Synchronization of time-varying time delayed neutral-type neural networks for finite-time in complex field

This paper deals with the problem of finite-time projective synchronization for a class of neutral-type complex-valued neural networks (CVNNs) with time-varying delays. A simple state feedback control protocol is developed such that slave CVNNs can be projective synchronized with the master system in finite time. By employing inequalities technique and designing new Lyapunov--Krasovskii functionals, various novel and easily verifiable conditions are obtained to ensure the finite-time projective synchronization. It is found that the settling time can be explicitly calculated for the neutral-type CVNNs. Finally, two numerical simulation results are demonstrated to validate the theoretical results of this paper.

The extended nonsymmetric block Lanczos methods for solving large-scale differential Lyapunov equations

In this paper, we present a new approach for solving large-scale differential Lyapunov equations. The proposed approach is based on projection of the initial problem onto an extended block Krylov subspace by using extended nonsymmetric block Lanczos algorithm then, we get a low-dimensional differential Lyapunov matrix equation. The latter differential matrix equation is solved by the Backward Differentiation Formula method (BDF) or Rosenbrock method (ROS), the obtained solution allows to build a low-rank approximate solution of the original problem. Moreover, we also give some theoretical results. The numerical results demonstrate the performance of our approach.

Asymptotic stepwise solutions of the Korteweg--de Vries equation with a singular perturbation and their accuracy

The paper deals with the Korteweg-de Vries equation with variable coefficients and a small parameter at the highest derivative. The asymptotic step-like solution to the equation is obtained by the non-linear WKB technique. An algorithm of constructing the higher terms of the asymptotic step-like solutions is presented. The theorem on the accuracy of the higher asymptotic approximations is proven. The proposed technique is demonstrated by example of the equation with given variable coefficients. The main term and the first asymptotic approximation of the given example are found, their analysis is done and statement of the approximate solutions accuracy is presented.

On approach to determine the internal potential and gravitational energy of ellipsoid

Formulas are derived for the calculation of the potential of bodies, which surface is a sphere or an ellipsoid, and the distribution function has a special form: a piecewise continuous one-dimensional function and a three-dimensional mass distribution. For each of these cases, formulas to calculate both external and internal potentials are derived. With their help, further the expressions are given for calculation of the potential (gravitational) energy of the masses of such bodies and their corresponding distributions. For spherical bodies, the exact and approximate relations for determining the energy are provided, which makes it possible to compare the iterative process and the possibility of its application to an ellipsoid. The described technique has been tested by a specific numerical example.

Mathematical modeling bringing the operation of air split conditioners heat pumps to the same internal temperature conditions

Nowadays, the use of heat pumps (HP) of air split-conditioners in air conditioning and heating systems of small industrial, public and residential facilities is becoming more common. It is known that the nominal heat capacity of HP of air split-conditioners is given in catalogs or reference literature under standard outdoor temperature conditions, namely: outdoor air temperature +7oС, indoor air temperature +21oС. At the same time, manufacturers of air split-conditioners do not ensure that, regardless of the size of heating capacity, all air split-conditioners have the same internal temperature conditions, namely: the evaporation temperature of the refrigerant and its condensation temperature. In this case, the thermodynamic efficiency, which can be best assessed by the exergetic output-input ratio (OIR) of different heating capacity of HP of air split-conditioners, is different; this, in our opinion, is incorrect. However, today there is a lack of mathematical models of bringing the operation of air split-conditioners HP to the similar internal temperature conditions, which will allow us to obtain the same exergetic OIR for different heating capacity of HP. To create the mathematical model of bringing the operation of HP of air split-conditioners to the equal internal temperature conditions, we have proposed them, namely: the evaporation temperature of the refrigerant +0.7oC and its condensation temperature +40oC. Taking these temperatures on the basis of the heat balances of the HP evaporator and HP condenser of air split-conditioners, we obtained the dependences for calculating air flow rates on the evaporator and condenser, which respectively maintain the proposed temperatures.

Statistical theory of catalytic hydrogen oxidation processes. Basic equations

A statistical description for the processes of catalytic hydrogen oxidation is proposed taking into account the reaction--diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface. The basic non-Markov transfer equations are obtained for the abbreviated description parameters of reaction-diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface in the method of nonequilibrium statistical Zubarev operator. Weakly nonequilibrium reaction-diffusion processes are also considered.

Use of Data Mining in the prediction of risk factors of Type 2 diabetes mellitus in Gulf countries

Prevalence of diabetes in Gulf countries is knowing a significant increase because of various risk factors, such as: obesity, unhealthy diet, physical inactivity and smoking. The aim of our proposed study is to use Data Mining and Data Analysis tools in order to determine different risk factors of the development of Type~2 diabetes mellitus (T2DM) in Gulf countries, from Gulf COAST dataset.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

TSDT theory for free vibration of functionally graded plates with various material properties

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

Numerical exploration of mixed convection heat transfer features within a copper-water nanofluidic medium occupied a square geometrical cavity

The phenomenon of mixed convection heat transfer in a homogeneous mixture is deliberated thoroughly in this study for cooper-water nanofluids flowing inside a lid-driven square cavity. By adopting the Oberbeck-Boussinesq approximation and using the single-phase nanofluid model, the governing partial differential equations modeling the present flow are stated mathematically based on the Navier--Stokes and thermal balance formulations, where the important features of the scrutinized medium are presumed to remain constant at the cold temperature. Note here that the density quantity in the buoyancy body force is a linear temperature-dependent function. The characteristic quantities are computed realistically via the commonly used phenomenological laws and the more accurate experimental correlations. A feasible non-dimensionalization procedure has been employed to derive the dimensionless conservation equations. The resulting nonlinear differential equations are solved numerically for realistic boundary conditions by employing the fourth-order compact finite-difference method (FOCFDM). After performing extensive validations with the previously published findings, the dynamical and thermal features of the studied convective nanofluid flow are revealed to be in good agreement for sundry values of the involved physical parameters. Besides, the present numerical outcomes are discussed graphically and tabularly with the help of streamlines, isotherms, velocity fields, temperature distributions, and local heat transfer rate profiles.