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For a second-order elliptic equation, we obtain oscillation and nonoscillation criteria of a new type in which, unlike well-known criteria, the majorant function is not a function of r = | x|. [ABSTRACT FROM AUTHOR]

This paper is concerned with the spectrum the Hill operator L( y) = − y′′ + Q( x) y in $${L^2_{{\rm per}}[0, \pi]}$$. We show that the eigenvalues of L can be characterized by knowing one of its eigenfunctions. Applications are given to nonlinear stability of a class of periodic problems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complex oscillation of differential polynomials generated by meromorphic solutions of differential equations where the coefficient A is meromorphic in the unit disc $$ \mathbb{D} $$ = { z: | z| < 1}. [ABSTRACT FROM AUTHOR]

The article reports on frequency-domain estimates intended for the calculation of periods of oscillation within discrete systems following nonlinearity. It highlights a theorem for nonlinear discrete system in which the system is composed of positive α and β without an existing nonzero N-periodic sequence xt. It also states different corollaries that support the factuality of the theorem pertaining to domain estimates. It tells that the logistic equation xt+1= Μ t(1-xt) is a nonlinear system which contains A= Μ b=―1, c=1 and ϕ (σ) = Μ (σ)2. Moreover, it asserts that nonlinearity ϕ is enclosed within slopes and lines based from calculations of t→+ &x221E;.

The Indian savings experience has been marked by varied oscillations since the inception of planning in India. In the period following the independence, India has witnessed a rising trend in the gross domestic saving rate, accompanied by many fluctuations over time though. Also, there have been many major shifts and substitutions within the composition of savings over the six decades. The objective of the present study is to examine the trend behavior and changing composition of savings in India over the planned economic era from 1950 to 2007. The study uses three indicators, namely, the trend growth of saving, the trend growth of saving rate and the average saving rate for an analysis of the trend behavior of savings in the country. On the basis of which, the entire six-decade period is decomposed into six distinct time periods or phases of saving-low-saving phase, increasing-saving phase, highsaving phase, stagnation phase, recovery phase and new-high-saving phase. For studying the changing composition of savings, the average share of saving components has been computed for different saving phases. After an extensive review of Indian savings, the study arrives at certain enlightening findings. There have been very important and major changes in the behavior and composition of savings in India over the analysis period. Household sector is the largest saver with the lion's share in GDS. Private corporate sector saves very low, while the public sector even dissaves. There have been some dramatic and drastic substitutions within the saving composition, with household preferences shifting from the conventionally most sought after saving instruments such as currency, life funds, provident and pension funds to bank deposits, shares and debentures, and other small-saving assets. [ABSTRACT FROM AUTHOR]

We have solved the rate equations for InGaAs/GaAs self-assembled quantum-dot laser considering homogeneous and inhomogeneous broadening of optical gain numerically using fourth-order Runge-Kutta method. Dynamic-characteristics are analyzed; relaxation oscillation frequency, modulation bandwidth, and turn-on delay improve as injection current increases. With enhancing of the full width at half maximum (FWHM) of homogeneous broadening, threshold current and turn-on delay increase, because of elevating of central group density of states. Simulation results of static-characteristics show that slope-efficiency increases as the FWHM of homogeneous broadening heightens due to enhancing of central group carriers. Exceeding of the FWHM of homogeneous broadening from FWHM of inhomogeneous broadening results in degradation of slope-efficiency and static-characteristics because empty DOS increas. Nonlinearity appears in light-current characteristics at a special interval from ratio of FWHM of homogeneous broadening to FWHM of inhomogeneous broadening. Differential gain decreases as initial relaxation time and recombination times heighten. Consequently, relaxation oscillation frequency and modulation bandwidth decline. [ABSTRACT FROM AUTHOR]

Mixed control-state constraints are used as a relaxation of originally state constrained optimal control problems for partial differential equations to avoid the intrinsic difficulties arising from measure-valued multipliers in the case of pure state constraints. In particular, numerical solution techniques known from the pure control constrained case such as active set strategies and interior-point methods can be used in an appropriately modified way. However, the residual-type a posteriori error estimators developed for the pure control constrained case can not be applied directly. It is the essence of this paper to show that instead one has to resort to that type of estimators known from the pure state constrained case. Up to data oscillations and consistency error terms, they provide efficient and reliable estimates for the discretization errors in the state, a regularized adjoint state, and the control. A documentation of numerical results is given to illustrate the performance of the estimators. [ABSTRACT FROM AUTHOR]

We consider a class of nonlinear partial difference equations with continuous variables. Some oscillation criteria are obtained using an integral transformation and inequalities. [ABSTRACT FROM AUTHOR]

We consider a weakly nonlinear multifrequency autonomous system of differential equations with a small parameter on the right-hand side under the condition that the unperturbed system has a quasiperiodic general solution. The system is reduced to a simpler form by averaging and separation. We establish sufficient conditions for the preservation of an invariant torus under a small perturbation. [ABSTRACT FROM AUTHOR]

Our aim is to establish some sufficient conditions for the oscillation of the second-order quasilinear neutral functional dynamic equation on a time scale $ \mathbb{T} $, where ∣ f( t, u)∣ ≥ q( t)∣ u∣, r, p, and q are real-valued rd-continuous positive functions defined on $$ \mathbb{T} $$, and γ and β > 0 are ratios of odd positive integers. Our results do not require that γ = β ≥ 1, p( t) ≥ 0, Some examples are considered to illustrate the main results. [ABSTRACT FROM AUTHOR]

We consider third order functional difference equation with discrete delay. We then develop few theorems related to the oscillatory behavior of the difference equation of the form Δ (b(n) Δ (a(n) Δ )))++Σmi= qi (n)f (x(σi (n-&3x03C4;))) = h(n). Examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper presents a complete overview of low-frequency oscillation phenomena in power systems. The definition of low-frequency oscillation and its classification are clearly explained. Some power system blackout incidents due to low-frequency oscillation and the lesson learned from those incidents are also reported in the paper. Widely used methodology for studying low-frequency oscillation among power utilities is presented. Methods for oscillation damping, at both the operational and the planning stages of a power system, are briefly discussed. A comprehensive case study of lowfrequency oscillation in a simple system is presented using eigenvalue analysis. Time domain results are presented to support the eigenvalue analysis. Conclusions are duly drawn. [ABSTRACT FROM AUTHOR]

In this paper we deal with nonlinear second-order neutral differential equation, which contains the unknown function both with and without delays, with several positive and negative coefficients. (x(t)-R(t)F(x(t-Τ)))n+i-1nΣ Pi(t)Gi(x(t-αi))- j=1mΣ Qj(t)Gj(x(t-βj)) = s (t) (x(t)-R(t)F(x(t-Τ)))n+i-1nΣ Pi(t)Gi(x(t-αi))- j=1mΣ Qj(t)Gj(x(t-βj)) = 0. Our criteria improve and extend many results known in the literature as results of Elabbasy, Saker [2], and Shoukaku [11]. In addition we prove that under appropriate hypotheses, if every solution of the associated linear equation zn(t) + i=1 n Σ Hi(t)(1-ϵi)≈(t-αi) = 0 oscillates, then every solution of the nonlinear equation homogeneous also oscillates. [ABSTRACT FROM AUTHOR]

Consider the first-order and the second-order delay difference equations Δx(n)+p(n)x(Τ(n)) = 0, n = 0, 1, 2, 2..., (1) and Δ 2x(n) + p (n)x(Τ(n)) = 0, n = 0, 1, 2,..., (2) where Δ x (n) = x(n+1) - x(n), Δ2 = Δ o Δ, p : N → R+ , Τ : N → N, → (n) ⩽ n - 1 and lim Τ (n) = + ∞ The most interesting oscillation criteria for Eq. (1), and Eq. (2). especially in the case where 0 < n→∞ lim inf i=Τ (n) n-1 Σ p(i) ⩽1/e and n→∞ lim sup i=Τ(n) for Eq. (1), are presented. [ABSTRACT FROM AUTHOR]

In this paper, a class of second order nonlinear differential equations with perturbation is studied. By using the generalized Riccati transformation, the integral averaging technique and the method of classification, new oscillation criteria are obtained for all solutions of the equations, which generalize and improve some known results. [ABSTRACT FROM AUTHOR]

Given a positive measure μ, d contractions on [0,1] and a function g on ℝ, we are interested in function series F that we call “ μ-similar functions” associated with μ, g and the contractions. These series F are defined as infinite sums of rescaled and translated copies of the function g, the dilation and translations depending on the choice of the contractions. The class of μ-similar functions F intersects the classes of self-similar and quasi-self-similar functions, but the heterogeneity we introduce in the location of the copies of g make the class much larger. We study the convergence and the global and local regularity properties of the μ-similar functions. We also try to relate the multifractal properties of μ to those of F and to develop a multifractal formalism (based on oscillation methods) associated with F. [ABSTRACT FROM AUTHOR]

Abstract  The simple free running multivibrator built around a single fractional capacitor is examined in this letter. Equations for the oscillation frequency of the multivibrator are derived taking into account the positive feedback factor around the multivibrator. We show that the use of the fractional capacitance allows the multivibrator to have very high frequencies of oscillation for reasonable time constants used. PSPICE simulation and experimental results demonstrate the analysis with an approximation to a fractional capacitor that yields a result, which is at least 1000 times in frequency compared to if a normal capacitor of the same value was employed. [ABSTRACT FROM AUTHOR]

We establish some necessary and sufficient conditions for oscillation of the solutions of the following two-dimensional difference system: Δxn - f(n, yn), Δyn = -g(n, xn), where f(n, u) and g(n, u) are strongly superlinear or sublinear functions. [ABSTRACT FROM AUTHOR]

We are concerned with the oscillation of the forced second-order neutral nonlinear differential equations with delayed argument in the form (r(t)(x(t) + a(t)x(σ(t)))')' + p(t)f(x(τ(t))) + Σn i=1 qi(t)∣x(t)∣λisngx(t) = e(t). No restriction is imposed on the potentials p(t), qi(t), ande(t) to be nonnegative. Our methodology is somewhat different from those of previous authors. [ABSTRACT FROM AUTHOR]

Some oscillation criteria for the following second-order neutral differential equation [x(t) ± r(t)f(x(t - λ))″ + p(t)g(x(t - α)) - q(t)g(x(t - β)) = s(t) where t ≥ t0 , λ, α, β ϵ ℝ+ with α ≥ β , r ? C²([t0,∞),ℝ+), p, q ϵ C([t0,8),ℝ+) and f, g ϵ C(ℝ, ℝ), s ϵ C([t0,∞),ℝ) have been obtained. Our results are not restricted with boundedness of solutions. [ABSTRACT FROM AUTHOR]

The analytic behaviour of classical and difference versions of Hermite polynomials is investigated from two different viewpoints: first using oscillation theory which is important in quantum oscillator systems and second using a factorization method which may serve as a stable numerical investigation of the function systems under investigation. The resulting polynomial systems are basically of type unbounded orthogonal polynomial systems. [ABSTRACT FROM AUTHOR]

The work describes the use of pole placement state-space method for parametric optimization of motor torque controller. Presented method is universal for any type of mathematical model in contrast to standard optimization (optimal shape or optimal modulus criterion). The general oscillatory element is analyzed. Mathematical models of separately excited and brushless DC motors are compared. Ready to use relationship for parametric optimization of motor torque controller is presented. The results of the simulation, in the environment MATLABSIMULINK, of the closed-loop control system are shown. [ABSTRACT FROM AUTHOR]

The frequency response of an oscillating structure can be tailored by attaching one or more subordinate oscillators. This paper shows how the magnitude and phase of the frequency response can be deliberately shaped by prescribing the distributions of the dynamic properties in an array of such subordinate oscillators. Exact analytic governing equations of motion are derived for the coupled system composed of the primary system and the subordinate array. For a relatively small number (<100) of attached oscillators whose total mass is small (<1%) relative to the primary structure, it is possible to engineer frequency-response functions of the primary oscillator to have, for example, nearly linear phase or constant amplitude over a frequency band of interest. The frequency range over which response shaping is achieved is determined by the band of the attached oscillators. It is shown that the common analytic methodology for designing a dynamic vibration absorber represents the limiting case of a single oscillator in the subordinate set. Moreover, increasing the number of subordinate oscillators (without increasing the total added mass) offers a number of advantages in reshaping the dominant system’s frequency response. [ABSTRACT FROM AUTHOR]

This article presents a hybrid differential transform/control-volume method to solve hyperbolic heat conduction problems. First, the governing equations are transformed using the differential transform technique. Second, the temperature spectra, given by predefined shape functions are calculated through a recursive formula after applying the control-volume method to each individual subinterval. Finally, the inverse differential transform technique is adopted to determine the temperature by a finite-term power series. Numerical oscillation can be effectively suppressed by choosing suitable values of the powers of shape functions, and the simulation results match well with the analytic solutions. [ABSTRACT FROM AUTHOR]

In this note we study the zeros of solutions of differential equations of the form u″ C pu = 0. A criterion for oscillation is found, and some sharper forms of the Sturm comparison theorem are given. [ABSTRACT FROM AUTHOR]

In this article, we show that the Chung-Smirnov property holds for Bernstein estimators of distribution functions under different conditions on the underlying distribution to be estimated. In doing so, we obtain general results that characterise the closeness between these Bernstein estimators and the empirical distribution function Fn. [ABSTRACT FROM AUTHOR]

Interval oscillation criteria are established for second-order difference equations in the form Δ(k (n)Δx(n))+p (n) x (g (n))+q (n) ∣x (g (n))∣㬱-1 x (g (n))=e (n) ; (Eγ) where n &#x2265 n0; n0 ϵ N = {0; 1; …}; γ > 1; k; p; q; e and g are sequences of real numbers; k (n) > 0 is nondecreasing; g(n) is nondecreasing, limn→∞ g(n) = ∞: Several oscillation criteria are given for equation (Eγ) considered as to separate delay and advanced difference equations when g(n) < n and g(n) > n respectively. Illustrative examples are included. [ABSTRACT FROM AUTHOR]

We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form (r (t) 횽alpha; (xΔ))Δ + f (t, xσ) = e(t), t ∈ [t0, ∞)T with f (t, x) = q(t) 횽alpha; (x) + ∑i=1n qi (t) 횽βi (x), 횽* (u) = |u|*-1 u, where [t0, ∞)T is a time scale interval with t0 ∈ T, the functions r, q, qi, e : [t0, ∞)T → R are right-dense continuous with r > 0, σ is the forward jump operator, xσ (t) : = x(σ (t)), and β1 >...> βm > α > β m+1 > ... βn > 0. All results obtained are new even for T = R and T = Z. In the special case when T = R and α = 1 our theorems reduce to (Y. G. Sun and J. S. W. Wong, Journal of Mathematical Analysis and Applications. 337 (2007), 549-560). Therefore, our results in particular extend most of the related existing literature from the continuous case to arbitrary time scale. [ABSTRACT FROM AUTHOR]

We employ Kranoselskii's fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation [x(t) + p(t) x (τ0(t))]ΔΔ + q1(t)x(τ1t)) - q2(t)x(τ2(t)) = e(t) on a time scale T. To dwell upon the importance of our results, one interesting example is also included. [ABSTRACT FROM AUTHOR]

We mainly study the global behavior of the nonlinear difference equation in the title, that is, the global asymptotical stability of zero equilibrium, the existence of unbounded solutions, the existence of period two solutions, the existence of oscillatory solutions, the existence, and asymptotic behavior of non-oscillatory solutions of the equation. Our results extend and generalize the known ones. [ABSTRACT FROM AUTHOR]

In this paper, a new approach is proposed to investigate Blackwell-type renewal theorems for weighted renewal functions systematically according to which of the tails of weighted renewal constants or the underlying distribution is asymptotically heavier. Some classical results are improved considerably. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the growth and the complex oscillation theory of the linear differential equation f(k) + Ak-1 f(k-1) + ߪ +A1f′ + A0f = F, where A0,A1, ߪ Ak-1, F ≢ 0 are entire functions. We also investigate the relation between the solutions of a pair non-homogeneous linear differential equations. We improve some results due to the author, S. Abbas and Z. X. Chen, S. A. Gao. [ABSTRACT FROM AUTHOR]

We study space mappings with branching that satisfy modulus inequalities. For classes of these mappings, we obtain several sufficient conditions for the normality of families. [ABSTRACT FROM AUTHOR]

In this paper, we will establish some new interval oscillation criteria for the forced second-order nonlinear dynamic equation[image omitted] on a time scale  where γ ≥ 1. As a special case when  =  our results not only include the oscillation results for second-order differential equations established by Wong (Oscillation criteria for a forced second-order linear differential equation, J. Math. Anal. Appl. 231 (1999), pp. 233-240) and Nasr (Sufficient condition for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. math. Soc. 126 (1998), pp. 123-125) but also improve these results. When  = ,  = h or  = qN, i.e. for difference equations, generalized difference equations or q-difference equations our results are essentially new and also can be applied on different types of time scales, as illustrated in several examples. [ABSTRACT FROM AUTHOR]

Several comparison theorems with respect to powers in nonlinearities for half-linear differential equations are presented. The Riccati transformation and the reciprocity principle are utilized. Some examples and an integral extension of the classical comparison result are presented as well. [ABSTRACT FROM AUTHOR]

Integro-differential and differential equations are derived for PLL systems with squarer and for the Costas loop. The equations are based on special asymptotic methods of high-frequency harmonic and pulse oscillations analysis. Methods to compute phase detector characteristics are proposed. New classes of such characteristics are introduced for highfrequency pulse clocks. [ABSTRACT FROM AUTHOR]

In Archimedean space (X,⊰) we study oscillation of all solutions of the second-order difference equation with a nonlinear damped term of the form a(k)Δ2y(k)+b(k)Δy(k)+c(k)y(k)+ f (k,y(k),y(k-r1(k)),…,y(k-rn(k))) = 0, where a;b;c : ℕ → ℝ, f : ℕ x Xn+1 → X, ri : ℕ → ℕ, i = 1,2,…,n. [ABSTRACT FROM AUTHOR]

Pure carbon nanotube (CNT) oscillators are compared to the corresponding CNT oscillators encapsulating copper nanowires (Cu@CNTs) by molecular dynamics simulations. The classical oscillation theory provides a fairly good estimate of the mass dependence of the operating frequency when the CNT surface is not deformed by the Cu nanowire. The structural deformations of the CNT induced by the encapsulated copper nanowire have a greater effect on the oscillation frequency than the mass of the copper nanowire. The excess forces of the Cu@CNT oscillator are slightly higher than those of the CNT oscillator and the excess van der Waals forces induced by the inter-wall interactions are 17 times higher than the excess forces induced by the Cu nanowire-CNT interactions. [ABSTRACT FROM AUTHOR]

By using the positive linear functional and the monotone subhomogeneous functional, including the general means and Riccati technique, some new oscillation criteria are established for the second order linear matrix differential system where P( t), R( t), Q( t) are n × n real continuous matrix functions, P( t) and R( t) are commutative. The results improve and generalize those given in some previous papers, which can be seen by the examples given at the end of this paper. [ABSTRACT FROM AUTHOR]

It has been known that a bottleneck RED (Random Early Detection) gateway can become oscillatory when regulating multiple identical TCP (Transmission Control Protocol) flows. However, a systematic explanation of such oscillatory behavior is not available. In this paper, we first use the fluid-flow model to derive the system characteristic frequency, and then compare with the frequencies of the RED queue length waveforms observed from "ns-2" simulations. The "ns-2" simulator is the only viable simulation tool accepted by industry for verification purposes. Analysis of the TCP source frequency distribution reveals the occurrence of period doubling when the system enters the instability region as the filter resolution varies. Since random events and a large number of TCP flows are involved in the process of generating the average system dynamics, a statistical viewpoint is taken in the analysis. Our results reflect the true system behavior as they are based on data from "ns-2" simulations rather than numerical simulations of analytical models. The physical mechanism of oscillation is explained in terms of the difference in the TCP source frequency and the TCP-RED system characteristic frequency. [ABSTRACT FROM AUTHOR]

Observed changes and variability in winter (DJF) mean temperature series at the 70 stations of Turkey and the circulation types at 500-hPa geopotential height level were investigated to explain atmospheric controls of the temperature variations during the extreme and normal phases of the Arctic Oscillation Index (AOI). The analysis was performed with respect to relationships between winter (monthly and seasonal) mean temperatures and the AOI and the composite winter (monthly and seasonal) temperature changes corresponding to the various phases of the AOI. Main conclusions and evaluations of the study are as follows: [ABSTRACT FROM AUTHOR]

The effect of the pressure recovery at glottal exit is introduced to modify the one-mass model. Using the modified one-mass model, the phonation critical condition, including phonation threshold pressure and phonation threshold flow, is analyzed by using the small-amplitude oscillation theory. It is found that the phonation threshold pressure is not sensitive to the change of the prephonatory glottal width at a wide glottal gap. This result agrees with previous experimental observations and suggests that the low slope of dependence of phonation threshold pressure on prephonatory gap found by Chan and Titze [J. Acoust. Soc. Am. 119, 2351–2362 (2006)] could be a consequence of the pressure recovery effect at the glottal exit. In addition, it is predicted that the phonation threshold flow is always significantly increased with the prephonatory gap even at a wide prephonatory glottal gap. Therefore, the phonation threshold flow has an advantage in assessing the phonatory system at a wide prephonatory gap in comparison with the phonation threshold pressure. The phonation threshold flow can be a useful aerodynamic parameter for pathological conditions in which the incomplete glottal gap is often seen. [ABSTRACT FROM AUTHOR]

A novel digital image stabilization technique is proposed in this paper. It is based on a fuzzy Kalman compensation of the global motion vector (GMV), which is estimated in the log-polar plane. The GMV is extracted using four local motion vectors (LMVs) computed on respective subimages in the logpolar plane. The fuzzy Kalman system consists of a fuzzy system with the Kalman filter's discrete time-invariant definition. Due to this inherited recursiveness, the output results into smoothed image sequences. The proposed stabilization system aims to compensate any oscillations of the frame absolute positions, based on the motion estimation in the log-polar domain, filtered by the fuzzy Kalman system, and thus the advantages of both the fuzzy Kalman system and the log-polar transformation are exploited. The described technique produces optimal results in terms of the output quality and the level of compensation. [ABSTRACT FROM AUTHOR]