testing non inferiority and equivalence between two diagnostic procedures in paired sample ordinal data before adopting a new diagnostic procedure which is more convenient and less expensive than the standard existing procedure it is essentially important to assess whether the diagnostic accuracy of the new procedure is non inferior or equivalent to that of the standard procedure in this paper we consider the situation where test responses are on an ordinal scale with more than two categories we give two definitions of non inferiority one in terms of the probability of correctly identifying the case for a randomly selected pair of a case and a non case over all possible cut off points and the other in terms of both the sensitivity and specificity directly on the basis of large sample theory we develop two simple test procedures for detecting non inferiority we further conduct monte carlo simulation to evaluate the finite sample performance of these test procedures we note that the two asymptotic test procedures proposed here can actually perform reasonably well in a variety of situations even when the numbers of studied subjects from the diseased and non diseased populations are not large to illustrate the use of the proposed test procedures we include an example of determining whether the diagnostic accuracy of using a digitized film is non inferior to that of using a plain film for screening breast cancer finally we note that the extension of these results to accommodate the case of detecting two sided equivalence is simply straightforward

interval estimation of the risk difference in non compliance randomized trials with repeated binary measurements in a randomized clinical trial rct we often encounter non compliance with the treatment protocol for a subset of patients the intention to treat itt analysis is probably the most commonly used method in a rct with non compliance however the itt analysis estimates the programmatic effectiveness rather than the biological efficacy in this paper we focus attention on the latter index and consider use of the risk difference rd to measure the effect of a treatment based on a simple additive risk model proposed elsewhere we develop four asymptotic interval estimators of the rd for repeated binary measurements in a rct with non compliance we apply monte carlo simulation to evaluate and compare the finite sample performance of these interval estimators in a variety of situations we find that all interval estimators considered here can perform well with respect to the coverage probability we further find that the interval estimator using a tanh 1 x transformation is probably more precise than the others while the interval estimator derived from a randomization based approach may cause a slight loss of precision when the number of patients per treatment is large and the probability of compliance to an assigned treatment is high we find that all interval estimators discussed here are essentially equivalent finally we illustrate use of these interval estimators with data simulated from a trial of using macrophage colony stimulating factor to reduce febrile neutropenia incidence in acute myeloid leukaemia patients copyright 2006 john wiley sons ltd

inverse eigenvalue problems for extended hessenberg and extended tridiagonal matrices in inverse eigenvalue problems one tries to reconstruct a matrix satisfying some constraints given some spectral information here two inverse eigenvalue problems are solved first given the eigenvalues and the first components of the associated eigenvectors called the weight vector an extended hessenberg matrix with prescribed poles is computed possessing these eigenvalues and satisfying the eigenvector constraints the extended hessenberg matrix is retrieved by executing particularly designed unitary similarity transformations on the diagonal matrix containing the eigenvalues this inverse problem closely links to orthogonal rational functions the extended hessenberg matrix contains the recurrence coefficients given the nodes eigenvalues poles poles of the extended hessenberg matrix and a weight vector first eigenvector components determining the discrete inner product moreover it is also sort of the inverse of the rational arnoldi algorithm instead of using the rational arnoldi method to compute a krylov basis to approximate the spectrum we will reconstruct the orthogonal krylov basis given the spectral info in the second inverse eigenvalue problem we do the same but refrain from unitarity as a result we execute possibly non unitary similarity transformations on the diagonal matrix of eigenvalues to retrieve a non symmetric extended tridiagonal matrix the algorithm will be less stable but it will be faster as the extended tridiagonal matrix admits a low cost factorization of o n n equals the number of eigenvalues whereas the extended hessenberg matrix does not again there is a close link with orthogonal function theory the extended tridiagonal matrix captures the recurrence coefficients of bi orthogonal rational functions moreover it is again sort of inverse of the nonsymmetric lanczos algorithm given spectral properties we reconstruct the two basis krylov matrices linked to the nonsymmetric lanczos algorithm

exact equivalence test for risk ratio and its sample size determination under inverse sampling when data are dichotomous this paper notes the utility of inverse sampling in establishing equivalence with respect to the risk ratio this paper develops an exact equivalence test that accounts for the risk ratio under inverse sampling and further discusses the relationship between the exact equivalence test and the exact conditional confidence limits also included are an exact and two asymptotic procedures for calculation of the minimum required number of index subjects for a desired power 1 beta at a given alpha level finally this paper provides a table that summarizes the minimum required number of index subjects for powers equal to 0 90 and 0 80 in application of the proposed exact equivalence test at 0 05 level in a variety of situations

explanatory and pragmatic estimates of the treatment effect when deviations from allocated treatment occur abstract in a randomized clinical trial comparing two treatments it can happen that certain patients receive the treatment other than that determined by random allocation significance testing is usually performed by intention to treat that is comparison of groups as determined by random allocation the difference between the mean values of the outcome variable for these two groups estimates the difference in practical use between two treatment policies corresponding to a pragmatic approach an attenuation factor can then be used to obtain an estimate of the underlying difference in effectiveness between the two treatments corresponding to an explanatory paradigm thus two distinct estimates are obtained in many instances both are valid but have distinct interpretations correspondingly in planning sample size requirements when deviations from allocated treatment can be anticipated the target treatment difference may be understood in either an explanatory or a pragmatic sense for the sample size assessment method it is necessary to take this distinction into account

stratified analysis in randomized trials with noncompliance this article develops methods for stratified analyses of additive or multiplicative causal effect on binary outcomes in randomized trials with noncompliance the methods are based on a weighted estimating function for an unbiased estimating function under randomization in each stratum when known weights are used the derived estimator is a natural extension of the instrumental variable estimator for stratified analyses and test based confidence limits are solutions of a quadratic equation in the causal parameter optimal weights that maximize asymptotic efficiency incorporate variability in compliance aspects across strata an assessment based on asymptotic relative efficiency shows that a substantial enhancement in efficiency can be gained by using optimal weights instead of conventional ones which do not incorporate the variability in compliance aspects across strata application to a field trial for coronary heart disease is provided

positive definite toeplitz matrices the arnoldi process for isometric operators and gaussian quadrature on the unit circle abstract we show that the well known levinson algorithm for computing the inverse cholesky factorization of positive definite toeplitz matrices can be viewed as a special case of a more general process the latter process provides a very efficient implementation of the arnoldi process when the underlying operator is isometric this is analogous with the case of hermitian operators where the hessenberg matrix becomes tridiagonal and results in the hermitian lanczos process we investigate the structure of the hessenberg matrices in the isometric case and show that simple modifications of them move all their eigenvalues to the unit circle these eigenvalues are then interpreted as abscissas for analogs of gaussian quadrature now on the unit circle instead of the real line the trapezoidal rule appears as the analog of the gauss legendre formula

stokes fourier and acoustic limits for the boltzmann equation convergence proofs we establish a stokes fourier limit for the boltzmann equation considered over any periodic spatial domain of dimension 2 or more appropriately scaled families of diperna lions renormalized solutions are shown to have fluctuations that globally in time converge weakly to a unique limit governed by a solution of stokes fourier motion and heat equations provided that the fluid moments of their initial fluctuations converge to appropriate l 2 initial data of the stokesfourier equations both the motion and heat equations are recovered in the limit by controlling the fluxes and the local conservation defects of the diperna lions solutions with dissipation rate estimates the scaling of the fluctuations with respect to knudsen number is essentially optimal the assumptions on the collision kernel are little more than those required for the diperna lions theory and that the viscosity and heat conduction are finite for the acoustic limit these techniques also remove restrictions to bounded collision kernels and improve the scaling of the fluctuations both weak limits become strong when the initial fluctuations converge entropically to appropriate l 2 initial data c 2002 john wiley sons inc

sensitivity analysis for szegő polynomials szeg polynomials are orthogonal with respect to an inner product on the unit circle numerical methods for weighted least squares approximation by trigonometric polynomials conveniently can be derived and expressed with the aid of szeg polynomials this paper discusses the conditioning of several mappings involving szeg polynomials and thereby sheds light on the sensitivity of some approximation problems involving trigonometric polynomials

a divide and conquer method for unitary and orthogonal eigenproblems leth n xn be a unitary upper hessenberg matrix whose eigenvalues and possibly also eigenvectors are to be determined we describe how this eigenproblem can be solved by a divide and conquer method in which the matrixh is split into two smaller unitary upper hessenberg matricesh 1 andh 2 by a rank one modification ofh the eigenproblems forh 1 andh 2 can be solved independently and the solutions of these smaller eigenproblems define a rational function whose zeros on the unit circle are the eigenvalues ofh the eigenvector ofh can be determined from the eigenvalues ofh and the eigenvectors ofh 1 andh 2 the outlined splitting of unitary upper hessenberg matrices into smaller such matrices is carried out recursively this gives rise to a divide and conquer method that is suitable for implementation on a parallel computer whenh n xn is orthogonal the divide and conquer scheme simplifies and is described separately our interest in the orthogonal eigenproblem stems from applications in signal processing numerical examples for the orthogonal eigenproblem conclude the paper

quasistationary hydrodynamics for the boltzmann equation the boltzmann equation solutions are considered for small knudsen number the main attention is devoted to certain deviations from the classical navier stokes description the equations for the quasistationary slow flows are derived these equations do not contain the knudsen number and provide in this sense a limiting description of hydrodynamic variables in the isothermal case the equations reduce to incompressible navier stokes equations for bulk velocity and pressure in the stationary case they coincide with the equations of slow nonisothermal flows it is shown that the derived equations unlike the burnett equations possess all principal properties of the boltzmann equation in one dimension the equations reduce to a nonlinear diffusion equation being exactly solvable for maxwell molecules multidimensional stationary heat transfer problems are also discussed it is shown that one can expect an essential difference between the boltzmann equation solution in the limit of continuous media and the corresponding solution of navier stokes equations

the numerically stable reconstruction of jacobi matrices from spectral data we present an expose of the elementary theory of jacobi matrices and in particular their reconstruction from the gaussian weights and abscissas many recent works propose use of the diagonal hermitian lanczos process for this purpose we show that this process is numerically unstable we recall rutishauser s elegant and stable algorithm of 1963 based on plane rotations implement it efficiently and discuss our numerical experience we also apply rutishauser s algorithm to reconstruct a persymmetric jacobi matrix from its spectrum in an efficient and stable manner

bias of two one sided tests procedures in assessment of bioequivalence the current applications of schuirmann s two one sided tests procedure for the original scale ignore the variability of the least squares mean of the reference formulation when it substitutes for the unknown reference average of pharmacokinetic responses we propose a modified two one sided test procedure that takes into account the variability of the least squares mean of the reference formulation the non parametric version of the modified procedure is also available we conducted a simulation study to examine the true level of significance and empirical power of four current parametric and non parametric two one sided tests procedures under a 2 x 2 crossover design with different combinations of sample size intrasubject variability and correlation between the two responses from a subject both theoretical results and empirical evidence show that the true level of significance of the current two one sided tests procedures converges to 0 5 when the correlation of the two responses approaches 1 however not only is the modified two one sided tests procedure a test of size alpha but empirical evidence indicates it is also an unbiased test the modified non parametric procedure also controls the size of the tests and is competitive even under normality assumption

fluid dynamic limits of kinetic equations ii convergence proofs for the boltzmann equation using relative entropy estimates about an absolute maxwellian it is shown that any properly scaled sequence of diperna lions renormalized solutions of some classical boltzmann equations has fluctuations that converge to an infinitesimal maxwellian with fluid variables that satisfy the incompressibility and boussinesq relations moreover if the initial fluctuations entropically converge to an infinitesimal maxwellian then the limiting fluid variables satisfy a version of the leray energy inequality if the sequence satisfies a local momentum conservation assumption the momentum densities globaly converge to a solution of the stokes equation a similar discrete time version of this result holds for the navier stokes limit with an additional mild weak compactness assumption the continuous time navier stokes limit is also discussed 01993 john wiley sons inc

the acoustic limit for the boltzmann equation the acoustic equations are the linearization of the compressible euler equations about a spatially homogeneous fluid state we first derive them directly from the boltzmann equation as the formal limit of moment equations for an appropriately scaled family of boltzmann solutions we then establish this limit for the boltzmann equation considered over a periodic spatial domain for bounded collision kernels appropriately scaled families of diperna lions renormalized solutions are shown to have fluctuations that converge entropically and hence strongly in l 1 to a unique limit governed by a solution of the acoustic equations for all time provided that its initial fluctuations converge entropically to an appropriate limit associated to any given l 2 initial data of the acoustic equations the associated local conservation laws are recovered in the limit

on investigating gmres convergence using unitary matrices for a given matrix a and right hand side b this paper investigates unitary matrices generating with some right hand sides c the same gmres residual norms as the pair a b we give characterizations of this class of unitary matrices and point out the relationship with krylov subspaces and krylov residual subspaces for the pair a b we investigate the eigenvalues of these unitary matrices in relation to the convergence behavior of gmres for the pair a b and describe the indispensable role of the eigenvector information we conclude with a formula for the gmres residual norms generated by a normal matrix b in terms of its eigenvalues and components of the right hand side c in the eigenvector basis

incompressible navier stokes and euler limits of the boltzmann equation we consider solutions of the boltzmann equation in a d dimensional torus d 2 3 for macroscopic times t n 1 t 0 when the space variations are on a macroscopic scale x n 1r n 2 x in the unit torus let u x t be for t t0 a smooth solution of the incompressible navier stokes equations ins for n 2 and of the incompressible euler equation ie for n 2 we prove that has solutions for t t0 which are close to o 2 in a suitable norm to the local maxwellian p 2 t d 2 exp v u x t 2 2t with constant density p and temperature t this is a particular case defined by the choice of initial values of the macroscopic variables of a class of such solutions in which the macroscopic variables satisfy more general hydrodynamical equations for n 3 these equations correspond to variable density ie while for n 2 they involve higher order derivatives of the density

a hybrid discontinuous galerkin scheme for multi scale kinetic equations abstract we develop a multi dimensional hybrid discontinuous galerkin method for multi scale kinetic equations this method is based on moment realizability matrices a concept introduced by d levermore w morokoff and b nadiga in 32 and used in 26 for one dimensional problem the main issue addressed in this paper is to provide a simple indicator to select the most appropriate model and to apply a compact numerical scheme to reduce the interface region between different models we also construct a numerical flux for the fluid model obtained as the asymptotic limit of the flux of the kinetic equation finally we perform several numerical simulations for time evolution and stationary problems

scaling and expansion of moment equations in kinetic theory the set of generalized 13 moment equations for molecules interacting with power law potentials struchtrup multiscalemodel simul 3 211 2004 forms the base for an investigation of expansion methods in the knudsen number and other scaling parameters the scaling parameters appear in the equations by introducing dimensionless quantities for all variables and their gradients only some of the scaling coefficients can be chosen independently while others depend on these chosen scales their size can be deduced from a chapman enskog expansion or from the principle that a single term in an equation cannot be larger in size by one or several orders of magnitude than all other terms

schur parameter pencils for the solution of the unitary eigenproblem abstract let u v be an n n pencil with unitary matrices u and v an algorithm is presented which reduces u and v simultaneously to unitary block diagonal matrices g o q h up and g e q h vp with block size at most two it is an o n 3 process using householder eliminations and it is backward stable in the special case v i the block diagonal matrices g o g h e can be normalized so that their entries are just the schur parameters of the hessenberg condensed form of u we call g o g e a schur parameter pencil it can also be derived from u v by a lanczos like process for the solution of the eigenvalue problem for g o g e a qr type algorithm can be developed based on this unitary reduction of a pencil u v to a schur parameter pencil the condensed form is preserved throughout the process each iteration step needs only o n operations this method of solving the unitary eigenvalue problem seems to be the closest possible analogy to the qr method for the hermitian eigenvalue problem

sample size determination for assessing equivalence based on proportion ratio under a randomized trial with non compliance and missing outcomes when a generic drug is developed it is important to assess the equivalence of therapeutic efficacy between the new and the standard drugs although the number of publications on testing equivalence and its relevant sample size determination is numerous the discussion on sample size determination for a desired power of detecting equivalence under a randomized clinical trial rct with non compliance and missing outcomes is limited in this paper we derive under the compound exclusion restriction model the maximum likelihood estimator mle for the ratio of probabilities of response among compliers between two treatments in a rct with both non compliance and missing outcomes using the mle with the logarithmic transformation we develop an asymptotic test procedure for assessing equivalence and find that this test procedure can perform well with respect to type i error based on monte carlo simulation we further develop a sample size calculation formula for a desired power of detecting equivalence at a nominal level to evaluate the accuracy of the sample size calculation formula we apply monte carlo simulation again to calculate the simulated power of the proposed test procedure corresponding to the resulting sample size for a desired power of 80 per cent at 0 05 level in a variety of situations we also include a discussion on determining the optimal ratio of sample size allocation subject to a desired power to minimize a linear cost function and provide a sensitivity analysis of the sample size formula developed here under an alterative model with missing at random copyright 2007 john wiley sons ltd

an interior point method for large constrained discrete ill posed problems ill posed problems are numerically underdetermined it is therefore often beneficial to impose known properties of the desired solution such as nonnegativity during the solution process this paper proposes the use of an interior point method in conjunction with truncated iteration for the solution of large scale linear discrete ill posed problems with box constraints an estimate of the error in the data is assumed to be available numerical examples demonstrate the competitiveness of this approach

eigenvalues of a symmetric tridiagonal matrix a divide and conquer approach the symmetric tridiagonal eigenproblem has been the topic of some recent work many methods have been advanced for the computation of the eigenvalues of such a matrix in this paper we present a divide and conquer approach to the computation of the eigenvalues of a symmetric tridiagonal matrix via the evaluation of the characteristic polynomial the problem of evaluation of the characteristic polynomial is partitioned into smaller parts which are solved and these solutions are then combined to form the solution to the original problem we give the update equations for the characteristic polynomial and certain auxiliary polynomials used in the computation furthermore this set of recursions can be implemented on a regulartree structure if the concurrency exhibited by this algorithm is exploited it can be shown that thetime for computation of all the eigenvalues becomeso nlogn instead ofo n2 as is the case for the approach where the order is increased by only one at every step we address the numerical problems associated with the use of the characteristic polynomial and present a numerically stable technique for the eigenvalue computation

generalized burnett hydrodynamics equations of hydrodynamics derived from the boltzmann equation beyond the navier stokes level are studied by a method proposed earlier by the author the main question we consider is the following what is the most natural replacement for classical ill posed burnett equations it is shown that in some sense it is a two parameter set of generalized burnett equations gbes derived in this paper some equations of this class are even simpler than original burnett equations the region of stability in the space of parameters and other properties of gbes are discussed

on an inverse eigenvalue problem for unitary hessenberg matrices abstract we show that a unitary upper hessenberg matrix with positive subdiagonal elements is uniquely determined by its eigenvalues and the eigenvalues of a modified principal submatrix this provides an analog of a well known result for jacobi matrices

green s matrices abstract our goal is to identify and understand matrices a that share essential properties of the unitary hessenberg matrices m that are fundamental for szego s orthogonal polynomials those properties include i recurrence relations connect characteristic polynomials rk x of principal minors of a ii a is determined by generators parameters generalizing reflection coefficients of unitary hessenberg theory iii polynomials rk x correspond not only to a but also to a certain cmv like five diagonal matrix iv the five diagonal matrix factors into a product bc of block diagonal matrices with 2 2 blocks v submatrices above and below the main diagonal of a have rank 1 vi a is a multiplication operator in the appropriate basis of laurent polynomials vii eigenvectors of a can be expressed in terms of those polynomials conditions v connects our analysis to the study of quasi separable matrices but the factorization requirement iv narrows it to the subclass of green s matrices that share properties i vii the key tool is twist transformations that provide 2n matrices all sharing characteristic polynomials of principal minors with a one such twist transformation connects unitary hessenberg to cmv another twist transformation explains findings of fiedler who noticed that companion matrices give examples outside the unitary hessenberg framework we mention briefly the further example of a daubechies wavelet matrix infinite matrices are included

hessenberg eigenvalue eigenmatrix relations abstract explicit relations between eigenvalues eigenmatrix entries and matrix elements of unreduced hessenberg matrices are derived the main result is based on the taylor expansion of the adjugate of zi h on the one hand and inherent properties of hessenberg matrix structure on the other hand this result is utilized to construct computable relations between eigenvalues eigenvector components eigenvalues of principal submatrices and products of lower diagonal elements generalizing similar identities for jacobi matrices

the relative efficiency of zelen s prerandomization design for clinical trials the prerandomization design due to zelen 1979 new england journal of medicine 300 1242 1245 for comparing an experimental treatment with a standard is studied and compared with the traditional randomization scheme two models for estimating the treatment effect are considered one applies when the response variables are continuous and normal and the other when they are binary relative efficiencies are computed and lower bounds expressed in terms of the probabilities of consent under the two schemes are given

an inverse eigenvalue problem and an associated approximation problem for generalized k centrohermitian matrices a partially described inverse eigenvalue problem and an associated optimal approximation problem for generalized k centrohermitian matrices are considered it is shown under which conditions the inverse eigenproblem has a solution an expression of its general solution is given in case a solution of the inverse eigenproblem exists the optimal approximation problem can be solved the formula of its unique solution is given

hydrodynamic limit of the stationary boltzmann equation in a slab we study the stationary solution of the boltzmann equation in a slab with a constant external force parallel to the boundary and complete accommodation condition on the walls at a specified temperature we prove that when the force is sufficiently small there exists a solution which converges in the hydrodynamic limit to a local maxwellian with parameters given by the stationary solution of the corresponding compressible navier stokes equations with no slip boundary conditions corrections to this maxwellian are obtained in powers of the knudsen number with a controlled remainder

the qr algorithm for unitary hessenberg matrices abstract let h be an n n unitary right hessenberg matrix with positive subdiagonal elements using what we call the schur parameterization of h we show how one step of the shifted qr algorithm for h can be carried out in o n arithmetic operations coupled with the shift strategy of eberlein and huang 3 this will permit computation of the spectrum of h to machine precision in o n 2 operations one potential application is the computation of gauss szego quadrature formulas 12 given the associated schur parameters 7 the weights can also be computed by direct analogy with 6

sensitivity of the lanczos recurrence to gaussian quadrature data how malignant can small weights be stability of passing from gaussian quadrature data to the lanczos recurrence coefficients is considered special attention is paid to estimates explicitly expressed in terms of quadrature data and not having weights in denominators it has been shown that the recent approach exploiting integral representation of hankel determinants implies quantitative improvement of d laurie s constructive estimate it has also been demonstrated that a particular implementation on the hankel determinant approach gives an estimate being unimprovable up to a coefficient the corresponding example involves quadrature data with a small but not too small weight it follows that polynomial increase of a general case upper bound in terms of the dimension is unavoidable

eigenvalue computation for unitary rank structured matrices in this paper we describe how to compute the eigenvalues of a unitary rank structured matrix in two steps first we perform a reduction of the given matrix into hessenberg form next we compute the eigenvalues of this resulting hessenberg matrix via an implicit qr algorithm along the way we explain how the knowledge of a certain shift correction term to the structure can be used to speed up the qr algorithm for unitary hessenberg matrices and how this observation was implicitly used in a paper due to william b gragg we also treat an analogue of this observation in the hermitian tridiagonal case

a numerical comparison of methods for solving secular equations numerical comparisons are carried out by the most prominent methods both second and higher order for solving secular equations these equations arise in several matrix problems and numerical linear algebra applications in addition to the comparisons we propose a new starting point our results show a clear advantage to higher order methods

on the derivation of the incompressible mavier stokes equation for hamiltonian particle systems we consider a hamiltonian paticle system interacting by means of a pair potetial we look at the behavior of the system on a space scale of order e 1 times of order e 2 and mean velocities of order e with e a scale parameter assuming that the phase space density of the particles is give by a series in e the analog of the chapman enskog expansion the behavior of the system under this rescaling is described to the lowest order in e by the incompressible navier stokes equations the viscosity is given in terms of microscopic correlations and its expression agrees with the green kubo formula

perturbation and interlace theorems for the unitary eigenvalue problem abstract two aspects of the perturbation problem for the eigenvalues of a unitary matrix u are treated firstly analogues of the hoffman wielandt theorem and a weyl type theorem proved by bhatia and davis are derived which are based on a different measure of the distance of spectra using a suitable parametrization of the unit circle by an angle the new results are called tangent theorems in contrast to the first mentioned well known results which are sine theorems moreover we illuminate the unknown minimizing permutations in the above weyl type theorems with respect to their angles the eigenvalues of u and the perturbed matrix are naturally ordered on the unit circle counterclockwise after a point is cut on the unit circle we prove a well known open conjecture there exists a cutting point such that the weyl type theorems both sine and tangent are true when the ordered eigenvalues of u and are paired with each other secondly the cauchy interlacing theorem for hermitian matrices is generalized it is shown that certain modified principal submatrices of u called the modified kth leading principal submatrices have the property that their eigenvalues interlace those of u finally we discuss block reflectors appearing in the description of the modified principal submatrices and generalize a result of schreiber and parlett

hilbert s 6th problem exact and approximate hydrodynamic manifolds for kinetic equations the problem of the derivation of hydrodynamics from the boltz mann equation and related dissipative systems is formulated as the problem of slow invariant manifold in the space of distributions we review a few in stances where such hydrodynamic manifolds were found analytically both as the result of summation of the chapman enskog asymptotic expansion and by the direct solution of the invariance equation these model cases comprising grad s moment systems both linear and nonlinear are studied in depth in order to gain understanding of what can be expected for the boltzmann equa tion particularly the dispersive dominance and saturation of dissipation rate of the exact hydrodynamics in the short wave limit and the viscosity modifica tion at high divergence of the flow velocity are indicated as severe obstacles to the resolution of hilbert s 6th problem furthermore we review the derivation of the approximate hydrodynamic manifold for the boltzmann equation using newton s iteration and avoiding smallness parameters and compare this to the exact solutions additionally we discuss the problem of projection of the boltzmann equation onto the approximate hydrodynamic invariant manifold using entropy concepts finally a set of hypotheses is put forward where we describe open questions and set a horizon for what can be derived exactly or proven about the hydrodynamic manifolds for the boltzmann equation in the future

addressing complications of intention to treat analysis in the combined presence of all or none treatment noncompliance and subsequent missing outcomes summary we study the combined impact that all or none compliance and subsequent missing outcomes can have on the estimation of the intention to treat effect of assignment in randomised studies in this setting a standard analysis which drops subjects with missing outcomes and ignores compliance information can be biased for the intention to treat effect to address all or none compliance that is followed by missing outcomes we construct a new estimation procedure for the intention to treat effect that maintains good randomisation based properties under more plausible nonignorable noncompliance and nonignorable missing outcome conditions the compound exclusion restriction on the effect of assignment and the latent ignorability of the missing data mechanism we present both theoretical results and a simulation study moreover we show how the two key concepts of compound exclusion and latent ignorability are relevant in more complicated settings such as right censoring of a time to event outcome

on monotonicity of zeros of paraorthogonal polynomials on the unit circle abstract the purpose of this note is to establish necessary and sufficient conditions for the monotonicity with respect to a real parameter of zeros of paraorthogonal polynomials on the unit circle it is also provided tractable sufficient conditions and an application example

the navier stokes limit of stationary solutions of the nonlinear boltzmann equation we consider the flow of a gas in a channel whose walls are kept at fixed different temperatures there is a constant external force parallel to the boundaries which may themselves also be moving the system is described by the stationary boltzmann equation to which are added maxwellian boundary conditions with unit accommodation coefficient we prove that when the temperature gap the relative velocity of the planes and the force are all sufficiently small there is a solution which converges in the hydrodynamic limit to a local maxwellian with parameters given by the stationary solution of the corresponding compressible navier stokes equations with no slip voundary conditions corrections to this maxwellian are obtained in powers of the knudsen number with a controlled remainder

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

a proposal for interpreting and reporting negative studies an issue of continuing interest is the interpretation and reporting of negative studies namely studies that do not find statistically significant differences the most common approach is the design power method which determines irrespective of the observed difference what differences the study could have been expected to detect we propose an alternative approach the application of equivalence testing methods where we define equivalence to mean that the actual difference lies within some specified limits this approach in contrast to the design power approach provides a way of quantifying with p values what was actually determined from the study instead of saying what the study may or may not have accomplished with some degree of certainty power for example a possible outcome of the equivalence testing approach is the conclusion at the 5 per cent level that two means or proportions do not differ by more than some specified amount the equivalence testing approach applies to any study design we illustrate the method with a cancer clinical trial and an epidemiologic case control study in addition for those studies in which one cannot specify limits a priori we propose the use of equivalence curves to summarize and present the study results

quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity in this paper we investigate the szego radau and szego lobatto quadrature formulas on the unit circle these are n m point formulas for which m nodes are fixed in advance with m 1 and m 2 respectively and which have a maximal domain of validity in the space of laurent polynomials this means that the free parameters free nodes and positive weights are chosen such that the quadrature formula is exact for all powers z j email protected email protected p with p p n m as large as possible

inverse unitary eigenproblems and related orthogonal functions this paper explores the relationship between certain inverse unitary eigenvalue problems and orthogonal functions in particular the inverse eigenvalue problems for unitary hessenberg matrices and for schur parameter pencils are considered the szego recursion is known to be identical to the arnoldi process and can be seen as an algorithm for solving an inverse unitary hessenberg eigenvalue problem reformulation of this inverse unitary hessenberg eigenvalue problem yields an inverse eigenvalue problem for schur parameter pencils it is shown that solving this inverse eigenvalue problem is equivalent to computing laurent polynomials orthogonal on the unit circle efficient and reliable algorithms for solving the inverse unitary eigenvalue problems are given which require only o mn arithmetic operations as compared with o mn 2 operations needed for algorithms that ignore the structure of the problem

weighting in instrumental variables and g estimation we propose here a simple scheme to use information on compliance and prerandomization covariates to improve analysis of randomized trials with non compliance we use the data to determine the effect of randomization on treatment received among various strata defined by pretreatment covariates when the effect of treatment received on the outcome of interest is the same across strata and pretreatment covariates predict non compliance weighting the estimating functions by the effect of randomization on treatment received can improve the precision of explanatory estimates of treatment effect and can increase the power of intent to treat tests of the null hypothesis efficiency gains under the weighting scheme are a simple increasing function of the variability of these weights such weighting schemes will often lead to improvements even when these conditions are not met we use a randomized trial of cholestyramine to illustrate these points