oscillation caused by impulses the present paper is devoted to the investigation of the oscillation of a kind of very extensively studied second order nonlinear delay differential equations with impulses some interesting results are obtained which illustrate that impulses play a very important role in giving rise to the oscillations of equations

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

interval criteria for oscillation of nonlinear second order dynamic equations on time scales interval oscillation criteria are established for a second order nonlinear dynamic equation on time scales by utilizing a generalized riccati technique and an integral averaging technique the theory can be applied to second order dynamic equations regardless of the choice of delta or nabla derivatives

necessary and sufficient conditions for oscillations of higher order delay differential equations we obtain necessary and sufficient conditions under which ail solutions of certain n th order delay differential equations oscillate when n is odd and necessary and sufficient conditions under which all bounded solutions oscillate when n is even the conditions derived involve the characteristic equation of the delay differential equation

random initial imperfections of structures abstract this paper is a theoretical study on random initial imperfections of structures the explicit form of probability density function of the load bearing capacity critical load of structures is derived for random initial imperfections based on a decomposition of the space of imperfection vectors into two orthogonal subspaces the subspace that asymptotically affects the load bearing capacity and the other that does not tight bounds on the range of load bearing capacity are presented for various types of simple critical points by means of the asymptotic theory of statistics we show the inefficiency of a conventional random method that approximates the minimum loadhearing capacity by the minimum load for a number of random initial imperfections the theoretical and empirical probability distribution functions for simple truss structures are compared to show the validity and effectiveness of the present method

on random imperfections for structures of regular polygonal symmetry a theoretical study is made on the effect of random initial imperfections on the load bearing capacities of structures of regular polygonal symmetry the group theoretic method is employed to implement the symmetry in the formulation in view of the concept of critical initial imperfection the explicit form of probability density function of the load bearing capacity of structures is derived for random initial imperfections in particular tight bounds on the range of load bearing capacity are presented for various types of simple and double critical points the theoretical and empirical probability distribution functions are compared for simple truss structures to show the validity and effectiveness of the present method

second order oscillation of forced functional differential equations with oscillatory potentials new oscillation criteria are established for second order differential equations containing both delay and advanced arguments of the form k t x t p t x t t a 1x t t q t x s t b 1x s t e t t 0 where a 1 and b 1 k p q e t s are continuous real valued functions k t 0 is nondecreasing t and o are nondecreasing t t t s t t and lim t t t the potentials p q and e are allowed to change sign and the information on the whole half line is not required as opposed to the usual case in most articles among others as an application of the results we are able to deduce that every solution of x t m 1sintx t p12 m 2costx t p6 cos2t m 1 m 2 0 is oscillatory provided that either m 1 orm 2 is sufficiently large

necessary and sufficient conditions for oscillations of second order neutral equations consider the neutral delay differential equation d2dt2 y t py t qy t 0 1 where p q r and r we proved that eq 1 oscillates if and only if the characteristic equation 2 2pe qe 0 has no real roots

probabilistic eigenvalue buckling analysis solved through the ratio of polynomial response surface an efficient procedure for the reliability analysis of frame structures with respect to the buckling limit state is proposed under the assumption that no imperfections are present and that the elastic parameters are uncertain and modeled as random variables the approach allows a deeper investigation of structures which are not sensitive to imperfections the procedure relies on a response surface method adopting simple ratio of polynomials without cross terms as performance function such a relationship approximates analytically the dependence between the buckling load and the basic variables furnishing a limit state equation which is very close to the exact one when a proper experimental design is adopted in this way a monte carlo simulation applied to the response surface leads to a good approximation with low computational effort several numerical examples show the accuracy and effectiveness of the method varying structural complexity correlation between basic variables and their distribution

a necessary and sufficient condition for the oscillation of neutral equations abstract consider the neutral differential equation d dt y t py t qy t 0 t t 0 where p q and are real numbers then a necessary and sufficient condition for the oscillation of is that the characteristic equation p e qe 0 has no real roots

existence for bounded positive solutions of schrodinger equations in two dimensional exterior domains in this paper by using the fixed point theory under quite general conditions on the nonlinear term we obtain an existence result of bounded positive solutions of schrodinger equations in two dimensional exterior domains

lower bounds to the performance of bit synchronization for bandwidth efficient pulse shaping bandwidth efficient signaling requires using pulse shaping that inherently has intersymbol interference isi except when the timing is perfect several lower bounds to the mean square error mse of non data aided bit synchronizers are derived for this case the optimal lower bound is derived using the maximum likelihood ml criterion for a sequence of binary pulse amplitude modulated pulses in the presence of isi and gaussian noise this lower bound is used as a benchmark to evaluate the performance of other synchronizers in a practical scenario it is shown that a previous lower bound based on the isi free ml synchronizer cannot be used to lower bound the mse of bit synchronizers a detection theory bound dtb also called ziv zakai bound is applied to the symbol timing recovery problem in the presence of isi and it is shown that this bound is a tight lower bound on the mse of the ml synchronizer a simple lower bound on this dtb is derived and it is shown that the simple bound is almost as tight as the well known modified cramer rao bound mcrb at moderate values of snr while it does not suffer from the shortcomings of the mcrb at small values of snr

statistics of normally distributed initial imperfections abstract this paper offers a theoretical study on the probabilistic nature of critical loads buckling loads of structures subject to normally distributed initial imperfections explicit form of probability density function of critical loads are derived for various types of critical points double bifurcation points of structures with regular polygonal symmetry are dealt with by means of the group theoretic bifurcation theory the distribution of minimum values of the critical loads is investigated to present a statistical design index the theoretical and empirical probability density functions for simple structures are compared to show the validity and effectiveness of this method the method is quite efficient when it is directly applicable otherwise the explicit forms at least can greatly supplement the inefficiency of the conventional random method

composite bound on the attainable mean square error in passive time delay estimation from ambiguity prone signals corresp the location of a radiating source can be determined by measuring the relative time delay of its signal wavefront to several spatially separated receivers a new technique is presented to investigate the performance of time delay measurement schemes based on a modified version of the ziv zakai lower bound this technique is shown to yield a tight bound on the attainable mean square measurement error for any prespecified signal to noise ratio conditions

the modified cramer rao bound and its application to synchronization problems we introduce the modified cramer rao bound crb which like the true crb is a lower bound to the error variance of any parameter estimator the modified crb proves useful when in addition to the parameter to be estimated the observed data also depend on other unwanted parameters the relationship between the modified and true crb is established and applications are discussed regarding the estimation of carrier frequency offset carrier phase and timing epoch in linearly modulated signals modified crbs for phase and timing estimation have been already discussed in previous works where it is shown that several practical carrier phase and clock recovery circuits do attain such bounds frequency discrimination instead is not so well represented in the literature and a significant contribution of this paper is the calculation of the modified crb for frequency estimation this bound is compared with the performance of some frequency detectors and it is concluded that further work is needed in search of more efficient frequency discrimination methods

oscillation theorems of nth order functional differential equations with forcing terms where a p q g h f r a co r are continuous b p t 0 q t 0 g r h t are nondecreasing c g t t and g t co as t co a function x t e cc 00 is called oscillatory if x t has arbitrarily large zeros in to co to o otherwise x t is called nonoscillatory we provide sufficient conditions for the above functional differential equations to be almost oscillatory in the sense that every solution x t of l 2 and 3 is either oscillatory or else it satisfies lim m x t 0 06i n 1

extended ziv zakai lower bound for vector parameter estimation the bayesian ziv zakai bound on the mean square error mse in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than mse the extended bound is evaluated for some representative problems in time delay and bearing estimation the resulting bounds have simple closed form expressions and closely predict the simulated performance of the maximum likelihood estimator in all regions of operation

analysis on evolution pattern of periodically distributed defects a similar pattern is formed in various materials when periodically distributed defects evolve mathematically this pattern formation is understood as the consequence of symmetry breaking while physically it is caused by interaction effect which vary depending on materials or defects in examining the nature of the interaction effects this paper analyzes the bifurcation induced growth of a periodic array of defects with the aid of group theoretic bifurcation analysis it is clearly shown that when the uniform pattern the evolution of all defects is broken only the alternate pattern the evolution of every second defect can take place for smaller defects as often observed in nature therefore two defects should be considered to examine a possible bifurcation of periodic defects furthermore the conclusion obtained can be extended to explain the phenomena whereby every second fourth and then eighth defect continue to evolve and whereby alternate bifurcation is repeated successively until the evolution is localized

a note on nasr s and wong s papers abstract in the case of oscillatory potentials we give sufficient conditions for the oscillation of the forced nonlinear second order differential equations with delayed argument in the form x t q t x t sgn x t f t in the linear 1 and the superlinear 1 cases

an oscillation criterion for second order sublinear differential equations abstract an oscillation criterion is given for the second order sublinear differential equation y a t f y 0 where a t is not assumed to be non negative and f y is non decreasing in y and yf y 0 for y 0 f y also satisfies a sublinear condition which includes the special case f y y y sgn y 0 this result extends earlier oscillation theorems of philos and the first author

oscillations of second order neutral functional differential equations abstract consider the second order neutral functional differential equation d 2 dt 2 x t n i 1 n i x t t i m j 1 j x t j 0 where 1 i i j and j i 1 2 n j 1 2 m are real numbers some new oscillation criteria are given for oscillation of e the results of this paper improve noticeably some known results

systematic description of imperfect bifurcation behavior of symmetric systems abstract a systematic method is presented for describing experimental curves of force vs strain of a system with regular polygonal dihedral group symmetry subject to bifurcation behavior with an aim toward overcoming the following problems 1 it is difficult to judge whether the system is undergoing bifurcation or not 2 the perfect behavior of the system cannot be known due to the presence of initial imperfections 3 those curves are often qualitatively different from bifurcation diagrams predicted by mathematics the tools employed are the asymptotic theory for imperfect bifurcation such as the koiter law and the stochastic theory of initial imperfections the former theory is extended in this paper to the system with regular polygonal symmetry to present asymptotic laws for recovering perfect curves with reference to the experimental ones these laws are formulated for physically observable displacements instead of the variables in the mathematical bifurcation diagrams in order to make them readily applicable to the experimental curves the stochastic theory is combined with an asymptotic law to develop a means to identify the multiplicity of the bifurcation point the systematic method for describing the experimental curves developed in this manner is applied to the bifurcation analysis of regular polygonal truss domes to testify its validity furthermore this method is applied to the shear behavior of cylindrical sand specimens to show that they in fact are undergoing bifurcation and in turn to demonstrate the importance of a viewpoint of bifurcation in the study of shear behavior of materials the need of a dual viewpoint of bifurcation and plasticity in the study of constitutive relationship of materials is emphasized to conclude the paper

three dimensional stochastic finite element method for elasto plastic bodies a new stochastic finite element method sfem is formulated for three dimensional softening elasto plastic bodies with random material properties the method is based on the karhunen loeve and polynomial chaos expansions and able to efficiently estimate complete probabilistic characteristics of the response such as moments or pdfs to reduce the computational complexity in the three dimensional setting two alterations are made with respect to the two dimensional sfem proposed earlier by the authors first a variability preserving modification of the karhunen loeve expansion is rigorously derived and applied in the stochastic discretization of random fields representing material properties second an efficient algorithm for parallel processing is developed with time consumption being the same order as for an ordinary fem rendering the proposed sfem an effective alternative to monte carlo simulation the applicability of the proposed method to stochastic analysis of strain localization is examined using monte carlo simulation then it is applied to a fault formation problem which is a recent concern of earthquake engineering ground surface layers are modelled by a softening elasto plastic body and the evolution of probabilistic characteristics of the rupture process is analysed in detail some practical observations are made regarding the nature of the fault formation from the stochastic viewpoint copyright 2001 john wiley sons ltd

a necessary and sufficient condition for the solutions of a functional differential equation to be oscillatory or tend to zero abstract it is shown that every solution of the nonhomogeneous functional differential equation d dt x t px t q t g x t f t wheref q c t 0 0 0 p 0 forx 0 gis nondecreasing lipschitzian and satisfy a sublinear condition 0 k dx g x and f s ds is either oscillatory or tends to zero asymptoticallyif and only if t q s ds

oscillation theorems for second order neutral functional differential equations some new oscillation criteria are given for second order neutral functional differential equations of the form d 2dt 2 x t lx t t mx t s qx t a px t b 0 where l t m s p and q are real numbers and a and b are real positive constants

existence for nonoscillatory solutions of second order nonlinear differential equations abstract in this paper the existence of nonoscillatory solutions of the second order nonlinear neutral differential equation r t x t p t x t i 1 m q i t f i x t i 0 t t 0 where m 1 is an integer 0 i 0 r p q i c t 0 r f i c r r i 1 2 m are studied some new sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for general p t and q i t i 1 2 m which means that we allow oscillatory p t and q i t i 1 2 m in particular our results improve essentially and extend some known results in the recent references

necessary and sufficient conditions for the oscillation of forced nonlinear second order differential equations with delayed argument abstract for a special class of the external force g t and nonnegative potential a t we give necessary and sufficient conditions for the oscillation of all solutions of a nonlinear second order forced differential equation with delayed argument of emden fowler type in the form x t a t x t sgn x t g t in the superlinear 1 and the sublinear cases

cramer rao bound on timing recovery of linearly modulated signals with no isi a new cramer rao lower bound for symbol timing recovery of linearly modulated quadrature amplitude modulation signals is presented contrary to some other works on the subject the transmitted data is assumed to be unknown at the receiver the bound is derived from a likelihood function that includes the symbol randomness for large number of symbols the bound is achievable at any signal to noise ratio the separation of symbol timing recovery and phase recovery schemes is investigated using the new results it is shown that the separation of these operations causes a degradation of less than 0 3 db compared to joint phase and timing recovery the bound is derived for symbol shaping limited to a single symbol length i e no intersymbol interference simulations for longer pulse shapes demonstrate that the new results provide better performance prediction than other known techniques

new oscillation criteria for a class of second order nonlinear forced differential equations abstract by using classical variational principle and averaging technique new oscillation criteria are established for second order nonlinear forced differential equations r t x t x t q t f x t e t t t 0 where the functions r q e c t 0 r and f c r r improve and extend some recent results

oscillation criteria for second order nonlinear differential equations with impulses abstract the present paper is devoted to the investigation of the oscillatory behavior of a kind of extensively studied second order nonlinear delay differential equations with impulses some interesting results are obtained which illustrate that impulses play a very important role in giving rise to the oscillations of equations

a sublinear oscillation theorem abstract an oscillation criterion is given for the second order nonlinear differential equation y a t y 0 where a t is continuous but is not assumed to be non negative for all large values of t and y is non decreasing in y and satisfies y y 0 for y 0 this result generalizes a recent extension of belohorec s theorem due to kwong and wong and also incorporates an earlier result of coles

oscillation of sublinear second order differential equations with integrable coefficients abstract an oscillation criterion is given for the second order sublinear differential equation y a t f y 0 where a t c 0 and f y c is nondecreasing with yf y 0 for y 0 and also satisfies a sublinear condition which covers the special case f y y sgn y 0 the coefficient a t is allowed to be negative for large values of t and its integral over the nonnegative reals is finite this result extends an earlier oscillation theorem of kwong and wong for the special case

finite symmetric systems and their analysis abstract symmetry of linear mechanical systems permits one to substantially reduce the effort in their analysis classification and structural analysis of the finite linear symmetric systems models are studied in this paper there are two variants of the symmetry approach mechanical and algebraic in accordance with the former a symmetric system is replaced by one or several small nonsymmetric subsystems which are subjected to special loads obtained from the initial set the total response of the original symmetric system is found by special superposition of partial responses of these subsystems the algebraic approach is based on the explicit block diagonal decomposition of the matrix equation corresponding to a symmetric system while both approaches have the same efficiency the latter is easier to implement and describe it is presented here the condtions under which the symmetry technique may be utilized do not include symmetry of the applied loads specifically symmetry of those loads which form the right side of the associated equations nevertheless if the loads are symmetric the efficiency of the symmetry approach substantially increases group theory which is widely used in this paper is the mathematical tool for the study of symmetry and all necessary notions are introduced

bifurcation hierarchy of a rectangular plate abstract the mechanism of the complex recursive bifurcation behavior of a four sides simply supported rectangular plate is investigated such complex behavior is due to the hidden symmetry of the plate associated with the periodic nature of the solutions the group theoretic bifurcation theory is employed to arrive at a lattice of subgroups which expresses the rule for the behavior this rule is shown to suffer degeneration due to the restriction by the boundaries compared with that of geometrical symmetry the governing equation of this plate is discretized by means of galerkin s method with the use of the double fourier series as shape functions the tangential stiffness matrix of the plate is shown to be block diagonalized by appropriately permuting the order of the fourier series following the rule presented the bifurcation analysis of the plate is carried out to assess the validity of the rule and to demonstrate the merit of the block diagonalization as a result of this the vital role of the bifurcation rule in the proper understanding and successful analysis of the complex bifurcation behavior has been demonstrated

oscillation criteria for forced first order neutral differential equations with variable coefficients abstract necessary and sufficient conditions are obtained so that every solution of y t p t y t q t g y t f t is oscillatory or tends to zero or to as t the problem is considered in various ranges for p t

oscillation criteria for second order sublinear differential equation abstract the basic purpose of this paper is to present a new oscillation criteria for second order sublinear differential equation a t x t x t q t t 0 t t 0 0 where a a c 1 t 0 is positive function q c t 0 has no restriction on its sign c 1 r are such that x 0 x x 0 for x 0

oscillation criteria for certain forced second order nonlinear differential equations with delayed argument some new sufficient conditions for the oscillation criteria are given for the forced second order nonlinear differential equations with delayed argument in the form x t q t f x t t e t the results are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our methodology is somewhat different from that of previous authors our results generalize and extend some earlier results of sun 1 furthermore we are able to answer the question in recent paper 1 for the oscillation of bounded solutions of the above equation when f x x lsgn x 0 l 1

oscillatory behavior of higher order nonlinear neutral forced differential equations with oscillating coefficients in this paper the higher order nonlinear neutral forced differential equations of the form x t p t x t t n i 1mq i t f i x s i t s t t t 0 where n m n n 2 and m 1 are studied a new necessary and sufficient theorem for the oscillation of bounded solutions and a sufficient criterion for the existence of bounded positive solutions of the above equations are obtained for general p t and s t in particular our results improve some known results

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

frequency domain interpretation of the cramer rao bound for carrier and clock synchronization the cramer rao bound is a fundamental lower bound on the variance of unbiased estimates applied to carrier phase and clock phase synchronization for digital communications it is shown that the corresponding bounds can be derived from the power density spectrum of the transmitted signal irrespective of the particular modulation scheme this allows the localization of the available information about the parameters in the frequency domain if the incoming signal is only partly exploited the resulting performance loss is now easily attainable

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

stability of a critical nonlinear neutral delay differential equation abstract this work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation a critical value of the coefficients is considered where only few results are known the difficulty follows from the fact that the spectrum of the linear operator is asymptotically closed to the imaginary axis an analysis based on the energy method provides new results about the asymptotic stability of constant and periodic solutions a complete analysis of the stability diagram is given in the linear homogeneous case under periodic forcing existence of periodic solutions is discussed involving a diophantine condition on the period of the source

oscillation of difference systems of the neutral type the authors consider the nonlinear difference systems d x n a nx s n p ng y n dy n dq nf x t n n n n 0 where d 1 a n p n and q n are real sequences s n and t n are real non negative sequences of integers and f g r r are continuous with uf u 0 and ug u 0 for u 0 the authors obtain sufficient conditions for all solutions of the system to be oscillatory examples to illustrate the results are included

a lower bound on the mean square error of symbol timing recovery for nrz rectangular signals in this paper which is based on previous work see ibid vol 40 p 1635 1992 a closed form lower bound on the mean square error of symbol timing recovery is reported for nrz rectangular pulse sequences the bound is a function of the fundamental parameters e sub b the symbol energy and n sub 0 the noise power spectral density

positive solutions of second order differential equations we prove a nonoscillation result for second order nonlinear ordinary differential equations an application to the schrodinger equation is also given c 2004 elsevier ltd all rights reserved

the existence and uniqueness of positive monotone solutions for a class of nonlinear schrdinger equations on infinite domains in this paper by constructing a new weighted norm method and analysis technique we establish the conditions for the existence and uniqueness of positive monotone solutions to a class of nonlinear schrdinger equations in planar exterior domains some examples are also given to demonstrate the application of our main results

on the application of the cramer rao and detection theory bounds to mean square error of symbol timing recovery a modified cramer rao bound is derived that takes account of the fact that the symbol timing estimate is restricted to a finite interval of one symbol duration a detection theory bound is also applied to the symbol timing problem results obtained using the cramer rao and detection theory bounds are compared it is shown that the detection theory bound is superior to the traditionally used cramer rao bound in particular the detection theory bound gives useful results for sharp pulse shapes and shows a dependence of the mean square error on the data sequence it also yields meaningful results for small signal to noise ratios

bifurcation hierarchy of symmetric structures abstract a group theoretic method for the analysis of bifurcation behavior of regular polygonal symmetric structures is described possible bifurcation paths and points of these structures are categorized in terms of dihedral and cyclic groups which express the symmetry in particular we offer a complete description of those double bifurcation points which occur due to group symmetry the type the number and the stability of bifurcation paths branching at these points are determined by deriving bifurcation equations the existence of a potential function plays a substantial role for the existence of bifurcation paths as a result of these all possible bifurcation process can be known a priori as a natural consequence of bifurcation hierarchy before actual numerical analysis an implementation of this method in numerical analysis shows its validity and usability

existence of global positive solutions of semilinear elliptic equations abstract using a very simple approach we prove the existence of asymptotically vanishing global positive solutions of the semilinear elliptic equation u f x u g x x u 0 in all of r n n 3 in particular earlier conditions on the negative part of the function f are dropped

bifurcation mechanism underlying echelon mode formation abstract this paper presents a theory on the underlying mathematical mechanism of the echelon mode a series of parallel short wrinkles that looks like a flight of stairs or wild geese arranged in formation which has been observed ubiquitously with uniform materials but which has long denied successful numerical simulations it is shown by means of the group theoretic bifurcation theory that the echelon mode formation can be explained as a recursive secondary tertiary symmetry breaking bifurcation if o 2 o 2 is chosen as the underlying symmetry to model the local uniformity of materials this implies for example that the use of periodic boundaries is essential to successfully realize the oblique stripe patterns and the subsequent echelon mode formation in numerical simulations in fact a recursive bifurcation analysis of a rectangular domain with periodic boundaries subject to uniform uniaxial compression yields various kinds of patterns such as diamond stripe and echelon modes which are often observed for materials under shear

on the performance limits of data aided synchronization this paper addresses data aided da synchronization in which the reference parameter acquisition is aided by a training sequence known to the receiver the cramer rao lower bound crb for the da timing and or carrier phase recovery is presented for da parameter estimation the crb typically varies with the training sequence this indicates that different training sequences offer fundamentally different performance in the literature the widely cited closed form crb for timing and carrier phase recovery was derived under the assumption that the training sequence is independent and identically distributed i i d and sufficiently long we derive a closed form crb for timing and carrier phase recovery with respect to an arbitrary training sequence and pulse shaping function for the over and under sampling cases it turns out that the crb is a weighted summation of the aperiodic correlation of the training sequence and the weighting factor is determined by the pulse shaping filter therefore this paper reveals the fundamental link between a training sequence and its corresponding performance limit

echelon modes in uniform materials abstract the mechanism of the echelon mode a series of parallel short wrinkles of soils that looks like a flight of stairs or wild geese arranged in formation observed in the triaxial compression test is revealed by means of the group theoretic bifurcation theory the study of the direct bifurcation of uniform materials in cylindrical domains with periodic boundaries has revealed the existence of various kinds of deformation patterns in particular a classical diamond checkerboard pattern solution and a pair of oblique stripe pattern solutions simultaneously branch at a bifurcation point of multiplicity four with the use of the periodic boundaries these oblique stripe solutions which cannot be directly obtained by the customary bifurcation analysis with non periodic boundaries have thus been made accessible the secondary bifurcation from these stripe solutions realizes the echelon mode the triaxial compression tests on soil specimens have demonstrated that the pattern of wrinkles shear bands and echelon modes of the specimens do indeed follow the present theory and can be understood as a natural consequence of pattern selection or in other words symmetry breaking bifurcation

on the asymptotic integration of nonlinear differential equations the aim of the present paper is twofold firstly the paper surveys the literature concerning a specific topic in asymptotic integration theory of ordinary differential equations the class of second order equations with bihari like nonlinearity secondly some general existence results are established with regard to a condition that has been found recently to be of significant use in the theory of elliptic partial differential equations

necessary and sufficient conditions for oscillations of neutral differential equations abstract consider the neutral delay differential equation x t px t qx t 0 t t 0 where q and are positive constants while p is a real parameter then a necessary and sufficient condition for all solutions of to oscillate is that the characteristic equation p e qe 0 of has no real roots

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

a picture of the global bifurcation diagram in ecological interacting and diffusing systems abstract this paper concerns global phenomena of pattern formation in stationary reaction diffusion equations possessing turing s diffusion induced instability which appear typically in mathematical biology global bifurcation diagrams with respect to two diffusion parameters are presented by integrating two complementary approaches analytical and numerical simple and double bifurcation analysis using group theoretic methods for the compact lie group d x results from singular perturbations when one diffusion constant is sufficiently small and a global existence theorem on primary bifurcated branches when the other diffusion is sufficiently large are the main analytical results a new numerical method is used to trace all bifurcating branches we examine interrelations between those local and semi global results under the light of global pictures obtained by numerical studies a variety of interesting and new diagrams near double eigenvalues are observed coexistence of multiple stable stationary states and global extension and deformation of local double structures are one of the main conclusions

critical initial imperfection of structures abstract a method is introduced for determining the critical initial imperfection of discretized structures that decreases the load bearing capacity most rapidly the effects of imperfections on simple critical points such as limit points of loads and simple bifurcation points are theoretically investigated based on the idea of the lyapunov schmidt decomposition developed in bifurcation theory imperfection sensitivity varies with the types of points nonetheless critical imperfection pattern is expressed in the same formula regardless of the types among various imperfections the most influential can be found in a quantitative manner the validity and the usability of the proposed method are illustrated through its application to simple example structures

interval oscillation of second order functional differential equations with oscillatory potentials abstract interval oscillation criteria are established for second order differential equations of the form e k t x t p t x g t q t x g t 1 x g t e t t 0 where 1 k p q e and g are continuous real valued functions k t 0 is nondecreasing g t is nondecreasing lim t g t we consider g t t and g t t separately illustrative examples are included

oscillations of mixed neutral functional differential equations abstract in this paper we establish several sufficient conditions for the oscillation of solutions of mixed neutral functional differential equations of the form d n dt n x t cx t h cx t h qx t g qx t g 0 where c c g g h and h are real constants and q and q are nonnegative real constants

on the existence of asymptotically decaying positive solutions of second order neutral differential equations abstract the existence of positive solutions of second order neutral differential equation x t cx t p t x g t 0 t t0 is investigated some sufficient conditions are given for the existence of positive solutions with asymptotic decay of for the cases of constant sign and nonconstant sign of coefficients it also is shown that one of these sufficient conditions is necessary

global existence of solutions with prescribed asymptotic behavior for second order nonlinear differential equations where the nonlinearity f satis9es certain monotonicity conditions speci9ed in the sequel we always assume without mentioning that the function f t u v is continuous in the domain d t u v t t0 u v r where t0 1 it is supposed also that all equations and inequalities involving t hold for t t0 unless otherwise speci9ed the symbols o and o have their standard meanings as t and we use the notation r def 0 eq 1 is often used for mathematical modelling of various physical chemical and biological systems and attracts constant interest of researchers a great deal of papers published during the last three decades are concerned with local and global existence of solutions of eq 1 and its numerous particular cases uniqueness of solutions

basic existence uniqueness and approximation results for positive solutions to nonlinear dynamic equations on time scales abstract this paper focuses on the qualitative and quantitative properties of solutions to certain nonlinear dynamic equations on time scales we present some new sufficient conditions under which these general equations admit a unique positive solution these positive and hence non oscillatory solutions extend across unbounded intervals and tend to a finite limit as the independent variable becomes large and positive our methods include banach s fixed point theorem including the method of picard iterations and weighted norms and metrics in the time scale setting due to the wide ranging nature of dynamic equations on time scales our results are novel for ordinary differential equations for difference equations for combinations of the two areas and for general time scales this is demonstrated via some examples furthermore we state an open problem of interest

critical imperfection of symmetric structures a method is presented to determine the critical most unfavorable initial imperfection of structures of regular polygonal symmetry denoted by dihedral groups a critical point of such structures is either simple or forced to be double by the symmetry and the group representation theory is employed to deal with the degeneracy due to symmetry the method is developed further to incorporate the symmetry of imperfections in many cases of practical interest the critical imperfection is given explicitly as the product of imperfection sensitivity matrix and the critical eigenvector it is shown that the symmetry in the critical eigenvectors of the tangent stiffness matrix is inherited to the symmetry in the critical imperfection mode

oscillation of second order nonlinear neutral differential equations abstract in this paper some sufficient conditions for oscillation and nonoscillation are obtained for the second order nonlinear neutral differential equation x t p t x t q t f x t 0 t 0 where 0 p t 1 q t 0 0