algebras of quotients of jordan algebras abstract we define a jordan analogue of lambek and utumi s associative algebra of quotients and we construct the maximal algebra of quotients for nondegenerate jordan algebras we apply those results to other classes of algebras of quotients appearing in the literature

diagnostics for the exponential normal growth curve model the exponential normal regression model provides a flexible parametric approach to constructing growth charts or centile curves we develop diagnostics for this model with a special emphasis towards assessing the impact of individual cases on estimated centile curves we also propose a standardized score residual that assesses the fit of individual cases to the location scale and skewness functions respectively an application of the proposed diagnostics is presented

a jordan canonical form for nilpotent elements in an arbitrary ring abstract in this paper we give an inductive new proof of the jordan canonical form of a nilpotent element in an arbitrary ring if a r is a nilpotent element of index n with von neumann regular a n 1 we decompose a e a 1 e a with e a e r e m n s a jordan block of size n over a corner s of r and 1 e a nilpotent of index a r of index n and von neumann regular a n 1 as a matrix ring over a unital domain

reference values obtained by kernel based estimation of quantile regressions in this paper we study the problem of estimating non parametrically a quantile regression curve as it applies to computing reference values we propose an automatic procedure that uses a symmetrized nearest neighbor kernel estimator of conditional distributions we also discuss ways of measuring the dispersion of quantile regression estimator one is based on the asymptotic distribution of such quantiles while the other relies on the bootstrap method the results of a small simulation study show that the methods of the paper perform rather well even in a situation where a good parametric solution is available as an example we analyze a small part of a data set that was collected to establish reference values for blood velocity in different parts of the umbilical cord of human fetuse as they grow toward birth

periodic solutions for p laplacian neutral rayleigh equation with a deviating argument abstract by using topological degree theory and some analytical skill some criteria to guarantee the existence of periodic solutions are derived for p laplacian neutral rayleigh equation with a deviating argument of the following form p x t c x t f x t g x t t e t

marginal versus joint box cox transformation with applications to percentile curve construction for igg subclasses and blood pressures when age specific percentile curves are constructed for several correlated variables the marginal method of handling one variable at a time has typically been used we address the question frequently asked by practitioners of whether we can achieve efficiency gains by joint estimation we focus on a simple but common method of box cox transformation and assess the statistical impact of a joint transformation to multivariate normality on the percentile curve estimation for correlated variables we find that there is little gain from the joint transformation for estimating percentiles around the median but a noticeable reduction in variances is possible for estimating extreme percentiles that are usually of main interest in medical and biological applications our study is motivated by problems in constructing percentile charts for igg subclasses of children and for blood pressures in adult populations both of which are discussed in the paper as examples and yet our general findings are applicable to a wide range of other problems

existence of periodic solutions for a lienard type p laplacian differential equation with a deviating argument by means of mawhin s continuation theorem a class of p laplacian type differential equation with a deviating argument of the form p x t f x t x t t g t x t t x e t is studied a new result related to t and the deviating argument t x is obtained it is significant that the growth degree with respect to the variable x in g t x is allowed to be greater than p 1 which could be achieved infrequently in previous papers

local orders in jordan algebras abstract making use of results on general algebras of quotients of jordan algebras we study a notion of local order based on the version for linear jordan algebras of the ideas of fountain and gould 14 as adapted to the jordan context by fernandez lopez and garcia rus in 7 in particular we characterize the set of lesieur croisot elements of a nondegenerate jordan algebra as those elements of the jordan algebra lying in the socle of its maximal algebra of quotients and apply this relationship to extend to quadratic jordan algebras the results of fernandez lopez and garcia rus on local orders in nondegenerate jordan algebras satisfying the descending chain condition on principal inner ideals and not containing ideals which are nonartinian quadratic factors

multi level repeated measures growth modelling using extended spline functions this paper explores the fitting of multi level models to growth data over a wide age range using a new class of extended spline models these extend conventional splines based on a function representation by allowing variable order functions and by including fractional polynomial terms the work focuses on modelling human growth in height and head circumference with example data sets the procedures can be used with covariates and for comparing population parameters

periodic solutions for lienard type p laplacian equation with two deviating arguments in this paper the lienard type p laplacian equation with two deviating arguments f p x t f x t x t g 1 t x t t 1 t g 2 t x t t 2 t e t is studied by applying the coincidence degree theory we obtain some new results on the existence of periodic solutions to this equation our results improve and extend some existing ones in the literature

jordan centers and martindale like covers abstract in this paper we show that the scalar center of a nondegenerate quadratic jordan algebra is contained in the scalar center of any of its martindale like covers

an abstract existence theorem at resonance and its applications abstract by using brouwer degree theory and a continuation theorem based on mawhin s coincidence degree an abstract existence theorem at resonance for operator equations is developed as applications of this result some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimension n n 2 the results due to nagle and sinkala are generalized improved and unified

existence and multiplicity results for periodic solutions of semilinear duffing equations we obtain existence an multiplicity of harmonic and subharmonic solutions to the periodically forced nonlinear duffing s equation x g x p t in the semi linear case 0 a g x x b for x large we introduce new conditions of nonresonance with respect to the spectrum of the associated linear differential operator x x and show by some nonlinear counterexamples that the results are sharp

periodic solutions for p laplacian neutral functional differential equation with deviating arguments by using the theory of coincidence degree we study a kind of periodic solutions to p laplacian neutral functional differential equation with multiple deviating arguments a new result on the existence of periodic solutions is obtained

computation of profile likelihood based confidence intervals for reference limits with covariates many biochemical quantities depend on age or some other covariate reference limits that allow for these dependencies help physicians to interpret the results of biochemical tests because reference limits must be estimated it is important to assess their precision with for example confidence intervals this paper relies on the assumption that data can be modeled by a generalized linear model and presents a method for calculating approximate profile likelihood based confidence intervals for reference limits the calculation of confidence intervals is based on a new method that draws on profile likelihood based confidence intervals in general statistical models the asset of this new method is that only two constrained optimization problems have to be solved instead of several in the standard method we motivate our confidence interval calculation method with two applications the first is for data on immunoglobulin concentration in the context of a generalized linear model with gamma distribution this model is compared with the often used lognormal model the second application handles data on serum alpha fetoprotein and is presented in a linear regression situation in the latter application the widths of the calculated profile confidence intervals are compared with exact and approximate regression based intervals and the actual confidence levels are determined by simulation

periodic solutions for a higher order p laplacian neutral functional differential equation with a deviating argument abstract in this paper a higher order p laplacian neutral functional differential equation with a deviating argument p x t c t x t n m f x t x t g t x t t e t has been studied by applying mawhin s continuation degree theorem some new criteria to guarantee the existence of periodic solutions are obtained it is interesting that the power of the variable x in function g is allowed to be greater than p 1

percentile smoothing using piecewise polynomials with covariates a nonparametric procedure for the joint smoothing of a series of percentile curves is presented it allows separate curves to be fitted over contiguous age ranges constraining them to join smoothly covariates can be incorporated thus allowing efficient estimation simultaneously for subgroups

periodic solutions for a rayleigh type p laplacian equation with sign variable coefficient of nonlinear term as p laplacian equations have been widely applied in the field of fluid mechanics and nonlinear elastic mechanics it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p laplacian by using lu s continuation theorem which is an extension of manasevich mawhin we study the existence of periodic solutions for a rayleigh type p laplacian equation f p x t f x t g 1 x email protected 1 t x email protected t g 2 x email protected 2 t x e t it is significant that the growth degree with respect to the variable u in g 1 u is allowed to be greater than p 1 and the coefficient b t of g 2 x email protected 2 t x can change sign in this paper which could be achieved rarely in the previous literature

a homotopic deformation along p of a leray schauder degree result and existence for u p 2u ƒ t u 0 u 0 u t 0 p 1 soit f 0 1 r r une fonction continue et soit o p r r definie par o p s s p 2 s pour p fixe 1 on considere le probleme de dirichlet suivant o p u f t u 0 u 0 u t 0 ou t est un nombre reel positif

reference curves based on non parametric quantile regression reference curves which take time into account such as those for age are often required in medicine but simple systematic and efficient statistical methods for constructing them are lacking classical methods are based on parametric fitting polynomial curves semi parametric methods are also widely used especially in europe here we propose a new methodology for the estimation of reference intervals for data sets based on non parametric estimation of conditional quantiles the derived methods should be applicable to all clinical or more generally biological variables that are measured on a continuous quantitative scale as an example we analyse a data set collected to establish reference curves for biophysical properties of the skin of healthy french women the results are compared to those obtained with royston s polynomial parametric method and the semi parametric lms approach

local pi theory of jordan systems ii abstract in this paper we study jordan systems having nonzero local algebras that satisfy a polynomial identity we prove that in nondegenerate jordan systems the set of elements at which the local algebra is pi is an ideal and that if it is nonzero it coincides with the socle when the system is primitive

outer fractions in quadratic jordan algebras abstract using new techniques of zelmanov c martinez improved on work of jacobson mccrimmon and parvathi to give a necessary and sufficient ore type condition for an arbitrary linear jordan algebra with no 2 or 3 torsion to have an algebra of fractions in this paper we extend to quadratic algebras the concept of algebras of outer fractions with respect to an ore monad and describe necessary and sufficient ore type conditions for the embedding in such an algebra of fractions the details of the actual embedding will appear in a subsequent paper

periodic solutions for a kind of lienard equation with a deviating argument abstract by means of continuation theorem of coincidence degree theory we study a kind of lienard equation with a deviating argument as follows x t f x t x t g x t t x t e t some new results on the existence of periodic solutions are obtained

the ring of fractions of a jordan algebra abstract we derive a necessary and sufficient ore type condition for a jordan algebra to have a ring of fractions

multi level models for longitudinal growth norms multi level models for estimating conditional and unconditional longitudinal growth norms are presented the procedure involves transforming the original growth measurements to normality and modelling these with a two level random coefficient model growth norms for any desired time interval and function can be derived height and weight data are used for illustration

the maximal symmetric ring of quotients abstract the maximal symmetric ring of quotients q r as defined by utumi is a symmetric version of the maximal ring of quotients of r for the most part we study this ring when r k g is a group algebra for example we show that if g is a free product of groups and if r k g is a domain then q r is usually equal to r on the other hand there are certainly groups for which q r is properly larger than r and we construct a number of such examples

periodic solutions for a kind of second order differential equation with multiple deviating arguments by means of continuation theorem of coincidence degree theory some new results on the existence and nonexistence of periodic solutions for a kind of second order functional differential equation with multiple deviating arguments are obtained

periodic solutions of neutral differential equation with multiple deviating arguments in this paper by means of an abstract continuous theorem of k set contractive operator and some analysis techniques the authors study the existence of periodic solution of the nonlinear neutral differential equation with multiple deviating argumentsddt x t cx email protected email protected i 1 email protected i t f x email protected i t email protected j 1 email protected j t g x email protected j t p t a new result is obtained

the structure of strongly prime quadratic jordan algebras abstract we extend the structure theory for strongly prime jordan algebras of arbitrary dimension to quadratic algebras of characteristic 2 we show that such j are either 1 hermitian forms h 0 a j h q a lying between an ample subspace of hermitian elements in a prime associative algebra a and those in its martindale ring of quotients q a 2 clifford forms with a scalar extension j j which is an algebra j j q 1 of a nondegenerate quadratic from q with basepoint 1 or 3 albert forms with a scalar extension j j which is a 27 dimensional split albert algebra j h 3 k of 3 3 hermitian matrices over an 8 dimensional split octonion algebra k as a consequence the simple jordan algebras of arbitrary dimension are either hermitian h 0 a for simple a or clifford forms in j q 1 or are albert algebras in particular our methods give an idempotent free classification of all simple finite dimensional algebras which are i special the key to this characterization is the existence of zel manov polynomials in the free special jordan algebra which are both hermitian polynomials whose values always look like hermitian elements and at the same time clifford polynomials nontrivial on 3 3 hermitian matrices hence on special algebras with 3 interconnected idempotents if a zel manov polynomial does not vanish on j then j is of hermitian type and if it does vanish on j then j is of clifford type one example of such a polynomial is q48 p16 x1 y1 z1 w1 p16 x2 y2 z2 w2 p16 x3 y3 z3 w3 for p16 d2x y z 2 dx y w dx y w dx y z x y z thus the structure of jordan algebras depends very directly on polynomial identities and commutators

primitivity in finitely generated special quadratic jordan algebras abstract primitive jordan algebras were introduced by zelmanov in the linear case 13 and hogben and mccrimmon in the quadratic case 4 a classification theorem for quadratic primitive jordan algebras in the spirit of the general classification of prime nondegenerate jordan algebras 9 is proven in 2 in that result besides albert and clifford type algebras there appear special algebras containing an ideal of the form h0 a for a primitive associative algebra a with involution to prove this result a key fact is that for a prime a primitivity can be transferred from h0 a to a and back the first part of this result stems from a more general theorem asserting that any tight associative envelope of a primitive jordan algebra is primitive 2 this can be extended to envelopes making use of the concept of primitivity any tight associative envelope of a primitive jordan algebra is primitive the aim of this paper is to examine the reciprocal of that theorem for finitely generated jordan algebras we prove in section 4 that a finitely generated special jordan algebra having a primitive envelope is primitive in the case of h a the proof makes uses of the herstein second construction 7 for a semiprime a with involution any nonzero ideal of h a contains some h0 i with i a nonzero ideal of a our proof will follow a similar pattern we prove in section 2 that the herstein mccrimmon construction can be extended to prime finitely generated jordan algebras with nonzero hermitian part for that we make use of some basic properties of hermitian ideals as defined in 9 in section 3 we treat algebras an anti hermitian type called here simply anti hermitian algebras separately and we collect the previous results in section 4 to prove our main theorem

primitive jordan pairs and triple systems abstract in this paper we give a characterization of primitivity of jordan pairs and triple systems in terms of their local algebras as a consequence of that local characterization we extend to jordan pairs and triple systems most of the known results about primitive jordan algebras in particular we describe primitive jordan pairs and triple systems over an arbitrary ring of scalars in the sense of the structure of primitive quadratic jordan algebras by j a anquela t cortes and f montaner 1995 j algebra172 530 553 5 1

local lesieur croisot theory of jordan algebras in this paper we study jordan algebras having nonzero local algebras that satisfy the property of being lesieur croisot i e being orders in nondegenerate jordan algebras of finite capacity we will prove that the set of the elements of a nondegenerate jordan algebra at which the local algebra is lesieur croisot is an ideal

the structure of primitive quadratic jordan algebras in this paper we give a complete description of primitive quadratic jordan algebras following the classification of strongly prime quadratic jordan algebras k mccrimmon and e i zel manov adv math 69 no 2 1988 133 222 the proof is based in two results of independent interest we show that every p i primitive jordan algebra is simple and unital with nonzero socle and prove that associative tight tight envelopes of special primitive jordan algebras are also primitive primitive as a consequence of the latter fact we see that an associative algebra a is one sided primitive if and only if a is primitive and an associative algebra a with involution is primitive if and only if an ample subspace h 0 a is primitive

algebras of quotients of nonsingular jordan algebras abstract we define a jordan analogue of johnson s associative algebra of quotients and study it under a suitable condition of nonsingularity of the jordan algebra which we call strong nonsingularity in particular we prove the existence and describe the maximal algebras of quotients of prime strongly nonsingular jordan algebras

periodic solutions to neutral differential equation with deviating arguments by employing the continuation theorem of coincidence degree theory and some analysis techniques we study a kind of neutral differential equation with deviating arguments as follows x t cx t r f x t g x t t p t some new results on the existence of periodic solutions are obtained our result generalizes main work of wang app math lett 12 1999 41 44

goldie theory for jordan algebras it is shown that zelmanov s version of goldie s conditions still characterizes quadratic jordan algebras having an artinian algebra of quotients which is nondegenerate at the same time jordan versions of the main notions of the associative theory such as those of the uniform ideal uniform element singular ideal and uniform dimension are studied moreover it is proved that the nondegenerate unital jordan algebras of finite capacity are precisely the algebras of quotients of nondegenerate jordan algebras having the property that an inner ideal is essential if and only if it contains an injective element 2002 elsevier science usa

on the analysis of mixed longitudinal growth data mixed longitudinal growth data consists of several observations on a characteristic over a limited age range for each individual in a study this data is then combined to model growth over the total age range of all individuals in the study the limited data collected on each individual precludes a subject specific approach to modelling so that a population based approach must be used here we propose a method for the analysis of mixed longitudinal data using linear models constructed from cubic splines to model both the mean and variance curves of an observed characteristic the method is illustrated on growth in height and head circumference for children in a recently collected mixed longitudinal data set concerning the growth of victorian schoolchildren where particular concern was the timing of growth spurts and increases in variability

jordan canonical form for finite rank elements in jordan algebras the usual jordan canonical form for matrices is extended first to nilpotent elements of the socle of a nondegenerate jordan algebra and then to elements of a nondegenerate jordan algebra which is reduced over an algebraically closed field 0 elsevier science inc 1997

on the existence of periodic solutions for p laplacian generalized lienard equation abstract by employing mawhin s continuation theorem the existence of periodic solutions of the p laplacian generalized lienard equation with deviating argument p x t f t x t x t t g x t t e t under various assumptions are obtained

maximal algebras of martindale like quotients of strongly prime linear jordan algebras abstract in this paper we prove the existence and give precise descriptions of maximal algebras of martindale like quotients for arbitrary strongly prime linear jordan algebras as a consequence we show that zelmanov s classification of strongly prime jordan algebras can be viewed exactly as the description of their maximal algebras of martindale like quotients as a side result we show that the martindale associative algebra of symmetric quotients can be expressed in terms of the symmetrized product i e in purely jordan terms

periodic solutions for a fourth order rayleigh type p laplacian delay equation abstract by applying mawhin s continuation theory and some new inequalities the existence of periodic solutions for a fourth order rayleigh type p laplacian delay equation is obtained moreover an example is given to illustrate the results

fitting decomposition in jordan systems in this note the well known fitting decomposition is extended to the context of jordan algebras pairs and triple systems recall fitting s lemma letfbe an endomorphism of a module m such that the sequences f m 3f2 m 1 and kerfc ker f2 c become stationary then m m1 m where m f m and mo ker f for all sufficiently large n now let c be the idempotent of a end m given by projection of m onto m and let a a 0 a 0 aoi 0 be the corresponding peirce decomposition of a where aeaii if and only if a mj cm and u m o then f fil fooea a and fil f im is invertible in ali whereas f 1 m is nilpotent in this form fitting s lemma makes sense for jordan algebras in fact if we consider a as a jordan algebra j then the jordan peirce spaces of c are j a j1 a a jo a and invertibility in j2 and nilpotence in j are jordan concepts we prove theorem 1 if j is a jordan algebra with dcc on principal inner ideals then for every a e j there exists a unique idempotent c of j such that a a2 a j2 jo in the peirce decomposition of j with respect to c where a2 is invertible in j and a is nilpotent in associative ring theory fitting s lemma implies that the endomorphism ring of an indecomposable module is local the jordan analogue is a unital jordan algebra with dcc on principal inner ideals containing no idempotents o 1 and such that this remains true in all isotopes is local the condition on the isotopes which cannot be dropped cf s indicates that this is really a result on jordan pairs thus it is natural to ask for a fitting decomposition in jordan pairs which indeed exists just as in the algebra case the sole difference being that the idempotent defining the peirce decomposition is merely unique up to association theorem 2 finally there is a fitting decomposition in jordan triple

diagonalization in jordan pairs as every student of linear algebra knows a rectangular matrix over a division ring can be diagonalized by elementary row and column operations similarly there are normal forms for alternating and hermitian matrices which can be achieved by simultaneous row and column operations since matrices of this kind form the main examples of jordan pairs it is natural to ask whether similar results hold in the jordan setting we show that this is in fact the case study the obstruction to diagonalizability the defect and also prove that nondegenerate jordan pairs admit a rank function sharing many properties with classical matrix rank let v v v be a jordan pair and s e e a set of orthogonal idempotents the s diagonal elements are those in xi 1 v e now suppose that v is nondegenerate and satisfies dcc on principal inner ideals an element x e v a i is called diagonalizabfe if x is s diagonal for some s consisting of division idempotents to see that for matrices this is the same as the usual notion of diagonalizability suppose that v has in addition act on principal inner ideals then v contains a frame that is a finite set f of orthogonal division idempotents such that v f 0 for rectangular or hermitian matrices over division rings f can be taken to consist of the diagonal matrix units e eii whereas for alternating matrices over a field e eli1 2ie zi the jordan analogues of elementary row and column operations are the inner automorphisms b v e v e and v e v e where e e f which generate the group of f elementary automorphisms of v 6 any set of orthogonal division idempotents can be transformed up to association into f by an f elementary automorphism 6 th 21 it follows that x is diagonalizable if and only if cp x is f diagonal for some elementary automorphism cp of v this shows the equivalence with the usual definition

the zelmanov approach to jordan homomorphisms of associative algebras abstract zelmanov s work on prime jordan algebras leads to an idempotent free version of martindale s theorem on the extension of jordan homomorphisms and derivations from the hermitian elements h r of an associative algebra of degree 2 with involution to associative homomorphisms and derivations on r the condition that j h r be of degree 2 is replaced by the intrinsic condition that j z j h a consist entirely of values of zelmanov polynomials

nondegenerate jordan algebras satisfying local goldie conditions abstract a structure theorem is given for nondegenerate jordan algebras j satisfying the ascending chain condition on annihilators of a single element and such that j contains no infinite direct sum of inner deals inside the inner ideal generated by each element x j as a consequence of this theorem and of the main results of a previous paper by the authors j algebra 174 1995 1024 1048 it is obtained that such jordan algebras j are precisely the local orders in nondegenerate jordan algebras satisfying dcc on principal inner ideals and without non artinian quadratic ideals which extends to local orders the zel manov theorem for goldie jordan algebras

existence of periodic solutions for a kind of second order neutral functional differential equation by means of the continuation theorem of coincidence degree theory we study a kind of second order neutral functional differential equation as followsd 2dt 2u t j 1 nc ju t r j f u t u t a t g u t j 1 n b j t g u t c j t p t some new results on the existence of periodic solutions are obtained