necessary and sufficient conditions for oscillation of second order neutral differential equations consider the second order nonlinear neutral differential equation with delays e d2 dt2 y t py t q t f y t 0 for t 0 where q t f x are continuous functions q t 0 yf y 0 if y 0 and 0 0 0 when f y satisfies either the superlinear or sublinear conditions which include the special case f y y y 1 of 1 and 0 1 respectively we give necessary and sufficient conditions for the oscillation of all continuable solutions of e when p 0 in e these results reduce to the well known theorems of atkinson and belohorec in the special case when f y y y 1 1

factorable fir nyquist filters with least stopband energy under sidelobe level constraints spectrally factorable nyquist filters are used in data communications to avoid intersymbol interference an approach is developed for obtaining a nyquist filter that is factorable having the smallest stopband energy for a given sidelobe level the resulting constrained minimization problem is solved efficiently and reliably using the goldfarb idnani 1983 algorithm some examples are presented comparing the present method with a previous approach from the literature

comment on the paper interval criteria for oscillation of second order nonlinear neutral differential equations comput math appl 46 5 6 2003 903 918

box constrained multi objective optimization a gradient like method without a priori scalarization abstract the aim of this paper is the development of an algorithm to find the critical points of a box constrained multi objective optimization problem the proposed algorithm is an interior point method based on suitable directions that play the role of gradient like directions for the vector objective function the method does not rely on an a priori scalarization and is based on a dynamic system defined by a vector field of descent directions in the considered box the key tool to define the mentioned vector field is the notion of vector pseudogradient we prove that the limit points of the solutions of the system satisfy the karush kuhn tucker kkt first order necessary condition for the box constrained multi objective optimization problem these results allow us to develop an algorithm to solve box constrained multi objective optimization problems finally we consider some test problems where we apply the proposed computational method the numerical experience shows that the algorithm generates an approximation of the local optimal pareto front representative of all parts of optimal front

oscillation criteria for second order nonlinear differential equations involving general means consider the second order nonlinear differential equation e y a t f y 0 where a t c 0 f y c1 f y 0 and yf y 0 for y 0 furthermore f y also satisfies either a superlinear or a sublinear condition which covers the nonlinear function f y y y 1 with 1 and 0 1 respectively commonly known as the emden fowler case here the coefficient function a t is allowed to be negative for arbitrarily large values of t kamenev type oscillation criteria involving integral averages for the linear equations l y a t y 0 are extended to the nonlinear equation e by using more general means the results extend similar results on general means by philos for the linear equation l and also results based upon kamenev s integral averaging method concerning the nonlinear equation e

integral inequalities and second order linear oscillation on the interval 0 a u 0 below by a solution we mean a non trivial solution a solution is oscillatory if it has an infinite number of zeros numerous oscillation criteria are known and diversified approaches have proved fruitful among these is the use of the associated riccati equation although the theory of differential and integral inequalities has been used by some investigators see e g hartman 4 71 the authors believe that it has not been fully exploited the non oscillation of 1 1 is equivalent to the existence of a solution of the associated riccati equation on a half line thus one technique of proving oscillation is to show that any solution of the riccati equation diverges to i co at a finite point the theory of differential and integral inequalities comes in handy in the estimation of the growth of such a solution below we describe some known results that are relevant to results established in this paper although these are stated here for the case i co in the rest of the paper we consider both cases a 0 and a 00 it is well known that if q is large in the mean then 1 1 is oscillatory a typical example of such a criterion is due to fite leighton and wintner if

interval criteria for oscillation of second order linear ordinary differential equations abstract new oscillation criteria are established for the equation py qy 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are more natural according to the sturm separation theorem and sharper than some previous results and can be applied to extreme cases such as t 0 q t dt

realization of root raised cosine roll off filters using a recursive fir filter structure root raised cosine roll off rrc filter is one of the most fundamental elements in modern digital communications this paper proposes a new method to efficiently realize the rrc filter the method employs cubic hermite interpolation to obtain a piecewise polynomial approximation for the impulse response of the rrc filter then the approximated impulse response is efficiently realized by using a transversal filter with a very small number of taps followed by integrators with a simple recursive structure named cascaded recursive finite impulse response cr fir filter as an example an rrc filter with roll off factor 0 5 is constructed by using the cr fir filter with only nine multipliers performance of the rrc filter in matched filtering is examined by computer simulations then it is shown that the constructed rrc matched filter has nearly the same performance as the ideal filter

optimum fir transmitter and receiver filters for data transmission over band limited channels the paper deals with the design of digital transmitter and receiver filters with finite impulse response fir for data transmission over band limited channels the filters are matched and satisfy a zero intersymbol interference constraint when cascaded for baseband transmission the filters achieve optimum spectral concentration in the frequency range 1 beta 2t 1 beta 2t mathematically the filter design leads to a generalized eigenvalue problem which is solved numerically by a projected gradient procedure for transmission over bandpass channels by combined amplitude and phase modulation the design technique is modified so that filters with complex valued impulse response and optimum spectral concentration in the range of positive bandpass frequencies f c 1 beta 2t f c 1 beta 2t are obtained in addition the complex formulation allows the design of impulse responses with enhanced spectral attenuation in the corresponding range of negative frequencies in order to minimize imageband interference results are shown in terms of filter coefficients signal spectra and spectral concentrations obtained for example filters designed for a voiceband data modem operating at a symbol rate of 2400 baud achieve a spectral concentration of 98 5 percent with 24 coefficients and beta 0 1 and with only 0 001 percent of the total energy in the imageband region

oscillation and nonoscillation for second order linear differential equations abstract new oscillation and nonoscillation theorems are obtained for the second order linear differential equation u p t u 0 where p t c 0 and p t 0 conditions only about the integrals of p t on every interval 2 n t 0 2 n 1 t 0 n 1 2 for some fixed t 0 0 are used in the results

energy optimization of band limited nyquist signals in the time domain this paper presents a theoretical consideration of the optimal design of band limited nyquist type signal shapes for data transmission which maximizes its energy in a given time interval and which generates no intersymbol interference at the periodic sampling instants a method based on a completely analytical approach is given for design of such signals the optimal signal is a solution of an inhomogeneous linear integral equation of fredholm type a technique for solving this equation is given the computation is straightforward and involves the determination of eigenvalues and eigenfunctions of a positive definite and symmetric kernel in terms of prolate spheroidal wave functions the constraint for intersymbol interference is shown to be easily included into the problem finally some numerical examples are given and the performance of the optimal signal shapes is compared to that resulting from the use of the raised cosine type of signals it is also concluded that especially for small values of rolloff factor the optimal signals thus obtained are almost maximally immune to small timing offsets at the sampling instants

oscillation by impulses for a second order delay differential equation we consider a certain second order nonlinear delay differential equation and prove that the all solutions oscillate when proper impulse controls are imposed an example is given

optimized signaling waveforms to reduce the effects of intersymbol interference and timing jitter the mainlobe energy of a member from the class of symbol waveforms with null derivatives at zero crossings is maximized thus a bandlimited pulse shape without intersymbol interference robust against jitter and timing errors is obtained comparisons to known pulses show advantages for these signals at the expense of bandwidth which linearly increases with the number of null derivatives

interval oscillation criteria for second order nonlinear differential equations with damping new oscillation criteria are established for the nonlinear damped differential equation ry py qf y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results and extend and improve the recent interval criteria of kong and huang and can be applied to extreme cases such as t0 q s ds in particular several examples that dwell upon the sharp conditions of our results are also included

oscillation for a second order neutral differential equation with impulses we consider a certain type of second order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations called impulses as a matter of fact some particular non impulsive cases of the system are oscillatory already thus we are interested in finding adequate impulse controls under which our system remains oscillatory

interval criteria for oscillation of second order nonlinear neutral differential equations some new oscillation criteria are established in this paper for the second order nonlinear neutral delay differential equation r t x t p t x t q t f x t 0 where and are nonnegative constants r p q c t0 r and f c r r these results are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results about neutral and delay differential equations in particular several examples that dwell upon the sharp conditions of our results are also included

a note on oscillation criteria of second order nonlinear neutral delay differential equations in recent years many results on oscillation criteria of second order nonlinear neutral delay differential equations have been obtained but some of these criteria are incorrect due to a mistake in a crucial auxiliary result this note examines several of these results provides some counterexamples and points out what causes the problems

riccati techniques and variational principles in oscillation theory for linear systems on etablit des conditions suffisantes pour que toutes les solutions soient oscillatoires on utilise les techniques de riccati et les principes variationnels

the self regulation problem as an inexact steepest descent method for multicriteria optimization abstract in this paper we study an inexact steepest descent method for multicriteria optimization whose step size comes with armijo s rule we show that this method is well defined moreover by assuming the quasi convexity of the multicriteria function we prove full convergence of any generated sequence to a pareto critical point as an application we offer a model for the psychology s self regulation problem using a recent variational rationality approach

design of orthogonal pulse shapes for communications via semidefinite programming in digital communications orthogonal pulse shapes are often used to represent message symbols for transmission through a channel in this paper the design of such pulse shapes is formulated as a convex semidefinite programming problem from which a globally optimal pulse shape can be efficiently found the formulation is used to design filters that achieve a the minimal bandwidth for a given filter length b the minimal filter length for a given bandwidth c the maximal robustness to timing error for a given bandwidth and filter length bandwidth is measured either in spectral energy concentration terms or with respect to a spectral mask the effectiveness of the method is demonstrated by the design of waveforms with substantially improved performance over the chip waveforms specified in standards for digital mobile telecommunications

on the oscillation of differential equations with an oscillatory coefficient we derive lower bounds for the distance between consecutive zeros of solutions of y q t y 0 when q takes both positive and negative values we apply our results to the limit point limit circle classifications of

integral averaging techniques for the oscillation of second order nonlinear differential equations abstract in this paper we enlist some known and establish some new oscillation criteria for the second order nonlinear differential equations of the form if a t x t t su p t t q t f x t 0 where the coefficients p t and q t are not assumed to be nonnegative for all large values of t these criteria are obtained by using integral averaging techniques and can be applied to some special cases where other classical oscillation results are not applicable a systematic study is attempted to extend improve and correlate a number of existing results

philos type oscillation criteria for emden fowler neutral delay differential equations philos type oscillation criteria are established for the emden fowler neutral delay differential equation x t c 1x t q 1 t y email protected a 1y email protected q 2 t y email protected b 1y email protected 0 t t 0 where x t y t p t y email protected the results obtained here essentially improve some known results in the literature in particular two interesting examples that point out the importance of our results are also included

design and hybrid realization of fir nyquist filters with quantized coefficients and low sensitivity to timing jitter a design of finite impulse response fir nyquist filters with zero intersymbol interference isi and low sensitivity to timing jitter is presented using an affine scaling linear programming algorithm a near optimum quantized coefficient set can be obtained in a feasible computational time by varying a parameter the design provides a tradeoff between the tail energy of the impulse response in the time domain and the stopband of the magnitude response in the frequency domain we also present a pipelined multiplier free fir filter realization with periodically time varying ptv coefficients based on a hybrid form the realizations exploit the coefficient symmetry to reduce the hardware by about one half by placing most of the shifts followed by addition toward the back end of the structure hardware is reduced due to the shorter wordlength of the adders the proposed structure has a provision to increase the speed by adjusting a design parameter but at the expense of more hardware

on two stage nyquist pulse shaping filters this correspondence outlines a method for designing two stage nyquist filters the nyquist filter is split into two equal and linear phase finite length impulse response spectral factors the per time unit multiplicative complexity of the overall structure is included as the objective function examples are then provided where nyquist filters are designed so as to minimize the multiplicative complexity subject to the constraints on the overall nyquist filter in comparison to the single stage case the two stage realization reduces the multiplicative complexity by an average of 48 for two stage sampling rate conversion src the correspondence shows that it is better to have a larger src ratio in the first stage