on estimating standardized risk differences from odds ratios an estimator proposed by greenland and holland 1991 biometrics 47 319 322 for a standardized risk difference parameter is shown to be a maximum likelihood estimator if the consistent estimator of the common odds ratio is appropriately chosen the statistical problem under consideration is reparameterized likelihood equations are derived

asymptotic behaviour of resolvents of abstract volterra equations abstract we give necessary and sufficient conditions for certain volterra integral and integrodifferential equations in some banach space to have a resolvent that belongs to some weighted l 1 space these conditions involve the invertibility of functions of the laplace transforms of the kernels

local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in banach spaces abstract in this work we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in banach spaces we suppose that the undelayed part admits a resolvent operator in the sense of grimmer r grimmer resolvent operators for integral equations in a banach space transactions of the american mathematical society 273 1982 333 349 the delayed part is assumed to be locally lipschitz firstly we show the existence of the mild solutions secondly we give sufficient conditions ensuring the existence of strict solutions

on linear volterra equations in banach spaces abstract in this paper we present the basic theory for a class of volterra differential integral equations of convolution type in banach spaces we show that existence of resolvent operator for such an equation is equivalent to its wellposedness and we obtain a hille yosida theorem unfortunately this result is not easy to apply and therefore it is important to have peturbation theorems available we present a result of this type which also contains an existence theorem and show by means of several examples that it cannot be improved

on the spreading and localization of risky information in social networks abstract we propose a model for the localization of risky information in social scale free networks where we assume that risky information can propagate only between mutually trusted nodes mtn we propose an algorithm to construct the mtn network and show that there is a critical value m c 2 of trusted nodes below which information localizes this critical value increases drastically if a fraction p of nodes does not transfer information at all we study the fraction of initial messengers needed to inform a desired fraction of the network as a function of the average number of trusted nodes m and discuss possible applications of the model also to marketing and to the spreading of a disease with very short incubation time

global behavior of positive solutions of nonlinear three point boundary value problems we investigate the structure of the positive solution set for nonlinear three point boundary value problems of the form u h t f u 0 u 0 0 u 1 lambdau eta where eta epsilon 0 1 is given lambda epsilon 0 1 n is a parameter f epsilon c 0 infinity 0 infinity satisfies f s 0 for s 0 and h epsilon c 0 1 0 infinity is not identically zero on any subinterval of 0 1 our main results demonstrate the existence of continua of positive solutions of the above problem c 2004 elsevier ltd all rights reserved

discrete opinion dynamics on networks based on social influence a model of opinion dynamics based on social influence on networks was studied the opinion of each agent can have integer values i 1 2 i and opinion exchanges are restricted to connected agents it was found that for any i 2 and self confidence parameter 0 u 1 when u is a degree independent constant the weighted proportion qi of the population that hold a given opinion i is a martingale and the fraction qi of opinion i will gradually converge to qi the tendency can slow down with the increase of degree assortativity of networks when u is degree dependent qi does not possess the martingale property however qi still converges to it in both cases for a finite network the states of all agents will finally reach consensus further if there exist stubborn persons in the population whose opinions do not change over time it was found that for degree independent constant u both qi and qi will converge to fixed proportions which only depend on the distribution of initial obstinate persons and naturally the final equilibrium state will be the coexistence of diverse opinions held by the stubborn people the analytical results were verified by numerical simulations on barabasi albert ba networks the model highlights the influence of high degree agents on the final consensus or coexistence state and captures some realistic features of the diffusion of opinions in social networks

percolation critical exponents in scale free networks we study the behavior of scale free networks having connectivity distribution p k k 2l close to the percolation threshold we show that for networks with 3 l 4 known to undergo a transition at a finite threshold of dilution the critical exponents are different than the expected mean field values of regular percolation in infinite dimensions networks with 2 l 3 possess only a percolative phase nevertheless we show that in this case percolation critical exponents are well defined near the limit of extreme dilution where all sites are removed and that also then the exponents bear a strong l dependence the regular mean field values are recovered only for l 4

regular problem for solutions of a retarded semilinear differential nonlocal equation abstract this paper deals with the regularity and existence of solutions of a retarded semilinear differential equation with nonlocal condition by using the fundamental solution in the case where the principal operators are unbounded operators

estimation of a common effect parameter from sparse follow up data breslow 1981 biometrika 68 73 84 has shown that the mantel haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications for cohort studies however estimation of a common risk ratio or risk difference can be of greater interest under a binomial sparse data model the mantel haenszel risk ratio and risk difference estimators are consistent in sparse stratifications while the maximum likelihood and weighted least squares estimators are biased under poisson sparse data models the mantel haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent while the weighted least squares estimators are again biased similarly of the common rate difference estimators the weighted least squares estimators are biased while the estimator employing mantel haenszel weights is consistent in sparse data variance estimators that are consistent in both sparse data and large strata can be derived for all the mantel haenszel estimators

approximate controllability of semi linear neutral integro differential systems with finite delay abstract this paper considers the approximate controllability of semilinear neutral integrodifferential systems with finite delay in hilbert space since the considered equation admits nonlinear terms involving spatial derivatives the fraction power theory and norm are used to discuss the problem so that the established results can be applied to them the results are obtained by using the sadovskii fixed point theorem and the theory of analytic resolvent operator an example is presented to illustrate the applications of the obtained results

existence of solutions for semilinear neutral stochastic functional differential equations with nonlocal conditions abstract in this paper by using fractional power of operators and sadovskii fixed point theorem the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions is studied the results are a generalization and continuation of the recent results on this issue an example is provided to illustrate the theory

the interpretation of multiplicative model parameters as standardized parameters under current conventions relative risk estimates obtained from multiplicative models are interpreted as estimates of a homogeneous effect such interpretations condition on the unverifiable assumption that the relative risk under study is homogeneous an assumption that is not likely to be correct even if the model fits well we propose that such estimates are better interpreted as estimates of standardized relative risks with a bias component that depends on the degree of model misspecification and on the study design to evaluate our proposal we present a study of the maximum likelihood estimators from poisson and logistic regression compared to the population standardized rate ratio the results indicate that our proposed interpretation would in practice be more cautious and accurate than the homogeneous effect interpretation

existence and regularity of solutions for some partial functional integrodifferential equations in banach spaces abstract in this work we study the existence and regularity of solutions for some partial functional integrodifferential equations in banach spaces we suppose that the undelayed part admits a resolvent operator in the sense given by grimmer in r grimmer resolvent operators for integral equations in a banach space transaction of american mathematical society 273 1982 333 349 the delayed part is assumed to be locally lipschitz firstly we show the existence of the mild solutions secondly we give sufficient conditions ensuring the existence of the strict solutions

asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions abstract of concern is a class of abstract semilinear integrodifferential equations with nonlocal initial conditions under some suitable hypotheses we establish some new theorems about the existence of asymptotically almost automorphic solutions to the integrodifferential equations moreover an example is given to illustrate our results

exponential stabilization of volterra integrodifferential equations in hilbert space we consider exponential stabilization of an abstract linear volterra integrodifferential equation in a hilbert space u e1au t e2 01k t s au s ds f t by a feedback control f t c0u t c1u t with bounded linear operators c0 and c1 of finite rank a is a positive semidefinite self adjoint unbounded operator k is nonnegative convex and decreasing with exponential decay k 0 being finite we introduce a concept of essential growth rate for resolvent operators similar to that for c0 semigroups and prove that the resolvent for the volterra equation has the same essential growth as the solution semigroup to u t e1au t e2k 0 e1u t f t stability can be checked by the location of poles and it is shown that exponential stabilization is possible with a decay rate of at most e2k 0 2e1 we apply our results to two problems concerning stabilization of motion of viscoelastic bodies

nonlocal cauchy problems governed by compact operator families abstract we study the existence of mild solutions for the nonlocal cauchy problem u t au t f t u t t t 0 t 0 t u t 0 g u u 0 and give new criterions which extend some existing results in this area

dynamics of rumor propagation on small world networks we study the dynamics of an epidemiclike model for the spread of a rumor on a small world network it has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network randomness here by numerical means we perform a quantitative characterization of the evolution in the two regimes the variant of dynamic small worlds where the quenched disorder of small world networks is replaced by randomly changing connections between individuals is also analyzed in detail and compared with a mean field approximation

empirical and counterfactual conditions for sufficient cause interactions summary sufficient component causes are discussed within the deterministic potential outcomes framework so as to formalize notions of sufficient causes synergism and sufficient cause in teractions doing so allows for the derivation of counterfactual and empirical conditions for detecting the presence of sufficient cause interactions the conditions are novel in that unlike other conditions in the literature they make no assumption about monotonicity the conditions can also be generalized and the conditions for three way sufficient cause interactions are given explicitly the statistical tests derived for sufficient cause interactions are compared with and contrasted to interaction terms in standard statistical models

on some fractional evolution equations abstract in this paper the solutions of some evolution equations with fractional orders in a banach space are considered conditions are given which ensure the existence of a resolvent operator for an evolution equation in a banach space

on almost automorphic type solutions of abstract integral equations a bohr neugebauer type property and some applications abstract in the present work we give some sufficient conditions to obtain a unique almost automorphic solution to abstract nonlinear integral equations which are simultaneously of advanced and delayed type and also a unique asymptotically almost automorphic mild solution to abstract integro differential equations with nonlocal initial conditions both situations are posed on banach spaces also we develop a bohr neugebauer type result for the abstract integral equations before that we introduce the notion of bounded functions develop the appropriate abstract theory and discuss the almost periodic situation as applications we study the existence of an asymptotically almost automorphic solution to integro differential equations modeling heat conduction in materials with memory and also the existence of the almost automorphic solution to semilinear parabolic evolution equations with finite delay

existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fbm with noncompact semigroup via monch fixed point abstract in this paper we investigate the existence and exponential stability of mild solutions for a class of impulsive neutral stochastic functional differential equations driven by fbm with noncompact semigroup in hilbert spaces sufficient conditions for the existence of mild solutions are obtained using the hausdorff measure of noncompactness and the monch fixed point theorem further we establish a new impulsive integral inequality to prove the exponential stability of mild solutions in the mean square moment finally an example is presented to illustrate our obtained results

estimating standardized parameters from generalized linear models although the traditional unrestricted non parametric estimators of directly standardized rates and rate differences remain unbiased in sparse data they tend to suffer from instability low precision as a result many authors have proposed more precise estimators based on parametric models for the rates this paper provides a general approach for constructing estimators of standardized parameters using generalized linear models and shows that in some common special cases these model based smoothed estimators can have an exceptionally simple form

impulsive neutral stochastic functional integro differential equations with infinite delay driven by fbm in this paper we study a class of impulsive neutral stochastic functional integro differential equations with infinite delay driven by a standard cylindrical wiener process and an independent cylindrical fractional brownian motion fbm with hurst parameter h 1 2 1 in the hilbert space we prove the existence and uniqueness of the mild solution for this kind of equations with the coefficients satisfying some non lipschitz conditions which include the classical lipschitz conditions as special case an example is provided to illustrate the theory some well known results are generalized and extended

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

existence results for impulsive differential inclusions with nonlocal conditions abstract in this paper we shall establish sufficient conditions for the existence of mild solutions for nonlocal impulsive differential inclusions on the basis of the fixed point theorems for multivalued maps and the technique of approximate solutions new results are obtained examples are also provided to illustrate our results

fractional variational principles with delay the fractional variational principles within riemann liouville fractional derivatives in the presence of delay are analyzed the corresponding euler lagrange equations are obtained and one example is analyzed in detail

existence results for systems with coupled nonlocal initial conditions abstract in this paper an existence theory is developed for first order differential systems with coupled nonlocal conditions given by stieltjes integrals the approach is based on the fixed point theorems of perov schauder and schaefer and on a vector method for treating systems which uses matrices having spectral radius less than one when the nonlocal conditions depend on functionals restricted to a proper subinterval the nonlinear integral operator associated to the system splits into two parts one of fredholm type and another one of volterra type correspondingly the sufficient conditions for the existence results will differ in the two parts of the interval some examples are presented to illustrate the theory

integral equations as evolution equations abstract we study a class of time dependent linear integrodifferential equations ve with the evolution equation approach we determine the generators of a time dependent evolution equation de which is equivalent to the given integrodifferential equation under very general assumptions we prove the well posedness and continuity of ve from the stability of de the related question of convergence of a family of approximate solutions is examined as an application we include an example of hyperbolic integro partial differential equation to illustrate the theory

the existence and asymptotic behavior of solutions to fractional stochastic evolution equations with infinite delay abstract we first prove the existence uniqueness and continuous dependence of mild solutions to stochastic delay evolution equations with a caputo fractional derivative d t c y t a y t f t y t g t y t d w t d t 1 2 1 then we investigate the asymptotic behavior of mild solutions to fractional stochastic delay evolution equations of the form d t c y t a y t i t 1 f t y t i t 1 g t y t d w t d t 0 1 in particular the existence of a global forward attracting set in the mean square topology is established a general theorem on the existence of mild solutions is obtained by using order fractional resolvent operator theory and the schauder fixed point theorem

nonlocal cauchy problem for analytic resolvent integrodifferential equations in banach spaces abstract in this paper we prove the existence of semi classical and mild solutions of nonlinear integrodifferential equations with nonlocal conditions in banach spaces the results are obtained by using the theory of analytic resolvents and schaefer s fixed point theorem

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

on s asymptotically ω periodic functions and applications abstract let x be a banach space and r a bounded function u c 0 x is called s asymptotically periodic if lim t u t u t 0 in this paper we establish conditions under which an s asymptotically periodic function is asymptotically periodic and we discuss the existence of s asymptotically periodic and asymptotically periodic solutions for an abstract integral equation some applications to partial differential equations and partial integro differential equations are considered

existence and regularity for a class of integrodifferential equations of parabolic type the method we use rests on the inversion of the formal laplace transform of r and allows one to analyze the regularity of the solution u problem 1 1 has been studied by several authors using various methods see for instance l 18 211 the laplace transform approach presented here has been used in s 7 9 14 153 in our previous papers s 7 93 we have in fact analyzed a more general situation while here we take full 36 0022 247x 85 3 00

a semilinear parabolic volterra integrodifferential equation abstract we consider the semilinear volterra integrodifferential equation u t a t u t t 0 t a t s g s u s ds t u t t t 0 u t 0 u 0 we assume that for each t 0 the linear operator a t is the negative generator of an analytic semigroup in a banach space x the nonlinear operator g t is lipschitz continuous on the domain of a 0 into x and the forcing term t u satisfies a holder condition in both variables we prove existence of solutions in the banach space x and uniqueness of solutions when x is a hilbert space we also consider an example where a t a a t s a t s and show that the corresponding solutions u t x converge as t to a solution u x of a related semilinear elliptic boundary value problem

existence and uniqueness theorem for a class of delay differential equations with left and right caputo fractional derivatives the existence and uniqueness theorems for functional right left delay and left right advanced fractional functional differential equations with bounded delay and advance respectively are proved the continuity with respect to the initial function for these equations is also proved under some lipschitz kind conditions the q operator is used to transform the delay type equation to an advanced one and vice versa an example is given to clarify the results

nonlocal nonlinear differential equations with a measure of noncompactness in banach spaces abstract in this paper we give the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions under the assumptions of the hausdorff measure of noncompactness in separable and uniformly smooth banach spaces

new uniqueness results of solutions for fractional differential equations with infinite delay in this paper by using fixed point theory and a new method we study the existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations and neutral differential equations with infinite delay and obtain two new existence and uniqueness results

existence of classical solutions to nonautonomous nonlocal parabolic problems abstract we obtain a new existence theorem for classical solutions to nonautonomous equations with nonlocal initial conditions u t a t u t f t u t t s t u s g u u 0 in a banach space x where t s 0 f g are given x valued functions and a t is a sectorial operator not necessarily densely defined in x for each t 0 t both banach s contraction principle and schauder s fixed point theorem as well as the theory of evolution families and interpolation spaces are employed in our approach a concrete example is shown to illustrate the existence theorem

existence and uniqueness of solutions to semilinear nonlocal parabolic equations abstract the banach contraction mapping theorem and the theory of analytic semigroups are used to prove the existence and uniqueness of solutions to nonlocal semilinear parabolic partial differential equations the equations consist of a parabolic boundary value problem and a relation connecting the initial value to values or weighted averages of values of the solution at other times

semilinear integrodifferential equations with nonlocal initial conditions abstract of concern is the cauchy problem for semilinear integrodifferential equations with nonlocal initial conditions under general and natural hypotheses we establish some new theorems about the existence and uniqueness of solutions for the cauchy problem as a consequence we unify and extend the corresponding theorems given previously for the cauchy problem for differential equations or integrodifferential equations with nonlocal initial conditions moreover we present two examples one of which comes from heat conduction in materials with memory to show that the existing results are not applicable to them in contrast with ours

nonlocal in time problem for anisotropic parabolic equations with variable exponents of nonlinearities abstract in this study we consider nonlinear parabolic equations with variable exponents of the nonlinearities the nonlocal problem for these equations is investigated and the existence and uniqueness theorems are proved for the problem

on the resolvent of linear nonautonomous partial functional differential equations abstract we give sufficient conditions for the existence of the resolvent operator for nonautonomous linear partial differential equations with delay where the highest order derivatives are undelayed furthermore we analyse the connection between the resolvent and the solution operator of the homogeneous equation

controllability of nonlinear neutral evolution integrodifferential systems sufficient conditions for controllability of nonlinear neutral evolution integrodifferential systems in a banach space are established the results are obtained by using the resolvent operators and the schaefer fixed point theorem an application to partial integrodifferential equation is given

standardized estimates from categorical regression models we consider the problem of interpreting categorical regression models such as the polytomous logistic model the continuation ratio model the stereotype model and the cumulative odds model we present a method to convert categorical regression coefficients into estimates of standardized fitted probabilities probability differences and probability ratios we use a delta method approach to estimate standard errors we then present a small simulation study to compare different transforms for setting confidence limits and provide an illustration of our approach in an observational study of drug therapy of polymyositis

a note on the covariance of the mantel haenszel log odds ratio estimator and the sample marginal rates a simple technique developed in phillips unpublished ph d dissertation university of windsor windsor ontario 1987 is used to approximate cov theta mh pi i 1 2 where theta mh is the mantel haenszel log odds ratio estimator for a 2 x 2 x k table and the pi are the sample marginal proportions these results are then applied to obtain an approximate variance estimate of an adjusted risk difference based on the mantel haenszel odds ratio estimator

stability and stabilizability of infinite dimensional systems in this paper we are concerned with stability problems for infinite dimensional systems first we review the theory for linear systems where the dynamics are governed by strongly continuous semigro

robustness of linear systems abstract in this paper we consider linear systems which are stable and examine the robustness of this property the perturbations are assumed to have unbounded structure and we determine the smallest perturbation which destroys stability we begin with an abstract analysis of the problem but in later sections specialize to three types of systems those whose mild solutions are given in terms of 1 a strongly continuous semigroups 2 b resolvent operators integrodifferential systems 3 c evolution operators time varying systems for b a banach space l2 t0 t b denotes the space of all square integrable functions defined on t0 t with values in b for b1 b2 banach spaces t0 t denotes the space of strongly measurable functions f t0 t l b1 b2 with ess sup f b 1 t0 l b1 b2 denotes the space of strongly measurable functions f t0 l b1 b2 with f t 0 and k l1 t0

existence of asymptotically almost automorphic solutions to some abstract partial neutral integro differential equations abstract the paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro differential equation with unbounded delay an example is given to illustrate our results

existence and uniqueness of global mild solutions for a class of nonlinear fractional reaction diffusion equations with delay abstract in this paper we study the mild solutions of a class of nonlinear fractional reaction diffusion equations with delay and caputo s fractional derivatives by the measure of noncompactness the theory of resolvent operators the fixed point theorem and the banach contraction mapping principle we develop various theorems for the existence and uniqueness of the global mild solutions for the problem

existence of solutions for neutral integro differential equations with state dependent delay in this paper we study the existence and regularity of solutions for a neutral functional integro differential equation with state dependent delay in banach space the mild solutions are investigated by sadovskii fixed point theorem under compactness condition for the resolvent operator and the theory of fractional power and a norm are also used in the discussion since the nonlinear terms of the system involve spacial derivatives the strict solutions are obtained under holder continuity condition hence this work extends and develops the existed results on this topic in the end an example is provided to illustrate the application of the obtained results

assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome this paper proposes a simple technique for assessing the range of plausible causal con clusions from observational studies with a binary outcome and an observed categorical covariate the technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response a medical study of coronary artery disease is used to illustrate the technique inevitably the results of clinical studies are subject to dispute in observational studies one basis for dispute is obvious since patients were not assigned to treatments at random patients at greater risk may be over represented in some treatment groups this paper proposes a method for assess ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response despite their limitations observational studies will continue to be a valuable source of information and therefore it is prudent to develop appropriate methods of analysis for them our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u under several sets of assumptions about u both cornfield et al 1959 and bross 1966 have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment that is whether the treatment effect after adjustment for u could be zero our method has two advantages first cornfield et al 1959 and bross 1966 adjust only for the unmeasured binary covariate u whereas we adjust for measured covariates in addition to the unmeasured covariate u second cornfield et al 1959 and bross 1966 1967 only judge whether the effect of the treatment could be zero having adjusted for u where cornfield et al 1959 employ an implicit yet extreme assumption about u in contrast we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u in principle the ith of the n patients under study has both a binary response r1i that would have resulted if he had received the new treatment and a binary response ro0 that would have resulted if he had received the control treatment in this formulation treatment effects are comparisons of r1i and roi such as r1i roi since each patient receives only one treatment either rli or ro0 is observed but not both and therefore comparisons of rli and roi imply some degree of speculation treatment effects defined as comparisons of the two potential responses r1i and roi of individual patients are implicit in fisher s 1953 randomization test of the sharp null

regularity of solutions of evolution integrodifferential equations with deviating argument abstract in this paper we prove the existence of mild and classical solutions of delay integrodifferential equation and delay integrodifferential evolution equations with nonlocal condition in banach spaces the regularity solutions of integrodifferential evolution equations interconnected with viscoelastic material is derived to guarantee the stabilization the results are established by using the resolvent operators and the fixed point principles finally an example is given to show the potential of the proposed techniques

existence of mild solutions for semilinear evolution equations with non local initial conditions abstract in this paper we study the existence of mild solutions for a class of semilinear evolution equations with non local initial conditions and extend some related results in this direction

nonlocal solutions of parabolic equations with strongly elliptic differential operators abstract the paper deals with second order parabolic equations on bounded domains with dirichlet conditions in arbitrary euclidean spaces their interest comes from being models for describing reaction diffusion processes in several frameworks a linear diffusion term in divergence form is included which generates a strongly elliptic differential operator a further linear part of integral type is present which accounts of nonlocal diffusion behaviours the main result provides a unifying method for studying the existence and localization of solutions satisfying nonlocal associated boundary conditions the cauchy multipoint and the mean value conditions are included in this investigation the problem is transformed into its abstract setting and the proofs are based on the homotopic invariance of the leray schauder topological degree a bounding function i e lyapunov like function theory is developed which is new in this infinite dimensional context it allows that the associated vector fields have no fixed points on the boundary of their domains and then it makes possible the use of a degree argument

a class of hyperbolic volterra integrodifferential equations on considere l existence des solutions pour l equation integrodifferentielle de volterra u t a t u t 0 t g t s u s ds f 0 t f 1 t u t t 0 u 0 u 0

analytic resolvent operators for integral equations in banach space on etudie l equation integrodifferentielle x t a 0 x t 0 t b t s x s ds f t t 0 x 0 x 0 ed a x et l equation integrale x t 0 t a t s x s ds f t dans un espace de banach x les operateurs a a 0 b t et a t sont des operateurs clos sur x a domaine dense

model based direct adjustment abstract direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population direct adjustment has several attractive features but when there are many subclasses it can attach large weights to small quantities of data often in a fairly erratic manner in the extreme direct adjustment can attach infinite weight to nonexistent data a noticeable inconvenience in practice this article proposes a method of model based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses the sample mean and conventional direct adjustment are both special cases of model based direct adjustment under two different extreme models for the subclass specific selection probabilities the discussion of this method provides some insights into the behavior of true and estimated propensity scores the estimated scores

some well posed functional equations which generate semigroups consider the abstract linear functional equation fe dx t f t t 0 x t t t 0 in a banach space b a theorem is proven which contains the following result as a special case let y r b be a lp space or c0 space on r t8 with a suitable weight function and with values in b let d be a closed unbounded causal linear operator in y r b which commutes with translations suppose that d i has a continuous causal inverse for some complex and that d restricted to those functions in y r b which vanish on r 0 has a continuous causal inverse then fe generates a strongly continuous semigroup of translation type on a banach space which is essentially the cross product of the restriction of the domain of d to r and y r b examples with b cn on how the theory applies to a neutral functional differential equation a difference equation a volterra integrodifferential equation with nonintegrable kernel but integrable resolvent and a fractional order functional differential equation are given also an abstract neutral functional differential equation in a hilbert space is studied and applications to an abstract volterra integrodifferential equation in a banach space are indicated

using empirical bayes methods in biopharmaceutical research a compound sampling model where a unit specific parameter is sampled from a prior distribution and then observed are generated by a sampling distribution depending on the parameter underlies a wide variety of biopharmaceutical data for example in a multi centre clinical trial the true treatment effect varies from centre to centre observed treatment effects deviate from these true effects through sampling variation knowledge of the prior distribution allows use of bayesian analysis to compute the posterior distribution of clinic specific treatment effects frequently summarized by the posterior mean and variance more commonly with the prior not completely specified observed data can be used to estimate the prior and use it to produce the posterior distribution an empirical bayes or variance component analysis in the empirical bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects in both the bayes and empirical bayes approaches estimated clinic effects are shrunken towards a common value from estimates based on single clinics this shrinkage produces more efficient estimates in addition the compound model helps structure approaches to ranking and selection provides adjustments for multiplicity allows estimation of the histogram of clinic specific effects and structures incorporation of external information this paper outlines the empirical bayes approach coverage will include development and comparison of approaches based on parametric priors for example a gaussian prior with unknown mean and variance and non parametric priors discussion of the importance of accounting for uncertainty in the estimated prior comparison of the output and interpretation of fixed and random effects approaches to estimating population values estimating histograms and identification of key considerations in the use and interpretation of empirical bayes methods

approximate controllability of nonlocal and impulsive neutral integro differential equations using the resolvent operator theory and an approximating technique abstract our purpose in this paper is to study the approximate controllability of nonlocal and impulsive neutral integro differential equations using the resolvent operator theory the approximating technique semigroup theory and the theory of fixed point we also derive a variation of constants formula for representing a solution of the given system by resolvent operators and then study the existence of a mild solution of the system we prove the main results by taking the impulsive functions to be continuous only and taking the nonlocal initial condition function to be lipschitz continuous in the first case and continuous only in the second case finally the main results are illustrated using examples

a semi bayes approach to the analysis of correlated multiple associations with an application to an occupational cancer mortality study thomas et al presented the application of empirical bayes methods to the problem of multiple inference in epidemiologic studies one limitation of their approach which they noted was the need to assume exchangeable log relative risk parameters and independent relative risk estimates numerical integration was also required here i generalize their approach to allow for non exchangeable parameters and non independent estimates the resulting method is bayesian in so far as some feature of the prior distribution are specified from prior information but is empirical bayes in so far as some explicit parameters in the prior distribution are estimated from the data estimation is based on approximations to the posterior distribution this allows one to implement the approach with standard software packages for matrix algebra the method is illustrated in an occupational mortality study of 84 exposure cancer associations

analysis of covariance and standardization as instances of prediction in this paper prediction provides the basis for unifying the procedures of covariances adjustment and standardization analysis of covariance is a method of forming predictions from a linear model it is used when qualitative effects are to be studied and the effects of continuous variables are to be adjusted for an essential feature is the division into effects of interest and effects for which adjustment is required covariates may also be qualitative as such they are used implicitly in experimental designs with blocks where treatment effects are adjusted for the effect of blocks the technique of standardization is well known in epidemiology and demography as a method of adjusting explicitly for qualitative effects the same division of effects applies when an analysis that uses generalized linear models is summarized two distinct types of prediction which give identical results in classical linear models are available prediction may be conditional on a fixed value of a covariate or marginal on a distribution of values such as the distribution in the set of data being analysed prediction methods are illustrated by the analysis of a table of proportions by use of a logit model

positive solutions to singular boundary value problems for fractional functional differential equations with changing sign nonlinearity in this work a boundary value problem is discussed for a singular delay differential equation of fractional order the nonlinearity may change sign by means of the krasnoselskii fixed point theorem existence results for positive solutions are obtained examples illustrating our main results are also given

nonlinear differential equations with nonlocal conditions in banach spaces abstract in this paper we study the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions in banach spaces we derive conditions under which the integral solutions exist

variance estimators for attributable fraction estimates consistent in both large strata and sparse data a number of variance formulae for the attributable fraction have been presented but none is consistent in sparse data such as found in individually matched case control studies this paper employs mantel haenszel estimation to derive variance estimators for attributable fractions that are dually consistent that is consistent in both sparse data and large strata the method may also be applied using conditional maximum likelihood extensions of these estimators to situations involving effect modification and preventive exposures are also derived examples of applications to individually matched case control studies are given

approximate controllability results for analytic resolvent integro differential inclusions in hilbert spaces abstractin this work we consider a nonlinear resolvent integro differential evolution inclusions in hilbert spaces this paper deals with the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces we use bohnenblust karlin s fixed point theorem to establish a set of sufficient conditions for the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces further we extend the result to study the approximate controllability concept with non local conditions an example is presented to demonstrate the obtained theory