existence and roughness of exponential dichotomies of linear dynamic equations on time scales in this paper we define the exponential dichotomy of linear dynamic equations on time scales then we present perturbation theorems on the roughness of exponential dichotomy and develop several explicit sufficient criteria for linear dynamic equations to have an exponential dichotomy as applications of the criteria of exponential dichotomy we derive some new sufficient conditions for the existence of periodic solutions of semi linear dynamic equations and nonlinear dynamic equations on time scales

regression analysis for a functional response functional responses are encountered when units are observed over time although the whole function itself is not observed a sufficiently large number of evaluations as is common with modern recording equipment are assumed to be available functional regression analysis relates the smooth functional response y t to known covariates x by a linear combination of parameter functions t which are to be estimated the model takes the standard form y t x t t t this approach provides an alternative to standard longitudinal data methods used in the biological sciences where less and noisier data necessitate parametric modeling the methodology is illustrated by an application in ergonomics

computer model calibration using high dimensional output this work focuses on combining observations from field experiments with detailed computer simulations of a physical process to carry out statistical inference of particular interest here is determining uncertainty in resulting predictions this typically involves calibration of parameters in the computer simulator as well as accounting for inadequate physics in the simulator the problem is complicated by the fact that simulation code is sufficiently demanding that only a limited number of simulations can be carried out we consider applications in characterizing material properties for which the field data and the simulator output are highly multivariate for example the experimental data and simulation output may be an image or may describe the shape of a physical object we make use of the basic framework of kennedy and o hagan however the size and multivariate nature of the data lead to computational challenges in implementing the framework to overcome these challenges we make use of basis repre

multivariate gaussian process emulators with nonseparable covariance structures the gaussian process regression model is a popular type of emulator used as a fast surrogate for computationally expensive simulators deterministic computer models for simulators with multivariate output common practice is to specify a separable covariance structure for the gaussian process though computationally convenient this can be too restrictive leading to poor performance of the emulator particularly when the different simulator outputs represent different physical quantities also treating the simulator outputs as independent can lead to inappropriate representations of joint uncertainty we develop nonseparable covariance structures for gaussian process emulators based on the linear model of coregionalization and convolution methods using two case studies we compare the performance of these covariance structures both with standard separable covariance structures and with emulators that assume independence between the outputs in each case study we find that only emulators with nons

exponential dichotomies almost periodic structurally stable differential systems and an example abstract in this paper we introduce concepts of almost periodic topological in short apt equivalence and almost periodic structural in short aps stability of differential systems and a necessary and sufficient condition for aps stability of differential systems furthermore we discuss the inheritability of the aps stability and density of aps stable differential systems in a certain space of uniformly almost periodic differential systems

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

precise error rate analysis of bandwidth efficient bpsk in nakagami fading and cochannel interference the bit error rate ber of bandlimited binary phase shift keying in a fading and cochannel interference cci environment is derived for the case of perfect coherent detection the fading and interference model assumed is general and of interest for microcellular system studies the model allows both desired signal and interfering signals to experience arbitrary amounts of fading severity a precise ber expression is derived using a characteristic function method using this accurate analytical result the impact of the interfering users fading severity on the desired user error rate is examined the bers obtained under perfect coherent detection are also valid as lower performance bounds for practical realizable receivers where ideal coherent detection is difficult to implement the error rate performance of a novel bandwidth efficient pulse shape is determined for the general fading and cci environment analysis and numerical results show that the new pulse can provide better ber performance than the widely used raised cosine pulse

exponential separation exponential dichotomy and almost periodicity of linear difference equations abstract in this paper we study the relation between the concept of exponential separation and those of reducibility exponential dichotomy and almost periodicity of linear difference equations

topological equivalence and structural stability for linear difference equations abstract in this paper first we prove that if two linear difference equations with invertible coefficient matrices are topologically equivalent and one of them has bounded coefficient matrix together with its inverse then the coefficient matrix of the other equation is also bounded together with its inverse we also prove that if a linear difference equation with bounded and invertible coefficient matrix is structurally stable then the inverse of the coefficient matrix is also bounded

performance of binary and quaternary direct sequence spread spectrum multiple access systems with random signature sequences the performance of synchronous and asynchronous binary and quaternary with and without offset direct sequence spread spectrum multiple access ds ssma communication systems using random signature sequences and arbitrary chip waveforms is investigated the average probability of error at the output of the correlation receiver is evaluated using a characteristic function approach for these systems numerical results are presented that illustrate performance comparisons between systems using random and deterministic signature sequences synchronous and asynchronous systems systems with rectangular or sinewave chip waveforms and binary and quaternary systems with the same data rates and bandwidth in all cases the accuracy of the gaussian approximation is also examined

bit to bit error dependence in slotted ds ssma packet systems with random signature sequences a technique is developed to find an accurate approximation to the probability of data bit error and the probability of packet success in a direct sequence spread spectrum multiple access ds ssma packet radio system with random signature sequences an improved gaussian approximation to the probability of data bit error is performed packet performance is analyzed by using the theory of moment spaces to gain insight into the effect of bit to bit error dependence caused by interfering signal relative delays and phases which are assumed constant over the duration of a desired packet numerical results show that if no error control exists in the desired packet or if block error control is used when multiple access interference is high the error dependence increases the average probability of packet success beyond that predicted by models which use independent bit errors however when block error control is used and the multiple access interference is low the bit error dependencies cause a reduction in packet error performance

robustness of nonuniform μ ν dichotomies in banach spaces abstract this paper focuses on the linear perturbation of dynamical systems in banach spaces which corresponds to a nonautonomous dynamical system admitting a nonuniform dichotomy we establish the robustness or roughness of nonuniform dichotomies in the sense that the linear dynamical system persists under a sufficiently small linear perturbation

analysis of computer experiments with functional response this article is motivated by a computer experiment conducted for optimizing residual stresses in the machining of metals although kriging is widely used in the analysis of computer experiments it cannot be easily applied to model the residual stresses because they are obtained as a profile the high dimensionality caused by this functional response introduces severe computational challenges in kriging it is well known that if the functional data are observed on a regular grid the computations can be simplified using an application of kronecker products however the case of irregular grid is quite complex in this article we develop a gibbs sampling based expectation maximization algorithm which converts the irregularly spaced data into a regular grid so that the kronecker product based approach can be employed for efficiently fitting a kriging model to the functional data supplementary materials are available online

necessary and sufficient criteria for the existence of exponential dichotomy on time scales necessary and sufficient criteria are established for the existence of exponential dichotomies for linear dynamic equations on time scales and are applied to derive some perturbation theorems on the roughness of exponential dichotomy

average bit error rate performance of band limited ds ssma communications direct sequence spread spectrum multiple access ds ssma communications strictly band limited transmitter chip waveforms with excess bandwidth in the interval between zero and one pseudo random spreading sequences an additive white gaussian noise channel and matched filter receivers are considered first a new expression for the average bit error rate ber is derived for systems with quaternary phase shift keying qpsk spreading the conventional matched filter receiver a coherent detector for binary phase shift keying bpsk data symbols and chip waveforms that result in no interchip interference the expression consists of a well known ber expression based on the standard gaussian approximation to multiple access interference and a few correction terms it enables accurate ber evaluations without any numerical integration for various choices of system parameters of interest the accuracy of the expression is guaranteed as long as the conditional gaussian approximation to the cross correlation coefficients between the desired user s spreading sequence and the interfering users spreading sequences is valid the expression well reflects the effect of filtering on the system performance extensions of the expression are discussed for systems with qpsk spreading and different detection schemes systems with bpsk spreading and systems with different transmit and receive filters monte carlo simulation results are also provided to verify the accuracy

reducibility of linear dynamic equations on measure chains the concepts of reducibility and kinematic similarity are of major significance in the theory of stability of linear differential and difference equations in this paper we generalize some fundamental results on reducibility from the finite dimensional differential equations context to dynamic equations on measure chains in arbitrary hilbert spaces in fact we derive sufficient conditions for dynamic equations to be kinematically similar to an equation with zero right hand side or to an equation in hermitian or block diagonal form

discretization of semilinear differential equations with an exponential dichotomy abstract a structural stability result for one step discretizations of semilinear differential equations with an exponential dichotomy in its linear part is presented and interpreted as a shadowing result estimates are given in terms of the stepsize and of the order of the discretization method chosen

uniformly rd piecewise almost periodic functions with applications to the analysis of impulsive δ dynamic system on time scales we introduce some new concepts of uniformly rd piecewise almost periodic functions on time scales and obtain some properties some new estimation inequalities and completely new theorems are established on time scales for impulsive dynamic systems several applications are given to illustrate our feasible results in the present work we introduce two equivalent concepts of uniformly rd piecewise almost periodic functions on time scales and their equivalence is proved based on this some basic properties of them are obtained then some new criteria of exponential dichotomy are established for homogeneous dynamic system on time scales also some completely new theorems are established on time scales for impulsive almost periodic dynamic systems such as favard s theorem and exponential dichotomy theorem as applications we provide a method to obtain an almost periodic solution for a given nonhomogeneous impulsive dynamic system furthermore we introduce an impulsive non autonomous nicholson s blowflies system model with patch structure and multiple nonlinear harvesting terms for which the existence and exponential stability of almost periodic solutions are studied which shows that our results can be applied feasibly and effectively

predicting the output from a complex computer code when fast approximations are available s we consider prediction and uncertainty analysis for complex computer codes which can be run at different levels of sophistication in particular we wish to improve efficiency by combining expensive runs of the most complex versions of the code with relatively cheap runs from one or more simpler approximations a bayesian approach is described in which prior beliefs about the codes are represented in terms of gaussian processes an example is presented using two versions of an oil reservoir simulator 1 c complex mathematical models implemented in large computer codes have been used to study real systems in many areas of scientific research sacks et al 1989 usually because physical experimentation is too costly and sometimes impossible as in the case of large environmental systems a computer experiment involves running the code with various input values for the purpose of learning something about the real system often a simulator can be run at different levels of complexity with versions ranging from the most sophisticated high level code to the most basic for example in 4 we consider two codes which simulate oil pressure at a well of a hydrocarbon reservoir both codes use finite element analysis in which the rocks comprising the reservoir are represented by small interacting grid blocks the flow of oil within the reservoir can be simulated by considering the interaction between the blocks the two codes differ in the resolution of the grid so that we have a very accurate slow version using many small blocks and a crude approximation using large blocks which runs much faster alternatively a mathematical model could be expanded to include more of the scientific laws underlying the physical processes simple fast versions of the code may well include the most important features and are useful for preliminary investigations in real time applications the number of runs from a high level simulator may be limited by expense then there is a need to trade off the complexity of the expensive code with the availability of the simpler approximations the purpose of the current paper is to explore ways in which runs from several levels of a code can be used to make inference about the output from the most complex code we may also have uncertainty about values for the input parameters which apply in any given application uncertainty analysis of computer codes describes how this uncertainty on the inputs affects our uncertainty about the output

exponential dichotomy integral separation and diagonalizability of linear systems of ordinary differential equations abstract this paper is concerned with linear systems of ordinary differential equations a criterion for integral separation in terms of exponential dichotomy is given as corollaries we obtain the roughness theorem for integral separation and the new result that an upper triangular system on a half line is integrally separated if and only if the system corresponding to its diagonal is we then show that a diagonal system on a half line is integrally separated if and only if a certain perturbed system is diagonalizable using this result we are able to deduce that the interior of the set of diagonalizable systems on a half line is the set of systems with integral separation and that the interior for the whole line is the set of systems which are integrally separated on both half lines

a simple accurate method to calculate spread spectrum multiple access error probabilities the exact calculation of error probabilities for direct sequence spread spectrum multiple access ds ssma systems has been addressed in the literature the exact calculation is computationally difficult so emphasis has been on approximations and bounds one particularly attractive approximation is to just use a signal to noise ratio in a gaussian approximation the standard approximation unfortunately that approximation is not generally accurate enough an improved gaussian approximation with good accuracy has recently been presented the author derives an accurate gaussian approximation which is also computationally very simple

performance evaluation for band limited ds cdma systems based on simplified improved gaussian approximation the standard gaussian approximation sga for error analysis of direct sequence code division multiple access ds cdma systems is very optimistic in many cases improved gaussian approximation iga is a technique that produces accurate error probabilities but is still computationally intensive simplified iga siga has complexity similar to that of sga and at the same time provides sufficient accuracy in this paper we consider siga for ds cdma systems employing random sequences in a band limited scenario the validity of iga for band limited systems is established in a rigorous mathematical sense then a key parameter in siga is derived via a frequency domain approach applications to a number of typical chip waveforms including the popular sinc and raised cosine pulses are investigated performance comparison with iga based lower and upper bounds shows that siga yields very accurate probability of error

a characterization of exponential separation in terms of reducibility for linear difference equations abstract the main aim of this paper is to show that a linear difference equation is exponentially separated if and only if all neighboring equations are reducible

ber performance of bandlimited ds cdma systems in nakagami fading accurate average bit error rate analysis of asynchronous bandlimited binary direct sequence code division multiple access ds cdma systems in nakagami m fading is studied the fading is assumed to be flat and slow the spectrum raised cosine src and beaulieu tan damen btd pulse shapes are employed a new method which combines the characteristic function cf method with the improved gaussian approximation ga is proposed for evaluating the ber of bandlimited ds cdma a substantial computational complexity reduction is achieved the well known standard ga holtzman s simplified improved ga and improved holtzman s ga methods are also considered the accuracies of the approximation methods are assessed using monte carlo simulation for a system employing a deterministic sequence for the desired user and random sequences for the active interfering users a cf method is employed to derive precise ber results the new btd pulse outperforms the src pulse in all situations

exponential separation exponential dichotomy and spectral theory for linear systems of ordinary differential equations abstract this paper is concerned with linear nonautonomous systems of ordinary differential equations a criterion for exponential separation in terms of exponential dichotomy is given as corollaries we obtain the roughness theorem for exponential separation and the new result that an upper triangular system on a half line is exponentially separated if and only if the system corresponding to its diagonal is a minimal decomposition into exponentially separated subspaces is defined it turns out that it is in general finer than the sacker sell spectral decomposition but that the two decompositions coincide for almost periodic systems

an optimal signal design for band limited asynchronous ds cdma communications an optimal signal design for band limited asynchronous direct sequence code division multiple access ds cdma communications with aperiodic random spreading sequences and a conventional matched filter receiver is considered in an additive white gaussian noise awgn channel with bandwidth defined in the strict sense two optimization problems are solved under finite bandwidth and zero interchip interference constraints first a chip waveform optimization is performed given the system bandwidth the data symbol transmission rate and the processing gain a technique to characterize a band limited chip waveform with a finite number of parameters is developed and it is used to derive optimum chip waveforms which minimize the effect of multiple access interference mai for any energy and delay profile of users next a joint optimization of the processing gain and the chip waveform is performed given the system bandwidth and the data symbol transmission rate a sufficient condition for a system to have lower average probability of bit error for any energy profile is found and it is used to derive some design strategies it is shown that the flat spectrum pulse with the processing gain leading to zero excess bandwidth results in the minimum average probability of bit error design examples and numerical results are also provided

structural stability via the density of a class of linear discrete systems abstract in this paper we prove that the set of multiplicatively separated linear discrete systems is dense in the set of linear systems and we find a relationship between the set of structurally stable systems and the set of the systems which have an exponential dichotomy

a simple and accurate method of probability of bit error analysis for asynchronous band limited ds cdma systems this paper considers probability of bit error p sub e analysis in asynchronous band limited direct sequence code division multiple access ds cdma systems it presents a simple and accurate method of p sub e analysis the proposed method can serve as an attractive alternative to the only two techniques currently available for band limited systems the standard gaussian approximation sga and the characteristic function method the former is prone to inaccuracy while the latter large computational complexity the method generalizes the simplified improved gaussian approximation siga derived previously for rectangular pulses this paper also outlines a generalization of another method referred to as the improved gaussian approximation iga numerical examples demonstrate the far greater accuracy of the generalized siga with respect to the sga the examples consider the is 95 and square root raised cosine sqrt rc pulses as well as uniform and nonuniform received power conditions

dichotomies in terms of lyapunov functions for linear difference equations abstract necessary and sufficient conditions that a linear difference equation have an exponential dichotomy on the set of the integer numbers are given in terms of lyapunov functions

conditions for kinematical similarity of a linear difference equation to a block upper triangular equation abstract in this paper we consider a linear difference equation in which the coefficient matrix is variable and depends on a positive parameter under some conditions we prove that the above equation is kinematically similar to a block upper triangular equation

gaussian process modeling of a functional output with information from boundary and initial conditions and analytical approximations a partial differential equation pde models a physical quantity as a function of space and time these models are often solved numerically with the finite element fe method and the computer outp