uniform decay for the unilateral problem associated to the kirchhoff type wave equations with nonlinear boundary damping in this article we study the existence of solutions and the uniform decay rate of the energy for nonlinear unilateral problem associated to the kirchhoff type wave equations with nonlinear boundary damping to obtain the existence of solutions we make use of faedo galerkin s approximation and also to show the uniform stabilization we use the perturbed energy method

a new augmented lyapunov krasovskii functional approach for stability of linear systems with time varying delays abstract this paper proposes improved delay dependent conditions for asymptotic stability of linear systems with time varying delays the proposed method employs a suitable lyapunov krasovskii s functional for new augmented system based on lyapunov method delay dependent stability criteria for the systems are established in terms of linear matrix inequalities lmis which can be easily solved by various optimization algorithms three numerical examples are included to show that the proposed method is effective and can provide less conservative results

on uniform decay of the solution for a damped nonlinear coupled system of wave equations with nonlinear boundary damping and memory term in this paper we are concerned with the existence and energy decay of the solution to the initial boundary value problem for the nonlinear coupled wave equations with nonlinear boundary damping and memory term

long time asymptotic expansion for the damped semilinear wave equation the first initial boundary value problem is considered for the damped semilinear wave equation with the quadratic nonlinearity for small initial data and homogeneous boundary conditions its solution is constructed in the form of a series in the eigenfunctions of the laplace operator the long time asymptotic expansion is obtained which shows the nonlinear effects of amplitude and frequency multiplication the same results hold for the admissible initial data that are not small

wirtinger based multiple integral inequality for stability of time delay systems abstractnote that the conservatism of the delay dependent stability criteria can be reduced by increasing the integral terms in lyapunov krasovskii functional lkf this brief revisits the stability problem for a class of linear time delay systems via multiple integral approach the novelty of this brief lies in that a wirtinger based multiple integral inequality is employed to estimate the derivative of a class of lkf with multiple integral terms based on these innovations a new delay dependent stability criterion is derived in terms of linear matrix inequalities two numerical examples are exploited to demonstrate the effectiveness and superiority of the proposed method

a distribution free procedure for comparing receiver operating characteristic curves from a paired experiment summary a distribution free permutation test procedure is proposed for comparing receiver operating characteristic curves based on continuous data from a paired design the method tests the hypothesis that the two curves are identical for all operating points unlike previously proposed methods which test the equivalence of the areas under the curves the new test is shown by simulation to have very similar operating characteristics to the standard method based on comparisons of the areas when the curves are parallel but markedly superior power when the curves cross that is when the curves are different but have similar areas the prospects of generalising the approach to unpaired experiments and to comparisons of ordinal rating data are discussed

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

transformations of the explanatory variables in the logistic regression model for binary data summary some results are presented on improving the fit of the logistic regression model for binary data by transforming the vector of explanatory variables the methods are based on consideration of the distributions of these variables conditional on outcome group the transformations required are the functions of the explanatory variables which appear in the log density ratio of the conditional distributions

an exact method for the stability analysis of time delayed linear time invariant lti systems a general class of linear time invariant systems with time delay is studied recently they attracted considerable interest in the systems and control community the complexity arises due to the exponential type transcendental terms in their characteristic equation the transcendentality brings infinitely many characteristic roots which are cumbersome to elaborate as evident from the literature a number of methodologies have been suggested with limited ability to assess the stability in the parametric domain of time delay this study offers an exact structured and robust methodology to bring a closure to the question at hand ultimately we present a unique explicit analytical expression in terms of the system parameters which not only reveals the stability regions pockets in the domain of time delay but it also declares the number of unstable characteristic roots at any given pocket the method starts with the determination of all possible purely imaginary resonant characteristic roots for any positive time delay to achieve this a simplifying substitution is used for the transcendental terms in the characteristic equation it is proven that the number of such resonant roots for a given dynamics is finite each one of these roots is created by infinitely many time delays which are periodically distributed an interesting property is also claimed next that the root crossing directions at these locations are invariant with respect to the delay and dependent only on the crossing frequency these two unique findings facilitate a simple and practical stability method which is the highlight of the work

improved approach to robust stability and h performance analysis for systems with an interval time varying delay abstract an improved delay and range dependent robust stability and h performance analysis criterion for systems with an interval time varying delay is investigated a novel lyapunov krasovskii functional containing triple integral terms is established and an extended free weighting matrix method double integral inequality method is subsequently proposed numerical examples validate the effectiveness of the proposed double integral inequality method and show that our approach is less conservative than existing methods

receiver operator characteristic roc curves and non normal data an empirical study this paper evaluates the performance of several diagnostic kits for assessing levels of serum prostatic acid phosphatase on patients at different stages of cancer of the prostate each patient was studied with several kits we compare results obtained for receiver operator characteristic roc curve methodology with data assumed to follow a normal distribution with log transformed data assumed to follow a normal distribution and when neither of these assumptions holds there were important differences between the results of the different approaches for these data the normal distribution assumption should be used with extreme caution the log transformed based results compared favourably with the non parametric but unconsidered application of the method should be avoided

stability for neural networks with time varying delays via some new approaches this paper considers the problem of delay dependent stability criteria for neural networks with time varying delays first by constructing a newly augmented lyapunov krasovskii functional a less conservative stability criterion is established in terms of linear matrix inequalities second by proposing novel activation function conditions which have not been proposed so far further improved stability criteria are proposed finally three numerical examples used in the literature are given to show the improvements over the existing criteria and the effectiveness of the proposed idea

best combination of multiple diagnostic tests for screening purposes in a medical diagnostic testing problem multiple diagnostic tests are often available in distinguishing between diseased and nondiseased subjects different diagnostic tests are usually sensitive to different aspects of the disease a desirable approach is to combine multiple diagnostic tests so as to obtain an optimal composite diagnostic test with higher sensitivity and specificity that detects the presence of the disease more accurately to accomplish this it has been observed via signal detection theory developed in the 1950s and 1960s that the optimal combination of different diagnostic variables i e the diagnostic test results is determined by the likelihood ratio function for the diseased and nondiseased groups the conventional approach is to fit parametric models for the diseased and nondiseased groups separately and then to use the fitted likelihood ratio function for the best combination of test results however this approach is not so robust if the underlying distribution functions are misspecified since the optimal combination depends only on the likelihood ratio function it would be more appropriate to model this function directly a two sample semiparametric inference technique is applied to the model for the likelihood ratio function we consider the best combination of multiple diagnostic tests and study semiparametric likelihood estimation of the optimal receiver operating characteristic curve and the area under the curve we present a bootstrap procedure along with some results on simulation and on analysis of two real data sets

using logistic regression procedures for estimating receiver operating characteristic curves summary estimation of a receiver operating characteristic roc curve is usually based either on a fully parametric model such as a normal model or on a fully nonparametric model in this paper we explore a semiparametric approach by assuming a density ratio model for disease and disease free densities this model has a natural connection with the logistic regression model the proposed semiparametric approach is more robust than a fully parametric approach and is more efficient than a fully nonparametric approach two real examples demonstrate that the roc curve estimated by our semiparametric method is much smoother than that estimated by the nonparametric method

existence uniqueness and asymptotic behavior for solutions of the nonlinear beam equation a mathematical model for the transverse deflection of an extensible beam of length l whose ends are held at fixed distance apart is equation 2 u t 2 4 u x 4 0 l u 2 t d 2 u x 2 0 which has been proposed by woinowsky and krieger 18 where is a positive constant is a constant not necessarily positive and the nonlinear term represents the change in the tension of the beam due to its extensibility

on coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term in this paper we prove the existence of the solution to the mixed problem for coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term moreover we discuss the uniform decay of the solution

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

semiparametric inference for a quantile comparison function with applications to receiver operating characteristic curves summary in studies to compare two samples more information may be available on one treatment than the other when one population is modelled parametrically and the other nonparametrically we study large sample properties of a semiparametric sample quantile comparison function and show that it can have substantially smaller asymptotic variance than its nonparametric counterpart especially near the boundaries we describe applications to both two sample tests and receiver operating characteristic curves

a family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data summary in this paper we study a broad class of nonparametric statistics for comparing two diagnostic markers one can compare the sensitivities of these diagnostic markers over restricted ranges of specificity by selecting an appropriate statistic from this class as special cases one can compare the entire area under the receiver operator curve hanley mcneil 1982 or one can compare the sensitivities at a fixed common specificity usually we would recommend a comparison based on an average of sensitivities over a restricted high level of specificities test procedures and confidence intervals are based on asymptotic normality these procedures are applicable for paired data in which both diagnostic markers are performed on each subject and for unpaired data the procedures may be used to compare two real functions of multiple diagnostic markers as well as to compare individual markers

stability and stabilization of discrete time tźs fuzzy systems with time varying delay via cauchyźschwartz based summation inequality this paper proposes new stability and stabilization conditions for discrete time fuzzy systems with time varying delays by constructing a suitable lyapunov krasovskii functional and introducing a new summation inequality based on the inequality of cauchy schwartz form which enhances the feasible region of the stability criterion for discrete time systems with time varying delay a stability criterion for such systems is established in order to show the effectiveness of the proposed inequality which provides more tight lower bound of a summation term of quadratic form a delay dependent stability criterion for such systems is derived within the framework of linear matrix inequalities which can be easily solved by various effective optimization algorithms going one step forward the proposed inequality is applied to a stabilization problem in discrete time fuzzy systems with time varying delays the advantages of the proposed stability and stabilization criteria are illustrated via two numerical examples

an augmented model for robust stability analysis of time varying delay systems stability analysis of linear systems with time varying delay is investigated in order to highlight the relations between the variation of the delay and the states redundant equations are introduced to construct a new modelling of the delay system new types of lyapunov krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion delay dependent stability conditions are then formulated in terms of linear matrix inequalities finally several examples show the effectiveness of the proposed methodology

global existence and blow up of solutions for some hyperbolic systems with damping and source terms abstract this paper deals with the global existence and blow up of solutions to some nonlinear hyperbolic systems with damping and source terms in a bounded domain by using the potential well method we obtain the global existence moreover for the problem with linear damping terms blow up of solutions is considered and some estimates for the lifespan of solutions are given

on the reachable set bounding of uncertain dynamic systems with time varying delays and disturbances in this paper improved conditions are proposed for finding an ellipsoidal bound of reachable sets which bound the state trajectories of uncertain dynamic systems with time varying delays and bounded peak disturbances a more generalized time derivative condition is considered in comparison with previous work by the use of convex hull properties and application of the lyapunov method sufficient conditions for finding an ellipsoidal bound of reachable sets of the concerned systems are established in terms of linear matrix inequalities lmis two numerical examples are included to show the superiority and effectiveness of our results

a singular perturbation problem for nonlinear damped hyperbolic equations on considere des equations hyperboliques non lineaires amorties u tt au t au a 2 u g u 0 ou a est un operateur positif et g est la derivee de gateaux d une fonctionnelle convexe on etudie le comportement asymptotique des solutions et la convergence des solutions fortes quand o

existence of periodic solutions for nonlinear differential equations abstract in this paper we shall study the existence of a periodic solution to the nonlinear differential equationxtt axt a xt a ax b t x f t x t 0 in some complex hilbert space using duality and variational methods

bayesian bootstrap estimation of roc curve receiver operating characteristic roc curve is widely applied in measuring discriminatory ability of diagnostic or prognostic tests this makes the roc analysis one of the most active research areas in medical statistics many parametric and semiparametric estimation methods have been proposed for estimating the roc curve and its functionals in this paper we propose the bayesian bootstrap bb a fully nonparametric estimation method for the roc curve and its functionals such as the area under the curve auc the bb method offers a bandwidth free smoothing approach to the empirical estimate and gives credible bounds the accuracy of the estimate of the roc curve in the simulation studies is examined by the integrated absolute error in comparison with other existing curve estimation methods the bb method performs well in terms of accuracy robustness and simplicity we also propose a procedure based on the bb approach to test the binormality assumption

global existence and stability for wave equation of kirchhoff type with memory condition at the boundary abstract we consider a nonlinear wave equation of kirchhoff type with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions we proved that the energy decay with the same rate of decay of the relaxation function that is the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially

input output approach to stability and l2 gain analysis of systems with time varying delays abstract stability and l 2 l 2 gain of linear continuous time and discrete time systems with uncertain bounded time varying delays are analyzed under the assumption that the nominal delay values are not equal to zero the delay derivatives in the continuous time are not assumed to be less than q 1 an input output approach is applied by introducing a new input output model which leads to effective frequency domain and time domain criteria the new method significantly improves the existing results for delays with derivatives not greater than 1 which were treated in the past as fast varying delays without any constraints on the delay derivatives new bounded real lemmas brls are derived for systems with state and objective vector delays and norm bounded uncertainties numerical examples illustrate the efficiency of the new method

two sample test for correlated data under outcome dependent sampling with an application to self reported weight loss data standard methods for two sample tests such as the t test and wilcoxon rank sum test may lead to incorrect type i errors when applied to longitudinal or clustered data recent alternatives of two sample tests for clustered data often require certain assumptions on the correlation structure and or noninformative cluster size in this paper based on a novel pseudolikelihood for correlated data we propose a score test without knowledge of the correlation structure or assuming data missingness at random the proposed score test can capture differences in the mean and variance between two groups simultaneously we use projection theory to derive the limiting distribution of the test statistic in which the covariance matrix can be empirically estimated we conduct simulation studies to evaluate the proposed test and compare it with existing methods to illustrate the usefulness proposed test we use it to compare self reported weight loss data in a friends referral group with the data from the internet self joining group

combining several screening tests optimality of the risk score the development of biomarkers for cancer screening is an active area of research while several biomarkers exist none is sufficiently sensitive and specific on its own for population screening it is likely that successful screening programs will require combinations of multiple markers we consider how to combine multiple disease markers for optimal performance of a screening program we show that the risk score defined as the probability of disease given data on multiple markers is the optimal function in the sense that the receiver operating characteristic roc curve is maximized at every point arguments draw on the neyman pearson lemma this contrasts with the corresponding optimality result of classic decision theory which is set in a bayesian framework and is based on minimizing an expected loss function associated with decision errors ours is an optimality result defined from a strictly frequentist point of view and does not rely on the notion of associating costs with misclassifications the implication for data analysis is that binary regression methods can be used to yield appropriate relative weightings of different biomarkers at least in large samples we propose some modifications to standard binary regression methods for application to the disease screening problem a flexible biologically motivated simulation model for cancer biomarkers is presented and we evaluate our methods by application to it an application to real data concerning two ovarian cancer biomarkers is also presented our results are equally relevant to the more general medical diagnostic testing problem where results of multiple tests or predictors are combined to yield a composite diagnostic test moreover our methods justify the development of clinical prediction scores based on binary regression

a class of logistic type discriminant functions summary in two group discriminant analysis the neyman pearson lemma establishes that the roc receiver operating characteristic curve for an arbitrary linear function is everywhere below the roc curve for the true likelihood ratio the weighted area between these two curves can be used as a risk function for finding good discriminant functions the weight function corresponds to the objective of the analysis for example to minimise the expected cost of misclassification or to maximise the area under the roc the resulting discriminant functions can be estimated by iteratively reweighted logistic regression we investigate some asymptotic properties in the near logistic setting where we assume the covariates have been chosen such that a linear function gives a reasonable but not necessarily exact

semiparametric methods for evaluating risk prediction markers in case control studies the performance of a well calibrated risk model for a binary disease outcome can be characterized by the population distribution of risk and displayed with the predictiveness curve better performance is characterized by a wider distribution of risk since this corresponds to better risk stratification in the sense that more subjects are identified at low and high risk for the disease outcome although methods have been developed to estimate predictiveness curves from cohort studies most studies to evaluate novel risk prediction markers employ case control designs here we develop semiparametric methods that accommodate case control data the semiparametric methods are flexible and naturally generalize methods previously developed for cohort data applications to prostate cancer risk prediction markers illustrate the methods

stability robustness of retarded lti systems with single delay and exhaustive determination of their imaginary spectra in this paper we consider the stability robustness of the general class of vector lti linear time invariant equations with a single delay dot bf x t bf a bf x t bf b bf x t tau bf x in bf r n the robustness is against the uncertain but constant delay tau in bf r we first present a set of novel propositions and state that the solution must start from the complete knowledge of imaginary spectra of the system and the corresponding delays the propositions claim that such spectra form a set of manageably small number of members and this number is upper bounded by n 2 regardless of the composition of bf a and bf b matrices they also claim that the infinite dimensional system at hand has an outstanding discipline regarding these imaginary spectra this discipline invites the recently developed concept called the cluster treatment of characteristic roots ctcr the ctcr procedure requires a complete and precise determination of the imaginary spectra of the system there are many procedures in the literature to achieve this they are in fact some variations of the five main methods of different levels of precision and complexity there is however no study known to the authors for presenting a comparison among these methods this paper addresses this need we first offer an overview of each of the five methods and then compare their numerical performances over an example case study

smooth semiparametric receiver operating characteristic curves for continuous diagnostic tests we propose a semiparametric kernel distribution function estimator based on which a new smooth semiparametric estimator of the receiver operating characteristic roc curve is constructed we derive the asymptotic bias and variance of the newly proposed distribution function estimator and show that it is more efficient than the traditional non parametric kernel distribution estimator we also derive the asymptotic bias and variance of our new roc curve estimator and show that it is more efficient than the smooth non parametric roc curve estimator proposed by zou et al stat med 1997 16 2143 2156 and lloyd j am stat assoc 1998 93 1356 1364 for our proposed estimators we derive data based methods for bandwidth selection in addition we present some results on the analysis of two real data sets finally a simulation study is presented to show that our estimators are better than the non parametric counterparts in terms of bias standard error and mean square error

an interpretation for the roc curve and inference using glm procedures the accuracy of a medical diagnostic test is often summarized in a receiver operating characteristic roc curve this paper puts forth an interpretation for each point on the roc curve as being a conditional probability of a test result from a random diseased subject exceeding that from a random nondiseased subject this interpretation gives rise to new methods for making inference about roc curves it is shown that inference can be achieved with binary regression techniques applied to indicator variables constructed from pairs of test results one component of the pair being from a diseased subject and the other from a nondiseased subject within the generalized linear model glm binary regression framework roc curves can be estimated and we highlight a new semiparametric estimator covariate effects can also be evaluated with the glm models the methodology is applied to a pancreatic cancer dataset where we use the regression framework to compare two different serum biomarkers asymptotic distribution theory is developed to facilitate inference and to provide insight into factors influencing variability of estimated model parameters

lyapunov equation for the stability of linear delay systems of retarded and neutral type in this note the delay independent stability of delay systems is studied it is shown that the strong delay independent stability is equivalent to the feasibility of certain linear matrix inequality lmi that is to the existence of a quadratic lyapunov krasovskii functional independent of the nonnegative value of the delay this constitutes the analogue of some well known properties of finite dimensional systems this result is then applied to study delay independent stability of systems with polytopic uncertainties

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

semiparametric roc surfaces for continuous diagnostic tests based on two test measurements we propose a semiparametric method for estimating roc surfaces for continuous diagnostic tests based on two test measurements such a three class diagnostic problem based on two test measurements arises naturally from some dna amplification related diagnostic scenarios simulation results show that our proposed semiparametric roc surface estimator is more efficient than the nonparametric counterpart and is quite comparable with the parametric counterpart when model assumption of the data is correctly specified for the parametric method moreover when the parametric model assumption is not true our proposed semiparametric method is superior to both nonparametric and parametric methods some discussions and a simulated example along with r programs for implementation of the proposed method are also provided

density estimation in the two sample problem with likelihood ratio ordering summary in this paper we propose a method for estimating the probability density functions in a two sample problem where the ratio of the densities is monotone this problem has been widely identified in the literature but effective solution methods in which the estimates should be probability densities and the corresponding density ratio should inherit monotonicity are unavailable if these conditions are not satisfied the applications of the resultant density estimates might be limited we propose estimates for which the ratio inherits the monotonicity property and we explore their theoretical properties one implication is that the corresponding receiver operating characteristic curve estimate is concave through numerical studies we observe that both the density estimates and the receiver operating characteristic curve estimate from our method outperform those resulting directly from kernel density estimates particularly when the sample size is relatively small

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

new approaches on stability criteria for neural networks with interval time varying delays abstract this paper concerns the problem of delay dependent stability criteria for neural networks with interval time varying delays first by constructing a newly augmented lyapunov krasovskii functional and combining with a reciprocally convex combination technique less conservative stability criterion is established in terms of linear matrix inequalities lmis which will be introduced in theorem 1 second by taking different interval of integral terms of lyapunov krasovskii functional utilized in theorem 1 further improved stability criterion is proposed in theorem 2 third a novel approach which divides the bounding of activation function into two subinterval are proposed in theorem 3 to reduce the conservatism of stability criterion finally through two well known numerical examples used in other literature it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea

maximum likelihood estimation of receiver operating characteristic roc curves from continuously distributed data we show that truth state runs in rank ordered data constitute a natural categorization of continuously distributed test results for maximum likelihood ml estimation of roc curves on this basis we develop two new algorithms for fitting binormal roc curves to continuously distributed data a true ml algorithm labroc4 and a quasi ml algorithm labroc5 that requires substantially less computation with large data sets simulation studies indicate that both algorithms produce reliable estimates of the binormal roc curve parameters a and b the roc area index az and the standard errors of those estimates

on a quasilinear wave equation with memory equation 1 l with a 0 and n 1 has its roots in a model for the small amplitude vibrations of a string in which the dependence of the tension on the deformation cannot be ignored see for example bernstein 2 carrier 3 41 dickey s and nishida 13 when a 0 1 1 may be used to describe the dynamics of an extensible string with fading memory this equation states that the dynamic equilibrium of a body depends not only on the present state of deformation but also on the previous history of the deformation gradient since the publication of the aforementioned papers equation 1 1 with a 0 has been the subject of intense scrutiny see for example arosio and spagnolo 11 lions 9 medeiros lo menzala ll nishihara 14 151 pohoiaev 16 and yamada 17 181 to name but a few among the facts thus far proved pohoiaev s results and their extension to the degenerate case of arosio and spagnolo are of particular significance they show that if the data satisfy an analytic type condition then solutions are global in time in spite of the abundant literature on the memoryless form of equation l l to our best knowledge equation 1 1 with a f 0 appears to be untouched our main results theorem 5 1 theorem 5 2 and theorem 5 4 will show that under appropriate assumptions on the kernel

augmented lyapunov krasovskii functional approaches to robust stability criteria for uncertain takagi sugeno fuzzy systems with time varying delays this paper considers the problem of robust stability analysis for uncertain takagi sugeno t s fuzzy systems with time varying delays by constructing an augmented lyapunov krasovskii functional and utilizing finsler s lemma a novel criterion for delay dependent robust stability of t s fuzzy model with time varying delay is derived in terms of linear matrix inequalities lmis also a further improved stability criterion is proposed by utilizing free weighting techniques finally three numerical examples are included to show the superiority of the proposed criteria

new and improved results on stability of static neural networks with interval time varying delays abstract in this paper the problem of stability analysis for static neural networks with interval time varying delays is considered by the consideration of new augmented lyapunov functionals new and improved delay dependent stability criteria to guarantee the asymptotic stability of the concerned networks are proposed with the framework of linear matrix inequalities lmis which can be solved easily by standard numerical packages the enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum delay bounds

small gain stability conditions for linear systems with time varying delays abstract in this paper we show that a variety of stability conditions both existing and new can be derived for linear systems subject to time varying delays in a unified manner in the form of scaled small gain conditions from a robust control perspective our development seeks to cast the stability problem as one of robust stability analysis and the resulting stability conditions are also reminiscent of robust stability bounds typically found in robust control theory the development is built on the well known conventional robust stability analysis requiring essentially no more than a straightforward application of the small gain theorem the derived conditions have conceptual appeal and they can be checked using standard robust control toolboxes

a goodness of fit test for logistic regression models based on case control data summary we test the logistic regression assumption under a case control sampling plan after reparameterisation the assumed logistic regression model is equivalent to a two sample semiparametric model in which the log ratio of two density functions is linear in data by identifying this model with a biased sampling model we propose a kolmogorov smirnovtype statistic to test the validity of the logistic link function moreover we point out that this test statistic can also be used in mixture sampling we present a bootstrap procedure along with some results on simulation and on analysis of two real datasets