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Effects of the road, such as speed bumps, can significantly affect a car's stability. This study focuses on how a quarter-car model is affected by a basic harmonic speed hump and how Cubic Negative Velocity Control (CNVC) is used to control the amplitude of disturbances. This study differs from earlier research in considering various control and force kinds that impact the system. The external forces in this context are a component of a non-linear dynamic system. Two-degree-of-freedom (2DOF) differential coupled equations describe the system's equation. Numerous numerical experiments have been conducted, including proportional derivative (PD), negative derivative feedback (NDF), positive position feedback (PPF), linear negative velocity control (LNVC), and CNVC; the results show that when the hump is represented as a simple harmonic hump, CNVC has the best effect and can regulate vibrations more precisely than the other approaches on this system. Subsequently, the vibration value of the system was numerically analyzed both before and after the control was implemented. Using the frequency response equation and phase plane approaches in conjunction with the Runge–Kutta fourth order method (RK-4) in the context of resonance situation analysis, the stability of the numerical solution has been evaluated. [ABSTRACT FROM AUTHOR]

Abstract The global focus has recently shifted away from fuel-based power sources, and one of the most important projects for energy production is wind energy. To maintain low costs, the current research examines the problem of vibrations affecting wind turbine towers’ performance (WTTs). In particular, the tower, resulting from excessive vibrations, can negatively affect a structure’s power output and service life, as it can cause fatigue. Therefore, we conducted numerical tests on various types of controlled systems. Our tests revealed that combining a new technique cubic negative velocity control (CNVC) and linear negative acceleration control (LNAC) was the most effective and cost-efficient option for vibration damping. This solution was derived by using an approximation method for the averaging technique. The external force is an important component of a nonlinear dynamic system and can be characterized by two-degree-of-freedom (2-DOF) differential coupled equations. After implementing the control measures, we conducted a numerical analysis of the vibration values before and after the operation. Stability is studied numerically. The numerical and approximate solutions were confirmed through the frequency response equation and time history with fourth-order Runge–Kutta (RK-4). Finally, we investigated the effect of parameters and compared our results with those of previously published studies.

Applying an averaging technique for the adapted Prüfer angle, we obtain an oscillation criterion for linear second order differential equations whose coefficients consist of products of powers of natural logarithm and general (bounded or unbounded) continuous functions. The presented criterion is illustrated by new corollaries and examples. The novelty is caused by the used averaging technique over unbounded intervals. [ABSTRACT FROM AUTHOR]

Time synchronization is essential in multicarrier systems such as filtered orthogonal frequency division multiplexing (F-OFDM) because it determines the whole system’s performance. Differ with OFDM, where subcarrier allocation is not flexible. In F-OFDM, the subcarrier allocation is more flexible, and the whole subcarrier in one symbol can be grouped into several subbands. The use of subcarriers that are limited to only one subband can reduce the performance of time synchronization based on autocorrelation (AC) methods. In this study, we first compare the performance of the AC-based time synchronization algorithms used in F-OFDM when training symbols are limited to one subband. Secondly, we made improvements to the AC-based time synchronization with the averaging technique of its timing metric, thus increasing the accuracy of time estimates in the F-OFDM system. The averaging technique of the timing metric improved the performance of the AC method in cases where the training symbol is limited to one subband, as shown in the simulation results. [ABSTRACT FROM AUTHOR]

We consider an exoplanetary system consisting of a star and two planets. The masses of the planets are significantly less than the mass of the star. The evolution of the orbital motion of exoplanets is studied within the framework of a double averaged unrestricted three-body problem. The main attention is paid to coplanar configurations, when the star and planets move in a certain plane that preserves a constant position. The possibility of reversing the orbital motion of the inner planet is noted. [ABSTRACT FROM AUTHOR]

In this article, we analyze the oscillation behavior of half-linear differential equation ... Applying the modified half-linear Prüfer angle and a general averaging technique over unbounded intervals, we prove an oscillation criterion for the studied equation. We point out that the presented oscillation criterion is new even in the linear case when p = 2. [ABSTRACT FROM AUTHOR]

Modeling of fractionally damped nanostructure is extremely important because of its inherent ability to capture the memory and hereditary effect of several viscoelastic materials extensively used in nanotechnology. The nonlinear free vibration characteristics of a simply-supported nanobeam with fractional-order derivative damping via nonlocal continuum theory are studied in this article. Using Newton's second law, the equation of motion for the nanobeam embedded in a viscoelastic matrix is derived. The Galerkin method is employed to transform the integro-partial differential equation of motion into a Duffing-type nonlinear ordinary differential equation. The fractional-order damping term is replaced by a combination of linear damping and linear stiffness term. The approximate analytical solution obtained via method of averaging is found to be in good agreement with solution obtained through numerical scheme. Detailed study of system parameters reveals that the fractional-order derivative damping has significant influence on the time response and effective natural frequency of the nanobeam. [ABSTRACT FROM AUTHOR]

Abstract Using a general averaging technique for the generalized adapted Prüfer angle, we prove an oscillation criterion concerning half-linear second order differential equations in the form (∗) t α − 1 r (t) Φ x ′ ′ + t α − 1 − p s (t) Φ (x) = 0 , Φ (x) = | x | p − 1 sgn x , where p > 1 , α ∈ R ∖︀ { p } , and r > 0 , s are continuous functions. We find simple conditions on r , s which imply that Eq. (∗) is oscillatory. The obtained result is new even in the linear case p = 2 for all considered α. [ABSTRACT FROM AUTHOR]

In this study, the authors aim to colourise a greyscale image using a fully automated framework which retrieves similar images from a reference database and then transfers the colour from the most similar retrieved images to perform colourisation. Inspired by the recent success of deep learning techniques in extracting semantic information from images, they first use fc7 features from AlexNet to retrieve similar images from the reference database. Top‐k retrieved images are considered for colour transfer to the target greyscale image, using various pixel level features. The images which result from the previous step are given a colour enhancement with Reinhard stain normalisation. They follow a pixel‐wise colour saturation based averaging technique to impart colour at pixel level. The final image is rectified using joint bilateral filtering. The resulting coloured images have a realistic appearance, similar in quality to the original coloured images. The proposed method outperforms several previous colourisation techniques, yielding superior performance both quantitatively and qualitatively. The method also enhances low‐contrast images. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the active vibration suppression of a fractional two-degree-of-freedom viscoelastic airfoil (TDOFVA) model with a harmonic external force by means of the sliding mode control (SMC) scheme. The viscoelastic behavior is described as a fractional-order derivative, leading to a new fractional TDOFVA model. Subsequently, an averaging technique is extended to derive the amplitude-frequency relations, and its correctness is verified by Monte Carlo simulations. In addition, effects of the system parameters on the dynamics are explored. To achieve a vibration suppression, we convert the TDOFVA system into a series of fractional-order differential equations. Then, a SMC strategy is employed, in which a fractional-order integral sliding surface is presented and asymptotical stability analysis of the SMC is performed. Several numerical results are presented to illustrate the performances of the proposed SMC scheme, which indicate that the given SMC methodology is effective to realize a vibration suppression of the TDOFVA model. [ABSTRACT FROM AUTHOR]

Averaging of accumulated data is a standard technique applied to processing data with low signal-to-noise ratios (SNR), such as image signals captured in ultra-high-speed imaging. The authors propose an architecture layout of an ultra-high-speed image sensor capable of on-chip signal accumulation. The very high frame rate is enabled by employing an image sensor structure with a multi-folded CCD in each pixel, which serves as an in situ image signal storage. The signal accumulation function is achieved by direct connection of the first and the last storage elements of the in situ storage CCD. It has been thought that the multi-folding is achievable only by driving electrodes with complicated and impractical layouts. Simple configurations of the driving electrodes to overcome the difficulty are presented for two-phase and four-phase transfer CCD systems. The in situ storage image sensor with the signal accumulation function is named Image Signal Accumulation Sensor (ISAS).

Denmark constitutes a low-enthalpy geothermal area, and currently geothermal production takes places from two sandstone-rich formations: the Bunter Sandstone and the Gassum formations. These formations form major geothermal reservoirs in the Danish area, but exploration is associated with high geological uncertainty and information about reservoir permeability is difficult to obtain. Prediction of porosity and permeability prior to drilling is therefore essential in order to reduce risks. Geologically these two formations represent excellent examples of sandstone diversity, since they were deposited in a variety of environments during arid and humid climatic conditions. The study is based on geological and petrophysical data acquired in deep wells onshore Denmark, including conventional core analysis data and well-logs. A method for assessing and predicting the average porosity and permeability of geothermal prospects within the Danish area is presented. Firstly, a porosity-depth trend is established in order to predict porosity. Subsequently, in order to predict permeability, a porosity-permeability relation is established and then refined in steps. Both one basin-wide and one local permeability model are generated. Two porosity-depth models are established. It is shown that the average permeability of a geothermal prospect can be modelled (predicted) using a local permeability model, i.e. a model valid for a geological province including the prospect. The local permeability model is related to a general permeability model through a constant, and the general model thus acts as a template. The applied averaging technique reduces the scatter that is normally seen in a porosity-permeability plot including all raw core analysis measurements and thus narrows the uncertainty band attached to the average permeability estimate for a reservoir layer. A 'best practice' technique for predicting average porosity and permeability of geothermal prospects on the basis of core analysis data and well-logs is suggested. The porosity is primarily related to depth, whereas the permeability also depends on porosity, mineralogy and grain size, which are controlled by the depositional environment. Our results indicate that porosity and permeability assessments should be based on averaged data and not raw conventional core analysis data. The uncertainty range of permeability values is significantly lower, when average values are used. [ABSTRACT FROM AUTHOR]

Active magnetic attitude control system providing given inertial attitude is considered. Control algorithm is constructed on the basis of a planar motion model. It decreases attitude discrepancy. Alternative approach is based on the PD-controller design. System behavior is analyzed for specific motion cases and sometimes for specific inertia tensor (axisymmetrical satellite) using averaging technique. Overall satellite angular motion is covered. Necessary attitude is found to be accessible for some control parameters. Stability is proven and optimal algorithm parameters are obtained. Floquet-based analysis is performed to verify and broaden analytical results. [ABSTRACT FROM AUTHOR]

A class of second order nonlinear damped differential equations is studied and several new oscillation conditions are obtained. Our results extend, improve and unify a number of existing results and handle the cases which are not covered by known criteria. [ABSTRACT FROM AUTHOR]

We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and the process is viewed in the timescale of mutations. Using averaging techniques due to Kurtz (in Lecture Notes in Control and Inform. Sci., vol. 177, pp. 186-209, ), we give a new proof of the convergence of the individual based model to the trait substitution sequence of Metz et al. (in Trends in Ecology and Evolution 7(6), 198-202, ), first worked out by Dieckman and Law (in Journal of Mathematical Biology 34(5-6), 579-612, ) and rigorously proved by Champagnat (in Theoretical Population Biology 69, 297-321, ): rigging the model such that 'invasion implies substitution', we obtain in the limit a process that jumps from one population equilibrium to another when mutations occur and invade the population. [ABSTRACT FROM AUTHOR]

The crack nucleation behavior of rough surfaces in line contact is investigated by means of a thermodynamically based continuum damage mechanics technique. The deterministic approach is employed to investigate the effect of roughness on the surface tractions and contact stresses. In order to treat the effect of high stress gradients, a special averaging technique, proposed previously for the case of smooth surface, is adopted in this study. The predictions of the crack nucleation life are compared with the relevant experimental data in the literature and indicate the validity of the analysis. [ABSTRACT FROM AUTHOR]

In this study, the controller is used to suppress the vibration due to rotor the helicopter blade flapping motion. The objective of this paper is to investigate the effect of time-delay absorber on the vibrating system when subjected to multi-parametric excitation forces. The equations of motion are described by coupled nonlinear differential equations. The averaging method is applied to obtain the frequency response equations near simultaneous sub-harmonic and internal resonance. The stability of the obtained nonlinear solution is studied and solved numerically. Numerical simulations show the steady state response amplitude versus the detuning parameter and the effects of the parameters system and controller. Effectiveness of the absorber E is about 2.7×10 of the main system ( X). [ABSTRACT FROM AUTHOR]

• A series of finite element methods with different averaging techniques are proposed and compared. • Our methods can avoid layer oscillations and guarantee the conservation of terminal currents. • No requirement for the dual Voronoi grid makes our methods' implementation much more convenient. • The fourth method (A4) performs well in semiconductor simulations in cases of high biases and poor-quality grids. Obtaining a satisfactory numerical solution of the classical three-dimensional drift-diffusion (DD) model, widely used in semiconductor device simulations, is still challenging nowadays, especially when the convection dominates the diffusion. In this work, we propose a series of finite element schemes with different types of averaging techniques to discretize the three-dimensional continuity equations. Our methods are based on the classical finite element framework, quite different from those mixed finite element/volume methods that also employ inverse averaging techniques. At first, the Slotboom variables are employed to transform the continuity equations into self-adjoint second-order elliptic equations with exponentially behaved coefficients. Then four averaging techniques, denoted with A1-A4, are introduced to approximate the exponential coefficient with its average on every tetrahedral element of the grid. The first scheme calculates the harmonic average of the exponential coefficient on a whole tetrahedron, and the other three schemes calculate the average of the exponential coefficient on each edge of a tetrahedral element. Our methods can avoid the spurious non-physical numerical oscillations and guarantee the conservation of the computed terminal currents with a terminal current evaluation approach. In fact, these methods not only maintain numerical stability but also overcome the disadvantages of some stabilization methods that cannot guarantee the conservation of the terminal currents, such as the streamline-upwind Petrov-Galerkin (SUPG) method. Moreover, the derivation of these discretization methods does not need the dual Voronoi grid as that of the finite volume Scharfetter-Gummel (FVSG) method or other mixed finite element/volume methods with inverse averaging techniques, which greatly reduces the complexity of parallel implementations of our methods. Simulations on two realistic three-dimensional semiconductor devices are carried out to test the accuracy and stability of our methods. According to numerical results, we conclude that scheme A4 can produce more accurate numerical solutions than the other three schemes, especially when the bias applied on the electrode is high. Numerical results also show that the scheme A4 is more robust than the Zlámal finite element method [1] in high-bias cases, and it also performs better than the FVSG method and a tetrahedral mixed finite element method [2] on poor-quality grids. Scheme A4 is also employed to study rich physical properties of the n -channel MOSFET. [ABSTRACT FROM AUTHOR]

Abstract: The angular motion of an axisymmetrical satellite equipped with an active magnetic attitude control system is considered. The dynamics of the satellite are analytically studied on the whole control loop. The control loop is as follows: preliminary reorientation along with nutation damping, spinning about the axis of symmetry, then precise reorientation of the axis of symmetry in inertial space. Reorientation starts right after separation from the launch vehicle. Active magnetic attitude control system time-response with respect to its parameters is analyzed. It is proven that low-inclined orbit forces low control system time-response. Comparison with the common control scheme shows the time-response gain. Numerical analysis of the disturbances effect is carried out and good pointing accuracy is proved. [Copyright &y& Elsevier]

Highlights: [•] Pressure and tangential traction distributions for cyclic loading is presented. [•] Influence of roughness on traction and sub-surface stress field is evaluated. [•] Crack initiation life subject to stick–slip fretting is predicted. [•] Crack initiation risk predictions are compared to experimental results. [ABSTRACT FROM AUTHOR]

Abstract: The angular motion of an axisymmetrical satellite equipped with the active magnetic attitude control system is examined. Attitude control system has to ensure necessary orientation of the axis of symmetry in the inertial space. It implements the following strategy: coarse reorientation of the axis of symmetry with nutation damping or “-Bdot” without initial detumbling; spinning-up about the axis of symmetry to achieve the property of a gyro; fine reorientation of the axis in the inertial space. Dynamics of the satellite is analytically studied using averaging technique on the complete control loop consisting of five algorithms. Solutions of the equations of motion are obtained in terms of quadratures for most cases or even in closed-form. The latter allowed to study the dependence of motion parameters including time-response with respect to the orbit inclination and other parameters for all algorithms. [Copyright &y& Elsevier]

Abstract: A thermodynamically based continuum damage mechanics (CDM) approach is employed as a propitious method for analyzing fretting crack nucleation. Intense fretting stress gradients in the contact region are examined and believed to be highly influential in the crack nucleation process. A methodology is proposed that allows for identification of an averaging zone as a function of the contact and loading parameters. The results predicted by this approach are verified by comparing the CDM crack nucleation predictions with the published experimental results on crack nucleation lives. Good agreement is observed between the predictions and the experiments. [Copyright &y& Elsevier]

Phase models represent the ideal framework to investigate the synchronization of a nonlinear oscillator with an external forcing. While many researches focused the attention to their analysis, little work has been done about the reduction of a physical system to the corresponding phase model. In this paper we show how, resorting to averaging techniques, it is possible to obtain the phase model corresponding to a given set of state equations. As examples, we derive the phase equations and investigate the synchronization properties of two popular nonlinear oscillators. [ABSTRACT FROM AUTHOR]

Averaging of accumulated data is a standard technique applied to processing data with low signal-to-noise ratios (SNR), such as image signals captured in ultra-high-speed imaging. The authors propose an architecture layout of an ultra-high-speed image sensor capable of on-chip signal accumulation. The very high frame rate is enabled by employing an image sensor structure with a multi-folded CCD in each pixel, which serves as an in situ image signal storage. The signal accumulation function is achieved by direct connection of the first and the last storage elements of the in situ storage CCD. It has been thought that the multi-folding is achievable only by driving electrodes with complicated and impractical layouts. Simple configurations of the driving electrodes to overcome the difficulty are presented for two-phase and four-phase transfer CCD systems. The in situ storage image sensor with the signal accumulation function is named Image Signal Accumulation Sensor (ISAS). [ABSTRACT FROM AUTHOR]

The synchronization of an oscillator with an external stimulus or between coupled elements is the subject of intense research in many areas of applied sciences. The most successful approach is based on phase modeling, founded on the idea to represent each oscillator by a phase variable. Phase models have been analyzed with a wealth of details and in a plethora of different variants, but little research has been done in view of the reduction of a physical system to the corresponding phase model. In this paper we investigate the possibility, at least within the context of analytical approximations, to obtain the phase model corresponding to a given nonlinear system. Both periodically driven and coupled oscillators are considered, and examples based on Stuart–Landau and van der Pol systems are given. [ABSTRACT FROM AUTHOR]

The Landau-Lifshitz (LL) dynamics of a uniformly magnetized particle is considered. The LL equation is written in the form of a Hamiltonian perturbed dynamical system. By using suitable averaging technique, the equation for the slow dynamics of the energy is derived. The averaging technique breaks up in the case of separatrix crossing. It is shown that, in the limit of small damping, the separatrix crossing can be described by using a probabilistic approach. [ABSTRACT FROM AUTHOR]

The application of FACTS devices in operating power systems has been growing. However, achieving the full advantages of these devices is severely dependent on their type, size, number and their location. Furthermore, their optimal size and placement are affected by their steady state models applied in power system studies. But the use of exact model of FACTS devices in steady state calculations is complex, due to their switching behavior. On the other hand, applying very simple models such as pure inductor/capacitor for FACTS devices leads to inaccurate results. In addition, in a power market the use of inaccurate models for power system components affects the electrical energy pricing system; while this is very crucial when FACTS devices are used for congestion management of the transmission systems. Average technique provides an appropriate time-domain representation of FACTS devices in which high frequency switching ripples are vanished. But average model can not be directly applied to the power system steady states. Thus this paper extends average models and presents average-neural (AN) models of STATCOM and SSSC as parallel and series FACTS devices, which are well-suited for analytical purposes in power system applications. To this extend, design and development of four neural identifiers are performed using the GAMMA, DNN, RBF and MLP. To verify the developed models, the exact solutions obtained from the average models of STATCOM and SSSC are compared with the outcomes of the identifiers. To show the accuracy of using the AN model, an optima] placement problem of STA TCOM is solved by applying the AN model and then the results are compared to those reported in literature. [ABSTRACT FROM AUTHOR]

By using the averaging technique, we establish some oscillation theorems for the second order damped elliptic differential equation which extend and improve some known results in the literature. [ABSTRACT FROM AUTHOR]

This paper introduces average circuit models for switch mode shunt converters coupled with power systems such as active filters and static compensators (STATCOM). These devices absorb or deliver reactive power to the utility network by employing either a fixed or a variable switching frequency (e.g., pulsewidth modulation voltage control or hysteresis current control). Analysis and simulation of these exact devices could be complex under transient and steady state conditions. Ongoing investigations on design of a practical STATCOM show that performing these kind of simulations (e.g., with PSpice) are very sluggish. Here both the fixed and variable switching frequency shunt devices are modeled using an averaging approach, by deriving their state-space equations. An average operator is defined, and applied to the state equation to get averaged mathematical models. Expansion of these models will eventually lead us to average circuit models. Further, the ripple is approximated to provide a correction to the average model. The resulting models produce much faster simulations than their exact devices. Theoretical considerations show that the averaged models agree well with the original system, and this is confirmed by PSPICE and MATLAB simulations. Additionally, experimental results are presented to validate the developed models. [ABSTRACT FROM AUTHOR]

Abstract: By using classical variational principle and averaging technique, new oscillation criteria are established for second-order nonlinear forced differential equations where the functions , and improve and extend some recent results. [Copyright &y& Elsevier]

In this paper, a novel method named pseudo-oscillator analysis is developed for the local dynamics near a Hopf bifurcation of scalar nonlinear dynamical systems with time delays. For this purpose, a pseudo-oscillator that is slightly perturbed from an undamped oscillator is firstly constructed, its fundamental frequency is the same as the frequency at the bifurcation point, and the disturbance is associated with the original system. Next, the pseudo-power function, defined as the power function of the pseudo-oscillator, is estimated along a harmonic function. Then we conclude that the local dynamics near the Hopf bifurcation can be justified from the variation of the averaged pseudo-power function. The new method features a clear physical intuition and easy computation, and it yields very accurate prediction for the periodic solution resulted from the Hopf bifurcation, as shown in three illustrative examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a simple but accurate modeling method for obtaining analytical solutions for the fundamental characteristics of electroosmotic flow through rectangular pumping channels without the Debye–Hückel approximation is presented. The Poisson–Boltzmann equation without the Debye–Hückel approximation for the electric potential distribution and the momentum equation for the velocity profile are averaged and solved analytically. To validate the modeling method proposed in the present work, electroosmotic flows through a rectangular capillary whose side is 50μm are experimentally investigated. The zeta potential at the silica–potassium phosphate buffered saline interface is measured by the streaming potential technique. The pressure driven flow characteristics of and the maximum electroosmotic flow rate through the capillary are measured. By comparing these experimental data and numerical solutions for original governing equations with the analytical solutions, the present analytical method is validated. It is found that the present modeling method is applicable when the ratio of a half of the channel width to the electric double layer thickness is larger than 3. From a parametric study for various configurations of the pumping channel based on the analytical solutions, it is shown that the pumping power can be increased by one order of magnitude with decreasing channel width. [Copyright &y& Elsevier]

In this paper, a novel method of energy analysis is developed for dynamical systems with time delays that are slightly perturbed from undamped SDOF/MDOF vibration systems. Being served frequently as the mathematical models in many applications, such systems undergo Hopf bifurcation including the classic "Hopf bifurcation" for SDOF systems and "multiple Hopf bifurcation" for MDOF systems, under certain conditions. An interesting observation of this paper is that the local dynamics near a Hopf bifurcation, including the stability of the trivial equilibrium and the bifurcating periodic solutions, of such systems, can be justified simply by the change of the total energy function. The key idea is that for the systems of concern, the total power (the total derivative of the energy function) can be estimated along an approximated solution with harmonic entries, the main part of the solution near the Hopf bifurcation. It shows that the present method works effectively for stability prediction of the trivial equilibrium and the bifurcating periodic solutions, and that it provides a high accurate estimation of the amplitudes of the bifurcating periodic solutions. Compared with the current methods such as the center manifold reduction which involves a great deal of symbolic computation, the energy analysis features a clear physical intuition and easy computation. Two illustrative examples are given to demonstrate the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

The effect of high-frequency vibrations of the field of external mass forces on convection in miscible fluids is considered for a system of convection equations obtained by an averaging technique. The structures of flows formed under initial conditions corresponding to physical experiments in microgravity are examined. [ABSTRACT FROM AUTHOR]

In this paper, the theoretical background for the failure analysis of fibre-reinforced composites under variable repeated loads in the framework of direct methods is presented. It is based on a local shakedown analysis in a representative volume element of the composite and the use of averaging techniques to study the influence of each component (matrix, fibre and interface) on the macroscopic response of such composite. [Copyright &y& Elsevier]

Abstract: This paper discusses a class of second-order nonlinear differential equations. By using the generalized Riccati technique and the averaging technique, new oscillation criteria are obtained for all solutions of the equation to be oscillatory. Asymptotic behavior for forced equations is also discussed. [Copyright &y& Elsevier]

For all solutions of a class of second order nonlinear damped differential equations, new oscillation criteria are established. Asympotic behavior for forced equations is also discussed. [ABSTRACT FROM AUTHOR]

The present work deals with the recovery of the in-boundary stress on smooth boundary parts in Boundary Element Method (BEM) in two dimensions. First, two Boundary Integral Representations (BIRs) of tangential derivative of boundary displacements, whose integral kernels multiplying either tangential derivative of displacements or displacements are smooth and bounded, are presented. Two procedures for an in-boundary stress recovery based on these BIRs are developed and analyzed. The first procedure, which directly uses the results obtained from a BEM analysis, displacements and tractions, requires the performing of integrations involved in these BIRs either over the real boundary of the solid or over a smooth approximation of the boundary part where the evaluation point is placed. The second procedure, which can be applied on a non-smooth (e.g. polygonal) approximation of the boundary, requires the use, in the first BIR introduced here, of an integral density which is previously smoothed by a local smoothing procedure. The third recovery procedure considered in this work is directly given by a local smoothing procedure of this kind. Results obtained by these three recovery procedures are compared in a series of numerical tests, the best results being obtained by the first procedure developed in this work. [ABSTRACT FROM AUTHOR]

By employing the generalized Riccati technique and the integral averaging technique, new Kamenev-type oscillation criteria are established for a class of second-order matrix differential systems. These criteria extend, improve, and unify a number of existing results and handle the cases which are not covered by known criteria. In particular, two interesting examples that illustrate the importance of our results are included. [Copyright &y& Elsevier]

The order reduction method for singularly perturbed optimal control systems consists of employing the system obtained while setting the small parameter to be zero. In many situations the differential-algebraic system thus obtained indeed provides an appropriate approximation to the singularly perturbed problem with a small parameter. In this paper we establish that if relaxed controls are allowed then the answer to the question whether or not this method is valid depends essentially on one simple parameter: the dimension of the fast variable, denoted n. More specifically, if n=1 then the order reduction method is indeed applicable, while if n>1 then the set of singularly perturbed optimal control systems for which it is not applicable is dense (in the L norm). [ABSTRACT FROM AUTHOR]