algebra then L becomes a dual skew HADL. Further we present different conditions on which an ADL with 0 becomes a dual skew HADL.

In this paper, we define new graph operations F-composition F (G)[H], where F (G) be one of the symbols S(G),M(G),Q(G),T(G),Λ(G),Λ[G],D₂(G),D₂[G]. Further, we give some results for the Wiener indices of the these graph operations.

A numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

Topological indices helps us to collect information about algebraic graphs and gives us mathematical approach to understand the properties of chemical structures. In this paper, we aim to compute multiplicative degree-based topological indices of Silicon-Carbon Si₂C₃−III[p,q] and SiC₃−III[p,q] .

In software definition networks, we allow transmission paths to be selected based on real-time data traffic monitoring to avoid congested channels. Correspondingly, this motivates us to study the existence of fractional factors in different settings. In this paper, we present several extend sufficient conditions for a graph admits ID-Hamiltonian fractional (g, f )factor. These results improve the conclusions originally published in the study by Gong et al. [2].

We extend the Boltzmann’s ideas that describe the evolution to the equilibrium of many body systems to the multifractal decomposition of the unitary interval 𝕀, in terms of sets J_α conformed by points with the same pointwise dimension, and obtain the D(α) singularity spectrum.

Inhomogeneous density of states in a discrete model of Standard & Poor’s 500 phase space leads to inequitable predictability of market events. Most frequent events might be efficiently predicted in the long run as expected from Mean reversion theory. Stocks have different mobility in phase space. Highly mobile stocks are associated with less unsystematic risk. Less mobile stocks might be cast into disfavor almost indefinitely. Relations between information components in Standard & Poor’s 500 phase space resemble of those in unfair coin tossing.

Biological systems exhibit unique phenotypes as the result of the expression of a genomic program. The regulation of this program is a complex phenomenon, wherein different regulatory mechanisms are involved. The deregulation of this program is at the centre of the emergence of diseases such as breast cancer. In particular, it has been observed that coregulation patterns between physically distant genes are lost in breast cancer.

In this work, we present a systematic study of chromosome-wide gene coregulation patterns in breast cancer as inferred by information theoretical measures over large (whole-genome expression in several hundred transcriptomes) experimental data corpora. We analyzed the chromosomal distance decay of correlations and found it to be with fat-tail distribution in breast cancer while being fundamentally constant in nontumour samples.

After model discrimination analyses, we concluded that the behaviour of the breast cancer distributions belongs to an intermediate regime between power law and Weibull distributions, with distinctive contributions corresponding to different chromosomes. This behaviour may have biological implications in terms of the organization of the gene regulatory program, and the changes found in this program between health and disease.

The method of isospectral network reduction allows one the ability to reduce a network while preserving the network’s spectral structure. In this paper we describe a number of recent applications of the theory of isospectral reductions. This includes finding hidden structures, specifically latent symmetries, in networks, uncovering different network hierarchies, and simultaneously determining different network cores. We also specify how such reductions can be interpreted as dynamical systems and describe the type of dynamics such systems have. Additionally, we show how the recent theory of equitable decompositions can be paired with the method of isospectral reductions to decompose networks.

A steady flow of a power law fluid through an artery with a stenosis has been analyzed. The equation governing the flow is derived under the assumption of mild stenosis. An exact solution of the governing equation is obtained, which is then used to study the effects of various parameters of interest on axial velocity, resistance to flow and shear stress distribution. It is found that axial velocity increases while resistance to flow decreases when going from shear-thinning to shear-thickening fluid. Moreover, the magnitude of shear stress decreases by increasing the tapering parameter. This problem was already addressed by Nadeem et al. [14], but the results presented by them were erroneous due to a mistake in the derivation of the governing equation of the flow. This mistake is highlighted in the "Formulation of the Problem" section.

In this work is presented a pedagogical point of view of multifractal analysis deoxyribonucleic acid (DNA) sequences is presented. The DNA sequences are formed by 4 nucleotides (adenine, cytosine, guanine, and tymine). Following Jeffrey’s paper we associated a simple contractive function to each nucleotide, and constructed the Hutchinson’s operator W, which was used to build covers of different sizes of the unitary square Q, thus W^k(Q) is a cover of Q, conformed by 4^k squares Q_k of size 2^−k, as each Q_k corresponds to a unique subsequence of nucleotides with length k : b₁b₂...b_k. Besides, it is obtained the optimal cover C_k to the fractal F generated for each DNA sequence was obtained. We made a multifractal decomposition of C_k in terms of the sets J_α conformed by the Q_k’s with the same value of the Holder exponent α, and determined f (α), the Hausdorff dimension of J_α, using the curdling theorem.

We consider a heteroclinic network in the framework of winnerless competition, realized by generalized Lotka-Volterra equations. By an appropriate choice of predation rates we impose a structural hierarchy so that the network consists of a heteroclinic cycle of three heteroclinic cycles which connect saddles on the basic level. As we have demonstrated in previous work, the structural hierarchy can induce a hierarchy in time scales such that slow oscillations modulate fast oscillations of species concentrations. Here we derive a Poincaré map to determine analytically the number of revolutions of the trajectory within one heteroclinic cycle on the basic level, before it switches to the heteroclinic connection on the second level. This provides an understanding of which parameters control the separation of time scales and determine the decisions of the trajectory at branching points of this network.