influence functions for testing abstract influence functions for testing are defined by applying hampel s influence function to transformed p values these influence functions describe the effect of an observation and an underlying distribution on the behavior of a test because these influence functions are not based on the test statistic alone they are applicable to both unconditional and conditional e g randomization tests the influence function of a transformed p value at a null hypothesis distribution is related to an influence function based on limiting power the influence functions of several one and two sample tests for location are discussed to illustrate the utility of this approach

the pressure corrected ice finite element method for compressible flows on unstructured meshes a new implicit continuous fluid eulerian ice scheme for simulating a wide range of transient and steady inviscid and viscous compressible flows on unstructured finite elements is presented this new computational fluid dynamics scheme termed the pressure corrected ice finite element method pcice fem represents an advancement in massmomentum coupled pressure based schemes the governing hydrodynamic equations for this scheme consist of the conservative forms of the momentum balance navier stokes mass conservation and total energy equations the pcice fem scheme is developed as a predictor corrector scheme by performing a fractional step splitting of the semi implicit temporal discretization of the governing equations into an explicit predictor phase and a semi implicit pressure correction phase coupled by a pressure poisson solution the result of this predictor corrector formulation is that the pressure poisson equation is provided with sufficient internal energy information to avoid iteration with the semi implicit pressure correction equations the pcice fem scheme combines a modified form of the two step taylor galerkin fem scheme as an explicit predictor for the fractional momentum equations and a time weighted fem method for the semi implicit form of the mass conservation and the total energy equations the pcice fem scheme employs flux corrected transport fct as a high resolution filter for shock capturing the ability of the pcice fem scheme to accurately and efficiently simulate a wide variety of flows from nearly incompressible to highly compressible is demonstrated

minimal nonsquare spectral factors we consider the problem of parametrizing the set of all nonsquare minimal spectral factors of a rational matrix function taking positive semidefinite values on the imaginary axis

j inner outer factorization j spectral factorization and robust control for nonlinear systems the problem of expressing a given nonlinear state space system as the cascade connection of a lossless system and a stable minimum phase system inner outer factorization is solved for the case of a stable system having state space equations affine in the inputs the solution is given in terms of the stabilizing solution of a certain hamilton jacobi equation the stable minimum phase factor is obtained as the solution of an associated nonlinear spectral factorization problem as an application one can arrive at the solution of the nonlinear h sub spl infin control problem for the disturbance feedforward case

an adaptive finite element procedure for compressible high speed flows abstract a two step explicit finite element procedure for obtaining time accurate solutions to the compressible euler equations is described the method is coupled with an adaptive mesh refinement process which enables steady state solutions of improved quality to be obtained

nonsquare spectral factors via factorizations of a unitary function abstract we consider the problem of parametrizing the set of nonsquare minimal spectral factors of a rational matrix function taking positive semidefinite values on the imaginary axis the tool here is the use of factorizations of a certain type of the function w 1w where w resp w is the minimal square spectral factor that has all its poles and zeros in the right resp left halfplane

spectral factorization via hermitian pencils abstract the spectral factorization problem is solved for state space systems via results on the canonical forms and inertia of hermitian matrix pencils these algebraic results then give a deflation method for spectral factorization

rational matrix functions with coisometric values on the imaginary line abstract given signature matrices j1 and j2 we obtain a necessary and sufficient condition for a rational matrix function w analytic at infinity to satisfy equation j1 w z j2w z on the imaginary axis the condition is based on a lyapunov equation involving matrices in an observable realization of w and generalizes the fact well known in the case where j1 j2 if the condition is satisfied for every observable realization a b c d of w there exists a unique possibly singular hermitian matrix g such that g satisfies the lyapunov equation and cg dj2b we call g the hermitian matrix associated with the realization the minimal factorizations w w1w2 where w1 and w2 satisfy equations j1 w1 z j1w1 z and j1 w2 z j2w2 z for z on the imaginary line can be characterized in terms of decompositions of the state space into subspaces determined by a possibly indefinite inner product induced by g as a corollary we obtain a sufficient condition for existence of a minimal factorization w w1w2 with w1 the multiplicative inverse of a blaschke potapov factor

null pole subspaces of nonregular rational matrix functions abstract given a not necessarily regular rational matrix function w and a subset of the extended complex plane we associate with it a free module l w over the ring of scalar rational functions which are analytic on called the null pole subspace of w over in the scalar case the information encoded in this module is equivalent to the knowledge of all the poles and zeros including their multiplicities at all points of in the general matrix case the null pole subspace encodes the more complicated zero pole structure of a rational matrix function which is the key tool for the understanding of many factorization problems in this paper we show how various other modules which have been introduced in the literature in connection with pole zero structure e g pole module zero module can be read off from the null pole subspace and how conversely the null pole subspace can be recovered from its various pieces pole module null module a null pole coupling operator and left annihilator we give an analytic coordinate dependent description of these modules which has connection with realization theory and which is useful for computations we also solve the converse problem of finding a rational matrix function which has a given admissible module as its null pole subspace

compressible multiphase semi implicit method with moment of fluid interface representation a unified method for simulating multiphase flows using an exactly mass momentum and energy conserving cell integrated semi lagrangian advection algorithm is presented the deforming material boundaries are represented using the moment of fluid method the new algorithm uses a semi implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed the asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows including stiff materials enabling large time steps characteristic of incompressible flow algorithms rather than the small time steps required by explicit methods shocks are captured and material discontinuities are tracked without the aid of any approximate or exact riemann solvers simulations of underwater explosions and fluid jetting in one two and three dimensions are presented which illustrate the effectiveness of the new algorithm at efficiently computing multiphase flows containing shock waves and material discontinuities with large impedance mismatch

a characterization of minimal square spectral factors two different well known approaches to the spectral factorization problem phi s w s w s are connected together by relating the geometric properties of the solution set of the underlying algebraic riccati equation to the structure of the all pass factor of each minimal solution w s

minimal square spectral factors abstract recently there has been renewed interest in the problem of spectral factorization and in particular the problem of parametrizing all square minimal spectral factors of a given spectrum for instance let us mention two recent papers in this journal one of which dealing with more computational aspects of this problem clements 1993 the other giving a parametrization under additional constraints ferrante et al 1993 this paper is motivated in a large part by ferrante et al 1993 in fact we shall show that a parametrization similar to the one given there can be achieved without one of the additional constraints imposed in ferrante et al 1993 a secondary aim of this paper is to give an overview of several parametrizations available in the literature

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

group sequential tests for delayed responses with discussion summary group sequential methods are used routinely to monitor clinical trials and to provide early stopping when there is evidence of a treatment effect a lack of an effect or concerns about patient safety in many studies the response of clinical interest is measured some time after the start of treatment and there are subjects at each interim analysis who have been treated but are yet to respond we formulate a new form of group sequential test which gives a proper treatment of these pipeline subjects these tests can be applied even when the continued accrual of data after the decision to stop the trial is unexpected we illustrate our methods through a series of examples we define error spending versions of these new designs which handle unpredictable group sizes and provide an information monitoring framework that can accommodate nuisance parameters such as an unknown response variance by studying optimal versions of our new designs we show how the benefits of lower expected sample size that are normally achieved by a group sequential test are reduced when there is a delay in response the loss of efficiency for larger delays can be ameliorated by incorporating data on a correlated short term end point fitting a joint model for the two end points but still making inferences on the original longer term end point we derive p values and confidence intervals on termination of our new tests

rational spectral factorization using state space methods abstract we describe a state space based algorithm to find the minimum phase spectral factor of any rational spectral density whether it be proper improper or polynomial

minimal representations of continuous time processes having spectral density with zeros in the extended imaginary axis given a process y with stationary increments and rational incremental spectral density s we parametrize minimal state space representations of dy we consider the case when s may have zeros on the imaginary axis including infinity and we analyze the zero structure of each state space representation

on a new class of realization formulas and their application abstract a new set of realization formulas is derived for a class of matrix valued functions w these include the standard realization formulas for rational w observability controllability and minimality are defined and characterized conditions for w to be j 1 j 2 isometric and or j 1 j 2 coisometric with respect to a pair of signature matrices j 1 and j 2 are given in terms of the realizations minimal factorizations for square w are considered and formulas for the factors are deduced associated reproducing kernel spaces of pairs too are discussed

on a hardy space approach to the analysis of spectral factors the paper presents a study of several problems related to spectral factorizations we assume only a very weak form of coercivity for the p x p spectral function phi and look at the set wm of all rectangular p x m spectral factors the main object is the arithmetization of the geometry of the set of minimal stable spectral factors by employing hardy space techniques and the arithmetic of inner functions particular attention is paid to the study of various partial orders associated with the set of spectral factors

on the lyapunov equation coinvariant subspaces and some problems related to spectral factorizations a geometric approach to stochastic realization theory and hence to spectral factorization problems has been developed by lindquist and picci 1985 1991 and lindquist et al 1995 most of this work was done abstractly fuhrmann and gombani 1998 adopted an entirely hardy space approach to this set of problems studying the set of rectangular spectral factors of given size for a weakly coercive spectral function the parametrization of spectral factors in terms of factorizations of related inner functions as developed in fuhrmann 1995 had to be generalized this led to a further understanding of the partial order introduced by lindquist and picci in the set of stable spectral factors in the present paper we study the geometry of finite dimensional coinvariant subspaces of a vectorial hardy space h 2 via realization theory emphasizing the role of the lyapunov equation in lifting the hardy space metric to the statespace domain we follow this by deriving state space formulas for rectangular spect

an improved finite element flux corrected transport algorithm an improved finite element flux corrected transport fe fct method for the numerical solution of hydrodynamic conservation equations is described based on the method developed by lohner and his collaborators to solve conservation equations in fluid mechanics and its application is extended to gas discharge problems the high and low order schemes used are the ones proposed by lohner who adds diffusion to the high order scheme by subtracting the lumped mass matrix from the consistent mass matrix to give the low order scheme the diffusion coefficient is adjusted globally a variable diffusion coefficient is introduced it is assumed to be constant in each element and is shown to transform the high order solution to a scheme equivalent to an upwind scheme which has minimal diffusion but ensures positive results this avoids the complexity of upwinding in fe especially in two dimensions it is also shown that the correct amount of real diffusion may be easily added to the algorithm when required for example for electrons results are presented which show that the high order scheme reduces to the upwind difference scheme when the new diffusion is used the proposed fct scheme is shown to give similar results in comparison with a fourth order fd fct algorithm finally the new method is applied to a streamer propagation problem in one dimension and the results obtained are shown to agree well with previously published results

riccati inequalities and reproducing kernel hilbert spaces natural connections between positive semidefinite solutions x of homogeneous algebraic riccati equations and finite dimensional reproducing kernel de branges spaces based on a j inner proper rational square matrix valued functions are known in this paper analogous connections between the positive semidefinite solutions x of nonhomogeneous algebraic riccati equations and finite dimensional reproducing kernel hilbert spaces based on rectangular j j coinner proper rational matrix valued functions are developed and are then applied to obtain factorization formulas for in terms of elementary factors enroute formulas for the factors in a version of a theorem of leech are also obtained

stable invariant lagrangian subspaces factorization of symmetric rational matrix functions and other applications several applications of earlier results by the authors concerning various notions of stability of invariant lagrangian subspaces are studied the applications include stability of symmetric minimal factorizations of real symmetric rational matrix functions stability of factorizations of certain classes of symmetric matrix polynomials and stably well posed matricial boundary value problems with symmetries an interpretation of many stability results in terms of equilibria of lie group actions on subspaces is given as well

parametrization of all minimal square spectral factors abstract two different parametrizations of minimal square spectral factors are given these parametrizations extend recent results by picci and pinzoni since they characterize spectral factors without specification on the zero or pole structure

on a connection between spectral factorization and geometric control theory we investigate here how the geometric control theory of basile marro and wonham can be obtained in a hilbert space context as the byproduct of the factorization of a spectral density with no zeros on the imaginary axis we show how controlled invariant subspaces can be obtained as images of orthogonal projections of co invariant subspaces onto a semi invariant markovian subspace of the hardy space of square integrable functions analytic in the right half plane output nulling subspaces are then related to a particular spectral factorization problem a similar construction is presented for controllability subspaces and a new algorithm for the computation of these subspaces is presented

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

short note notes on the pcice method simplification generalization and compressibility properties the pressure based pcice numerical method r c martineau r a berry the pressure corrected ice finite element method pcice fem for compressible flows on unstructured meshes j comput phys 198 2004 659 for computing transient fluid flows of all speeds from nearly incompressible to high supersonic with strong shocks is simplified and generalized its behavior is examined in the nearly incompressible limit and in the fully compressible limit in the nearly incompressible limit the pcice algorithm is found to reduce to a generalization of the incompressible mac method which includes the density gradient as a driving function in the pressure poisson equation in the fully compressible regime it is found to reduce to an expression equivalent to density based methods for high speed flow

zeros of spectral factors the geometry of splitting subspaces and the algebraic riccati inequality in this paper it is shown how the zero dynamics of not necessarily square spectral factors relate to the splitting subspace geometry of stationary stochastic models and to the corresponding algebraic riccati inequality the notion of output induced subspace of a minimal markovian splitting subspace which is the stochastic analogue of the supremal output nulling subspace in geometric control theory is introduced through this concept the analysis can be made coordinate free and straightforward geometric methods can be applied it is shown how the zero structure of the family of spectral factors relates to the geometric structure of the family of minimal markovian splitting subspaces in the sense that the relationship between the zeros of different spectral factors is reflected in the partial ordering of minimal splitting subspaces finally the well known characterization of the solutions of the algebraic riccati equation is generalized in terms of lagrangian subspaces invariant under the corresponding hamiltonian to the larger solution set of the algebraic riccati inequality

qualitative robustness of tests abstract a test is qualitatively robust by definition if its sequence of n 1 log transformed p values n being a measure of the sample size is continuous as a point function of the observations and weakly equicontinuous as a function of discrete probability measures this definition is applitable both to unconditional and to conditional tests under weak regularity conditions an unconditional test is qualitatively robust if and only if its test statistic is continuous a counterexample shows that conditional tests do not share this property the sample mean student s t and ybar xbar permutation tests are not qualitatively robust the sign wilcoxon huber censored likelihood and normal scores tests are qualitatively robust

the algebraic riccati equation a polynomial approach abstract polynomial models are used to give a unified approach to the problem of classifying the set of all real symmetric solutions of the algebraic riccati equation

parametrization of minimal spectral factors of discrete time rational spectral densities in this paper the problem of providing a complete parametrization of the minimal spectral factors of a discrete time rational spectral density is considered the desired parametrization given in terms of the all pass divisors of a certain all pass function is established in the most general setting after several partial results mostly in the continuous time case this is indeed the first complete parametrization obtained without resorting to any facilitating assumption this result provides a positive answer to a conjecture raised in 2016

rerandomization inference on regression and shift effects computationally feasible methods abstract an idea due to quade 1973 is used to develop a method that reduces the computational load for rerandomization inferences in certain situations and for experiments carried out with a sufficiently small reference set of randomizations makes computations entirely feasible consider an experimental design for n units for which an experimental plan e is to be chosen randomly from a set of k plans plan e will assign treatment dosage de u to unit u with postulated additive effect de u reflected in the observation zu rerandomization inferences are to be carried out by means of pivotal statistics te e z be z be z 1 be d e where z and d e are observation and dosage vectors and be mdot is the regression slope onto d e the dosages under plan e a the p value of a test of the hypotheses versus is essentially the proportion of te e z values e that are at most b if t l e z is the lth largest of the te e z s e then a l l k confi

non linear minimal square spectral factorization recent work has identified a correspondence between minimal square spectral factors of a given spectral density invariant subspaces of an associated hamiltonian matrix solutions of an appropriate algebraic riccati equation and minimal unitary left divisors of a certain unitary function on the imaginary line the purpose of this report is to obtain a natural extension of these ideas to a non linear setting at least for the special case where only minimal square stable spectral factors are considered