Search

This paper chapter studies the dynamic modeling and nonlinear control problems in electrical network integration of wind farm system with Synchronous Generators. So, comprehensive models of various components of this system are presented. Then, the nonlinear control of the inverter and rectifiers are introduced. The Sliding Mode Controllers (SMC) are designed to maximize the extracted power from turbines, to maintain a stable voltage of DC-bus for the inverter and to regulate the powers injected into the network. The control equations have been giving. Theory of Lyapunov stability has been utilized to evince the regulators stability. The efficiency of the control techniques is validated with simulations in MATLAB/Simulink. The proposed method reveals better results than VC technique under different network power voltage conditions. [ABSTRACT FROM AUTHOR]

A method for choosing an appropriate initial condition to simulate stochastic differential equations stably is proposed. We apply Lyapunov stability and asymptotic stability theories to show how to choose initial conditions without causing blow up of numerical simulations, and carry out specific analysis through the stochastic nonlinear Kubo oscillator. [ABSTRACT FROM AUTHOR]

This paper deals with the effect of rotation on the onset of convection in magnetic nanofluids (MNF) with magnetic field dependent (MFD) viscosity using linear stability theory. As suggested by J. Buongiorno [1], Brownian motion and thermophoresis are important slip mechanisms in nanofluid. Since this work is based on MNF therefore, magnetophoresis is included as the third slip mechanism in addition to those mentioned above. Numerical method is employed along with MATLAB's EIG function to solve the resulting eigen value problem. Analysis is done graphically for ester-based MNF (EMNF) and water-based MNF (WMNF) through neutral stability curves (NSCs) and Critical stability curves (CSCs) for rigid-free boundary condition (Bcs) in gravity environment. The most significant parameter here is Taylor number (TA) which investigates the effect of rotation and the analysis shows that system gets stabilized with increase in the value of TA. [ABSTRACT FROM AUTHOR]

The aim of this paper is to describe an epidemic model when two SI-type of diseases are transmitted vertically as well as horizontally through one population. The population contains two subclasses: susceptible and infectious, while the infectious are divided into three subgroups: those infected by AIDS disease, HCV disease, and by both diseases. A nonlinear mathematical model for AIDS and HCV diseases is Suggested and analyzed. Both local and global stability for each feasible equilibrium point are determined theoretically by using the stability theory of differential equations, Routh-Hurwitz and Gershgorin theorem. Moreover, the numerical simulation was carried out on the model parameters in order to determine their impact on the disease dynamics, and the results are displayed graphically and discussed. [ABSTRACT FROM AUTHOR]

A hypersonic flow at M=16 over a double cone geometry was simulated using Direct Simulation Monte Carlo method. The simulation was done using a fully three dimensional setting and the results were compared with the corresponding axisymmetric simulations at the same conditions. It was observed that the well-defined closed separation bubble in the axisymmetric simulations does not exist for the three dimensional simulations. Breaking of axial symmetry in the separation bubble and shear and shock layers surrounding the separation bubble was shown with periodic structures appearing in these layers. Further analysis is being conducted for the origins of these instabilities using linear stability theory. [ABSTRACT FROM AUTHOR]

The application of the numerical analytical method of boundary elements for solving problems of flat bending stability of thin-walled rod systems under any arbitrary combination of transverse loads is presented. The basic cases when the bending moment is zero and when it is constant are considered. A solution is also constructed for the case when clean bending takes place only in some part of the rod. In the considered cases the rod is hinged at the ends, which does not influence in any way the generality of the solution because of peculiarities of NA BEM; the difference will be only in expressions of constants of integration and fundamental functions of this or that problem. Numerical realization of the developed algorithm is shown on the example of an I-beam cross-section rod. The value of the minimum critical moment calculated in the paper is exactly equal to its value determined by S. P. Timoshenko's formula It is pointed out that this approach allows us to obtain the solutions of the complex problems of the theory of stability of thin-walled rods when restrictions on boundary conditions are removed, different transverse loadings and any structure of rod systems including frames and uncut beams can be taken into account. With an arbitrary law of bending moment change, it is proposed to replace this arbitrary law by a stepwise dependence, i.e., a system with distributed parameters is replaced by a set of systems with constant parameters. [ABSTRACT FROM AUTHOR]

For systems with geometric constraints, the stability of steady motions is only possible in critical cases with the obligatory presence of zero roots in the number equal to the number of connections. Earlier, by rigorous methods of analytical mechanics and nonlinear stability theory, the asymptotic stability of such motions was established when the real parts of the remaining roots of the characteristic equation were negative. In this work, these abstract theoretical results are developed, and the main stages of their qualified application in engineering practice are given. In the presence of cyclic coordinates, additional zero roots of the characteristic equation appear. This circumstance significantly complicates the study of stability when using Lagrange variables. Here, we propose a transition to Routh variables with the introduction of pulses instead of velocities of cyclic coordinates. Such an approach makes it possible to apply both the Malkin theorem on stability under constantly acting perturbations and Kamenkov's theorem on stability in the special case of zero roots in an amount equal to the sum of the numbers of geometric constraints and cyclic coordinates. When applying Malkin's theorem (the initial perturbations of cyclic pulses are considered as constantly acting perturbations), only non-asymptotic stability is established. With a rigorous application of Kamenkov's theorem, in addition to the general conclusion about non-asymptotic stability, we obtain a strictly substantiated conclusion about the asymptotic stability with respect to positional velocities. Obviously, the property of the asymptotic stability of steady motions with respect to positional velocities can be essential in eapplications. [ABSTRACT FROM AUTHOR]

This article concerned with the combined Synchronization among the complex Chen, Lü and Lorenz systems. Combined Synchronization along with the nonlinear control function is used to guarantee the synchronization of the master and slave systems. Lyapunov stability theory is used to stabilize the proposed controllers. The chaotic behavior of complex dynamical systems in three-dimensional space is shown through the phase portraits. Finally numerical results are depicted through graphs to validate the effectiveness of the suggested method. [ABSTRACT FROM AUTHOR]

The article proposes to consider the choice of parameters of the mathematical model of the network for its optimization. The analysis of the network behavior is estimated using the Lyapunov stability theory. This can serve as a rough estimate of the state of the networked system. The simulation results presented the performance of the models is proved, their sensitivity to change in initial data. [ABSTRACT FROM AUTHOR]

The influence of foreign gas injection on the boundary layer stability of the Mach 6 nozzle of the Transit-M wind tunnel is investigated within the framework of the linear stability theory. The N-factors of the Görtler vortices and the first and second Mack modes are obtained. For a given nozzle, the most unstable disturbances are Görtler vortices. It is shown that the light gas injection leads to a significant slowdown in the growth of Görtler vortices, and the higher the mass flow rate, the stronger this effect. However, an increase in the mass flow rate of a light gas leads to an acceleration of the second mode growth in the boundary layer of M = 6 nozzle; the second mode can lead to a transition earlier than the Görtler vortices at some parameters of the injections. Heavy gas injection accelerates the growth of Görtler vortices and second mode disturbances. The growth of the first Mack mode is slower during the injection of both light and heavy gases. [ABSTRACT FROM AUTHOR]

There is a proposal to use models of sliding and spinning friction for the dynamics of a humanoid robot's walking. These models have exact expressions in analytical functions, and, in addition, have simplified Padé approximations for net friction force and net moment of friction forces. The use of these models in the theories of gait stability will provide new insights into the walking of humanoid robots. [ABSTRACT FROM AUTHOR]

This paper investigates about the method to control three species system of generalized Lotka-Volterra method. The system's stability is investigated by applying stability theory on Lyapunov function. The backstepping measure which is an iterative process is applied to control the system. In backstepping computations the Lyapunov exponents are not essential. Hence this backstepping technique is the most effective one. In order to validate the result numerical simulation is derived. [ABSTRACT FROM AUTHOR]

Multipliers of the number of phases are used in automation devices, electronic equipment, communications in cases where there is no possibility to use multiphase circuits or their use is associated with certain technical or economic difficulties. The most widely used devices of this type in the form of a multiplier of the number of phases, which are used in single-phase circuits for powering three-phase consumers. From the point of view of circuitry, the simplest are phase multipliers based on nonlinear LC circuits, which have high reliability and relatively small dimensions when powering devices of low and medium power. However, phase multipliers based on LC circuits can operate in resonant modes under certain conditions, hence, voltage or current surges may occur in them. The work of a parametric phase number multiplier operating at the fundamental frequency and used in single-phase circuits for powering three-phase consumers is considered from the point of view of the theory of stability of oscillatory processes. The stability of the phase number multiplier is studied according to the Hurwitz stability criterion. The characteristic circuit design and operating parameters of the phase multiplier based on LC circuits and their influence on its stable operation are analyzed. It is concluded that the change in the load of the phase number converter based on LC circuits from short circuit to no-load does not affect the stability mode. It is concluded that from the point of view of the theory of vibration stability, the proposed circuit is suitable for the development of real frequency multipliers of low and medium power. [ABSTRACT FROM AUTHOR]

The orbital stability of solitary waves to double dispersion equation with quadratic–cubic nonlinearity is investigated. The stability of solitary waves with velocity c, |c|<1, is analyzed by means of the Grillakis, Shatah and Strauss' stability theory. The orbital stability results are proved for the special set of parameters of the problem, which has not been considered so far. Explicit analytical formulas for the function, crucial for the orbital stability, and its second derivative are derived. The dependence of the stability of the solitary waves on parameters of the problem is theoretically studied. [ABSTRACT FROM AUTHOR]

This manuscript deals with an investigation of hybrid projective synchronization (HPS) scheme between chaotic identical chemical reactor systems via active control design (ACD) in a comprehensive manner. Using master- slave framework, ACD is proposed and studied systematically to control the microscopic chaos existing in the considered system. The criterion of asymptoticstability in state vectors of given system is derived using appropriate controllers and Lyapunov stability theory. In addition, MATLAB software is used to perform numerical simulations to illustrate the efficacy and supremacy of the discussed strategy. Remarkably, both the analytic and computational results are in exceptional agreement. [ABSTRACT FROM AUTHOR]

The unsteady problem of a shock wave / laminar boundary layer interaction development is considered for the case of sudden deflection the shock wave generator. The unsteady process of the separation zone growth and movement of the laminar-turbulent transition location was studied both numerically and experimentally. The position of the transition location was predicted in CFD by two approaches, namely by eN method based on linear stability theory (LST) [1], and by Menter model [2] κ-ω-γ-Reѳ in RANS simulation of the flow. [ABSTRACT FROM AUTHOR]

The effect of the local surface heating on the stability of the boundary layer of the contoured nozzle M6 has been studied numerically for the hypersonic wind tunnel Transit-M ITAM SB RAS. Boundary layer profiles on the nozzle surface are found by the numerical simulation. Disturbance stability in the boundary layer is calculated in the context of the linear stability theory. It is shown that the local heating results in the slow-down of Goertler vortices amplification and Mack first mode in respect to the basic case; the stronger the heating, the stronger the effect. The second mode stabilizes at the local surface heating up to the temperature approaching to the stagnation temperature and de-stabilizes at further temperature rise. The optimal temperature of the local surface heating has been determined for the contoured nozzle M6 to stabilize disturbances in the boundary layer. [ABSTRACT FROM AUTHOR]

The paper presents results of a theoretical study on the properties of a supersonic boundary layer and its linear stability under conditions of surface material sublimation. Calculations were performed for an adiabatic-wall boundary layer over a camphor coated flat-plate model at a free-stream Mach number of M=2. In the boundary layer, surface sublimation generates a binary mixture flow of air and foreign vapors. This flow is studied using boundary layer equations in approximation of local self-similarity. It is shown that increase of the flow stagnation temperature leads to the wall material sublimation. Increasing evaporation causes significant wall cooling and an increase in the near-wall density of the binary mixture. Such modification of the boundary layer profiles leads to a decrease of the amplification rates of the first mode perturbations, which were computed by means of the linear stability theory. It is concluded that application of a camphor coating facilitates the supersonic adiabatic-wall boundary-layer stabilization with increasing flow stagnation temperature. [ABSTRACT FROM AUTHOR]

Numerical and theoretical stability studies are conducted for a supersonic M = 2.0 flow over a flat plate with a spanwise strip of distributed suction. Propagation of artificially excited 3D wave trains relevant to the first-mode instability are considered. Direct numerical simulations (DNS) as well as assessments based on the linear stability theory (LST) are performed using the in-house code "HSFlow++" (High Speed Flow solver). It is shown that, despite strong spatial nonuniformities of the mean flow near the suction strip ends, the e-N method based on the local-parallel LST gives reasonable estimates of the laminar flow control performance of the suction strip. [ABSTRACT FROM AUTHOR]

The evolution of artificial disturbances in a laminar boundary layer on a flat plate model in the presence of an incident shock wave is considered. The flow is supersonic with the freestream Mach number M = 1.43. The results obtained in the two-dimensional computation are compared with the results obtained using the linear stability theory. The simulation is carried out in order to determine the possibility of using an electric discharge in the experiment as a source of first-mode disturbances. The discharge is simulated as a heat source. The results show a good agreement of two-dimensional computation with linear stability theory. It was demonstrated that discharge may be used as the source of first-mode disturbances. [ABSTRACT FROM AUTHOR]

Catastrophe theory generally discusses systems that regularly behave by analyzing the critical points and explaining the radical jumps that occur as they pass through these critical points continuously from stable to unstable state. This study aims to analyze the critical points in the field of landslides and the application of catastrophe theory related to the stability of slopes in the landslide case. The factor of safety (FS) values are used to determine the critical points. The results showed that the critical points occurred at the FS value of 1.61 to 0.92. Based on these FS values, it can be seen the change from a stable to an unstable state that indicates the catastrophic phenomenon. [ABSTRACT FROM AUTHOR]

The exponential stability plays a central role in the theory of asymptotic behaviors for evolution equations. The aim of this paper is to define, to illustrate by examples and to characterize several general concepts of stability for skew-evolution semiflows on Banach spaces [ABSTRACT FROM AUTHOR]

The development of two-dimensional subsonic disturbances in a supersonic boundary layer of a vibrationally excited gas on a flat plate was studied on the basis of the linear stability theory. A system of two-temperature gas dynamics including the Landau–Teller relaxation equation used as initial model. The unperturbed flow was described by a selfsimilar boundary layer solution for a perfect gas. In the linearized system of equations the temperature disturbances of the transport coefficients were taken into account. The neutral stability curves for the first and second most unstable modes are calculated. It is shown that for both modes the critical Reynolds numbers at maximum excitation exceed by approximately thirteen percentages the corresponding values for a perfect gas. For independently verification of the direct numerical solution neutral stability curves are also calculated on the basis of the asymptotic approach. It is shown that the thus-calculated neutral stability curves agree well with the results of the numerical solution of the original spectral problem. [ABSTRACT FROM AUTHOR]

Numerical calculations of the flow in a plane supersonic boundary layer of vibrationally excited gas in locally self-similar and original formulations were carried out. Some characteristic conditions of the external flow and heat transfer at the boundary were considered. It is shown that in all the cases of locally self-similar solutions the profiles of hydrodynamic variables converge to some limit values for the longitudinal coordinate x ≥ 8 — 15. For all regimes, the maximum local deviation of these limits from profiles calculated in the full formulation does not exceed 5 %. This justifies the use of easily calculated locally self-similar solutions in corresponded problems of the linear stability theory. [ABSTRACT FROM AUTHOR]

The modified hybrid projective synchronization between two fractional order complex chaotic systems with time delays is exposed in detail in this article. The error between the deportment of the system is identified and the controller is then modeled to synchronize the systems via the stability theory of two fractional order complex chaotic structures. Finally numerical solution is investigated and verified to support it. The corresponding numerical results prove the effectiveness and robustness of the controller. [ABSTRACT FROM AUTHOR]

In this manuscript, a systematic procedure for investigating hybrid projective synchronization (HPS) scheme in two identical hyperchaotic systems has been designed. Based on Lyapunov stability theory (LST), an active control technique (ACT) has been presented to achieve the desired HPS scheme. The considered HPS scheme is a significant scheme for synchronization as it includes anti-synchronization, complete synchronization, projective synchronization and hybrid synchronization as its particular cases. Moreover, computer simulations are implemented to validate the efficacy and feasibility of the considered approach by using MATLAB. Remarkably, the analytic and computational results are in complete agreement. Also, the considered HPS scheme is very efficient as it has numerous applications in image encryption and secure communication. [ABSTRACT FROM AUTHOR]

Direct Numerical Simulation (DNS) is used to investigate linear and nonlinear stages of development of unstable disturbances and the transition to turbulence in a supersonic boundary layer on a flat plate with the Mach number of the external flow M = 6. The computations are carried out for the case of a cooled surface at a ratio of the plate temperature to the free-stream temperature Tw/T∞ = 1.4. According to linear stability theory calculations, the two-dimensional waves of the first mode in the boundary layer are completely stabilized at the considered flow parameters. The growth rates are maximum for unstable twodimensional disturbances of the second mode, while the three-dimensional waves of the second mode are also unstable. The results of DNS of linear and nonlinear stages of development of such disturbances are compared with the results of earlier computations of the laminar-turbulent transition on a flat plate with a temperature corresponding to the case of a thermally insulated surface, Tw/T∞ = 7. [ABSTRACT FROM AUTHOR]

An asymptotic theory of the neutral stability curve for a supersonic boundary layer of a vibrationally excited molecular gas on a plate is developed. The initial mathematical model of flow consists of equations of two-temperature viscous heat-conducting gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the “inviscid” and “viscous” parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. [ABSTRACT FROM AUTHOR]

This paper deals with stability analysis of diffusive three species predator-prey model (Lotka-volterra model) with interval biological parameter harvesting. The boundedness and equilibrium points of the prey predator model has been found and discussed about stability analysis of predator-prey model involving intra-specific coefficient with randomness exist. Mean square stability of the model is achieved by the construction of Lyapunov stability theory. Finally comparing prey predator model and model with randomness are analyzed by the numerical simulation. [ABSTRACT FROM AUTHOR]

We are studying a nonlinear nonlocal Dirichlet parabolic problem associated with the following p(x)-laplacian equation ∂u/∂t - a(∫Ω |∇u|p(x)/p(x)) Δ p(x)u = f(x,t). We apply Galerkin’s approximation technique, some uniform estimates and a compactness arguments to prove the existence result. Then we investigate the uniqueness of solutions, finally we give an answer to the asymptotic behavior question. [ABSTRACT FROM AUTHOR]

The presented paper deals with the problems of stability of motion of dynamical systems when integrally small perturbations forces affect the system in the finite time interval. It is assumed that the perturbation force is selected from a rather broad class of functions, of a class of generalized functions (they may be impulse functions). The need for such studies is dictated by the practice, when you have to take into account the continuous perturbation or impulse effects that can qualitatively change the behavior of the object. Feature of research is that we are not going to follow the "letter" of the classical notion of stability but propose a modification of the concept, tailored applications. So, we admit the possibility of strong perturbations of the object at a finite time interval. If after a specified period of time perturbations in the motion of the object will be small and will remain little longer, then these movement is called stable under small perturbations of the integral. Obviously, such notion of stability is different from the Lyapunov stability, since it permits "fluctuation" instability at a certain interval. However, this instability is not fatal to the nature of the object, since replaced by the steady state of motion. [ABSTRACT FROM AUTHOR]

We offer a new logical method for a parametric synthesizing linear static regulator in binary dynamic systems. To describe the dynamics in the general case of a nonlinear object and linear regulator state equations are used. The required dynamics property (in our case the property of stability) specification of a closed system is given in the formal logic language. In this formulation, the synthesis problem is reduced to the qualitative analysis problem - the verification of the truth of the quantified Boolean formula with the simultaneous search for the feedback matrix. The proposed method allows the natural parallelization based on data and high scalability with increasing the problem dimension in case of it is implemented in a high-performance computing environment. We develop a service-oriented solver, including the tools intended to automatically create a Boolean model of the original problem and solve the synthesis problem of a linear regulator using this model. [ABSTRACT FROM AUTHOR]

This work is devoted to analyse different kinds of stabilities for higher order integro-differential equations within appropriate metric spaces. We will consider the σ-semi-Hyers-Ulam stability which is a new kind of stability somehow between the Hyers-Ulam and the Hyers-Ulam-Rassias stabilities. Sufficient conditions are obtained in view to guarantee Hyers-Ulam, σ-semi-Hyers-Ulam and Hyers-Ulam-Rassias stabilities for such a class of integro-differential equations. We will be considering finite and infinite intervals as integration domains. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. [ABSTRACT FROM AUTHOR]

We study the stability of limit cycles that appear due to a constant delay introduced in the control of an unmanned vehicle. Stability switches of the equilibrium point shows the existence of a Hopf bifurcation. For the delay differential equations with constant delay, we establish the formulae required to calculate the Lyapunov coeffcient and determine an approximation of the solution. Numerical simulations are used to illustrate the results. [ABSTRACT FROM AUTHOR]

We deduce the formula of the asymptotics of the spectrum of the linear problem on the stability of stationary flow of an incompressible polymeric fluid with volume charge. [ABSTRACT FROM AUTHOR]

The paper is based on results obtained within an international project 'RECEPT' of the European Framework Program FP7. The experiments were carried out in a three-dimensional boundary layer developing on an experimental model of a long-laminar-run swept airfoil (sweep angle of 35°). The model was mounted in a test section of the lowturbulence wind-tunnel MTL (KTH, Stockholm) at an angle of attack of -5° and equipped with sidewalls provided satisfaction of infinite-span conditions. The cross-flow (CF) instability modes were predominant in this case, while the Tollmien-Schlichting (TS) waves were suppressed by a favorable pressure gradient. The main measurements were carried out by means of hot-wire anemometry at conditions of excitation of fully controlled, unsteady surface and flow perturbations. These perturbations were excited by special sources: (1) a row of oscillating membranes and (2) a vibrating wire, at frequencies of fs and fv, respectively. A very good, quantitative agreement between the measured and calculated (by linear stability theory based on PSE approach) amplification curves was found at surface frequency fs. However, the evolution of the CF-modes excited at difference combination frequency fsv- = fs - fv turned out to be very much different from the theoretical one. Thorough analysis of the obtained results has shown that the only explanation of these discrepancies can be associated with presence of a distributed receptivity mechanism due to scattering of freestream vortices on the CF-instability waves excited by surface vibrations. Another unusual and unexpected phenomenon found in the present experiments is associated with anomalous amplification of difference combination modes with the zero spanwise wavenumbers β′. This phenomenon was observed in the flow, which is stable with respect to both CF- and TS-waves having β′ = 0 for all frequencies. There is no explanation of this finding at present. [ABSTRACT FROM AUTHOR]

This scientific paper shows complex numbers, wave and particle nature of light, electromagnetic spectrum: range from radio waves to gamma rays. It includes complete and detailed understanding of how energy converted from kinetic to potential, potential to kinetic and electric field to magnetic field, magnetic field to the electric field, also cocludes that net energy is constant (law of conservation of energy). It also pays attention to system stability and how energy is converted into another form of energy to create new stability. sin2wt +cos2 wt =1 is everything. [ABSTRACT FROM AUTHOR]

We identify sufficient conditions for the stability of some well-known finite difference schemes for the solution of the multivariable reaction-diffusion equations that model chemical reaction networks. Since the equations are mainly nonlinear, these conditions are obtained through local linearization. A recurrent condition is that the Jacobian matrix of the reaction part evaluated at some positive unknown solution is either D-semi-stable or semi-stable. We demonstrate that for a single reversible chemical reaction whose kinetics are monotone, the Jacobian matrix is D-semi-stable and therefore such schemes are guaranteed to work well. [ABSTRACT FROM AUTHOR]

The paper studies the stability of linear systems of difference equations with single delay x(k+1)=A(k)+∑s=1lBs(k)x(k-ms(k)), k=0,1, ... where l ≥ 1, A is a constant n × n matrix, Bs(k) are n × n matrices, ms(k) ∈ N ∪ {0} and ms ≤ m for an m ∈ N. Sufficient conditions for the stability are derived using the method of Lyapunov functions. [ABSTRACT FROM AUTHOR]

This paper is devoted to a numerical approach of the biomechanics behavior modeling of a dental implant supported prothesis made up of three elements, and the surrounding bone under the masticatory forces loading. A clinical situation involving both biological (the bone tissue) and non-biological (the three elements of implant prosthesis) materials is simulated. This problem involves fine technical structure details - the threads, tapers, etc with a great impact in masticatory force transmission. Modeling the contact between the implant and the bone tissue is important to a proper bone-implant interface model and implant design. A three-dimensional numerical model is proposed in order to calculate the state of stress and displacement of this complex structure in order to evaluate its stability by determining the risk zones of stress concentration. The results of numerical modeling are in good agreement with other numerical results and clinical cases A comparison between this numerical analysis and clinical cases is performed and a good agreement is obtained. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to approximate some matrix functions by using a family of high-order Newton-type iterative methods. We analyse the semilocal convergence and the speed of convergence of these methods. Concerning stability, it is well known that even the simplified Newton method can be unstable. Despite it, we present stable versions of our family of algorithms for several matrix functions. We test numerically the methods: we check the numerical robustness and stability by considering matrices that are close to be singular and badly conditioned. We find algorithms of the family with better numerical behavior than the Newton and the Halley methods. These two algorithms are basically the iterative methods proposed in the literature to solve many of this type of problems. [ABSTRACT FROM AUTHOR]

A family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is constructed by using weight function procedure. From its error equation, different iterative schemes with memory can be designed increasing the order of convergence up to six. The stability of the families, with and without memory, is studied in terms of the values of the parameters, in order to select the elements of the families with good properties of stability and avoid those that present chaotic behavior in the iterative process. [ABSTRACT FROM AUTHOR]

In this paper, we shall construct a new numerical scheme for fourth-order fractional diffusion wave model. The solvability, stability and convergence of proposed method are established in l2 norm and it is shown that the numerical scheme improves the earlier work done. Simulation is carried out to verity the accuracy and efficiency of the numerical scheme. [ABSTRACT FROM AUTHOR]

The IBR-2M pulse reactor is characterized by a high level of reactivity fluctuations and consequently by a high level of fluctuations in the regulated parameter as well as in the amplitude of the power pulses. Fluctuations of the regulated parameter relative to the average level in the standard stabilization regime usually fall within the range of 20% with certain peaks up to 40%, which is close to the limits of the emergency protection operation (50%). Under these conditions the automatic regulator may receive contradictory requirements. In this paper, the results of stability analysis of the IBR-2M reactor in the automatic regulating regime at various levels of average power are presented. It is shown that stability margins of the amplitude and the phase are enough, especially for the IBR-2M reactor operation with automatic regulator. [ABSTRACT FROM AUTHOR]

This paper reports the results of an ongoing research to develop and validate scales for two psychological constructs: "preference diversity" and "openness to novelty", that we believe to be important factors in users' responses to movie recommendations. Question items were created based on literature review and the results of a focus group interview. A questionnaire interview that consists of the candidate question items were performed so the validation and purification of the scales can be performed (N=191). Through exploratory factor analysis, five items were eventually selected for each construct. A user study (N=293) were subsequently followed which collected both users' responses to the scales and their actual movie viewing history of a sample of 220 movies. The scales were shown to possess both stability and internal consistency. Results showed that the participants' preference diversity score were correlated with the diversity of the movies seen, as measured by the number of movies, the number of movie genres, and the average dissimilarity of the movies seen. Furthermore, those who have higher openness to novelty also tended to watch and appreciate more obscure films. [ABSTRACT FROM AUTHOR]

In the present manuscript, we briefly discuss the differences between ordinary Q-balls and U(1) gauged Q-balls. We focus on the differences in the existence of Q-ball solutions for appropriate values of the model parameters, as well as on the differences in classical stability of such Q-balls. [ABSTRACT FROM AUTHOR]

In this paper, we study an eco-epidemiology model which is derived from S I epidemic model with bilinear incidence rate and modified Leslie Gower predator-prey model with harvesting on susceptible prey. Existence condition and stability of all equilibrium points are discussed for the proposed model. Furthermore, we show that the model exhibits a Hopf bifurcation around interior equilibrium point which is driven by the rate of infection. Our numerical simulations using some different value of parameters confirm our analytical analysis. [ABSTRACT FROM AUTHOR]

In this paper we discuss a fractional order predator-prey model with ratio-dependent functional response. The dynamical properties of this model is analyzed. Here we determine all equilibrium points of this model including their existence conditions and their stability properties. It is found that the model has two type of equilibria, namely the predator-free point and the co-existence point. If there is no co-existence equilibrium, i.e. when the coefficient of conversion from the functional response into the growth rate of predator is less than the death rate of predator, then the predator-free point is asymptotically stable. On the other hand, if the co-existence point exists then this equilibrium is conditionally stable. We also construct a nonstandard Grnwald-Letnikov (NSGL) numerical scheme for the propose model. This scheme is a combination of the Grnwald-Letnikov approximation and the nonstandard finite difference scheme. This scheme is implemented in MATLAB and used to perform some simulations. It is shown that our numerical solutions are consistent with the dynamical properties of our fractional predator-prey model. [ABSTRACT FROM AUTHOR]

The aim of the present work is using some new matrix measure results to establish explicit conditions for global asymptotic stability of the zero solution of incommensurate neutral linear fractional differential system with distributed delays. The derivatives in the system can be in Riemann-Liouville or Caputo type. The proposed conditions allow the studying for global asymptotic stability of the zero solution of the considered neutral system to be replaced with studying of the same problem for the corresponding (auxiliary) retarded linear fractional systems, which is a significantly simpler task. [ABSTRACT FROM AUTHOR]

To investigate global asymptotic stability in general of an equilibrium position of an autonomous system of ordinary differential equations, considered by V.A. Pliss, a function different from the Lyapunov functions is applied. V.A. Pliss proved that for this system it is impossible to construct the Lyapunov function as a sum of a quadratic form and an integral of some nonlinear function defined by the right-hand side of the system. [ABSTRACT FROM AUTHOR]