the control of confounding by intermediate variables in epidemiologic studies of the effect of an exposure on disease the crude association of exposure with disease may fail to reflect a causal association due to confounding by one or more covariates most previous discussions of confounding in the epidemiologic literature have considered only point exposure studies that is studies that measure exposure and covariate status only once at start of follow up in this paper we offer definitions of confounding suitable for longitudinal studies that obtain data on exposure covariate and vital status at several points in time an important difference between longitudinal studies and point exposure studies is that in longitudinal studies a time dependent covariate can be simultaneously a confounder and an intermediate variable on the causal pathway from exposure to disease in this paper i propose an estimator the extended standardized risk difference that provides control for confounding by a covariate that is simultaneously a confounder and an intermediate variable

supercyclic subspaces spectral theory and weighted shifts abstract a vector x in a banach space b is called hypercyclic for a bounded operator t if the orbit t n x n 0 is dense in b if the scalar multiples of the elements in the orbit are dense then the vector x is called supercyclic we give a general sufficient condition for a bounded operator on a banach space to have an infinite dimensional closed subspace of supercyclic vectors as a consequence we also obtain a spectral sufficient condition for the existence of such a subspace for an operator these results allow us to characterize unilateral and bilateral weighted shifts that have an infinite dimensional closed subspace of supercyclic vectors surprisingly there are weighted shift operators that have supercyclic vectors but in which all closed subspaces of supercyclic vectors are finite dimensional our results complement recent work on hypercyclic subspaces and supercyclic subspaces they also suggest that the problem of the existence of infinite dimensional closed subspaces of supercyclic vectors is not only different but also more difficult to handle than the corresponding problem for hypercyclic vectors

a general approach to read s type constructions of operators without non trivial invariant closed subspaces we present a general method for constructing operators without non trivial invariant closed subsets on a large class of non reflexive banach spaces in particular our approach unifies and generalizes several constructions due to read of operators without non trivial invariant subspaces on the spaces l 1 c 0 or circle plus l2 j and without non trivial invariant subsets on l 1 we also investigate how far our methods can be extended to the hilbertian setting and construct an operator on a quasi reflexive dual banach space which has no non trivial w closed invariant subspace

bounded analytic functions in the dirichlet space in this paper we study the hilbert space of analytic functions with finite dirichlet integral in a connected open set c2 in the complex plane we show that every such function can be represented as a quotient of two bounded analytic functions each of which has a finite dirichlet integral this has several consequences for the structure of invariant subspaces of the algebra of multiplication operators on the dirichlet space in case f2 is simply connected namely we show that every nontrivial invariant subspace contains a nontrivial bounded function that each two nontrivial invariant subspaces have a nontrivial intersection that is the algebra is cellular indecomposable and that each nontrivial invariant subspace has the codimension one property with respect to certain multiplication operators

stabilization effect of magnetic fields on two dimensional compressible current vortex sheets we analyze the linear stability of rectilinear compressible current vortex sheets in two dimensional isentropic magnetohydrodynamics which is a free boundary problem with the boundary being characteristic in the case when the magnitude of the magnetic field has no jump on the current vortex sheets we find a necessary and sufficient condition of linear stability for the rectilinear current vortex sheets showing that magnetic fields exert a stabilization effect on compressible vortex sheets in addition a loss of regularity with respect to the source terms both in the interior domain and on the boundary occurs in a priori estimates of solutions to the linearized problem for a rectilinear current vortex sheet as the kreiss lopatinskii determinant associated with this linearized boundary value problem has roots on the boundary of frequency spaces in this study the construction of symmetrizers for a reduced differential system which has poles at which the kreiss lopatinskii condition may fail simultaneously plays a crucial role in the a priori estimates

weak stability of the plasma vacuum interface problem abstract we consider the free boundary problem for the two dimensional plasma vacuum interface in ideal compressible magnetohydrodynamics mhd in the plasma region the flow is governed by the usual compressible mhd equations while in the vacuum region we consider the maxwell system for the electric and the magnetic fields at the free interface driven by the plasma velocity the total pressure is continuous and the magnetic field on both sides is tangent to the boundary we study the linear stability of rectilinear plasma vacuum interfaces by computing the kreiss lopatinski determinant of an associated linearized boundary value problem apart from possible resonances we obtain that the piecewise constant plasma vacuum interfaces are always weakly linearly stable independently of the size of tangential velocity magnetic and electric fields on both sides of the characteristic discontinuity we also prove that solutions to the linearized problem obey an energy estimate with a loss of regularity with respect to the source terms both in the interior domain and on the boundary due to the failure of the uniform kreiss lopatinski condition as the kreiss lopatinski determinant associated with this linearized boundary value problem has roots on the boundary of the frequency space in the proof of the a priori estimates a crucial part is played by the construction of symmetrizers for a reduced differential system which has poles at which the kreiss lopatinski condition may fail simultaneously

properties of a nonparametric test for early comparison of treatments in clinical trials in the presence of surrogate endpoints summary a nonparametric test is derived for comparing treatments with respect to the final endpoint in clinical trials in which the final endpoint has been observed for a random subset of patients but results are available for a surrogate endpoint for a larger sample of patients the test is an adaptation of the wilcoxon mann whitney two sample test with an adjustment that involves a comparison of the ranks of the surrogate endpoints between patients with and without final endpoints the validity of the test depends on the assumption that the patients with final endpoints represent a random sample of the patients registered in the study this assumption is viable in trials in which the final endpoint is evaluated at a landmark timepoint in the patients natural history a small sample simulation study demonstrates that the test has a size that is close to the nominal value for all configurations evaluated when compared with the conventional test based only on the final endpoints the new test delivers substantial increases in power only when the surrogate endpoint is highly correlated with the true endpoint our research indicates that in the absence of modeling assumptions auxiliary information derived from surrogate endpoints can provide significant additional information only under special circumstances

the existence of current vortex sheets in ideal compressible magnetohydrodynamics we prove the local in time existence of solutions with a surface of current vortex sheet tangential discontinuity of the equations of ideal compressible magnetohydrodynamics in three space dimensions provided that a stability condition is satisfied at each point of the initial discontinuity this paper is a natural completion of our previous analysis trakhinin in arch ration mech anal 177 331 366 2005 where a sufficient condition for the weak stability of planar current vortex sheets was found and a basic a priori estimate was proved for the linearized variable coefficients problem for nonplanar discontinuities the original nonlinear problem is a free boundary hyperbolic problem since the free boundary is characteristic the functional setting is provided by the anisotropic weighted sobolev spaces h m the fact that the kreiss lopatinski condition is satisfied only in a weak sense yields losses of derivatives in a priori estimates therefore we prove our existence theorem by a suitable nash moser type iteration scheme

the structure of almost invariant half spaces for some operators abstract given a banach space x and an operator t l x an almost invariant half space aihs is a closed subspace y satisfying t y y f for some finite dimensional subspace f and dim y dim x y in this paper we study the connection between aihs and noncompactness of some subsets of the unit ball chains of t invariant subspaces and different parts of spectrum of t and t we describe a simple template for such subspaces and show that if t is quasinilpotent or weakly compact then it admits an aihs y

a generalization of jensen s inequality for polynomials having concentration at low degrees in this paper we give some asymptotic estimates for the best lower bound c d k p of the jensen s functional j f email protected 0 2 plog f e i q email protected p for when the polynomial f has a concentration d at low degrees k measured by the l p norm under the l p norm p 2

orbital and strongly orbital spaces abstract we say that a countably dimensional topological vector space x is orbital if there is t l x and a vector x x such that x is the linear span of the orbit t n x n 0 1 we say that x is strongly orbital if additionally x can be chosen to be a hypercyclic vector for t of course x can be orbital only if the algebraic dimension of x is finite or infinite countable we characterize orbital and strongly orbital metrizable locally convex spaces we also show that every countably dimensional metrizable locally convex space x does not have the invariant subset property that is there is t l x such that every non zero x x is a hypercyclic vector for t finally assuming the continuum hypothesis we construct a complete strongly orbital locally convex space as a byproduct of our constructions we determine the number of isomorphism classes in the set of dense countably dimensional subspaces of any given separable infinite dimensional frechet space x for instance in x l 2 there are exactly 3 pairwise non isomorphic as topological vector spaces dense countably dimensional subspaces

operators similar to their restrictions to invariant subspaces abstract an operator t on a separable infinite dimensional banach space x is called crystal like if for each nonzero invariant subspace m of t there exists a positive number r such that t m the restriction of t to m is similar to rt in this paper we investigate some elementary properties of crystal like operators such as the spectrum cyclicity strong irreducibility essential similarity reflectivity and the commutativity of the commutant

a priori estimates for 3d incompressible current vortex sheets we consider the free boundary problem for current vortex sheets in ideal incompressible magneto hydrodynamics it is known that current vortex sheets may be at most weakly neutrally stable due to the existence of surface waves solutions to the linearized equations the existence of such waves may yield a loss of derivatives in the energy estimate of the solution with respect to the source terms however under a suitable stability condition satisfied at each point of the initial discontinuity and a flatness condition on the initial front we prove an a priori estimate in sobolev spaces for smooth solutions with no loss of derivatives the result of this paper gives some hope for proving the local existence of smooth current vortex sheets without resorting to a nash moser iteration such result would be a rigorous confirmation of the stabilizing effect of the magnetic field on kelvin helmholtz instabilities which is well known in astrophysics

analysis of factorial survival experiments several new methodological issues that arise within two way factorial designs for survival experiments are discussed within the framework of asymptotic theory for the proportional hazards model with two binary treatment covariates these issues include the proper formulation of null hypotheses and alternatives the choice among log rank and adjusted or stratified log rank statistics the asymptotic correlation between test statistics for the separate main effects the asymptotic power under the various possible methods of analysis of tests to detect main effects and interactions the comparison of power to detect main effects within a 2 x 2 factorial design with power in a three group trial where no patients are randomized simultaneously to both treatments and the problems of analysis arising when accrual or exposure to one of the treatments is terminated early for ethical reasons

every operator has almost invariant subspaces abstract we show that any bounded operator t on a separable reflexive infinite dimensional banach space x admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension in the non reflexive spaces we show that the same is true for operators which have non eigenvalues in the boundary of their spectrum in the hilbert space our methods produce perturbations that are also small in norm improving on an old result of brown and pearcy

the invariant subspace problem for non archimedean kothe spaces abstract in this study a proof is given that if a non archimedean kothe space which is generated by an infinite matrix b b n k k n n such that b n k b n 1 k for k n n and for each k l n m n exists such that b n k 1 b n l k for n m then a continuous operator t exists that has no nontrivial closed invariant subspaces

an extension of lomonosov s techniques to non compact operators the existence of invariant subspaces for bounded linear operators acting on an infinite dimensional hilbert space appears to be one of the most difficult questions in the theory of linear transformations the question is known as the invariant subspace problem very few affirmative answers are known regarding this problem one of the most prominent ones is the theorem on the existence of hyper invariant subspaces for compact operators due to v i lomonosov

invariant subspaces for non normable frechet spaces abstract a frechet space x satisfies the hereditary invariant subspace resp subset property if for every closed infinite dimensional subspace m in x each continuous operator on m possesses a non trivial invariant subspace resp subset in this paper we exhibit a family of non normable separable infinite dimensional frechet spaces satisfying the hereditary invariant subspace property and we show that many non normable frechet spaces do not satisfy this property we also state sufficient conditions for the existence of a continuous operator without non trivial invariant subset and deduce among other examples that there exists a continuous operator without non trivial invariant subset on the space of entire functions h c

what price kaplan meier summary the asymptotic efficiency of the kaplan meier product limit estimator relative to the maximum likelihood estimator of a parametric survival function is examined under a random censoring model

existence of compressible current vortex sheets variable coefficients linear analysis we study the initial boundary value problem resulting from the linearization of the equations of ideal compressible magnetohydrodynamics and the rankine hugoniot relations about an unsteady piecewise smooth solution this solution is supposed to be a classical solution of the system of magnetohydrodynamics on either side of a surface of tangential discontinuity current vortex sheet under some assumptions on the unperturbed flow we prove an energy a priori estimate for the linearized problem since the tangential discontinuity is characteristic the functional setting is provided by the anisotropic weighted sobolev space w21 despite the fact that the constant coefficients linearized problem does not meet the uniform kreiss lopatinskii condition the estimate we obtain is without loss of smoothness even for the variable coefficients problem and nonplanar current vortex sheets the result of this paper is a necessary step in proving the local in time existence of current vortex sheet solutions of the nonlinear equations of magnetohydrodynamics

well posedness in smooth function spaces for the moving boundary three dimensional compressible euler equations in physical vacuum we prove well posedness for the three dimensional compressible euler equations with moving physical vacuum boundary with an equation of state given by p c for 1 the physical vacuum singularity requires the sound speed c to go to zero as the square root of the distance to the moving boundary and thus creates a degenerate and characteristic hyperbolic free boundary system wherein the density vanishes on the free boundary the uniform kreiss lopatinskii condition is violated and manifest derivative loss ensues nevertheless we are able to establish the existence of unique solutions to this system on a short time interval which are smooth in sobolev spaces all the way to the moving boundary and our estimates have no derivative loss with respect to initial data our proof is founded on an approximation of the euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term chosen to preserve as much of the geometric structure of the euler equations as possible we first construct solutions to this degenerate parabolic regularization using a higher order version of hardy s inequality we then establish estimates for solutions to this degenerate parabolic system which are independent of the artificial viscosity parameter solutions to the compressible euler equations are found in the limit as the artificial viscosity tends to zero our regular solutions can be viewed as degenerate viscosity solutions our methodology can be applied to many other systems of degenerate and characteristic hyperbolic systems of conservation laws

hyperbolic boundary value problems for symmetric systems with variable multiplicities abstract we extend the kreiss majda theory of stability of hyperbolic initial boundary value and shock problems to a class of systems notably including the equations of magnetohydrodynamics mhd for which majda s block structure condition does not hold namely simultaneously symmetrizable systems with characteristics of variable multiplicity satisfying at points of variable multiplicity either a totally nonglancing or a nonglancing and linearly splitting condition at the same time we give a simple characterization of the block structure condition as geometric regularity of characteristics defined as analyticity of associated eigenprojections the totally nonglancing or nonglancing and linearly splitting conditions are generically satisfied in the simplest case of crossings of two characteristics and likewise for our main physical examples of mhd or maxwell equations for a crystal together with previous analyses of spectral stability carried out by gardner kruskal and blokhin trakhinin this yields immediately a number of new results of nonlinear inviscid stability of shock waves in mhd in the cases of parallel or transverse magnetic field and recovers the sole previous nonlinear result obtained by blokhin trakhinin by direct dissipative integral methods of stability in the zero magnetic field limit we also discuss extensions to the viscous case

linear stability of compressible vortex sheets in two dimensional elastodynamics abstract the linear stability of rectilinear compressible vortex sheets is studied for two dimensional isentropic elastic flows this problem has a free boundary and the boundary is characteristic a necessary and sufficient condition is obtained for the linear stability of the rectilinear vortex sheets more precisely it is shown that besides the stable supersonic zone the elasticity exerts an additional stable subsonic zone we also find that there is a class of states in the interior of subsonic zone where the stability of such states is weaker than the stability of other states in the sense that there is an extra loss of tangential derivatives with respect to the source terms this is a new feature that the euler flow does not possess one of the difficulties for the elastic flow is that the non differentiable points of the eigenvalues may coincide with the roots of the lopatinskii determinant as a result the kreiss symmetrization cannot be applied directly instead we perform an upper triangularization of the system to separate only the outgoing modes at all points in the frequency space so that an exact estimate of the outgoing modes can be obtained moreover all the outgoing modes are shown to be zero due to the l 2 regularity of solutions the estimates for the incoming modes can be derived directly from the lopatinskii determinant this new approach avoids the lengthy computation and estimates for the outgoing modes when kreiss symmetrization is applied this method can also be applied to the euler flow and mhd flow

stability of multidimensional thermoelastic contact discontinuities we study the system of nonisentropic thermoelasticity describing the motion of thermoelastic nonconductors of heat in two and three spatial dimensions where the frame indifferent constitutive relation generalizes that for compressible neo hookean materials thermoelastic contact discontinuities are characteristic discontinuities for which the velocity is continuous across the discontinuity interface mathematically this renders a nonlinear multidimensional hyperbolic problem with a characteristic free boundary we identify a stability condition on the piecewise constant background states and establish the linear stability of thermoelastic contact discontinuities in the sense that the variable coefficient linearized problem satisfies a priori tame estimates in the usual sobolev spaces under small perturbations our tame estimates for the linearized problem do not break down when the strength of thermoelastic contact discontinuities tends to zero the missing normal derivatives are recovered from the estimates of several quantities relating to physical involutions in the estimate of tangential derivatives there is a significant new difficulty namely the presence of characteristic variables in the boundary conditions to overcome this difficulty we explore an intrinsic cancellation effect which reduces the boundary terms to an instant integral then we can absorb the instant integral into the instant tangential energy by means of the interpolation argument and an explicit estimate for the traces on the hyperplane

stability of incompressible current vortex sheets abstract we revisit the study in y trakhinin on the existence of incompressible current vortex sheets study of a linearized free boundary value problem math methods appl sci 28 2005 917 945 where an energy a priori estimate for the linearized free boundary value problem for planar current vortex sheets in ideal incompressible magnetohydrodynamics was proved for a part of the whole stability domain found a long time ago in s i syrovatskij the stability of tangential discontinuities in a magnetohydrodynamic medium zh eksper teor fiz 24 1953 622 629 in russian w i axford note on a problem of magnetohydrodynamic stability canad j phys 40 1962 654 655 in this paper we derive an a priori estimate in the whole stability domain the crucial point in deriving this estimate is the construction of a symbolic symmetrizer for a nonstandard elliptic problem for the small perturbation of total pressure this symmetrizer is an analogue of kreiss type symmetrizers as in hyperbolic theory the failure of the uniform lopatinski condition i e the fact that current vortex sheets are only weakly neutrally stable yields loss of derivatives in the energy estimate the result of this paper is a necessary step to prove the local in time existence of stable nonplanar incompressible current vortex sheets by a suitable nash moser type iteration scheme

on quasinilpotent operators and the invariant subspace problem abstract we show that a bounded quasinilpotent operator t acting on an infinite dimensional banach space has an invariant subspace if and only if there exists a rank one operator f and a scalar c 0 1 such that t f and t f are also quasinilpotent we also prove that for any fixed rank one operator f almost all perturbations t f have invariant subspaces of infinite dimension and codimension

hypercyclic operators on non normable frechet spaces abstract every infinite dimensional separable non normable frechet space admits a continuous hypercyclic operator a large class of separable countable inductive limits of banach spaces with the same property is given but an example of a separable complete inductive limit of banach spaces which admits no hypercyclic operator is provided it is also proved that no compact operator on a locally convex space is hypercyclic

short time structural stability of compressible vortex sheets with surface tension assume we start with an initial vortex sheet configuration which consists of two inviscid fluids with density bounded below flowing smoothly past each other where a strictly positive fixed coefficient of surface tension produces a surface tension force across the common interface balanced by the pressure jump we model the fluids by the compressible euler equations in three space dimensions with a very general equation of state relating the pressure entropy and density such that the sound speed is positive we prove that for a short time there exists a unique solution of the equations with the same structure

semiparametric efficiency in multivariate regression models with missing data abstract we consider the efficiency bound for the estimation of the parameters of semiparametric models defined solely by restrictions on the means of a vector of correlated outcomes y when the data on y are missing at random we show that the semiparametric variance bound is the asymptotic variance of the optimal estimator in a class of inverse probability of censoring weighted estimators and that this bound is unchanged if the data are missing completely at random for this case we study the asymptotic performance of the generalized estimating equations gee estimators of mean parameters and show that the optimal gee estimator is inefficient except for special cases the optimal weighted estimator depends on unknown population quantities but for monotone missing data we propose an adaptive estimator whose asymptotic variance can achieve the bound

infinite matrices with few non zero entries and without non trivial invariant subspaces in this paper we investigate a family of infinite matrices that act on l1 we derive a condition sufficient to guarantee that a matrix has no non trivial closed invariant subspaces as a result a simplest known operator on l1 without invariant subspaces is obtained all entries of the matrix of the example but one are non negative

nonlinear stability of the current vortex sheet to the incompressible mhd equations in this paper we solve a long standing open problem nonlinear stability of the current vortex sheet in the ideal incompressible magnetohydrodynamics under the syrovatskij stability condition this result gives the first rigorous confirmation of the stabilizing effect of the magnetic field on kelvin helmholtz instability 2017 wiley periodicals inc

structural stability of shock waves in 2d compressible elastodynamics we study the two dimensional structural stability of shock waves in a compressible isentropic inviscid elastic material in the sense of the local in time existence and uniqueness of discontinuous shock front solutions of the equations of compressible elastodynamics in two space dimensions by the energy method based on a symmetrization of the wave equation and giving an a priori estimate without loss of derivatives for solutions of the constant coefficients linearized problem we find a condition sufficient for the uniform stability of rectilinear shock waves comparing this condition with that for the uniform stability of shock waves in isentropic gas dynamics we make the conclusion that the elastic force plays stabilizing role in particular we show that as in isentropic gas dynamics all compressive shock waves are uniformly stable for convex equations of state moreover for some particular deformations and general equations of state by the direct test of the uniform kreiss lopatinski condition we show that the stability condition found by the energy method is not only sufficient but also necessary for uniform stability as is known uniform stability implies structural stability of corresponding curved shock waves

local existence for the free boundary problem for nonrelativistic and relativistic compressible euler equations with a vacuum boundary condition we study the free boundary problem for the equations of compressible euler equations with a vacuum boundary condition our main goal is to recover in eulerian coordinates the earlier well posedness result obtained by lindblad 11 for the isentropic euler equations and extend it to the case of full gas dynamics for technical simplicity we consider the case of an unbounded domain whose boundary has the form of a graph and make short comments about the case of a bounded domain we prove the local in time existence in sobolev spaces by the technique applied earlier to weakly stable shock waves and characteristic discontinuities 5 21 it contains in particular the reduction to a fixed domain using the good unknown of alinhac 1 and a suitable nash moser type iteration scheme a certain modification of such an approach is caused by the fact that the symbol associated to the free surface is not elliptic this approach is still directly applicable to the relativistic version of our problem in the setting of special relativity and we briefly discuss its extension to general relativity 2009 wiley periodicals inc

the compressible euler equations in a bounded domain existence of solutions and the incompressible limit a short time existence theorem is proven for the euler equations for nonisentropic compressible fluid flow in a bounded domain and solutions with low mach number and almost incompressible initial data are shown to be close to corresponding solutions of the equations for incompressible flow

almost invariant and essentially invariant halfspaces abstract in this paper we study sufficient conditions for an operator to have an almost invariant half space as a consequence we show that if x is an infinite dimensional complex banach space then every operator t l x admits an essentially invariant half space we also show that whenever a closed algebra of operators possesses a common aihs then it has a common invariant half space as well

a complete 2d stability analysis of fast mhd shocks in an ideal gas an algorithm of numerical testing of the uniform lopatinski condition for linearized stability problems for 1 shocks is suggested the algorithm is used for finding the domains of uniform stability neutral stability and instability of planar fast mhd shocks a complete stability analysis of fast mhd shock waves is first carried out in two space dimensions for the case of an ideal gas main results are given for the adiabatic constant 5 3 mono atomic gas that is most natural for the mhd model the cases 7 5 two atomic gas and 5 3 are briefly discussed not only the domains of instability and linear in the usual sense stability but also the domains of uniform stability for which a corresponding linearized stability problem satisfies the uniform lopatinski condition are numerically found for different given angles of inclination of the magnetic field behind the shock to the planar shock front as is known uniform linearized stability implies the nonlinear stability that is local existence of discontinuous shock front solutions of a quasilinear system of hyperbolic conservation laws

nonlinear stability and existence of compressible vortex sheets in 2d elastodynamics abstract the nonlinear stability and local existence of compressible vortex sheets for the two dimensional isentropic elastic fluid are established in the usual sobolev spaces the problem has a characteristic free boundary and the kreiss lopatinski condition is satisfied only in a weak form this paper completes the previous works 6 7 of the first three authors where the weakly linear stability of the rectilinear vortex sheets is proved by means of an upper triangularization technique our proof is based on certain higher order energy estimates and an appropriate modification of the nash moser iteration in particular the estimate for the normal derivatives of the characteristic variables can be recovered from that for the linearized divergences and vorticities

invariant subspace problem for classical spaces of functions abstract we construct continuous linear operators without non trivial invariant subspaces on several classical non banach spaces of analysis the schwartz space of rapidly decreasing functions the space of smooth functions on a compact smooth manifold the space of holomorphic functions on the unit disc or on an arbitrary polydisc the space of entire functions on c d for d 2 as these are reflexive spaces the result gives an analogous statement for the dual spaces e g the space of tempered distributions the construction works with kothe sequence spaces and is based on methods developed by read to construct his famous example on the space l 1

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

two dimensional vortex sheets for the nonisentropic euler equations nonlinear stability we study the linear stability of contact discontinuities for the nonisentropic compressible euler equations in two space dimensions assuming the jump of the tangential velocity across the discontinuity surface is sufficiently large we derive a suitable energy estimate for the linearized boundary value problem the found estimate extends to nonisentropic compressible flows the main result of coulombel secchi for the isentropic euler equations compared with this latter case when the jump of the tangential velocity of the unperturbed flow attains a certain critical value in the region of weak stability here an additional loss of regularity appears this is related to the presence of a double root of the lopatinskii determinant associated to the problem

on the well posedness of a linearized plasma vacuum interface problem in ideal compressible mhd abstract we study the initial boundary value problem resulting from the linearization of the plasma vacuum interface problem in ideal compressible magnetohydrodynamics mhd we suppose that the plasma and the vacuum regions are unbounded domains and the plasma density does not go to zero continuously but jumps for the basic state upon which we perform linearization we find two cases of well posedness of the frozen coefficient problem the gas dynamical case and the purely mhd case in the gas dynamical case we assume that the jump of the normal derivative of the total pressure is always negative in the purely mhd case this condition can be violated but the plasma and the vacuum magnetic fields are assumed to be non zero and non parallel to each other everywhere on the interface for this case we prove a basic a priori estimate in the anisotropic weighted sobolev space h 1 for the variable coefficient problem

a priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows in the present paper we prove the a priori estimates of sobolev norms for a free boundary problem of the incompressible inviscid magnetohydrodynamics equations in all physical spatial dimensions n 2 and 3 by adopting a geometrical point of view used in christodoulou and lindblad commun pure appl math 53 1536 1602 2000 and estimating quantities such as the second fundamental form and the velocity of the free surface we identify the well posedness condition thattheouternormalderivativeofthetotalpressureincludingthefluidandmagnetic pressuresisnegativeonthefreeboundary whichissimilartothephysicalcondition taylor sign condition for the incompressible euler equations of fluids

rota s universal operators and invariant subspaces in hilbert spaces a hilbert space operator is called universal in the sense of rota if every operator on the hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces we exhibit an analytic toeplitz operator whose adjoint is universal in the sense of rota and commutes with a quasi nilpotent injective compact operator with dense range in particular this new universal operator invites an approach to the invariant subspace problem that uses properties of operators that commute with the universal operator

inference using surrogate outcome data and a validation sample summary in the context of estimating 3 from the regression model p yi x relating response y to covariates x suppose that only a surrogate response s is available for most study subjects suppose that for a random subsample of the study cohort termed the validation sample the true outcome y is available in addition to s we consider maximum likelihood estimation of 3 from such data and show that it is nonrobust to misspecification of the distribution relating the surrogate to the true outcome p s i y x an alternative semiparametric method is also considered which is nonparametric with respect to p s i y x large sample distribution theory for maximum estimated likelihood estimates is developed an illustrative example is presented

well posedness of characteristic symmetric hyperbolic systems we consider the initial boundary value problem for quasi linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity we show the well posedness in hadamard s sense i e existence uniqueness and continuous dependence of solutions on the data of regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary

well posedness of the free boundary problem in incompressible elastodynamics abstract in this paper we prove the local well posedness of the free boundary problem in incompressible elastodynamics under a natural stability condition which ensures that the evolution equation describing the free boundary is strictly hyperbolic our result gives a rigorous confirmation that the elasticity has a stabilizing effect on the rayleigh taylor instability

invariant subspaces of operator lie algebras and lie algebras with compact adjoint action it is proved that a lie algebra of compact operators with a non zero volterra ideal is reducible has a nontrivial invariant subspace a number of other criteria of reducibility for collections of operators is obtained the results are applied to the structure theory of lie algebras of compact operators and normed lie algebras with compact adjoint action

symmetric positive systems with boundary characteristic of constant multiplicity the theory of maximal positive boundary value problems for symmetric positive systems is developed assuming that the boundary is characteristic of constant multiplicity no such hypothesis is needed on a neighborhood of the boundary both regularity theorems and mixed initial boundary value problems are discussed many classical ideas are sharpened in the process

semiparametric two sample tests in clinical trials with a post randomisation response indicator in many clinical trials involving survival endpoints one has additional data on some binary indicator of response such as initial tumour shrinkage in cancer trials this paper studies the case of randomised clinical trials where the response indicator is available shortly after randomisation and where one can assume that within each stratum defined by the response indicator a two treatment group proportional hazards model holds the same model may also describe some incompletely randomised or observational studies asymptotic relative efficiencies for kaplan meier based estimators versus maximum partial likelihood estimators are examined under this model for estimating either the difference in survival probabilities at a specified time or the parameter estimated by the logrank numerator it is shown that the efficiency gains using the model are more promising when estimating the difference in survival probabilities an example is given comparing the long term survival experience of two groups of patients with advanced hodgkin s disease

on the initial boundary value problem for the linearized equations of magnetohydrodynamics we study the initial boundary value problem for the linearized equations of ideal magnetohydrodynamics defined on a bounded domain whose boundary is a regular magnetic surface we show that it is well posed in h 1 omega and that the loss of regularity of solutions always occurs for some initial data in h l omega l geq 2

jensen s functional and polynomials in several variables in this paper we obtain some lower bounds of the integral 0 2 p 0 2 plog p e i q 1 e i q n d q 12 p d q n2 p if the polynomial p z 1 z n in several variables has a concentration at low degrees measured by 1 l p norm under l p norm 1 p 2 2 l p norm under l p norm p 2 3 l p quasi norm under l p quasi norm 0

stability of contact discontinuities in three dimensional compressible steady flows abstract in this paper we study the stability of contact discontinuities in three dimensional compressible isentropic steady flows by developing kreiss coulombel and secchi s arguments for a boundary value problem of hyperbolic equations involving poles in coefficients derived from the linearized problem at a supersonic contact discontinuity we obtain a necessary and sufficient condition for the linear weak stability of contact discontinuities and observe that only weak kreiss lopatinskii condition holds both of planar and non planar contact discontinuities are studied the energy estimates of solutions to the linearized problem at a planar contact discontinuity are obtained in the weakly stable region by constructing the kreiss symmetrizers microlocally away from the poles of the coefficient matrices and studying the equations directly at each pole the linear stability of non planar contact discontinuities is studied by developing the argument of the planar case and using the calculus of paradifferential operators the failure of the uniform kreiss lopatinskii condition results in a loss of tangential derivatives of solutions to the linearized boundary value problem with respect to the source terms and boundary data

well posedness of the linearized problem for mhd contact discontinuities abstract we study the free boundary problem for contact discontinuities in ideal compressible magnetohydrodynamics mhd they are characteristic discontinuities with no flow across the discontinuity for which the pressure the magnetic field and the velocity are continuous whereas the density and the entropy may have a jump under the rayleigh taylor sign condition p n 0 on the jump of the normal derivative of the pressure satisfied at each point of the unperturbed contact discontinuity we prove the well posedness in sobolev spaces of the linearized problem for 2d planar mhd flows

a hereditarily indecomposable mathcal l _ infty space that solves the scalar plus compact problem we construct a hereditarily indecomposable banach space with dual space isomorphic to l1 every bounded linear operator on this space is expressible as i k with a scalar and k compact

volterra type operators on sp d spaces abstract cuckovic and paudyal characterized the lattice of invariant subspaces of the operator t in the hardy hilbert space h 2 d where they studied the special case when p 2 of the space s p d we generalize some of their works to the general case when 1 p and determine that m is an invariant subspace of t on h p d if and only if t z m is an invariant subspace of m z on s 0 p d if and only if t z m is a closed ideal of s 0 p d furthermore we provide certain beurling type invariant subspaces of m z on s p d and s 0 p d then we investigate the boundedness of the operators t g and i g on s p d finally we investigate the spectrum of multiplication operator m g on s p d the isometric multiplication operators and the isometric zero divisors on s p d

spectral theory and hypercyclic subspaces a vector x in a hilbert space h is called hypercyclic for a bounded operator t h h if the orbit tnx n 1 is dense in h our main result states that if t satisfies the hypercyclicity criterion and the essential spectrum intersects the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is true even if t is a hypercyclic operator which does not satisfy the hypercyclicity criterion as a consequence other characterizations are obtained for an operator t to have an infinite dimensional closed subspace of hypercyclic vectors these results apply to most of the hypercyclic operators that have appeared in the literature in particular they apply to bilateral and backward weighted shifts perturbations of the identity by backward weighted shifts multiplication operators and composition operators the main result also applies to the differentiation operator and the translation operator t f z f z 1 defined on certain hilbert spaces consisting of entire functions we also obtain a spectral characterization of the norm closure of the class of hypercyclic operators which have an infinite dimensional closed subspace of hypercyclic vectors

topologically irreducible representations and radicals in banach algebras it is shown that the topologically irreducible representations of a normed algebra define a certain topological radical in the same way that the strictly irreducible representations define the jacobson radical and that this radical can be strictly smaller than the jacobson radical an abstract theory of topological radicals in topological algebras is developed and used to relate this radical to the baer radical prime radical the relations with topologically transitive representations and standard representations in the sense of meyer are also explored 1991 mathematics subject classification 46h15 46h25 16nxx

a comparison of tests of the difference in the proportion of patients who are cured we compared by simulation the likelihood ratio wald and score tests based on a mixture model similar to that proposed by farewell 1982 biometrics 38 1041 1046 and a simple nonparametric test based on the plateau value of the product limit estimate for testing the difference in cured proportions between two groups the parametric tests obtained their asymptotic properties even in small samples provided that one could assume equal failure rates in the two groups otherwise good agreement with predictions required that essentially all potential failures had been observed the comparative properties of the parametric tests depended on whether the population survival functions crossed with the power of the wald test as good as or better than the others in the common situation when the survival functions do not cross however its size was sometimes less than nominal the score test was often not defined and is therefore of limited value the product limit test often performed as well as the parametric tests and despite being biased in some circumstances may be a useful alternative to these especially in small samples when some potential failures have not been observed

on almost invariant subspaces and approximate commutation abstract a closed subspace y of a banach space x is almost invariant for a collection s of bounded linear operators on x if for each t s there exists a finite dimensional subspace f t of x such that t y y f t in this paper we study the existence of almost invariant subspaces for algebras of operators we show in particular that if a closed algebra of operators on a hilbert space has a non trivial almost invariant subspace then it has a non trivial invariant subspace we also examine the structure of operators which admit a maximal commuting family of almost invariant subspaces in particular we prove that if t is an operator on a separable hilbert space and if t p p t has finite rank for all projections p in a given maximal abelian self adjoint algebra m then t m f where m m and f is of finite rank

well posedness of the free boundary problem in compressible elastodynamics abstract we study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid at the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure vanishes outside the flow domain we prove the local in time existence of a unique smooth solution of the free boundary problem provided that among three columns of the deformation gradient there are two which are non collinear vectors at each point of the initial free boundary if this non collinearity condition fails the local in time existence is proved under the classical rayleigh taylor sign condition satisfied at the first moment by constructing an hadamard type ill posedness example for the frozen coefficients linearized problem we show that the simultaneous failure of the non collinearity condition and the rayleigh taylor sign condition leads to rayleigh taylor instability

the fixed boundary value problems for the equations of ideal magneto hydrodynamics with a perfectly conducting wall condition the equations of ideal magneto hydrodynamics are investigated concerning initial boundary value problems with a perfectly conducting wall condition the local in time solution is proved to exist uniquely provided that the normal component of the initial magnetic field vanishes everywhere or nowhere on the boundary