model inconsistency illustrated by the cox proportional hazards model we consider problems involving the comparison of two or more treatments where we have the opportunity to adjust for relevant covariates either conditionally in a regression model or implicitly in repeated measures data for example in crossover trials it is seen that for data arising from non normal distributions there is the possibility that models adjusting for covariates and those not adjusting for covariates will be inconsistent that is at most one of the models can be valid alternatively even if conditional and unconditional models are valid parameters in each model may have different interpretations we note that this presents difficulties for the specification and interpretation of the analysis it is also clear that model validation is critical specific attention is paid to survival data analysed by the cox proportional hazards model

weight enumerators of extremal singly even 60 30 12 codes conway and sloane 1990 have listed the possible weight enumerators for extremal self dual codes up to length 72 in this correspondence we construct extremal singly even self dual 60 30 12 codes whose weight enumerator does not appear in this list in addition we present the possible weight enumerators for extremal self dual codes of length 60

on the algebraic structure of quasi cyclic codes i finite fields a new algebraic approach to quasi cyclic codes is introduced the key idea is to regard a quasi cyclic code over a field as a linear code over an auxiliary ring by the use of the chinese remainder theorem crt or of the discrete fourier transform dft that ring can be decomposed into a direct product of fields that ring decomposition in turn yields a code construction from codes of lower lengths which turns out to be in some cases the celebrated squaring and cubing constructions and in other cases the u spl upsi u spl upsi and vandermonde constructions all binary extended quadratic residue codes of length a multiple of three are shown to be attainable by the cubing construction quinting and septing constructions are introduced other results made possible by the ring decomposition are a characterization of self dual quasi cyclic codes and a trace representation that generalizes that of cyclic codes

half linear differential equations linearization technique and its application abstract oscillatory properties of the half linear second order differential equation r t x c t x 0 x x p 2 x p 1 are investigated where is viewed as a perturbation of an equation of the same form and these properties are compared with the oscillatory behavior of a certain associated linear second order differential equation as a corollary a conjecture posed by the first author in the paper o dosl perturbations of the half linear euler weber differential equations j math anal appl 323 2006 426 440 is proved and some new research problems are formulated

integral conditions for nonoscillation of second order nonlinear differential equations an extension of the fubini theorem is presented and applied in studying the possible coexistence of nonoscillatory solutions for the differential equation r t x sgnx q t x sgnx some discrepancies among the cases and are illustrated and compared with the linear case in addition when an application to the integral characterization of principal solutions which answers an open problem stated in o dosl a elbert integral characterization of the principal solution of half linear second order differential equations studia sci math hungar 36 2000 455 469 is given

on the insensitivity of the score test for heterogeneity to omitted covariates in multivariate failure time models the multivariate weibull distribution often provides a point of departure for modelling repeated or a sequence of failure times for a particular individual it is then natural to want to test the implied assumption of homogeneity and a number of authors have derived a score test for this purpose see for example kimber 1996 in the present paper it is shown that the proposed score test for neglected heterogeneity can be insensitive to specification error in the implied log linear regression structure

extremal self dual codes with an automorphism of order 2 a method to design binary self dual codes with an automorphism of order two without fixed points is presented extremal self dual codes with lengths 40 42 44 54 58 68 are constructed many of them have weight enumerators for which extremal codes were previously not known to exist

nonoscillatory half linear differential equations and generalized karamata functions abstract we introduce a natural generalization of the concept of regularly varying functions in the sense of karamata and show that the class of generalized karamata functions is a well suited framework for the study of the asymptotic behavior of nonoscillatory solutions of the half linear differential equation of the type a p t y 1 y q t y 1 y 0

semiparametric regression analysis for recurrent event interval counts this paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation we consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow up at each visit the patient reports the number of events that occurred since the previous visit or an examination reveals the number of accumulated events such as skin cancers the exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow up times each patient s record thus consists of a sequence of clinic visit dates event counts corresponding to the successive time intervals between clinic visits and baseline covariates we propose a semiparametric regression model extending the fully parametric model of thall 1988 biometrics 44 197 209 to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time varying nature of the underlying event rate covariate effects enter the model parametrically while the underlying time varying event rate is modelled nonparametrically the method of severini and wong 1992 annals of statistics 20 1768 1802 is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution a simulation study and application to a data set are provided

some new extremal self dual 58 29 10 codes the authors discuss extremal self dual 60 30 12 codes and then go on to present new extremal self dual 58 29 10 codes

new extremal self dual codes of lengths 36 38 and 58 we construct new extremal self dual binary codes of lengths 36 38 and 58 we show that there are at least 14 inequivalent extremal self dual 38 18 8 codes and that there are at least 368 inequivalent extremal self dual 38 19 8 codes for length 58 we construct 11 extremal self dual 58 29 10 codes whose weight enumerators were previously unknown

on the structure of binary self dual codes having an automorphism of order a square of an odd prime we describe a method for constructing binary self dual codes having an automorphism of order p sup 2 for an odd prime p using this method we classify the optimal self dual codes of lengths 36 spl les n spl les 44 and n 54 having an automorphism of order 9 we obtain all self dual 56 28 12 58 29 10 and 60 30 12 codes having an automorphism of order 9 without cycles of length 3 some of the constructed codes of lengths 54 58 and 60 have weight enumerators for which the existence of codes was not known before

a general family of distributions for longitudinal dependence with special reference to event histories event histories play an increasingly important role in medical studies examples include times between recurrences of tumours as with bladder cancer and between repeated infections as with chronic granulotomous disease a general method for generating new distributions is proposed by introducing an intensity function into a density this procedure yields as special cases several distributions already proposed in the literature the families of distributions based on the pareto distribution are of particular interest for event history analysis because of their relationship to the laplace transform of a gamma distribution they can yield multivariate distributions with longitudinal serial dependence by a procedure similar to updating in the kalman filter and with uniform dependence in a similar way to copulas for longitudinal dependence several such updating procedures are proposed

existence of certain extremal self dual codes two new singly even extremal self dual codes are given these are a 42 21 8 code and a 58 29 10 code

a method for constructing self dual codes with an automorphism of order 2 in this paper we investigate binary self dual codes with an automorphism of order 2 with c cycles and f fixed points a method for constructing such codes using self orthogonal codes of length c and self dual codes of length f is presented we apply this method to construct extremal self dual codes of lengths 40 42 44 52 54 and 58 some of them have weight enumerators for which self dual codes were previously not known to exist we prove that there do not exist self dual 50 25 10 and 96 48 20 codes with an automorphism of order 2 with f fixed points for f 0 in their automorphism groups

asymptotic formulae for solutions of half linear differential equations we establish asymptotic formulae for regularly varying solutions of the half linear differential equation r t y 1 sgn y p t y 1 sgn y where r p are positive continuous functions on a and 1 the results can be understood in several ways some open problems posed in the literature are solved results for linear differential equations are generalized some of the observations are new even in the linear case a refinement on information about behavior of solutions in standard asymptotic classes is provided a precise description of regularly varying solutions which are known to exist is given regular variation of all positive solutions is proved

distinguishing heterogeneity from decreasing hazard rates different copies of a repairable machine or units often exhibit different failure rates if this heterogeneity is ignored a statistical model of the time until failure may estimate a spurious decreasing hazard rate resulting in incorrect inferences concerning the risk following repair this article develops a renewal proces model that accommodates both heterogeneity across units and decreasing hazard rates failure times for each unit are assumed weibull and the weibull scale parameter is assumed to vary across units according to a gamma distribution the model is illustrated using both proschan s air conditioner data and data on a u s navy radar

a comparison of frailty models for multivariate survival data this paper reviews some of the main approaches to the analysis of multivariate censored survival data such data typically have correlated failure times the correlation can be a consequence of the observational design for example with clustered sampling and matching or it can be a focus of interest as in genetic studies longitudinal studies of recurrent events and other studies involving multiple measurements we assume that the correlation between the failure or survival times can be accounted for by fixed or random frailty effects we then compare the performance of conditional and mixture likelihood approaches to estimating models with these frailty effects in censored bivariate survival data we find that the mixture methods are surprisingly robust to misspecification of the frailty distribution the paper also contains an illustrative example on the times to onset of chest pain brought on by three endurance exercise tests during a drug treatment trial of heart patients

a method for constructing inequivalent self dual codes with applications to length 56 necessary and sufficient conditions are presented for two doubly even codes with an automorphism of odd prime order to be equivalent under certain assumptions for the codes as an application we obtain all extremal doubly even codes of length 56 with an automorphism of order 13 sixteen such codes are inequivalent

asymptotic formulas for non oscillatory solutions of perturbed half linear euler equation abstract we establish asymptotic formulas for non oscillatory solutions of the half linear second order differential equation x t p x c t x 0 where this equation is viewed as a perturbation of the half linear euler equation

an asymptotic analysis of nonoscillatory solutions of q difference equations via q regular variation abstract we do a thorough asymptotic analysis of nonoscillatory solutions of the q difference equation d q r t d q y t p t y q t 0 considered on the lattice q k k n 0 q 1 we classify the solutions according to various aspects that take into account their asymptotic behavior we show relations among the asymptotic classes for every positive solution we establish asymptotic formulae several discrepancies are revealed when comparing the results with their existing differential equations or difference equations counterparts however it should be noted that many of our observations in the q case have not their continuous or discrete analogies yet important roles in our considerations are played by the theory of q regular variation and various transformations the results are illustrated by examples

binary self dual codes with automorphisms of composite order in this paper we present some results concerning a decomposition of binary self dual codes having an automorphism of an order which is the product of two odd prime numbers these results are applied to construct self dual 72 36 12 codes with an automorphism of order 15 furthermore it is proved that the automorphism group of a putative binary extremal self dual 72 36 16 code contains at most 28 nontrivial types of automorphisms of odd order a complete list of these possible types of automorphisms is presented

decomposing and shortening codes using automorphisms corresp codes possessing certain types of automorphisms are examined in one case the code can be decomposed as a direct sum of two subcodes which can be viewed as shorter length codes in a second case the code itself corresponds to a shorter length code related results and applications are given

a distributional model for repeated failure time measurements summary a standard model for repeated measurements is based on the multivariate normal distribution with equicorrelated variables a corresponding analysis is developed for weibull failure times the resulting distribution has some attractive properties for practical application to multivariate failure times

de haan type increasing solutions of half linear differential equations abstract we study asymptotic behavior of eventually positive increasing solutions to the half linear equation r t y 1 sgn y p t y 1 sgn y where r p are positive continuous functions and 1 we give conditions which guarantee that any such a solution is in the class in the de haan sense we also discuss regularly varying solutions and connections with a generalized regular variation and other related concepts the results can be viewed as a half linear extension of existing statements for linear equations but in some aspects they are new also in the linear case

a family of distributions for modelling non elliptically symmetric multivariate data summary the paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation we present a relatively simple family of distributions for use in describing data which are not elliptically symmetric properties of the family are discussed and it is shown that multivariate pareto burr and logistic distributions are special cases in addition simulation methods for applications in monte carlo robustness studies are outlined and finally the fit to a data set on uranium exploration is compared to that obtained using the usual bivariate normal distribution

some new extremal self dual codes with lengths 44 50 54 and 58 we construct extremal self dual codes with lengths 44 50 54 and 58 they have weight enumerators for which extremal codes were previously not known to exist two methods are used for constructing the codes using self dual codes of same or smaller length to obtain the codes we use a combinatorial optimization search

automorphisms of codes with applications to extremal doubly even codes of length 48 general results on automorphisms of self dual binary codes are given these results are applied to the study of extremal self dual doubly even binary codes of length 48 the main theorem proved is that an extremal self dual doubly even code of length 48 with a nontrivial automorphism of odd order is equivalent to the extended quadratic residue code interesting constructions of the binary extended golay code as well as a conjecture about a possible connection between an extremal self dual doubly even code of length 72 and an extremal quaternary code of length 24 arc yielded by techniques used in the proof

new extremal self dual codes of length 62 and related extremal self dual codes new extremal self dual codes of length 62 are constructed with weight enumerators of three different types two of these types were not represented by any known code up till now all these codes possess an automorphism of order 15 some of them are used to construct extremal self dual codes of length 60 by the method of subtracting by additional subtracting an extremal self dual 58 29 10 code was obtained having a weight enumerator which does not correspond to any code known so far

a new upper bound on the minimal distance of self dual codes it is shown that the minimal distance d of a binary self dual code of length n or 74 is at most 2 n 6 10 this bound is a consequence of some new conditions on the weight enumerator of a self dual code obtained by considering a particular translate of the code called its shadow these conditions also enable one to find the highest possible minimal distance of a self dual code for all n or 60 to show that self dual codes with d or 22 with d or 8 exist precisely for n 24 32 and n or 26 and with d or 10 exist precisely for n or 46 and to show that there are exactly eight self dual codes of length 32 with d 8 several of the self dual codes of length 34 have trivial group this appears to be the smallest length where this can happen