a survey on oscillation of impulsive delay differential equations this paper presents a systematic development of the oscillatory results for the linear and nonlinear impulsive delay differential equations we also discuss linearized oscillation theory and give some applications to mathematical biology

principal and nonprincipal solutions of impulsive differential equations with applications we introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained the arguments are based on polya and trench factorizations as in non impulsive differential equations so we first establish these factorizations making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations examples are provided with numerical simulations to illustrate the relevance of the results

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

i optimal curve for impulsive lotka volterra predator prey model abstract for the classical lotka volterra predator prey system new notion i optimal curve i is introduced this curve is disposed in the phase space of the system the curve i intersects each trajectory c of lotka volterra system at least once the points of i possess the following optimal property if m m i c0 then after a jump with magnitude i to the origin of coordinates it hits a trajectory c1 and c 1 is minimal i e c 1 is the nearest to the stable centre the minimality concerns the rest points of initial trajectory c 0 from which the impulsive jumps subtractings with magnitude i to 0 0 are realized the monotonicity continuity and linear asymptotical behaviour of i curve are proved

estimation of the negative binomial parameter κ by maximum quasi likelihood we investigate estimation of the parameter k of the negative binomial distribution for small samples using a method of moments estimate mme and a maximum quasi likelihood estimate mqle previous work is reviewed the importance of indirect estimation of k through its reciprocal a and of allowance for negative estimates of k or a are discussed samples of size 50 are simulated 10 000 times for each of several parameter combinations to examine the properties of the estimates samples of sizes 10 20 30 and 50 are simulated 1 000 times to investigate the effect of sample size both estimators perform reasonably well except when the mean is small and the sample size does not exceed 20 three examples are given one of a designed experiment for which the mqle is especially suited confidence limits are derived for the mqle further work along these lines is required for adequate assessment of the usual maximum likelihood estimate

forced oscillation of super half linear impulsive differential equations by using a picone type formula in comparison with oscillatory unforced half linear equations we derive new oscillation criteria for second order forced super half linear impulsive differential equations having fixed moments of impulse actions in the superlinear case the effect of a damping term is also considered

oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations new oscillation criteria are obtained for second order forced mixed nonlinear impulsive differential equations of the form r t f a x q t f a x k 1nq k t f b k x e t t q ix q i a ix q i x q i b ix q i where f c s s c 1s and b 1 b 2 b m a b m 1 b n 0 if a 1 and the impulses are dropped then the results obtained by sun and wong y g sun j s w wong oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities j math anal appl 334 2007 549 560 are recovered examples are given to illustrate the results

second order quasilinear oscillation with impulses abstract sufficient conditions for oscillation of all solutions of a class of second order quasilinear differential equations with fixed moments of impulse effect are found

interval oscillation of a general class of second order nonlinear impulsive differential equations with nonlinear damping in this paper a general class of second order nonlinear impulsive differential equations with damping is studied several interval oscillation criteria which generalize and extend some known ones are established moreover examples are given to illustrate the effectiveness and non emptiness of our results

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

impulsive control of a nuclear spin generator in this paper several new theorems on the stability of impulsive control systems are presented these theorems are then used to find the conditions under which the nuclear spin generator can be asymptotically controlled to the equilibrium point by using impulsive control given the parameters of the nuclear spin generator and the impulsive control law we also present a theory of impulsive synchronization of two nuclear spin generators moreover a larger upper bound of impulsive intervals for the stabilization and synchronization can be obtained

linearized oscillation theory for a nonlinear delay impulsive equation for a scalar nonlinear impulsive delay differential equation y t k 1m rk t fk y hk t 0 t j y j ij y j with rk t 0 hk t t limj j such an auxiliary linear impulsive delay differential equation x t k 1m rk t ak t x hk t 0 x j bjx j is constructed that oscillation nonoscillation of the nonlinear equation can be deduced from the corresponding properties of the linear equation coefficients rk t and delays are not assumed to be continuous explicit oscillation and nonoscillation conditions are established for some nonlinear impulsive models of population dynamics such as the impulsive logistic equation and the impulsive generalized lasota wazewska equation which describes the survival of red blood cells it is noted that unlike nonimpulsive delay logistic equations a solution of a delay impulsive logistic equation may become negative

interval estimation of the over dispersion parameter in the analysis of one way layout of count data the over dispersion parameter is an important and versatile measure in the analysis of one way layout of count data in biological studies for example it is commonly used as an inverse measure of aggregation in biological count data its estimation from finite data sets is a recognized challenge many simulation studies have examined the bias and efficiency of different estimators of the over dispersion parameter for finite data sets see for example clark and perry biometrics 1989 45 309 316 and piegorsch biometrics 1990 46 863 867 but little attention has been paid to the accuracy of the confidence intervals cis of it in this paper we first derive asymptotic procedures for the construction of confidence limits for the over dispersion parameter using four estimators that are specified by only the first two moments of the counts we also obtain closed form asymptotic variance formulae for these four estimators in addition we consider the asymptotic ci based on the maximum likelihood ml estimator using the negative binomial model it appears from the simulation results that the asymptotic cis based on these five estimators have coverage below the nominal coverage probability to remedy this we also study the properties of the asymptotic cis based on the restricted estimates of ml extended quasi likelihood and double extended quasi likelihood by eliminating the nuisance parameter effect using their adjusted profile likelihood and quasi likelihoods it is shown that these cis outperform the competitors by providing coverage levels close to nominal over a wide range of parameter combinations two examples to biological count data are presented copyright 2010 john wiley sons ltd

bias corrected maximum likelihood estimator of the negative binomial dispersion parameter nous decrivons un estimateur du maximum de vraisemblance avec correction du premier ordre pour le biais sur le parametre de dispersion d une distribution binomiale negative cet estimateur est compare en terme debiais et d efficacite avec l estimateur du maximum de vraisemblance etudie par piegorsch 1990 biometrics 46 863 867 les estimateurs de moment et du maximum de quasi vraisemblance etendue de clark et perry 1989 biometrics 45 309 316 et un estimateur de double quasi vraisemblance etendue l estimateur du maximum de vraisemblance avec correction du biais a des proprietes de biais et d efficacite superieures dans la plupart des cas pour faciliter la comparaison nous donnons les resultats pour le modele binomial negatif a deux parametres cependant un exemple impliquant la regression binomiale negative est donne

picone s formula for linear non selfadjoint impulsive differential equations in this paper we derive a picone type formula for second order linear non selfadjoint impulsive differential equations having fixed moments of impulse actions and obtain a wirtinger type inequality a leighton type comparison theorem and a sturm picone comparison theorem for such equations moreover several oscillation criteria are also derived as applications

global attractivity in a food limited population model with impulsive effects abstract sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay logistic equation with impulsive effect n t r t n t k n p t k c t n p t n k n k exp i k ln n k k p where r t c t are continuous functions p k are positive constants and k k 1 denotes the sequence of impulsive time which assumed to be strictly increasing some special cases are also considered

sturmian comparison theory for linear and half linear impulsive differential equations in this paper we investigate sturmian comparison theory for second order half linear differential equations with fixed moments of impulse actions it is shown that impulse actions may greatly change the behavior of solutions in comparison several oscillation criteria are also derived to illustrate the results

less conservative conditions for asymptotic stability of impulsive control systems this note studies the stability of impulsive control systems a new comparison theorem for asymptotic stability of impulsive differential system is presented based on the new result we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also enlarged

oscillations of second order nonlinear impulsive ordinary differential equations consider the second order impulsive ordinary differential equation r t x t f t x t 0 t t 0 t t k k 1 2 x t k g k x t k x t k h k x t k k 1 2 e where 0 t 0 1 k k t k is any quotient of positive odd integers we obtain some sufficient conditions ensuring that all solutions of e oscillate

sturmian theory for second order differential equations with mixed nonlinearities in the paper sturmian comparison theory is developed for the pair of second order differential equations first of which is the nonlinear differential equations 1 m t y s t y i 1 n q i t y i 1 y 0 with mixed nonlinearities 1 m 1 m 1 n and the second is the nonselfadjoint differential equations 2 k t x r t x p t x 0 under the assumption that the solution of eq 2 has two consecutive zeros we obtain sturm picone type and leighton type comparison theorems for eq 1 by employing the new nonlinear version of picone s formula that we derive wirtinger type inequalities and several oscillation criteria are also attained for eq 1 examples are given to illustrate the relevance of the results

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

some necessary conditions for codes to be good for error detection codes for error detection on a q ary symmetric channel are studied whether a code is good or not for error detection in the technical sense depends on the structure of the code for some combinations of the main parameters length size and minimum distance all code are good and for some other combinations all are ugly stronger than not good the purpose of this paper is to give bounds on the parameters for codes that are not good for error detection in particular it is shown that if the minimum distance is below some bound which depends on the length and size of the code as well as a lower bound on the number of codewords of minimum distance then the code is ugly and hence not good for error detection

boundedness for impulsive delay differential equations and applications to population growth models abstract in this paper criteria on uniform ultimate boundedness are derived for impulsive delay differential equations using lyapunov functions and razumikhin techniques it should be noted that the boundedness criteria establish global existence of solutions as well as boundedness without assuming a priori that solutions can necessarily be continued to infinity those criteria are then used to obtain permanence results for population growth models some examples are discussed to illustrate the theorems