orthogonalization process by recurrence relations an orthogonalization process is proposed applicable to spaces which are realizations of abstract hilbert space it is simpler than the gram schmidt process a recurrence relation which orthogonalizes a physical space is proposed and it is shown that the generalized langevin equation is contained therein this process serves as a basis for understanding the nature of the dynamic many body formalism

initial value problems for systems of integrodifferential equations in banach spaces in this paper by the use of new comparison results and mixed monotone iterative techniques the existence of solutions of initial value problems for systems of integrodifferential equations in banach spaces is discussed the results obtained in this paper generalize and improve the results corresponding to those obtained by others our result is new even in finite dimensional spaces

on the solvability of periodic boundary value problems with impulse in this work we obtain some new results concerning the existence of solutions to an impulsive first order nonlinear ordinary differential equation with periodic boundary conditions the ideas involve differential inequalities and schaefer s fixed point theorem

blind multiuser detection from moe to subspace methods the minimum output energy moe multiuser receiver has been shown to approach the minimum mean square error mmse receiver at high signal to noise ratio snr however performance degradation is incurred by noise induced channel estimation error in this paper we propose a power of r por technique to significantly improve the performance of the moe receiver it is shown that the new receiver asymptotically converges to the mmse receiver without performance penalty the convergence is established either under high snr with large exponent raised in the power of the covariance matrix or with sufficiently large number of data samples connection between our por method and a widely studied subspace method is investigated from the respective optimization criteria asymptotic equivalence between these two methods is also established extensive simulations based on finite data samples show that the proposed method significantly outperforms the subspace method in systems with medium to heavy loading severe multipath distortion or smaller processing gain moreover adaptive implementation of the proposed method exhibits very robust performance in a dynamic loading environment

dimensionality dependence of dynamical correlations exact results from a quantum many body system using one of the simplest model interacting quantum many body systems it is shown that the relaxation function behaves remarkably differently at low temperatures depending upon whether the lattice dimensionality of the system d t t c in quantum many body systems

performance of blind and group blind multiuser detectors in blind or group blind linear multiuser detection the detector is estimated from the received signals with the prior knowledge of only the signature waveform of the desired user or the signature waveforms of some but not all users the performance of a number of such estimated linear detectors including the direct matrix inversion dmi blind linear minimum mean square error mmse detector the subspace blind linear mmse detector and the form i and form ii group blind linear hybrid detectors are analyzed asymptotic limit theorems for each of the estimates of these detectors when the signal sample size is large are established based on which approximate expressions for the average output signal to interference plus noise ratios sinrs and bit error rates bers are given to gain insights on these analytical results the performance of these detectors in an equicorrelated code division multiple acces cdma system is compared examples are provided to demonstrate the excellent match between the theory developed here and the simulation results

variational methods to the second order impulsive differential equation with dirichlet boundary value problem in this paper we study the existence of solutions for a class of second order impulsive differential equation by using the critical point theorem of y jabri and an even functional theorem we give some new criteria to guarantee that the impulsive differential equation has at least one solution infinitely many solutions under the assumption that a nonlinear term satisfies sublinear superlinear asymptotically linear respectively some recent results are extended and conditions of assumptions are simplified finally some examples are presented to illustrate our main results

on dynamic equations with deviating arguments abstract in this paper we study the existence of solutions of dynamic equations with deviating arguments on time scales we formulate sufficient conditions under which such problems have a minimal and a maximal solution in a corresponding region bounded by upper lower solutions

spin dynamics of the quantum xy chain and ladder in a random field abstract we investigate the hamiltonian dynamics of two low dimensional quantum spin systems in a random field at the infinite temperature limit the xy chain and the two leg xy ladder with interchain ising interactions we determine the longitudinal spin autocorrelation functions of the spin 1 2 xy chain and ladder in the presence of disordered fields by using the method of recurrence relations the first six basis vectors for the chain and the first four basis vectors for the ladder of the dynamic hilbert spaces of jz t as well as the corresponding recurrents and moments of the time dependent autocorrelation function are analytically computed for bimodal distributions of the fields we did find a remarkable result in the disordered models cases with a fraction of p sites under field bb and a fraction of 1 p sites under the field ba have the same longitudinal dynamics as those with p sites under field ba and 1 p sites under the field bb we also find that both the xy chain and the two leg xy ladder with ising interchain coupling in the presence of random fields are sensitive to the percentage of disorder but not to the intensity of the fields

dynamics of a transverse ising model with four spin interactions abstract we report the first study of the dynamics of a transverse ising model with four spin interactions we consider finite chains of increasing size in order to determine the time dependent correlation function as well as the longitudinal relaxation function of the infinite chain up to 8 exact 5 approximate moments of the infinite chain were also obtained the correlation function is oscillatory for large values of the transverse field and is monotonically decreasing for small values of the transverse field the system undergoes a crossover from a collective mode excitation regime to a central mode type of dynamics as the strenght of field is lowered the present model does not allow gaussian decay for the correlation function

heisenberg langevin and current equations via the recurrence relations approach some years ago the heisenberg equation of motion was formally solved by the recurrence relations approach it is shown here that the langevin equation represents a structural property of the recurrence relations the langevin equation is useful for studying the time evolution of the current the resulting current current correlation function is compared with luttinger s phenomenological theory geometric interpretations are made for the conductivity and the dielectric function

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

ruelle resonances in kicked quantum spin chain abstract we study exponential decay of high temperature time correlation functions in a non integrable quantum spin chain problem namely ising spin 1 2 chain kicked with tilted homogeneous magnetic field for this purpose we define a master propagator over a suitable banach space of quantum observables quantum many body analogue of perron frobenius operator whose leading eigenvalue determines the asymptotic decay of correlations this is demonstrated with explicit calculation for which a fast algorithm for the construction of the master propagator is developed

on the relaxation of fluctuations in the steady state of the stratonovich model a detailed investigation has been carried out of the relaxation of fluctuations in the steady state of the stratonovich model also known as the random growing rate model the autocorrelation time of this system driven by parametric white noise in the linear term has been measured for an electronic circuit model computed by digital simulation and calculated by use of a continued fraction expansion method the results are all consistent with each other and with those obtained from the matrix continued fraction method of jung and risken 1985 provided that explicit account is taken of the ways in which any macroscopic real physical system is bound to differ from the idealisation represented by the original form of the stratonovich model in particular it is necessary to recognise the existence of weak additive noise and a small additive constant the physical origins of some earlier seemingly discrepant calculations and experimental data are discussed

dynamics of the independent oscillator io model in the einstein and pseudo debye limits abstract the independent oscillator model is thought to be a simple model for brownian motion explored extensively by ford lewis and o connell this model does not specify the distribution of the oscillators frequencies by considering the distribution to be of two standard limits otherwise preserving the hermiticity of the model we obtain the memory function exactly by the method of recurrence relations in one limit the memory function is purely oscillatory while in the other limit it shows a decreasing amplitude with an oscillation relevance to transport theory is briefly pointed out

gronwall bellman type nonlinear delay integral inequalities on time scales abstract in this paper some gronwall bellman type nonlinear delay integral inequalities on time scales are established which provide a handy tool in deriving boundedness of solutions of certain delay dynamic equations on time scales our results generalize some of the main results in lipovan 2006 1 pachpatte 2000 2 ferreira and torres 2009 3 zhang and meng 2008 4 cheung and ren 2006 5 kim 2009 6 and some of our results unify continuous and discrete analysis in the literature

asymptotically near optimal blind estimation of multipath cdma channels in this paper correlation matching techniques are applied to estimate multipath code division multiple access cdma channels we arrange unknown multipath parameters for each of j active users in a vector then the output correlation matrix is parameterized by j unknown rank one matrices with each one formulated from the corresponding channel vector this correlation matrix is further compared with its sample average the resulting error can be first minimized to obtain unbiased estimates of j unknown rank one matrices in closed forms thus our estimator for each channel vector is derived by singular value decomposition svd on the associated rank one matrix within a scalar ambiguity it turns out that the performance of our estimator can be improved by introducing an asymptotically optimal weighting matrix in our cost function this weighting matrix can be estimated directly from data samples only with a small penalty on the asymptotic performance the asymptotic covariance of our estimator is also derived and can be compared with the cramer rao lower bound both in closed forms simulation results show the applicability of the proposed methods and consistency with our theoretical analysis

solving the liouville equation for conservative systems continued fraction formalism and a simple application abstract there are very few formalisms available to solve the liouville equation for energy conserved systems the continued fraction formalism introduced through the works of zwanzig mori kubo lee grigolini and others is described here a detailed discussion is presented on ways to apply the continued fraction formalism to solve for relaxation functions and for the dynamical variable itself for a simple and exactly solvable quantum spin system

multiuser detection in mismatched multiple access channels we consider an additive white gaussian noise multiple access channel and investigate the performance degradation of several multiuser detectors due to imperfect knowledge of the channel parameters induced by either estimation errors or sampling quantization of the receiver s sufficient statistics the symbol error rates and the asymptotic multiuser efficiencies ames of these detectors are examined as functions of both true and approximated channel parameters for 2 asynchronous users the results quantify the loss of near far resistance due to parameter estimation errors and demonstrate that detectors which are optimal for ideal conditions are often more sensitive to parameter mismatch examples are given which illustrate a reverse ordering of the symbol error rates for these detectors in the high signal to noise regime and also illustrate cases when the conventional matched filter detector exhibits superior performance over multiuser detectors

global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics in this paper we shall consider the following nonlinear impulsive delay differential equation x t v t x t xn t m n xn t m t a e t 0 t tk x tk 1 1 bk x tk k 1 2 where m and n are positive integers v t and t are positive periodic continuous functions with period 0 in the nondelay case m 0 we show that the above equation has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate periodic impulsive perturbations the impulsive delay equation shown above preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

fluctuation dissipation dispersion relation and quality factor for slow processes a generalization of the callen welton formula for systems with slowly varying parameters is given using the momentum method and the time multiscale technique it is shown that not only the dissipation but also the dispersive contributions determine the spectral function of the fluctuations in these systems the general formalism is illustrated for an oscillating electrical circuit and the influence of the dispersion contributions on the quality factor of the system is discussed

transition behaviour in the asymptotic long time limit and theoretical approach to explore the two different long time limit behaviours decaying and non decaying to zero for t of a dynamical quantity we present a theoretical approach which analyses a continued fraction cf representation of the quantity on the basis of our analysis we show that the two asymptotic behaviours are characterized by a structure of cf coefficients and that there exists a certain condition that determines the transition between the two limits in addition a measure is introduced to predict the transition we apply our theory to various systems to confirm its validity the nondecay behaviour involves a kind of feedback process in a dynamical system the appearance of a dynamical similarity near the transition is discussed

initial value problem for first order integro differential equation of volterra type on time scales abstract in this paper we combine the monotone iterative technique with fixed point theory to investigate the extremal solutions of nonlinear integro differential equations on time scales several important lemmas and existence criteria are obtained

statistical performance analysis of the algebraic constant modulus algorithm this paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm acma method for blindly separating constant modulus sources this can be used to predict the signal to interference plus noise ratio sinr performance of these beamformers as well as their deviation from the nonblind wiener receivers to which they asymptotically converge the analysis is based on viewing acma as a subspace fitting optimization where the subspace is spanned by the eigenvectors of a fourth order covariance matrix the theoretical performance is illustrated by numerical simulations and shows a good match

generalized gronwall bellman type delay dynamic inequalities on time scales and their applications abstract in this paper we establish some new gronwall bellman type delay dynamic inequalities on time scales which can be used as a handy tool in the investigation of qualitative as well as quantitative analysis of solutions of delay dynamic equations on time scales our results generalize the main results of ou iang l ou iang the boundedness of solutions of linear differential equations y a t y 0 shuxue jinzhan 3 1957 409 415 jiang f c jiang f w meng explicit bounds on some new nonlinear integral inequality with delay j comput appl math 205 2007 479 486 and yuan z l yuan x w yuan f w meng some new delay integral inequalities and their applications appl math comput 208 2009 231 237

blind equalization and multiuser detection in dispersive cdma channels the problem of blind demodulation of multiuser information symbols in a high rate code division multiple access cdma network in the presence of both multiple access interference mai and intersymbol interference isi is considered the dispersive cdma channel is first cast into a multiple input multiple output mimo signal model framework by applying the theory of blind mimo channel identification and equalization it is then shown that under certain conditions the multiuser information symbols can be recovered without any prior knowledge of the channel or the users signature waveforms including the desired user s signature waveform although the algorithmic complexity of such an approach is prohibitively high however in practice the signature waveform of the user of interest is always available at the receiver it is shown that by incorporating this knowledge the impulse response of each user s dispersive channel can be identified using a subspace method it is further shown that based on the identified signal subspace parameters and the channel response two linear detectors that are capable of suppressing both mai and isi i e a zero forcing detector and a minimum mean square error mmse detector can be constructed in closed form at almost no extra computational cost data detection can then be furnished by applying these linear detectors obtained blindly to the received signal the major contribution of this paper is the development of these subspace based blind techniques for joint suppression of mai and isi in the dispersive cdma channels

relaxation and phase space singularities in time series of human magnetoencephalograms as indicator of photosensitive epilepsy to analyze the crucial role of fluctuation and relaxation effects for the function of the human brain we studied some statistical quantifiers that support the information characteristics of neuromagnetic brain responses magnetoencephalogram meg the signals to a flickering stimulus of different color combinations have been obtained from a group of control subjects which is then contrasted with those of a patient suffering photosensitive epilepsy pse we found that the existence of the specific stratification of the phase clouds and the concomitant relaxation singularities of the corresponding nonequilibrium dynamics of the chaotic behavior of the signals in separate areas in a patient provide likely indicators for the zones which are responsible for the appearance of pse

relaxation in a duffing potential abstract the solution of the equation of motion for a particle in a duffing potential v x 1 x 2 2 2 x 4 4 1 2 0 for arbitrary anharmonicity strength is characterized by the presence of odd frequencies which implies that velocity and position autocorrelation functions of such an oscillator in a microcanonical ensemble are also characterized by odd frequencies it is however non trivial to determine whether such discrete frequencies also characterize the autocorrelation functions in a canonical ensemble as discussed recently by fronzoni et al j stat phys 41 1985 553 we recover and extend upon the results of fronzoni et al to show analytically via mori lee theory that essentially discrete i e well defined peaks with finite but small width temperature dependent frequencies characterize the autocorrelation functions in a canonical ensemble

blind adaptive algorithms for minimum variance cdma receivers constrained optimization methods have received considerable attention as a means to derive blind multiuser receivers with low complexity the receiver s output variance is minimized subject to appropriate constraints which depend on the multipath structure of the signal of interest when multipath is present the constraint equations can be written in parametric form and the constraint parameters jointly optimized with the linear receiver s parameters we develop adaptive solutions for this joint constrained optimization problem both stochastic gradient and recursive least square type algorithms are developed the performance of the proposed methods is compared with other blind and trained methods and turns out to be close to the trained minimum mean square error receiver

a survey stability and boundedness of volterra difference equations abstract volterra difference equations arise in the modeling of many real phenomena in this survey stability and boundedness problems of some volterra nonlinear difference equations are investigated stability conditions and boundedness are formulated in terms of the characteristics of equations

periodic boundary value problems of integro differential equation of volterra type on time scales in this paper we prove a new comparison result and develop the monotone iterative technique to show the existence of extremal solutions of the following periodic boundary value problems pbvp of nonlinear integro differential equation on time scales x 1 t f t x z t 0 k t s x s 1s t 2 0 a

some pachpatte type inequalities on time scales in this paper using the comparison theorem we investigate some pachpatte type integral inequalities on time scales which provide explicit bounds on unknown functions our results extend some known dynamic inequalities on time scales unify and extend some continuous inequalities and their corresponding discrete analogues some applications of the main results are given in the end of this paper

derivation of the generalized langevin equation by a method of recurrence relations the generalized langevin equation was first derived by mori using the gram schmidt orthogonalization process this equation can also be derived by a method of recurrence relations for a physical space commonly used in statistical mechanics the recurrence relations are simple and they lead directly to the langevin equation the langevin equation is shown to be composed of one homogeneous and one inhomogeneous equation

periodic boundary value problem for non lipschitzian impulsive functional differential equations we consider a class of first order impulsive functional differential equations where the functional dependence is not necessarily a lipschitzian function the new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented we give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution

on the second order statistics of the weighted sample covariance matrix the second order statistics of the sample covariance are encountered in many covariance based processing algorithms this paper derives closed form expressions for the covariance of the weighted sample covariance matrix with an arbitrary weight for both a real system and complex system given a system model the results explicitly rely on the second order and fourth order statistics of the channel noise and inputs they are shown to coincide with the existing results when the channel inputs and noise are gaussian distributed our results can be directly applied to analyze the statistical properties of subspace based channel estimation methods for single input multiple output simo systems and code division multiple access cdma systems numerical examples are provided to further verify analyses

extremal solutions of nonlinear impulsive integrodifferential equations in banach spaces abstract in this paper we combine the monotone iterative technique with fixed point theory to investigate the extremal solutions of nonlinear impulsive integrodifferential equations in banach spaces existence criteria are obtained and several examples are worked out

periodic solutions for ordinary differential equations with sublinear impulsive effects abstract the continuation method of topological degree is used to investigate the existence of periodic solutions for ordinary differential equations with sublinear impulsive effects the applications of the abstract approach include the generalizations of some classical nonresonance theorem for impulsive equations for instance the existence theorem for asymptotically positively homogeneous differential systems and the existence theorem for second order equations with landesman lazer conditions

some new dynamic inequalities on time scales in this paper based on some known dynamic inequalities we investigate certain new dynamic inequalities on time scales which provide explicit bounds on unknown functions our results unify and extend some continuous inequalities and their corresponding discrete analogues

perturbation analysis for subspace decomposition with applications in subspace based algorithms subspace decomposition has been exploited in different applications due to perturbations from various sources such as finite data samples and measurement noise perturbations arise in subspaces therefore some loss is introduced to performance of subspace based algorithms although first order perturbation results have been proposed in the literature and applied to various problems up to second order perturbation analysis can provide more accurate analytical results and is studied in this paper based on the orthogonality principle perturbations of subspaces and singular values or eigenvalues are derived explicitly as functions of a perturbation in the objective matrix up to the second order respectively all in closed forms it is shown that by keeping only the first order terms the derived results reduce to those from existing approaches examples to apply the proposed results to both matrix computation and subspace based channel estimation are provided to verify our analysis

limiting periodicity of the solutions for some volterra difference equations conditions of the limiting of periodicity of the solutions for some volterra difference equations are derived these conditions are formulated immediately in terms of the coefficients of equations and their resolvent using the second liapunov method and fixed point theorem

nonlinear integro differential equations and optimal control problems on time scales this paper is mainly concerned with a class of optimal control problems of a system governed by the nonlinear integro differential equation on time scales using the contraction mapping principle the existence and uniqueness of a weak solution of the nonlinear integro differential equation on time scales are proved discussing l t 1 strong weak lower semicontinuity of integral functional on time scales we give sufficient conditions for the existence of optimal control by the virtue of the integration by parts formula on time scales the necessary conditions of optimality are derived

blind multiuser detection a subspace approach a new multiuser detection scheme based on signal subspace estimation is proposed it is shown that under this scheme both the decorrelating detector and the linear minimum mean square error mmse detector can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest the consistency and asymptotic variance of the estimates of the two linear detectors are examined a blind adaptive implementation based on a signal subspace tracking algorithm is also developed it is seen that compared with the previous minimum output energy blind adaptive multiuser detector the proposed subspace based blind adaptive detector offers lower computational complexity better performance and robustness against signature waveform mismatch two extensions are made within the framework of signal subspace estimation first a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel secondly a multiuser detection scheme using spatial diversity in the form of an antenna array is considered a blind adaptive technique for estimating the array response for diversity combining is proposed it is seen that under the proposed subspace approach blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection with little attendant increase in complexity

aspects of non ergpdicity in hermitian systems abstract it is shown that some of the simplest interacting many body systems exhibiting non ergodicity necessarily satisfy certain identities involving their equilibrium multipoint static correlations these identities may be useful in the study of model non ergodic systems being analysed or simulated some examples of pertinent model non ergodic systems are given to illustrate the material discussed

relaxation in nonlinear systems nonconvergent infinite continued fractions and sensitive relaxation processes abstract the mori lee treatment of linear response theory demonstrates that the laplace transform of any relaxation function of a dynamical variable can be expressed as a continued fraction for certain simple nonlinear systems the continued fraction representation of the relaxation functions cannot be evaluated perturbatively it turns out that many body systems with even a single on site nonlinearity can dramatically alter the relaxation behavior in such systems we argue that nonperturbative continued fractions in the mori lee formalism are necessarily associated with systems that exhibit relaxation that is sensitive to the presence of nonlinearities

impulsive control of discrete systems with time delay this note deals with impulsive control of discrete systems with time delay it s the first time that an impulsive controller was introduced for discrete systems with time delay firstly some stability criteria for delay discrete systems with impulse effects are obtained by using lyapunov functionals and razumikhin technique these stability criteria show that if the impulses satisfy some conditions then the original stable systems can keep their stability property even with impulse effects then by using lyapunov functionals or lyapunov functions together with razumikhin technique two stability criteria for the discrete systems with time delay under impulsive control are given these two results show that unstable systems can be stable under impulsive control some examples are also presented to illustrate the efficiency of the obtained results

ergodicity in simple and not so simple systems and kubo s condition abstract the ergodic hypothesis is approached from the side of time averaging to ascertain regions of its validity a necessary and sufficient condition is formulated in terms of certain infinite products and tested in models of nn coupled harmonic oscillators the validity of the hypothesis requires energy delocalizability indicated by the existence of coherent translation modes kubo s condition is re examined to see the origin of its limitations

a unique solution of initial value problems for first order impulsive integro differential equations of mixed type in banach spaces in this paper we investigate initial value problem for first order impulsive integro differential equation of mixed type in a banach space without any compactness type assumption we obtain a unique solution of the equation an explicit iterative approximation of the solution and an error estimate of the approximation sequence our result improves and extends many recent results

generalized langevin equation and recurrence relations the generalized langevin equation gle is a reformulation of the heisenberg equation of motion and hence an exact equation it is the basis of the memory function approach a very widely used method for studying dynamics of classical and quantum fluids the gle was first derived by mori in a very formal way a much simpler and more physically motivated derivation was given by us some years later in this work we provide perhaps the simplest possible derivation of the gle the simplicity of the derivation helps to bring out the subtleties present in this important dynamical relationship

why irreversibility is not a sufficient condition for ergodicity khinchin s theorem of ergodicity is examined by means of linear response theory the resulting ergodic condition shows that contrary to the theorem irreversibility is not a sufficient condition for ergodicity by the recurrence relations method we prove that irreversibility is broader in scope than ergodicity showing why it can only be a necessary condition for ergodicity

momentum autocorrelation function of an impurity in a classical oscillator chain with alternating masses iii some limiting cases abstract the momentum autocorrelation function of a mass impurity in a classic diatomic chain is studied using the recurrence relations method general expressions for the contributions of branch cuts and resonant poles have been derived and illustrated in previous papers i and ii respectively in the present paper a series of limiting cases that any one of the three masses m 0 m 1 m 2 approaches to zero or infinity are analyzed it is found that the cases m 0 0 and 2 m 2 are closely related to each other and that the general expressions for the amplitudes are valid also in the limits 0 and the ergodicity in the case m 2 0 is studied and the ratio of two specific infinite products is obtained

an application of variational method to second order impulsive differential equation on the half line abstract in this paper we study the multiplicity of solutions for second order impulsive differential equation with a parameter on the half line by using a variational method and a three critical points theorem we give some new criteria to guarantee that the impulsive problem has at least three classical solutions also an example is given in this paper to illustrate the main results

momentum autocorrelation function of an impurity in a classical oscillator chain with alternating masses ii illustrations abstract a classic diatomic chain with a mass impurity is studied using the recurrence relations method the dependence of frequency and amplitude upon two mass ratios is illustrated in detail by examining the figures we can learn a lot about the model such as the widths of the acoustic and optical branches as well as the gap between them the frequency and amplitude of the resonant modes etc the momentum autocorrelation functions of the impurity in different regions of the configuration space are numerically calculated and illustrated a theorem is obtained governing the upper and lower frequencies of the acoustic and optical branches the envelope of the integrand of the cut contribution is determined the convergence of numerical calculations of time integration for parameter w to its theoretical value is confirmed

the existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method abstract in this paper we study the existence and multiplicity of classical solutions for a second order impulsive differential equation with periodic boundary conditions by using a variational method and critical point theory we give some new criteria to guarantee that the impulsive problem has at least one solution two solutions and infinitely many solutions when the parameter pair c lies in different intervals respectively some examples are given in this paper to illustrate the main results

robust constrained linear receivers for cdma wireless systems for code division multiple access cdma communication systems many constrained linear receivers have been developed to suppress multiple access interference the linearly constrained formulations are generally sensitive to multipath fading and other types of signal mismatch we develop robust linear receivers by exploring appropriate constraints multiple linear constraints are exploited to preserve the output energy that is scattered in multipath channels in addition a quadratic inequality constraint on the weight vector norm is used to improve robustness with respect to imprecise signal modeling these constraints can be applied to the minimum output energy moe detector to mitigate the signal mismatch problem and to the decision directed minimum mean square error mmse detector to prevent error propagation and eliminate the need for training sequences at startup adaptive implementations for the proposed detectors are presented using recursive least square rls updating in both the direct form and the partitioned linear interface canceller plic structure simulations are performed in a multipath propagation environment to illustrate the performance of the proposed detectors

momentum autocorrelation function of an impurity in a classical oscillator chain with alternating masses i general theory abstract a chain composed of classic harmonic oscillators with alternating masses and one mass impurity is studied using the recurrence relations method the dynamics of the momentum autocorrelation function of the impurity mass is contributed by three branch cuts corresponding to acoustic and optic modes and by two pairs of poles for resonant modes one pair of the poles are located beyond the optic branch and the other in the gaps between the branches criteria for the resonances are established general expressions for frequencies and amplitudes of the resonant modes are derived ergodic behavior of the momentum of the impurity is analyzed

effects of imperfect blind channel estimation on performance of linear cdma receivers in a code division multiple access cdma system signal detection under multipath distortion typically requires estimation of unknown channel parameters first in such a scenario performance of receivers highly relies on the accuracy of channel estimates in this paper effects of channel estimation errors on the performance of linear cdma receivers due to finite data samples are studied when channel parameters are estimated blindly by a recently proposed covariance matching technique those receivers include zero forcing zf direct matrix inversion dmi minimum mean square error mmse subspace mmse and rake receivers their output signal to interference plus noise ratios sinrs and bit error rates bers are adopted for performance measures expressions for performance indicators under such an imperfect condition are derived from a perturbation perspective and verified by simulation examples

impulsive periodic boundary value problems of first order differential equations in this paper by using schaeffer s theorem we prove new existence theorems for a nonlinear periodic boundary value problem of first order differential equations with impulses our results improve and generalize some known results

testing boltzmann s ergodic hypothesis with electron gas models kubo proposed a physical approach to proving the validity of boltzmann s ergodic hypothesis it is to perform the time averages on dynamical functions thereby avoiding the difficulties of measure theory inherent in the classical approach to perform time averaging properly one must have a general solution for the heisenberg equation of motion such as by the recurrence relations method a time averaging carried over with a recurrence relations solution is found to yield an ergodic condition in the form of an infinite product it is linked to the energy transfer mechanisms hence to the ergodicity itself the electron gas models are fertile ground for testing ergodicity by this approach for several static domains we have evaluated the infinite product and drawn from them a general physical picture that underlies the ergodic hypothesis

maximum principles for periodic impulsive first order problems we present some comparison results for the periodic boundary value problem for first order ordinary differential equations with impulses at fixed moments then the upper and lower solution method and the monotone iterative scheme are presented